Subgroups — C₇₃×#62583 #32971987

Order 18688.

1978 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3373	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3308	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3298	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#3238	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#3213	C₂	1	2	yes	maximal, complemented
13	C₇₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#489×C₇₃	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₇₃	—	2	1	no	—
19	#559×C₇₃	C₂²	1	1	yes	characteristic
20	#556×C₇₃	C₂²	1	1	yes	characteristic
21	#555×C₇₃	—	2	1	no	—
22	#551×C₇₃	—	2	2	no	—
23	D₄×Q₈×C₇₃	—	2	1	no	—
24	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
26	#548×C₇₃	C₂²	1	2	yes	—
27	#547×C₇₃	—	2	1	no	—
28	#547×C₇₃	—	2	2	no	—
29	#547×C₇₃	C₂²	1	2	yes	—
30	#547×C₇₃	C₂²	1	4	yes	complemented
31	#546×C₇₃	—	2	1	no	—
32	#546×C₇₃	C₂²	1	2	yes	—
33	D₄²×C₇₃	C₂²	1	1	yes	characteristic
34	#542×C₇₃	—	2	1	no	—
35	#538×C₇₃	—	2	2	no	—
36	#536×C₇₃	—	2	2	no	—
37	#536×C₇₃	—	2	1	no	—
38	#532×C₇₃	C₂²	1	1	yes	characteristic
39	#532×C₇₃	C₂²	1	2	yes	complemented
40	#532×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
42	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#529×C₇₃	C₂²	1	2	yes	—
44	#529×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×#124×C₇₃	C₂²	1	2	yes	—
46	#518×C₇₃	—	2	1	no	—
47	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
48	#501×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	#501×C₇₃	C₂²	1	2	yes	complemented
50	#496×C₇₃	C₂²	1	1	yes	characteristic
51	#496×C₇₃	C₂²	1	2	yes	complemented
52	#490×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	#489×C₇₃	C₂²	1	2	yes	—
54	#489×C₇₃	C₂²	1	4	yes	—
55	#489×C₇₃	C₂²	1	1	yes	characteristic
56	#489×C₇₃	C₂²	1	2	yes	complemented
57	#489×C₇₃	C₂²	1	2	yes	complemented
58	#489×C₇₃	C₂²	1	4	yes	complemented
59	#489×C₇₃	C₂²	1	2	yes	complemented
60	#487×C₇₃	C₂²	1	2	yes	complemented
61	#486×C₇₃	C₂²	1	2	yes	—
62	#484×C₇₃	C₂²	1	2	yes	complemented
63	#483×C₇₃	C₂²	1	4	yes	complemented
64	#481×C₇₃	C₂²	1	2	yes	—
65	#480×C₇₃	C₂²	1	4	yes	—
66	#477×C₇₃	C₂²	1	4	yes	complemented
67	#476×C₇₃	C₂²	1	4	yes	complemented
68	#475×C₇₃	C₂²	1	2	yes	complemented
69	#474×C₇₃	C₂²	1	2	yes	—
70	#469×C₇₃	C₂²	1	2	yes	—
71	#468×C₇₃	C₂²	1	2	yes	complemented
