Subgroups — C₇₃×#61451 #32970855

Order 18688.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#3345	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₇₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#3180	C₂	1	2	yes	maximal, complemented
17	C₇₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#3114	C₂	1	2	yes	maximal, complemented
19	C₇₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇₃×#3109	C₂	1	2	yes	maximal, complemented
21	C₇₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#442×C₇₃	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₇₃	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
27	#559×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
29	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
30	#553×C₇₃	—	2	1	no	—
31	#553×C₇₃	C₂²	1	2	yes	complemented
32	#551×C₇₃	—	2	2	no	—
33	#550×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	#548×C₇₃	—	2	1	no	—
36	#547×C₇₃	C₂²	1	1	yes	characteristic
37	#547×C₇₃	C₂²	1	2	yes	complemented
38	#546×C₇₃	—	2	1	no	—
39	#546×C₇₃	—	2	1	no	—
40	#546×C₇₃	—	2	2	no	—
41	#546×C₇₃	C₂²	1	2	yes	complemented
42	D₄²×C₇₃	C₂²	1	1	yes	characteristic
43	D₄²×C₇₃	C₂²	1	2	yes	complemented
44	D₄²×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#532×C₇₃	C₂²	1	2	yes	complemented
46	#532×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	#532×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	#529×C₇₃	—	2	1	no	—
49	#529×C₇₃	C₂²	1	2	yes	complemented
50	#525×C₇₃	—	2	2	no	—
51	#525×C₇₃	—	2	2	no	—
52	#525×C₇₃	—	2	1	no	—
53	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₇₃	—	2	1	no	—
56	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
58	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
59	#501×C₇₃	C₂²	1	2	yes	complemented
60	#498×C₇₃	C₂²	1	1	yes	characteristic, complemented
61	#496×C₇₃	C₂²	1	2	yes	complemented
62	#493×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#490×C₇₃	C₂²	1	2	yes	complemented
64	#489×C₇₃	C₂²	1	2	yes	complemented
65	#486×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	#486×C₇₃	C₂²	1	1	yes	characteristic, complemented
67	#483×C₇₃	C₂²	1	2	yes	complemented
68	#482×C₇₃	C₂²	1	2	yes	complemented
69	#481×C₇₃	C₂²	1	2	yes	complemented
70	#481×C₇₃	C₂²	1	2	yes	complemented
71	#481×C₇₃	C₂²	1	2	yes	complemented
72	#480×C₇₃	C₂²	1	2	yes	complemented
73	#478×C₇₃	C₂²	1	2	yes	complemented
74	#478×C₇₃	C₂²	1	2	yes	complemented
75	#476×C₇₃	C₂²	1	1	yes	characteristic, complemented
76	#476×C₇₃	C₂²	1	2	yes	complemented
77	#476×C₇₃	C₂²	1	1	yes	characteristic, complemented
78	#476×C₇₃	C₂²	1	2	yes	complemented
79	#475×C₇₃	C₂²	1	1	yes	characteristic, complemented
80	#474×C₇₃	C₂²	1	1	yes	characteristic, complemented
81	#469×C₇₃	C₂²	1	2	yes	complemented
82	#469×C₇₃	C₂²	1	2	yes	complemented
83	#466×C₇₃	C₂²	1	2	yes	complemented
84	#466×C₇₃	C₂²	1	2	yes	complemented
85	#465×C₇₃	C₂²	1	2	yes	complemented
86	#465×C₇₃	C₂²	1	2	yes	complemented
87	#463×C₇₃	C₂²	1	2	yes	complemented
88	#463×C₇₃	C₂²	1	2	yes	complemented
89	#460×C₇₃	C₂²	1	1	yes	characteristic, complemented
90	#459×C₇₃	C₂²	1	1	yes	characteristic
91	#459×C₇₃	C₂²	1	2	yes	complemented
92	#459×C₇₃	C₂²	1	1	yes	characteristic, complemented
93	#459×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	#459×C₇₃	C₂²	1	2	yes	complemented
95	#450×C₇₃	C₂²	1	2	yes	complemented
96	#449×C₇₃	C₂²	1	2	yes	complemented
97	#447×C₇₃	C₂²	1	2	yes	—
98	#447×C₇₃	C₂²	1	2	yes	complemented
99	#447×C₇₃	C₂²	1	2	yes	complemented
100	#447×C₇₃	C₂²	1	2	yes	complemented
101	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
102	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
103	#442×C₇₃	C₂²	1	2	yes	—
104	#442×C₇₃	C₂²	1	1	yes	characteristic
105	#442×C₇₃	C₂²	1	2	yes	complemented
106	#442×C₇₃	C₂²	1	2	yes	complemented
107	#442×C₇₃	C₂²	1	2	yes	complemented
108	#442×C₇₃	C₂²	1	2	yes	complemented
109	#442×C₇₃	C₂²	1	1	yes	characteristic, complemented
110	#442×C₇₃	C₂²	1	2	yes	complemented
111	#442×C₇₃	C₂²	1	2	yes	complemented
112	#442×C₇₃	C₂²	1	2	yes	complemented
113	#442×C₇₃	C₂²	1	2	yes	complemented
114	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
115	#440×C₇₃	C₂²	1	2	yes	complemented
116	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	#435×C₇₃	C₂²	1	2	yes	complemented
122	#435×C₇₃	C₂²	1	2	yes	complemented
123	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#432×C₇₃	C₂²	1	2	yes	complemented
126	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#428×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₂×#106×C₇₃	C₂²	1	2	yes	complemented
129	#418×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#417×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#102×C₇₃	C₂²	1	2	yes	complemented
132	C₂×#102×C₇₃	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₇₃	—	2	1	no	—
136	C₂×#41×C₇₃	—	2	1	no	—
137	C₂×#41×C₇₃	—	2	2	no	—
138	C₂×#41×C₇₃	—	2	2	no	—