72	#466×C₇₃	C₂²	1	4	yes	—
73	#465×C₇₃	C₂²	1	4	yes	complemented
74	#463×C₇₃	C₂²	1	4	yes	—
75	#463×C₇₃	C₂²	1	4	yes	complemented
76	#461×C₇₃	C₂²	1	2	yes	complemented
77	#459×C₇₃	C₂²	1	2	yes	—
78	#449×C₇₃	C₂²	1	4	yes	complemented
79	#448×C₇₃	C₂²	1	4	yes	complemented
80	#447×C₇₃	C₂²	1	4	yes	—
81	#446×C₇₃	C₂²	1	2	yes	complemented
82	#442×C₇₃	C₂²	1	4	yes	complemented
83	#440×C₇₃	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₇₃	C₂²	1	2	yes	—
86	#435×C₇₃	C₂²	1	4	yes	complemented
87	C₈×D₄×C₇₃	C₂²	1	2	yes	—
88	#432×C₇₃	C₂²	1	2	yes	complemented
89	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
90	#417×C₇₃	C₂²	1	4	yes	complemented
91	C₂×#103×C₇₃	C₂²	1	4	yes	complemented
92	C₂×#102×C₇₃	C₂²	1	4	yes	—
93	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
95	2₋¹⁺⁴×C₇₃	—	4	8	no	—
96	C₂×#41×C₇₃	—	2	2	no	—
97	C₂×#41×C₇₃	—	2	4	no	—
98	C₂×#41×C₇₃	—	2	2	no	—
99	C₂×#41×C₇₃	—	2	1	no	—
100	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
101	C₂×#41×C₇₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₇₃	—	2	2	no	—
103	C₂²×Q₈×C₇₃	—	2	2	no	—
104	C₂²×Q₈×C₇₃	—	2	1	no	—
105	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₇₃	—	2	1	no	—
107	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
110	C₂×D₈×C₇₃	C₂³	1	2	yes	—
111	C₂×D₈×C₇₃	C₂³	1	4	yes	—
112	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₇₃	—	2	1	no	—
115	C₄⋊Q₈×C₇₃	—	2	2	no	—
116	C₄⋊Q₈×C₇₃	—	2	1	no	—
117	C₄⋊Q₈×C₇₃	—	2	1	no	—
118	C₄⋊Q₈×C₇₃	—	2	2	no	—
119	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
123	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	#127×C₇₃	C₂³	1	1	yes	characteristic
125	#127×C₇₃	C₂³	1	1	yes	characteristic
126	#126×C₇₃	—	2	2	no	—
127	#126×C₇₃	—	2	2	no	—
128	#126×C₇₃	—	2	1	no	—
129	#125×C₇₃	C₂³	1	1	yes	characteristic
130	#124×C₇₃	—	2	1	no	—
131	#124×C₇₃	—	2	2	no	—
132	#124×C₇₃	—	2	2	no	—
133	#124×C₇₃	—	2	2	no	—
134	#124×C₇₃	—	2	2	no	—
135	#124×C₇₃	—	2	1	no	—
136	#124×C₇₃	C₂³	1	2	yes	—
137	#124×C₇₃	C₂³	1	2	yes	—
138	#124×C₇₃	C₂³	1	1	yes	characteristic
139	#124×C₇₃	C₂³	1	2	yes	—
140	#123×C₇₃	—	2	1	no	—
141	#123×C₇₃	—	2	2	no	—
142	#123×C₇₃	—	2	2	no	—
143	#123×C₇₃	—	2	2	no	—
144	#123×C₇₃	—	2	4	no	—
145	#123×C₇₃	—	2	4	no	—
146	#123×C₇₃	—	2	4	no	—
147	C₂²⋊Q₈×C₇₃	—	2	1	no	—
148	C₂²⋊Q₈×C₇₃	—	2	2	no	—
149	C₂²⋊Q₈×C₇₃	—	2	4	no	—
150	C₂²⋊Q₈×C₇₃	—	2	2	no	—
151	C₂²⋊Q₈×C₇₃	—	2	4	no	—
152	C₂²⋊Q₈×C₇₃	—	2	2	no	—
153	C₂²⋊Q₈×C₇₃	—	2	2	no	—
154	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
156	#121×C₇₃	—	2	2	no	—
157	#121×C₇₃	—	2	1	no	—
158	#121×C₇₃	—	2	1	no	—
159	#121×C₇₃	—	2	2	no	—
160	#121×C₇₃	—	2	1	no	—
161	#121×C₇₃	—	2	1	no	—
162	#121×C₇₃	—	2	2	no	—
163	#121×C₇₃	C₂³	1	4	yes	—
164	#121×C₇₃	C₂³	1	2	yes	—
165	#121×C₇₃	C₂³	1	2	yes	—
166	#121×C₇₃	C₂³	1	1	yes	characteristic
167	#120×C₇₃	—	2	2	no	—
168	#120×C₇₃	—	2	2	no	—
169	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
170	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₇₃	—	2	1	no	—
174	C₄×D₄×C₇₃	—	2	2	no	—
175	C₄×D₄×C₇₃	—	2	1	no	—
176	C₄×D₄×C₇₃	—	2	1	no	—
177	C₄×D₄×C₇₃	—	2	2	no	—
178	C₄×D₄×C₇₃	—	2	1	no	—
179	C₄×D₄×C₇₃	—	2	1	no	—
180	C₄×D₄×C₇₃	—	2	1	no	—
181	C₄×D₄×C₇₃	—	2	2	no	—
182	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₇₃	D₄	1	2	yes	—
184	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₇₃	C₂³	1	2	yes	—
186	C₄×D₄×C₇₃	C₂³	1	4	yes	—
187	C₄×D₄×C₇₃	C₂³	1	2	yes	—
188	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₇₃	C₂³	1	2	yes	—
190	#117×C₇₃	—	2	1	no	—
191	#117×C₇₃	—	2	1	no	—
192	#117×C₇₃	—	2	2	no	—
193	#117×C₇₃	D₄	1	2	yes	—
194	#117×C₇₃	D₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
202	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
204	#107×C₇₃	C₂³	1	2	yes	—
205	#107×C₇₃	C₂³	1	4	yes	—
206	#106×C₇₃	C₂³	1	2	yes	—
207	#106×C₇₃	C₂³	1	4	yes	—
208	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
209	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
210	#103×C₇₃	C₂³	1	2	yes	—
211	#103×C₇₃	C₂³	1	4	yes	—
212	#103×C₇₃	C₂³	1	4	yes	—
213	#103×C₇₃	C₂³	1	4	yes	—
214	#103×C₇₃	C₂³	1	4	yes	—
215	#102×C₇₃	C₂³	1	2	yes	—
216	#102×C₇₃	C₂³	1	4	yes	—
217	#102×C₇₃	C₂³	1	4	yes	—
218	#102×C₇₃	C₂³	1	4	yes	—
219	#102×C₇₃	C₂³	1	4	yes	—
220	#102×C₇₃	C₂³	1	2	yes	—
221	#102×C₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
223	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
224	#97×C₇₃	C₂³	1	1	yes	characteristic
225	#97×C₇₃	C₂³	1	2	yes	—
226	#97×C₇₃	C₂³	1	4	yes	—
227	#97×C₇₃	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₇₃	C₂³	1	2	yes	—
229	C₂⁴×C₇₃	—	2	2	no	—
230	#41×C₇₃	—	2	4	no	—
231	#41×C₇₃	—	4	8	no	—
232	#41×C₇₃	—	4	4	no	—
233	#41×C₇₃	—	4	4	no	—
234	#41×C₇₃	—	4	16	no	—