139	C₂×#41×C₇₃	—	2	1	no	—
140	C₂×#41×C₇₃	—	2	1	no	—
141	C₂×#41×C₇₃	—	4	8	no	—
142	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
143	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₇₃	—	2	1	no	—
145	C₂²×D₄×C₇₃	—	2	1	no	—
146	C₂²×D₄×C₇₃	—	2	1	no	—
147	C₂²×D₄×C₇₃	—	2	2	no	—
148	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
149	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₇₃	—	2	2	no	—
152	C₂³×C₄×C₇₃	—	2	1	no	—
153	C₂³×C₄×C₇₃	—	2	2	no	—
154	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
155	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
158	C₂×D₈×C₇₃	—	2	8	no	—
159	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₇₃	C₂³	1	2	yes	—
161	C₂×D₈×C₇₃	C₂³	1	2	yes	—
162	C₂×D₈×C₇₃	C₂³	1	2	yes	—
163	C₂×D₈×C₇₃	C₂³	1	2	yes	—
164	C₂×D₈×C₇₃	C₂³	1	2	yes	—
165	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
169	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
173	#127×C₇₃	C₂³	1	1	yes	characteristic
174	#127×C₇₃	C₂³	1	2	yes	—
175	#127×C₇₃	C₂³	1	1	yes	characteristic
176	#126×C₇₃	—	2	2	no	—
177	#126×C₇₃	—	2	2	no	—
178	#125×C₇₃	—	2	1	no	—
179	#125×C₇₃	C₂³	1	2	yes	—
180	#124×C₇₃	—	2	1	no	—
181	#124×C₇₃	—	2	1	no	—
182	#124×C₇₃	—	2	2	no	—
183	#124×C₇₃	—	2	1	no	—
184	#124×C₇₃	C₂³	1	2	yes	—
185	#123×C₇₃	—	2	2	no	—
186	#123×C₇₃	—	2	2	no	—
187	#123×C₇₃	—	2	2	no	—
188	#123×C₇₃	—	2	2	no	—
189	#123×C₇₃	—	2	2	no	—
190	#123×C₇₃	—	2	2	no	—
191	#123×C₇₃	—	2	2	no	—
192	C₂²⋊Q₈×C₇₃	—	2	1	no	—
193	C₂²⋊Q₈×C₇₃	—	2	1	no	—
194	C₂²⋊Q₈×C₇₃	—	2	2	no	—
195	C₂²⋊Q₈×C₇₃	—	2	1	no	—
196	C₂²⋊Q₈×C₇₃	—	2	2	no	—
197	C₂²⋊Q₈×C₇₃	—	2	2	no	—
198	C₂²⋊Q₈×C₇₃	—	2	2	no	—
199	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
200	#121×C₇₃	—	2	2	no	—
201	#121×C₇₃	—	2	2	no	—
202	#121×C₇₃	—	2	1	no	—
203	#121×C₇₃	—	2	1	no	—
204	#121×C₇₃	—	2	1	no	—
205	#121×C₇₃	—	2	2	no	—
206	#121×C₇₃	—	2	1	no	—
207	#121×C₇₃	—	2	2	no	—
208	#121×C₇₃	—	2	1	no	—
209	#121×C₇₃	—	2	2	no	—
210	#121×C₇₃	C₂³	1	2	yes	—
211	#121×C₇₃	C₂³	1	2	yes	—
212	#121×C₇₃	C₂³	1	2	yes	—
213	#121×C₇₃	C₂³	1	2	yes	—
214	#121×C₇₃	C₂³	1	2	yes	—
215	#120×C₇₃	—	2	2	no	—
216	#120×C₇₃	—	2	2	no	—
217	#120×C₇₃	—	2	2	no	—
218	#120×C₇₃	—	2	2	no	—
219	#120×C₇₃	—	2	2	no	—
220	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
221	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₇₃	—	2	1	no	—
225	C₄×D₄×C₇₃	—	2	2	no	—
226	C₄×D₄×C₇₃	—	2	1	no	—
227	C₄×D₄×C₇₃	—	2	1	no	—
228	C₄×D₄×C₇₃	—	2	1	no	—
229	C₄×D₄×C₇₃	—	2	2	no	—
230	C₄×D₄×C₇₃	—	2	1	no	—
231	C₄×D₄×C₇₃	—	2	1	no	—
232	C₄×D₄×C₇₃	—	2	2	no	—
233	C₄×D₄×C₇₃	—	2	2	no	—
234	C₄×D₄×C₇₃	—	2	1	no	—
235	C₄×D₄×C₇₃	—	2	2	no	—
236	C₄×D₄×C₇₃	—	2	2	no	—
237	C₄×D₄×C₇₃	—	2	1	no	—
238	C₄×D₄×C₇₃	—	2	2	no	—
239	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
240	C₄×D₄×C₇₃	D₄	1	2	yes	—
241	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₇₃	C₂³	1	2	yes	—
246	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₇₃	C₂³	1	2	yes	—
249	C₄×D₄×C₇₃	C₂³	1	2	yes	—
250	C₄×D₄×C₇₃	C₂³	1	2	yes	—
251	C₄×D₄×C₇₃	C₂³	1	2	yes	—
252	C₄×D₄×C₇₃	C₂³	1	2	yes	—
253	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₇₃	C₂³	1	2	yes	—
255	#117×C₇₃	—	2	1	no	—
256	#117×C₇₃	—	2	2	no	—
257	#117×C₇₃	D₄	1	2	yes	—
258	#117×C₇₃	D₄	1	1	yes	characteristic
259	#117×C₇₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
268	C₂×C₄²×C₇₃	—	2	1	no	—
269	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
270	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
271	#107×C₇₃	C₂³	1	1	yes	characteristic
272	#107×C₇₃	C₂³	1	1	yes	characteristic
273	#107×C₇₃	C₂³	1	2	yes	—
274	#106×C₇₃	C₂³	1	1	yes	characteristic
275	#106×C₇₃	C₂³	1	2	yes	—
276	#106×C₇₃	C₂³	1	2	yes	—
277	#106×C₇₃	C₂³	1	2	yes	—
278	#106×C₇₃	C₂³	1	1	yes	characteristic
279	#106×C₇₃	C₂³	1	2	yes	—
280	#106×C₇₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
284	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
285	#103×C₇₃	C₂³	1	1	yes	characteristic
286	#103×C₇₃	C₂³	1	1	yes	characteristic
287	#103×C₇₃	C₂³	1	2	yes	—
288	#102×C₇₃	C₂³	1	1	yes	characteristic
289	#102×C₇₃	C₂³	1	1	yes	characteristic
290	#102×C₇₃	C₂³	1	2	yes	—
291	#102×C₇₃	C₂³	1	2	yes	—
292	#102×C₇₃	C₂³	1	2	yes	—
293	#102×C₇₃	C₂³	1	2	yes	—
294	#102×C₇₃	C₂³	1	2	yes	—
295	#102×C₇₃	C₂³	1	2	yes	—
296	#102×C₇₃	C₂³	1	1	yes	characteristic
297	#102×C₇₃	C₂³	1	1	yes	characteristic
298	#102×C₇₃	C₂³	1	1	yes	characteristic
299	#102×C₇₃	C₂³	1	1	yes	characteristic
300	#102×C₇₃	C₂³	1	2	yes	—
301	#102×C₇₃	C₂³	1	2	yes	—
302	#102×C₇₃	C₂³	1	2	yes	—
303	#102×C₇₃	C₂³	1	2	yes	—
304	#102×C₇₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
308	#97×C₇₃	C₂³	1	1	yes	characteristic
309	#97×C₇₃	C₂³	1	2	yes	—
310	#97×C₇₃	C₂³	1	2	yes	—
311	#97×C₇₃	C₂³	1	2	yes	—
312	#97×C₇₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₇₃	—	2	2	no	—
316	C₂⁴×C₇₃	—	2	1	no	—
317	C₂⁴×C₇₃	—	2	2	no	—
318	#41×C₇₃	—	2	4	no	—
319	#41×C₇₃	—	2	2	no	—