235	#41×C₇₃	—	4	8	no	—
236	C₂×Q₈×C₇₃	—	2	4	no	—
237	C₂×Q₈×C₇₃	—	2	2	no	—
238	C₂×Q₈×C₇₃	—	2	2	no	—
239	C₂×Q₈×C₇₃	—	2	1	no	—
240	C₂×Q₈×C₇₃	—	2	2	no	—
241	C₂×Q₈×C₇₃	—	4	8	no	—
242	C₂×Q₈×C₇₃	—	4	4	no	—
243	C₂×Q₈×C₇₃	—	4	4	no	—
244	C₂×Q₈×C₇₃	—	4	8	no	—
245	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₇₃	—	2	2	no	—
249	C₂×D₄×C₇₃	—	2	2	no	—
250	C₂×D₄×C₇₃	—	2	4	no	—
251	C₂×D₄×C₇₃	—	2	1	no	—
252	C₂×D₄×C₇₃	—	2	2	no	—
253	C₂×D₄×C₇₃	—	2	1	no	—
254	C₂×D₄×C₇₃	—	2	1	no	—
255	C₂×D₄×C₇₃	—	2	1	no	—
256	C₂×D₄×C₇₃	—	2	1	no	—
257	C₂×D₄×C₇₃	—	2	2	no	—
258	C₂×D₄×C₇₃	—	4	4	no	—
259	C₂×D₄×C₇₃	—	4	4	no	—
260	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇₃	—	2	2	no	—
266	C₂²×C₄×C₇₃	—	2	4	no	—
267	C₂²×C₄×C₇₃	—	2	2	no	—
268	C₂²×C₄×C₇₃	—	2	1	no	—
269	C₂²×C₄×C₇₃	—	2	4	no	—
270	C₂²×C₄×C₇₃	—	2	2	no	—
271	C₂²×C₄×C₇₃	—	2	2	no	—
272	C₂²×C₄×C₇₃	—	2	2	no	—
273	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
279	SD₁₆×C₇₃	—	4	4	no	—
280	SD₁₆×C₇₃	—	4	2	no	—
281	D₈×C₇₃	—	4	4	no	—
282	D₈×C₇₃	—	4	2	no	—
283	M₁₆×C₇₃	—	4	2	no	—
284	C₂×C₈×C₇₃	—	4	4	no	—
285	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₇₃	—	2	1	no	—
289	C₄⋊C₄×C₇₃	—	2	2	no	—
290	C₄⋊C₄×C₇₃	—	2	4	no	—
291	C₄⋊C₄×C₇₃	—	2	2	no	—
292	C₄⋊C₄×C₇₃	—	2	2	no	—
293	C₄⋊C₄×C₇₃	—	2	4	no	—
294	C₄⋊C₄×C₇₃	—	2	1	no	—
295	C₄⋊C₄×C₇₃	—	2	1	no	—
296	C₄⋊C₄×C₇₃	—	2	1	no	—
297	C₄⋊C₄×C₇₃	—	2	1	no	—
298	C₄⋊C₄×C₇₃	—	2	2	no	—
299	C₄⋊C₄×C₇₃	—	2	1	no	—
300	C₄⋊C₄×C₇₃	—	2	2	no	—
301	C₄⋊C₄×C₇₃	—	2	1	no	—
302	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
310	C₂²⋊C₄×C₇₃	—	2	2	no	—
311	C₂²⋊C₄×C₇₃	—	2	1	no	—
312	C₂²⋊C₄×C₇₃	—	2	2	no	—
313	C₂²⋊C₄×C₇₃	—	2	1	no	—
314	C₂²⋊C₄×C₇₃	—	2	1	no	—
315	C₂²⋊C₄×C₇₃	—	2	1	no	—
316	C₂²⋊C₄×C₇₃	—	2	2	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	2	no	—
319	C₂²⋊C₄×C₇₃	—	2	2	no	—
320	C₂²⋊C₄×C₇₃	—	2	2	no	—
321	C₂²⋊C₄×C₇₃	—	2	2	no	—
322	C₂²⋊C₄×C₇₃	—	2	2	no	—
323	C₂²⋊C₄×C₇₃	—	2	4	no	—
324	C₂²⋊C₄×C₇₃	—	2	1	no	—
325	C₂²⋊C₄×C₇₃	—	2	2	no	—
326	C₂²⋊C₄×C₇₃	—	2	4	no	—
327	C₂²⋊C₄×C₇₃	—	2	2	no	—
328	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
331	C₄²×C₇₃	—	2	2	no	—
332	C₄²×C₇₃	—	2	1	no	—
333	C₄²×C₇₃	C₂×D₄	1	2	yes	—
334	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇₃	C₂×D₄	1	2	yes	—
337	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
338	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₇₃	C₂⁴	1	2	yes	—
340	C₂³×C₇₃	—	2	1	no	—
341	C₂³×C₇₃	—	2	2	no	—
342	C₂³×C₇₃	—	2	2	no	—
343	C₂³×C₇₃	—	4	4	no	—
344	C₂³×C₇₃	—	8	2	no	—
345	C₂³×C₇₃	—	8	2	no	—
346	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
348	Q₈×C₇₃	—	2	2	no	—
349	Q₈×C₇₃	—	2	2	no	—
350	Q₈×C₇₃	—	2	4	no	—
351	Q₈×C₇₃	—	4	4	no	—
352	Q₈×C₇₃	—	4	2	no	—
353	Q₈×C₇₃	—	4	8	no	—
354	Q₈×C₇₃	—	4	4	no	—
355	Q₈×C₇₃	—	8	2	no	—
356	D₄×C₇₃	—	2	4	no	—
357	D₄×C₇₃	—	2	2	no	—
358	D₄×C₇₃	—	2	2	no	—
359	D₄×C₇₃	—	2	2	no	—
360	D₄×C₇₃	—	2	4	no	—
361	D₄×C₇₃	—	4	2	no	—
362	D₄×C₇₃	—	4	2	no	—
363	D₄×C₇₃	—	4	4	no	—
364	D₄×C₇₃	—	4	4	no	—
365	D₄×C₇₃	—	4	8	no	—
366	D₄×C₇₃	—	4	2	no	—
367	D₄×C₇₃	—	8	1	no	—
368	D₄×C₇₃	—	8	2	no	—
369	D₄×C₇₃	—	8	1	no	—
370	D₄×C₇₃	—	8	2	no	—
371	D₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
372	C₂×C₄×C₇₃	—	2	4	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	4	no	—
375	C₂×C₄×C₇₃	—	2	2	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	1	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	2	no	—
380	C₂×C₄×C₇₃	—	2	4	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	4	2	no	—
383	C₂×C₄×C₇₃	—	4	1	no	—
384	C₂×C₄×C₇₃	—	4	8	no	—
385	C₂×C₄×C₇₃	—	4	4	no	—
386	C₂×C₄×C₇₃	—	4	8	no	—
387	C₂×C₄×C₇₃	—	4	2	no	—
388	C₂×C₄×C₇₃	—	4	4	no	—
389	C₂×C₄×C₇₃	—	8	2	no	—
390	C₂×C₄×C₇₃	—	8	2	no	—
391	C₂×C₄×C₇₃	—	8	2	no	—
392	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
401	C₈×C₇₃	—	2	2	no	—
402	C₈×C₇₃	—	2	4	no	—
403	C₈×C₇₃	—	2	2	no	—
404	C₂²×C₇₃	—	2	2	no	—
405	C₂²×C₇₃	—	2	2	no	—
406	C₂²×C₇₃	—	2	1	no	—
407	C₂²×C₇₃	—	2	1	no	—
408	C₂²×C₇₃	—	2	1	no	—
409	C₂²×C₇₃	—	4	2	no	—
410	C₂²×C₇₃	—	4	2	no	—
411	C₂²×C₇₃	—	4	1	no	—
412	C₂²×C₇₃	—	4	2	no	—
413	C₂²×C₇₃	—	4	1	no	—
414	C₂²×C₇₃	—	4	2	no	—
415	C₂²×C₇₃	—	4	2	no	—
416	C₂²×C₇₃	—	4	1	no	—
417	C₂²×C₇₃	—	4	2	no	—
418	C₂²×C₇₃	—	16	4	no	—
419	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
420	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₇₃	—	2	1	no	—
422	C₄×C₇₃	—	2	2	no	—
423	C₄×C₇₃	—	2	1	no	—
424	C₄×C₇₃	—	2	1	no	—
425	C₄×C₇₃	—	2	2	no	—
426	C₄×C₇₃	—	2	1	no	—
427	C₄×C₇₃	—	2	2	no	—
428	C₄×C₇₃	—	4	1	no	—
429	C₄×C₇₃	—	4	2	no	—
430	C₄×C₇₃	—	4	1	no	—
431	C₄×C₇₃	—	4	4	no	—
432	C₄×C₇₃	—	4	2	no	—
433	C₄×C₇₃	—	4	1	no	—
434	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
435	C₄×C₇₃	#585	1	2	yes	—