320	#41×C₇₃	—	4	1	no	—
321	#41×C₇₃	—	4	8	no	—
322	#41×C₇₃	—	4	4	no	—
323	#41×C₇₃	—	4	8	no	—
324	#41×C₇₃	—	4	4	no	—
325	#41×C₇₃	—	4	4	no	—
326	#41×C₇₃	—	8	2	no	—
327	C₂×Q₈×C₇₃	—	2	2	no	—
328	C₂×Q₈×C₇₃	—	2	1	no	—
329	C₂×Q₈×C₇₃	—	2	1	no	—
330	C₂×Q₈×C₇₃	—	4	4	no	—
331	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₇₃	—	2	4	no	—
334	C₂×D₄×C₇₃	—	2	2	no	—
335	C₂×D₄×C₇₃	—	2	4	no	—
336	C₂×D₄×C₇₃	—	2	1	no	—
337	C₂×D₄×C₇₃	—	2	2	no	—
338	C₂×D₄×C₇₃	—	2	2	no	—
339	C₂×D₄×C₇₃	—	2	2	no	—
340	C₂×D₄×C₇₃	—	2	2	no	—
341	C₂×D₄×C₇₃	—	2	2	no	—
342	C₂×D₄×C₇₃	—	2	1	no	—
343	C₂×D₄×C₇₃	—	2	2	no	—
344	C₂×D₄×C₇₃	—	2	2	no	—
345	C₂×D₄×C₇₃	—	2	1	no	—
346	C₂×D₄×C₇₃	—	2	2	no	—
347	C₂×D₄×C₇₃	—	2	1	no	—
348	C₂×D₄×C₇₃	—	2	2	no	—
349	C₂×D₄×C₇₃	—	2	1	no	—
350	C₂×D₄×C₇₃	—	2	1	no	—
351	C₂×D₄×C₇₃	—	4	2	no	—
352	C₂×D₄×C₇₃	—	4	2	no	—
353	C₂×D₄×C₇₃	—	4	1	no	—
354	C₂×D₄×C₇₃	—	4	8	no	—
355	C₂×D₄×C₇₃	—	4	4	no	—
356	C₂×D₄×C₇₃	—	4	4	no	—
357	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
358	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
360	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
361	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇₃	—	2	1	no	—
365	C₂²×C₄×C₇₃	—	2	2	no	—
366	C₂²×C₄×C₇₃	—	2	2	no	—
367	C₂²×C₄×C₇₃	—	2	1	no	—
368	C₂²×C₄×C₇₃	—	2	1	no	—
369	C₂²×C₄×C₇₃	—	2	1	no	—
370	C₂²×C₄×C₇₃	—	2	2	no	—
371	C₂²×C₄×C₇₃	—	2	1	no	—
372	C₂²×C₄×C₇₃	—	2	1	no	—
373	C₂²×C₄×C₇₃	—	2	2	no	—
374	C₂²×C₄×C₇₃	—	2	2	no	—
375	C₂²×C₄×C₇₃	—	2	1	no	—
376	C₂²×C₄×C₇₃	—	2	2	no	—
377	C₂²×C₄×C₇₃	—	2	1	no	—
378	C₂²×C₄×C₇₃	—	2	2	no	—
379	C₂²×C₄×C₇₃	—	2	2	no	—
380	C₂²×C₄×C₇₃	—	4	8	no	—
381	C₂²×C₄×C₇₃	—	4	4	no	—
382	C₂²×C₄×C₇₃	—	8	4	no	—
383	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
389	SD₁₆×C₇₃	—	2	2	no	—
390	SD₁₆×C₇₃	—	2	2	no	—
391	SD₁₆×C₇₃	—	4	2	no	—
392	D₈×C₇₃	—	2	4	no	—
393	D₈×C₇₃	—	2	4	no	—
394	D₈×C₇₃	—	2	2	no	—
395	D₈×C₇₃	—	2	4	no	—
396	D₈×C₇₃	—	4	2	no	—
397	D₈×C₇₃	—	4	2	no	—
398	D₈×C₇₃	#41	1	4	yes	complemented
399	M₁₆×C₇₃	—	2	2	no	—
400	M₁₆×C₇₃	—	4	1	no	—
401	C₂×C₈×C₇₃	—	2	4	no	—
402	C₂×C₈×C₇₃	—	4	2	no	—
403	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
407	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₇₃	—	2	1	no	—
410	C₄⋊C₄×C₇₃	—	2	2	no	—
411	C₄⋊C₄×C₇₃	—	2	1	no	—
412	C₄⋊C₄×C₇₃	—	2	2	no	—
413	C₄⋊C₄×C₇₃	—	2	2	no	—
414	C₄⋊C₄×C₇₃	—	2	1	no	—
415	C₄⋊C₄×C₇₃	—	2	1	no	—
416	C₄⋊C₄×C₇₃	—	2	2	no	—
417	C₄⋊C₄×C₇₃	—	2	2	no	—
418	C₄⋊C₄×C₇₃	—	2	2	no	—
419	C₄⋊C₄×C₇₃	—	2	1	no	—
420	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂²⋊C₄×C₇₃	—	2	2	no	—
431	C₂²⋊C₄×C₇₃	—	2	1	no	—
432	C₂²⋊C₄×C₇₃	—	2	1	no	—
433	C₂²⋊C₄×C₇₃	—	2	1	no	—
434	C₂²⋊C₄×C₇₃	—	2	2	no	—
435	C₂²⋊C₄×C₇₃	—	2	2	no	—
436	C₂²⋊C₄×C₇₃	—	2	2	no	—
437	C₂²⋊C₄×C₇₃	—	2	1	no	—
438	C₂²⋊C₄×C₇₃	—	2	2	no	—
439	C₂²⋊C₄×C₇₃	—	2	2	no	—
440	C₂²⋊C₄×C₇₃	—	2	1	no	—
441	C₂²⋊C₄×C₇₃	—	2	2	no	—
442	C₂²⋊C₄×C₇₃	—	2	1	no	—
443	C₂²⋊C₄×C₇₃	—	2	2	no	—
444	C₂²⋊C₄×C₇₃	—	2	2	no	—
445	C₂²⋊C₄×C₇₃	—	2	1	no	—
446	C₂²⋊C₄×C₇₃	—	2	2	no	—
447	C₂²⋊C₄×C₇₃	—	2	2	no	—
448	C₂²⋊C₄×C₇₃	—	2	2	no	—
449	C₂²⋊C₄×C₇₃	—	2	2	no	—
450	C₂²⋊C₄×C₇₃	—	2	2	no	—
451	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
454	C₄²×C₇₃	—	2	1	no	—
455	C₄²×C₇₃	—	2	1	no	—
456	C₄²×C₇₃	—	2	1	no	—
457	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₇₃	C₂×D₄	1	2	yes	—
460	C₄²×C₇₃	C₂×D₄	1	2	yes	—
461	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
462	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
463	C₄²×C₇₃	C₂⁴	1	2	yes	—
464	C₂³×C₇₃	—	2	1	no	—
465	C₂³×C₇₃	—	2	1	no	—
466	C₂³×C₇₃	—	2	2	no	—
467	C₂³×C₇₃	—	2	2	no	—
468	C₂³×C₇₃	—	2	1	no	—
469	C₂³×C₇₃	—	4	4	no	—
470	C₂³×C₇₃	—	4	4	no	—
471	C₂³×C₇₃	—	4	2	no	—
472	C₂³×C₇₃	—	4	2	no	—
473	C₂³×C₇₃	—	4	4	no	—
474	C₂³×C₇₃	—	4	4	no	—
475	C₂³×C₇₃	—	8	2	no	—
476	C₂³×C₇₃	—	8	2	no	—
477	C₂³×C₇₃	—	8	1	no	—
478	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
480	Q₈×C₇₃	—	2	2	no	—
481	Q₈×C₇₃	—	2	1	no	—
482	Q₈×C₇₃	—	2	1	no	—
483	Q₈×C₇₃	—	4	4	no	—
484	Q₈×C₇₃	—	4	2	no	—
485	Q₈×C₇₃	—	8	1	no	—
486	D₄×C₇₃	—	2	4	no	—
487	D₄×C₇₃	—	2	2	no	—
488	D₄×C₇₃	—	2	2	no	—
489	D₄×C₇₃	—	2	1	no	—
490	D₄×C₇₃	—	2	1	no	—
491	D₄×C₇₃	—	2	1	no	—
492	D₄×C₇₃	—	2	2	no	—
493	D₄×C₇₃	—	2	1	no	—
494	D₄×C₇₃	—	2	2	no	—
495	D₄×C₇₃	—	4	2	no	—
496	D₄×C₇₃	—	4	4	no	—
497	D₄×C₇₃	—	4	4	no	—
498	D₄×C₇₃	—	4	4	no	—
499	D₄×C₇₃	—	4	2	no	—
500	D₄×C₇₃	—	4	4	no	—
501	D₄×C₇₃	—	4	4	no	—
502	D₄×C₇₃	—	4	4	no	—
503	D₄×C₇₃	—	4	4	no	—
504	D₄×C₇₃	—	4	2	no	—
505	D₄×C₇₃	—	4	2	no	—
506	D₄×C₇₃	—	8	2	no	—
507	D₄×C₇₃	—	8	1	no	—
508	D₄×C₇₃	—	8	1	no	—
509	D₄×C₇₃	—	8	2	no	—
510	D₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	complemented
511	D₄×C₇₃	C₂×#41	1	2	yes	—
512	D₄×C₇₃	C₂×#41	1	2	yes	complemented
513	C₂×C₄×C₇₃	—	2	4	no	—
514	C₂×C₄×C₇₃	—	2	2	no	—
515	C₂×C₄×C₇₃	—	2	2	no	—
516	C₂×C₄×C₇₃	—	2	1	no	—
517	C₂×C₄×C₇₃	—	2	2	no	—
518	C₂×C₄×C₇₃	—	2	1	no	—
519	C₂×C₄×C₇₃	—	2	1	no	—
520	C₂×C₄×C₇₃	—	2	1	no	—
521	C₂×C₄×C₇₃	—	2	1	no	—
522	C₂×C₄×C₇₃	—	2	2	no	—
523	C₂×C₄×C₇₃	—	2	1	no	—
524	C₂×C₄×C₇₃	—	2	2	no	—
525	C₂×C₄×C₇₃	—	2	1	no	—
526	C₂×C₄×C₇₃	—	4	2	no	—
527	C₂×C₄×C₇₃	—	4	1	no	—
528	C₂×C₄×C₇₃	—	4	2	no	—
529	C₂×C₄×C₇₃	—	4	2	no	—
530	C₂×C₄×C₇₃	—	4	4	no	—
531	C₂×C₄×C₇₃	—	4	4	no	—
532	C₂×C₄×C₇₃	—	4	2	no	—
533	C₂×C₄×C₇₃	—	4	4	no	—
534	C₂×C₄×C₇₃	—	4	2	no	—
535	C₂×C₄×C₇₃	—	4	4	no	—
536	C₂×C₄×C₇₃	—	4	2	no	—
537	C₂×C₄×C₇₃	—	4	4	no	—
538	C₂×C₄×C₇₃	—	4	2	no	—
539	C₂×C₄×C₇₃	—	4	2	no	—
540	C₂×C₄×C₇₃	—	4	2	no	—
541	C₂×C₄×C₇₃	—	8	2	no	—
542	C₂×C₄×C₇₃	—	8	2	no	—
543	C₂×C₄×C₇₃	—	8	2	no	—
544	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
553	C₈×C₇₃	—	2	2	no	—
554	C₈×C₇₃	—	2	1	no	—
555	C₈×C₇₃	—	2	1	no	—
556	C₈×C₇₃	—	2	2	no	—
557	C₈×C₇₃	—	2	1	no	—
558	C₈×C₇₃	C₂×#41	1	2	yes	complemented
559	C₂²×C₇₃	—	2	2	no	—
560	C₂²×C₇₃	—	2	2	no	—
561	C₂²×C₇₃	—	2	1	no	—
562	C₂²×C₇₃	—	2	1	no	—
563	C₂²×C₇₃	—	2	2	no	—
564	C₂²×C₇₃	—	2	2	no	—
565	C₂²×C₇₃	—	2	1	no	—
566	C₂²×C₇₃	—	4	1	no	—
567	C₂²×C₇₃	—	4	1	no	—
568	C₂²×C₇₃	—	4	1	no	—
569	C₂²×C₇₃	—	4	1	no	—
570	C₂²×C₇₃	—	4	2	no	—
571	C₂²×C₇₃	—	4	2	no	—
572	C₂²×C₇₃	—	4	1	no	—
573	C₂²×C₇₃	—	4	2	no	—
574	C₂²×C₇₃	—	4	2	no	—
575	C₂²×C₇₃	—	4	1	no	—
576	C₂²×C₇₃	—	4	2	no	—
577	C₂²×C₇₃	—	4	1	no	—
578	C₂²×C₇₃	—	4	2	no	—
579	C₂²×C₇₃	—	8	8	no	—
580	C₂²×C₇₃	—	8	8	no	—
581	C₂²×C₇₃	—	8	4	no	—
582	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
583	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₇₃	—	2	1	no	—
585	C₄×C₇₃	—	2	2	no	—
586	C₄×C₇₃	—	2	1	no	—
587	C₄×C₇₃	—	2	1	no	—
588	C₄×C₇₃	—	2	2	no	—
589	C₄×C₇₃	—	2	1	no	—
590	C₄×C₇₃	—	2	2	no	—
591	C₄×C₇₃	—	4	1	no	—
592	C₄×C₇₃	—	4	2	no	—
593	C₄×C₇₃	—	4	1	no	—
594	C₄×C₇₃	—	4	1	no	—
595	C₄×C₇₃	—	4	2	no	—
596	C₄×C₇₃	—	4	1	no	—
597	C₄×C₇₃	—	4	1	no	—
598	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
599	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
600	C₄×C₇₃	#585	1	1	yes	characteristic
601	#61451	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
602	C₂×C₇₃	—	2	4	no	—
603	C₂×C₇₃	—	4	1	no	—
604	C₂×C₇₃	—	4	2	no	—
605	C₂×C₇₃	—	4	2	no	—
606	C₂×C₇₃	—	8	2	no	—
607	C₂×C₇₃	—	8	2	no	—
608	C₂×C₇₃	—	8	1	no	—
609	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
610	C₂×C₇₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
611	C₂×C₇₃	#3585	1	1	yes	characteristic
612	#3481	C₂×C₇₃	1	1	yes	characteristic, complemented
613	D₄×#41	C₂×C₇₃	1	1	yes	characteristic, complemented
614	#3399	C₂×C₇₃	1	1	yes	characteristic, complemented
615	#3384	C₂×C₇₃	1	1	yes	characteristic, complemented
616	#3373	C₂×C₇₃	1	1	yes	characteristic, complemented
617	#3366	C₂×C₇₃	1	1	yes	characteristic, complemented
618	#3345	C₂×C₇₃	1	2	yes	complemented
619	#3335	C₂×C₇₃	1	1	yes	characteristic, complemented
620	#3318	C₂×C₇₃	1	2	yes	complemented
621	#3306	C₂×C₇₃	1	2	yes	complemented
622	#3295	C₂×C₇₃	1	1	yes	characteristic, complemented
623	#3294	C₂×C₇₃	1	1	yes	characteristic, complemented
624	D₄×D₈	C₂×C₇₃	1	1	yes	characteristic, complemented
625	#3264	C₂×C₇₃	1	2	yes	complemented
626	#3184	C₂×C₇₃	1	1	yes	characteristic, complemented
627	#3180	C₂×C₇₃	1	2	yes	complemented
628	#3115	C₂×C₇₃	1	1	yes	characteristic, complemented
629	#3114	C₂×C₇₃	1	2	yes	complemented
630	#3109	C₂×C₇₃	1	1	yes	characteristic, complemented
631	#3109	C₂×C₇₃	1	2	yes	complemented
632	#2970	C₂×C₇₃	1	1	yes	characteristic, complemented
633	C₄×AGL(1,ℤ/8)	C₂×C₇₃	1	1	yes	characteristic, complemented
634	C₂×#442	C₂×C₇₃	1	2	yes	complemented
635	C₇₃	#61451	1	1	yes	characteristic, direct product factor, Sylow
636	C₂²×#41	—	2	1	no	—
637	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic
638	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
639	#559	C₂²×C₇₃	1	1	yes	characteristic, complemented
640	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
641	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
642	#553	—	2	1	no	—
643	#553	C₂²×C₇₃	1	2	yes	complemented
644	#551	—	2	2	no	—
645	#550	C₂²×C₇₃	1	1	yes	characteristic, complemented
646	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
647	#548	—	2	1	no	—
648	#547	C₂²×C₇₃	1	1	yes	characteristic
649	#547	C₂²×C₇₃	1	2	yes	complemented
650	#546	—	2	1	no	—
651	#546	—	2	1	no	—
652	#546	—	2	2	no	—
653	#546	C₂²×C₇₃	1	2	yes	complemented
654	D₄²	C₂²×C₇₃	1	1	yes	characteristic
655	D₄²	C₂²×C₇₃	1	2	yes	complemented
656	D₄²	C₂²×C₇₃	1	1	yes	characteristic, complemented
657	#532	C₂²×C₇₃	1	2	yes	complemented
658	#532	C₂²×C₇₃	1	1	yes	characteristic, complemented
659	#532	C₂²×C₇₃	1	1	yes	characteristic, complemented
660	#529	—	2	1	no	—
661	#529	C₂²×C₇₃	1	2	yes	complemented
662	#525	—	2	2	no	—
663	#525	—	2	2	no	—
664	#525	—	2	1	no	—
665	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
666	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic, complemented
667	C₂×C₄×D₄	—	2	1	no	—
668	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
669	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
670	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
671	#501	C₂²×C₇₃	1	2	yes	complemented
672	#498	C₂²×C₇₃	1	1	yes	characteristic, complemented
673	#496	C₂²×C₇₃	1	2	yes	complemented
674	#493	C₂²×C₇₃	1	1	yes	characteristic, complemented
675	#490	C₂²×C₇₃	1	2	yes	complemented
676	#489	C₂²×C₇₃	1	2	yes	complemented
677	#486	C₂²×C₇₃	1	1	yes	characteristic, complemented
678	#486	C₂²×C₇₃	1	1	yes	characteristic, complemented
679	#483	C₂²×C₇₃	1	2	yes	complemented
680	#482	C₂²×C₇₃	1	2	yes	complemented
681	#481	C₂²×C₇₃	1	2	yes	complemented
682	#481	C₂²×C₇₃	1	2	yes	complemented
683	#481	C₂²×C₇₃	1	2	yes	complemented
684	#480	C₂²×C₇₃	1	2	yes	complemented
685	#478	C₂²×C₇₃	1	2	yes	complemented
686	#478	C₂²×C₇₃	1	2	yes	complemented
687	#476	C₂²×C₇₃	1	1	yes	characteristic, complemented
688	#476	C₂²×C₇₃	1	2	yes	complemented
689	#476	C₂²×C₇₃	1	1	yes	characteristic, complemented
690	#476	C₂²×C₇₃	1	2	yes	complemented
691	#475	C₂²×C₇₃	1	1	yes	characteristic, complemented
692	#474	C₂²×C₇₃	1	1	yes	characteristic, complemented
693	#469	C₂²×C₇₃	1	2	yes	complemented
694	#469	C₂²×C₇₃	1	2	yes	complemented
695	#466	C₂²×C₇₃	1	2	yes	complemented
696	#466	C₂²×C₇₃	1	2	yes	complemented
697	#465	C₂²×C₇₃	1	2	yes	complemented
698	#465	C₂²×C₇₃	1	2	yes	complemented
699	#463	C₂²×C₇₃	1	2	yes	complemented
700	#463	C₂²×C₇₃	1	2	yes	complemented
701	#460	C₂²×C₇₃	1	1	yes	characteristic, complemented
702	#459	C₂²×C₇₃	1	1	yes	characteristic
703	#459	C₂²×C₇₃	1	2	yes	complemented
704	#459	C₂²×C₇₃	1	1	yes	characteristic, complemented
705	#459	C₂²×C₇₃	1	2	yes	complemented
706	#459	C₂²×C₇₃	1	1	yes	characteristic, complemented
707	#450	C₂²×C₇₃	1	2	yes	complemented
708	#449	C₂²×C₇₃	1	2	yes	complemented
709	#447	C₂²×C₇₃	1	2	yes	—
710	#447	C₂²×C₇₃	1	2	yes	complemented
711	#447	C₂²×C₇₃	1	2	yes	complemented
712	#447	C₂²×C₇₃	1	2	yes	complemented
713	#446	C₂²×C₇₃	1	1	yes	characteristic, complemented
714	#446	C₂²×C₇₃	1	1	yes	characteristic, complemented
715	#442	C₂²×C₇₃	1	2	yes	—
716	#442	C₂²×C₇₃	1	1	yes	characteristic
717	#442	C₂²×C₇₃	1	2	yes	complemented
718	#442	C₂²×C₇₃	1	2	yes	complemented
719	#442	C₂²×C₇₃	1	1	yes	characteristic, complemented
720	#442	C₂²×C₇₃	1	2	yes	complemented
721	#442	C₂²×C₇₃	1	2	yes	complemented
722	#442	C₂²×C₇₃	1	2	yes	complemented
723	#442	C₂²×C₇₃	1	2	yes	complemented
724	#442	C₂²×C₇₃	1	2	yes	complemented
725	#442	C₂²×C₇₃	1	2	yes	complemented
726	#440	C₂²×C₇₃	1	1	yes	characteristic, complemented
727	#440	C₂²×C₇₃	1	2	yes	complemented
728	#440	C₂²×C₇₃	1	1	yes	characteristic, complemented
729	C₄×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
730	C₄×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
731	C₄×D₈	C₂²×C₇₃	1	1	yes	characteristic
732	C₄×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
733	#435	C₂²×C₇₃	1	2	yes	complemented
734	#435	C₂²×C₇₃	1	2	yes	complemented
735	C₈×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
736	C₈×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
737	#432	C₂²×C₇₃	1	2	yes	complemented
738	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
739	#428	C₂²×C₇₃	1	1	yes	characteristic, complemented
740	C₂×#106	C₂²×C₇₃	1	2	yes	complemented
741	#418	C₂²×C₇₃	1	1	yes	characteristic, complemented
742	#417	C₂²×C₇₃	1	1	yes	characteristic, complemented
743	C₂×#102	C₂²×C₇₃	1	2	yes	complemented
744	C₂×#102	C₂²×C₇₃	1	2	yes	complemented
745	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
746	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
747	C₂×#41	—	2	1	no	—
748	C₂×#41	—	2	1	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	4	8	no	—
754	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
755	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
756	C₂²×Q₈	—	2	1	no	—
757	C₂²×D₄	—	2	1	no	—
758	C₂²×D₄	—	2	1	no	—
759	C₂²×D₄	—	2	2	no	—
760	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
761	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
762	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
763	C₂³×C₄	—	2	2	no	—
764	C₂³×C₄	—	2	1	no	—
765	C₂³×C₄	—	2	2	no	—
766	AGL(1,ℤ/8)	—	2	4	no	—
767	C₂×SD₁₆	C₂³×C₇₃	1	1	yes	characteristic
768	C₂×SD₁₆	C₂³×C₇₃	1	1	yes	characteristic
769	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
770	C₂×D₈	—	2	8	no	—
771	C₂×D₈	C₂³×C₇₃	1	2	yes	—
772	C₂×D₈	C₂³×C₇₃	1	2	yes	—
773	C₂×D₈	C₂³×C₇₃	1	2	yes	—
774	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
775	C₂×D₈	C₂³×C₇₃	1	2	yes	—
776	C₂×D₈	C₂³×C₇₃	1	2	yes	—
777	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
778	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
779	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
780	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
781	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
782	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
783	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
784	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
785	#127	C₂³×C₇₃	1	1	yes	characteristic
786	#127	C₂³×C₇₃	1	2	yes	—
787	#127	C₂³×C₇₃	1	1	yes	characteristic
788	#126	—	2	2	no	—
789	#126	—	2	2	no	—
790	#125	—	2	1	no	—
791	#125	C₂³×C₇₃	1	2	yes	—
792	#124	—	2	1	no	—
793	#124	—	2	1	no	—
794	#124	—	2	2	no	—
795	#124	—	2	1	no	—
796	#124	C₂³×C₇₃	1	2	yes	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	1	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	2	no	—
818	#121	—	2	1	no	—
819	#121	—	2	2	no	—
820	#121	—	2	1	no	—
821	#121	—	2	2	no	—
822	#121	C₂³×C₇₃	1	2	yes	—
823	#121	C₂³×C₇₃	1	2	yes	—
824	#121	C₂³×C₇₃	1	2	yes	—
825	#121	C₂³×C₇₃	1	2	yes	—
826	#121	C₂³×C₇₃	1	2	yes	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	—	2	2	no	—
832	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
835	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
852	C₄×D₄	D₄×C₇₃	1	2	yes	—
853	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₇₃	1	2	yes	—
856	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₇₃	1	2	yes	—
858	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₇₃	1	2	yes	—
860	C₄×D₄	C₂³×C₇₃	1	2	yes	—
861	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₇₃	1	2	yes	—
863	C₄×D₄	C₂³×C₇₃	1	2	yes	—
864	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₇₃	1	2	yes	—
867	#117	—	2	1	no	—
868	#117	—	2	2	no	—
869	#117	D₄×C₇₃	1	2	yes	—
870	#117	D₄×C₇₃	1	1	yes	characteristic
871	#117	C₂³×C₇₃	1	1	yes	characteristic
872	C₂×C₄⋊C₄	—	2	1	no	—
873	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
874	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₂²⋊C₄	—	2	1	no	—
878	C₂×C₂²⋊C₄	—	2	2	no	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₄²	—	2	1	no	—
881	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
882	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
883	#107	C₂³×C₇₃	1	1	yes	characteristic
884	#107	C₂³×C₇₃	1	1	yes	characteristic
885	#107	C₂³×C₇₃	1	2	yes	—
886	#106	C₂³×C₇₃	1	1	yes	characteristic
887	#106	C₂³×C₇₃	1	2	yes	—
888	#106	C₂³×C₇₃	1	2	yes	—
889	#106	C₂³×C₇₃	1	2	yes	—
890	#106	C₂³×C₇₃	1	1	yes	characteristic
891	#106	C₂³×C₇₃	1	2	yes	—
892	#106	C₂³×C₇₃	1	2	yes	—
893	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
894	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
895	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
896	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
897	#103	C₂³×C₇₃	1	1	yes	characteristic
898	#103	C₂³×C₇₃	1	1	yes	characteristic
899	#103	C₂³×C₇₃	1	2	yes	—
900	#102	C₂³×C₇₃	1	1	yes	characteristic
901	#102	C₂³×C₇₃	1	1	yes	characteristic
902	#102	C₂³×C₇₃	1	2	yes	—
903	#102	C₂³×C₇₃	1	2	yes	—
904	#102	C₂³×C₇₃	1	2	yes	—
905	#102	C₂³×C₇₃	1	2	yes	—
906	#102	C₂³×C₇₃	1	2	yes	—
907	#102	C₂³×C₇₃	1	2	yes	—
908	#102	C₂³×C₇₃	1	1	yes	characteristic
909	#102	C₂³×C₇₃	1	1	yes	characteristic
910	#102	C₂³×C₇₃	1	1	yes	characteristic
911	#102	C₂³×C₇₃	1	1	yes	characteristic
912	#102	C₂³×C₇₃	1	2	yes	—
913	#102	C₂³×C₇₃	1	2	yes	—
914	#102	C₂³×C₇₃	1	2	yes	—
915	#102	C₂³×C₇₃	1	2	yes	—
916	#102	C₂³×C₇₃	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
920	#97	C₂³×C₇₃	1	1	yes	characteristic
921	#97	C₂³×C₇₃	1	2	yes	—
922	#97	C₂³×C₇₃	1	2	yes	—
923	#97	C₂³×C₇₃	1	2	yes	—
924	#97	C₂³×C₇₃	1	1	yes	characteristic
925	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
926	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
927	C₂⁴	—	2	2	no	—
928	C₂⁴	—	2	1	no	—
929	C₂⁴	—	2	2	no	—
930	#41	—	2	4	no	—
931	#41	—	2	2	no	—
932	#41	—	4	1	no	—
933	#41	—	4	8	no	—
934	#41	—	4	4	no	—
935	#41	—	4	8	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	#41	—	8	2	no	—
939	C₂×Q₈	—	2	2	no	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	4	4	no	—
943	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	4	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	1	no	—
966	C₂×D₄	—	4	8	no	—
967	C₂×D₄	—	4	4	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
970	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
971	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
972	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
973	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
975	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	4	8	no	—
993	C₂²×C₄	—	4	4	no	—
994	C₂²×C₄	—	8	4	no	—
995	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
998	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
1000	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	2	2	no	—
1003	SD₁₆	—	4	2	no	—
1004	D₈	—	2	4	no	—
1005	D₈	—	2	4	no	—
1006	D₈	—	2	2	no	—
1007	D₈	—	2	4	no	—
1008	D₈	—	4	2	no	—
1009	D₈	—	4	2	no	—
1010	D₈	#41×C₇₃	1	4	yes	complemented
1011	M₁₆	—	2	2	no	—
1012	M₁₆	—	4	1	no	—
1013	C₂×C₈	—	2	4	no	—
1014	C₂×C₈	—	4	2	no	—
1015	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
1020	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
1041	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
1065	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
1070	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
1071	C₄²	C₂×D₄×C₇₃	1	2	yes	—
1072	C₄²	C₂×D₄×C₇₃	1	2	yes	—
1073	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
1074	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
1075	C₄²	C₂⁴×C₇₃	1	2	yes	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	4	4	no	—
1082	C₂³	—	4	4	no	—
1083	C₂³	—	4	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	4	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	8	2	no	—
1088	C₂³	—	8	2	no	—
1089	C₂³	—	8	1	no	—
1090	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
1091	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	1	no	—
1094	Q₈	—	2	1	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	8	1	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	4	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	1	no	—
1121	D₄	—	8	2	no	—
1122	D₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	complemented
1123	D₄	C₂×#41×C₇₃	1	2	yes	—
1124	D₄	C₂×#41×C₇₃	1	2	yes	complemented
1125	C₂×C₄	—	2	4	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	4	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1159	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1164	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
1165	C₈	—	2	2	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	1	no	—
1170	C₈	C₂×#41×C₇₃	1	2	yes	complemented
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	1	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	8	8	no	—
1192	C₂²	—	8	8	no	—
1193	C₂²	—	8	4	no	—
1194	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	4	yes	—
1195	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
1211	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
1212	C₄	#585×C₇₃	1	1	yes	characteristic
1213	C₂	—	2	4	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	8	2	no	—
1218	C₂	—	8	1	no	—
1219	C₂	—	8	2	no	—
1220	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
1221	C₂	C₂²×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
1222	C₂	C₇₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₄×#41×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇₃×#3481	C₂	semidirect
2. D₄×#41×C₇₃	C₂	semidirect
3. C₇₃×#3399	C₂	semidirect
4. C₇₃×#3384	C₂	semidirect
5. C₇₃×#3373	C₂	semidirect
6. C₇₃×#3366	C₂	semidirect
7. C₇₃×#3345	C₂	semidirect
8. C₇₃×#3335	C₂	semidirect
9. C₇₃×#3318	C₂	semidirect
10. C₇₃×#3306	C₂	semidirect
11. C₇₃×#3295	C₂	semidirect
12. C₇₃×#3294	C₂	semidirect
13. D₄×D₈×C₇₃	C₂	semidirect
14. C₇₃×#3264	C₂	semidirect
15. C₇₃×#3184	C₂	semidirect
16. C₇₃×#3180	C₂	semidirect
17. C₇₃×#3115	C₂	semidirect
18. C₇₃×#3114	C₂	semidirect
19. C₇₃×#3109	C₂	semidirect
20. C₇₃×#3109	C₂	semidirect
21. C₇₃×#2970	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₇₃	C₂	semidirect
23. C₂×#442×C₇₃	C₂	semidirect
27. #559×C₇₃	C₂²	semidirect
28. #554×C₇₃	C₂²	semidirect
29. #554×C₇₃	C₂²	semidirect
31. #553×C₇₃	C₂²	semidirect
33. #550×C₇₃	C₂²	semidirect
34. D₄×Q₈×C₇₃	C₂²	semidirect
37. #547×C₇₃	C₂²	semidirect
41. #546×C₇₃	C₂²	semidirect
43. D₄²×C₇₃	C₂²	semidirect
44. D₄²×C₇₃	C₂²	semidirect
45. #532×C₇₃	C₂²	semidirect
46. #532×C₇₃	C₂²	semidirect
47. #532×C₇₃	C₂²	semidirect
49. #529×C₇₃	C₂²	semidirect
54. C₄×#41×C₇₃	C₂²	semidirect
56. C₂×C₄×D₄×C₇₃	C₂²	semidirect
57. C₂×C₄×D₄×C₇₃	C₂²	semidirect
58. C₂×C₄×D₄×C₇₃	C₂²	semidirect
59. #501×C₇₃	C₂²	semidirect
60. #498×C₇₃	C₂²	semidirect
61. #496×C₇₃	C₂²	semidirect
62. #493×C₇₃	C₂²	semidirect
63. #490×C₇₃	C₂²	semidirect
64. #489×C₇₃	C₂²	semidirect
65. #486×C₇₃	C₂²	semidirect
66. #486×C₇₃	C₂²	semidirect
67. #483×C₇₃	C₂²	semidirect
68. #482×C₇₃	C₂²	semidirect
69. #481×C₇₃	C₂²	semidirect
70. #481×C₇₃	C₂²	semidirect
71. #481×C₇₃	C₂²	semidirect
72. #480×C₇₃	C₂²	semidirect
73. #478×C₇₃	C₂²	semidirect
74. #478×C₇₃	C₂²	semidirect
75. #476×C₇₃	C₂²	semidirect
76. #476×C₇₃	C₂²	semidirect
77. #476×C₇₃	C₂²	semidirect
78. #476×C₇₃	C₂²	semidirect
79. #475×C₇₃	C₂²	semidirect
80. #474×C₇₃	C₂²	semidirect
81. #469×C₇₃	C₂²	semidirect
82. #469×C₇₃	C₂²	semidirect
83. #466×C₇₃	C₂²	semidirect
84. #466×C₇₃	C₂²	semidirect
85. #465×C₇₃	C₂²	semidirect
86. #465×C₇₃	C₂²	semidirect
87. #463×C₇₃	C₂²	semidirect
88. #463×C₇₃	C₂²	semidirect
89. #460×C₇₃	C₂²	semidirect
91. #459×C₇₃	C₂²	semidirect
92. #459×C₇₃	C₂²	semidirect
93. #459×C₇₃	C₂²	semidirect
94. #459×C₇₃	C₂²	semidirect
95. #450×C₇₃	C₂²	semidirect
96. #449×C₇₃	C₂²	semidirect
98. #447×C₇₃	C₂²	semidirect
99. #447×C₇₃	C₂²	semidirect
100. #447×C₇₃	C₂²	semidirect
101. #446×C₇₃	C₂²	semidirect
102. #446×C₇₃	C₂²	semidirect
105. #442×C₇₃	C₂²	semidirect
106. #442×C₇₃	C₂²	semidirect
107. #442×C₇₃	C₂²	semidirect
108. #442×C₇₃	C₂²	semidirect
109. #442×C₇₃	C₂²	semidirect
110. #442×C₇₃	C₂²	semidirect
111. #442×C₇₃	C₂²	semidirect
112. #442×C₇₃	C₂²	semidirect
113. #442×C₇₃	C₂²	semidirect
114. #440×C₇₃	C₂²	semidirect
115. #440×C₇₃	C₂²	semidirect
116. #440×C₇₃	C₂²	semidirect
117. C₄×SD₁₆×C₇₃	C₂²	semidirect
118. C₄×SD₁₆×C₇₃	C₂²	semidirect
120. C₄×D₈×C₇₃	C₂²	semidirect
121. #435×C₇₃	C₂²	semidirect
122. #435×C₇₃	C₂²	semidirect
123. C₈×D₄×C₇₃	C₂²	semidirect
124. C₈×D₄×C₇₃	C₂²	semidirect
125. #432×C₇₃	C₂²	semidirect
126. #432×C₇₃	C₂²	semidirect
127. #428×C₇₃	C₂²	semidirect
128. C₂×#106×C₇₃	C₂²	semidirect
129. #418×C₇₃	C₂²	semidirect
130. #417×C₇₃	C₂²	semidirect
131. C₂×#102×C₇₃	C₂²	semidirect
132. C₂×#102×C₇₃	C₂²	semidirect
133. C₄×M₁₆×C₇₃	C₂²	semidirect
134. C₂×#97×C₇₃	C₂²	semidirect
398. D₈×C₇₃	#41	semidirect
510. D₄×C₇₃	AGL(1,ℤ/8)	semidirect
512. D₄×C₇₃	C₂×#41	semidirect
558. C₈×C₇₃	C₂×#41	semidirect
601. #61451	C₇₃	direct (N × H)
612. #3481	C₂×C₇₃	semidirect
613. D₄×#41	C₂×C₇₃	semidirect
614. #3399	C₂×C₇₃	semidirect
615. #3384	C₂×C₇₃	semidirect
616. #3373	C₂×C₇₃	semidirect
617. #3366	C₂×C₇₃	semidirect
618. #3345	C₂×C₇₃	semidirect
619. #3335	C₂×C₇₃	semidirect
620. #3318	C₂×C₇₃	semidirect
621. #3306	C₂×C₇₃	semidirect
622. #3295	C₂×C₇₃	semidirect
623. #3294	C₂×C₇₃	semidirect
624. D₄×D₈	C₂×C₇₃	semidirect
625. #3264	C₂×C₇₃	semidirect
626. #3184	C₂×C₇₃	semidirect
627. #3180	C₂×C₇₃	semidirect
628. #3115	C₂×C₇₃	semidirect
629. #3114	C₂×C₇₃	semidirect
630. #3109	C₂×C₇₃	semidirect
631. #3109	C₂×C₇₃	semidirect
632. #2970	C₂×C₇₃	semidirect
633. C₄×AGL(1,ℤ/8)	C₂×C₇₃	semidirect
634. C₂×#442	C₂×C₇₃	semidirect
635. C₇₃	#61451	direct (N × H)
639. #559	C₂²×C₇₃	semidirect
640. #554	C₂²×C₇₃	semidirect
641. #554	C₂²×C₇₃	semidirect
643. #553	C₂²×C₇₃	semidirect
645. #550	C₂²×C₇₃	semidirect
646. D₄×Q₈	C₂²×C₇₃	semidirect
649. #547	C₂²×C₇₃	semidirect
653. #546	C₂²×C₇₃	semidirect
655. D₄²	C₂²×C₇₃	semidirect
656. D₄²	C₂²×C₇₃	semidirect
657. #532	C₂²×C₇₃	semidirect
658. #532	C₂²×C₇₃	semidirect
659. #532	C₂²×C₇₃	semidirect
661. #529	C₂²×C₇₃	semidirect
666. C₄×#41	C₂²×C₇₃	semidirect
668. C₂×C₄×D₄	C₂²×C₇₃	semidirect
669. C₂×C₄×D₄	C₂²×C₇₃	semidirect
670. C₂×C₄×D₄	C₂²×C₇₃	semidirect
671. #501	C₂²×C₇₃	semidirect
672. #498	C₂²×C₇₃	semidirect
673. #496	C₂²×C₇₃	semidirect
674. #493	C₂²×C₇₃	semidirect
675. #490	C₂²×C₇₃	semidirect
676. #489	C₂²×C₇₃	semidirect
677. #486	C₂²×C₇₃	semidirect
678. #486	C₂²×C₇₃	semidirect
679. #483	C₂²×C₇₃	semidirect
680. #482	C₂²×C₇₃	semidirect
681. #481	C₂²×C₇₃	semidirect
682. #481	C₂²×C₇₃	semidirect
683. #481	C₂²×C₇₃	semidirect
684. #480	C₂²×C₇₃	semidirect
685. #478	C₂²×C₇₃	semidirect
686. #478	C₂²×C₇₃	semidirect
687. #476	C₂²×C₇₃	semidirect
688. #476	C₂²×C₇₃	semidirect
689. #476	C₂²×C₇₃	semidirect
690. #476	C₂²×C₇₃	semidirect
691. #475	C₂²×C₇₃	semidirect
692. #474	C₂²×C₇₃	semidirect
693. #469	C₂²×C₇₃	semidirect
694. #469	C₂²×C₇₃	semidirect
695. #466	C₂²×C₇₃	semidirect
696. #466	C₂²×C₇₃	semidirect
697. #465	C₂²×C₇₃	semidirect
698. #465	C₂²×C₇₃	semidirect
699. #463	C₂²×C₇₃	semidirect
700. #463	C₂²×C₇₃	semidirect
701. #460	C₂²×C₇₃	semidirect
703. #459	C₂²×C₇₃	semidirect
704. #459	C₂²×C₇₃	semidirect
705. #459	C₂²×C₇₃	semidirect
706. #459	C₂²×C₇₃	semidirect
707. #450	C₂²×C₇₃	semidirect
708. #449	C₂²×C₇₃	semidirect
710. #447	C₂²×C₇₃	semidirect
711. #447	C₂²×C₇₃	semidirect
712. #447	C₂²×C₇₃	semidirect
713. #446	C₂²×C₇₃	semidirect
714. #446	C₂²×C₇₃	semidirect
717. #442	C₂²×C₇₃	semidirect
718. #442	C₂²×C₇₃	semidirect
719. #442	C₂²×C₇₃	semidirect
720. #442	C₂²×C₇₃	semidirect
721. #442	C₂²×C₇₃	semidirect
722. #442	C₂²×C₇₃	semidirect
723. #442	C₂²×C₇₃	semidirect
724. #442	C₂²×C₇₃	semidirect
725. #442	C₂²×C₇₃	semidirect
726. #440	C₂²×C₇₃	semidirect
727. #440	C₂²×C₇₃	semidirect
728. #440	C₂²×C₇₃	semidirect
729. C₄×SD₁₆	C₂²×C₇₃	semidirect
730. C₄×SD₁₆	C₂²×C₇₃	semidirect
732. C₄×D₈	C₂²×C₇₃	semidirect
733. #435	C₂²×C₇₃	semidirect
734. #435	C₂²×C₇₃	semidirect
735. C₈×D₄	C₂²×C₇₃	semidirect
736. C₈×D₄	C₂²×C₇₃	semidirect
737. #432	C₂²×C₇₃	semidirect
738. #432	C₂²×C₇₃	semidirect
739. #428	C₂²×C₇₃	semidirect
740. C₂×#106	C₂²×C₇₃	semidirect
741. #418	C₂²×C₇₃	semidirect
742. #417	C₂²×C₇₃	semidirect
743. C₂×#102	C₂²×C₇₃	semidirect
744. C₂×#102	C₂²×C₇₃	semidirect
745. C₄×M₁₆	C₂²×C₇₃	semidirect
746. C₂×#97	C₂²×C₇₃	semidirect
1010. D₈	#41×C₇₃	semidirect
1122. D₄	AGL(1,ℤ/8)×C₇₃	semidirect
1124. D₄	C₂×#41×C₇₃	semidirect
1170. C₈	C₂×#41×C₇₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇₃×#3481	2
D₄×#41×C₇₃	2
C₇₃×#3399	2
C₇₃×#3384	2
C₇₃×#3373	2
C₇₃×#3366	2
C₇₃×#3345	2
C₇₃×#3335	2
C₇₃×#3318	2
C₇₃×#3306	2
C₇₃×#3295	2
C₇₃×#3294	2
D₄×D₈×C₇₃	2
C₇₃×#3264	2
C₇₃×#3184	2
C₇₃×#3180	2
C₇₃×#3115	2
C₇₃×#3114	2
C₇₃×#3109	2
C₇₃×#2970	2
C₄×AGL(1,ℤ/8)×C₇₃	2
C₂×#442×C₇₃	2
#61451	73

Subgroups — C73×#61451 #32970855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#61451 #32970855