436	#62583	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂×C₇₃	—	2	4	no	—
438	C₂×C₇₃	—	4	1	no	—
439	C₂×C₇₃	—	8	2	no	—
440	C₂×C₇₃	—	8	2	no	—
441	C₂×C₇₃	—	8	1	no	—
442	C₂×C₇₃	#3500	1	1	yes	characteristic
443	C₂×C₇₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
444	C₂×C₇₃	#3586	1	1	yes	characteristic
445	#3514	C₂×C₇₃	1	1	yes	characteristic, complemented
446	#3499	C₂×C₇₃	1	1	yes	characteristic, complemented
447	#3373	C₂×C₇₃	1	2	yes	complemented
448	#3367	C₂×C₇₃	1	2	yes	complemented
449	#3308	C₂×C₇₃	1	4	yes	complemented
450	#3306	C₂×C₇₃	1	4	yes	complemented
451	#3298	C₂×C₇₃	1	2	yes	complemented
452	#3294	C₂×C₇₃	1	2	yes	complemented
453	#3239	C₂×C₇₃	1	1	yes	characteristic, complemented
454	#3238	C₂×C₇₃	1	2	yes	complemented
455	#3214	C₂×C₇₃	1	1	yes	characteristic, complemented
456	#3213	C₂×C₇₃	1	2	yes	complemented
457	#3180	C₂×C₇₃	1	2	yes	complemented
458	#3171	C₂×C₇₃	1	1	yes	characteristic, complemented
459	#3141	C₂×C₇₃	1	1	yes	characteristic, complemented
460	C₂×#489	C₂×C₇₃	1	2	yes	complemented
461	#2970	C₂×C₇₃	1	1	yes	characteristic, complemented
462	C₇₃	#62583	1	1	yes	characteristic, direct product factor, Sylow
463	C₂×2₋¹⁺⁴	—	2	1	no	—
464	#559	C₂²×C₇₃	1	1	yes	characteristic
465	#556	C₂²×C₇₃	1	1	yes	characteristic
466	#555	—	2	1	no	—
467	#551	—	2	2	no	—
468	D₄×Q₈	—	2	1	no	—
469	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
470	D₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
471	#548	C₂²×C₇₃	1	2	yes	—
472	#547	—	2	1	no	—
473	#547	—	2	2	no	—
474	#547	C₂²×C₇₃	1	2	yes	—
475	#547	C₂²×C₇₃	1	4	yes	complemented
476	#546	—	2	1	no	—
477	#546	C₂²×C₇₃	1	2	yes	—
478	D₄²	C₂²×C₇₃	1	1	yes	characteristic
479	#542	—	2	1	no	—
480	#538	—	2	2	no	—
481	#536	—	2	2	no	—
482	#536	—	2	1	no	—
483	#532	C₂²×C₇₃	1	1	yes	characteristic
484	#532	C₂²×C₇₃	1	1	yes	characteristic, complemented
485	#532	C₂²×C₇₃	1	2	yes	complemented
486	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	complemented
487	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
488	#529	C₂²×C₇₃	1	1	yes	characteristic
489	#529	C₂²×C₇₃	1	2	yes	—
490	C₂×#124	C₂²×C₇₃	1	2	yes	—
491	#518	—	2	1	no	—
492	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
493	#501	C₂²×C₇₃	1	1	yes	characteristic, complemented
494	#501	C₂²×C₇₃	1	2	yes	complemented
495	#496	C₂²×C₇₃	1	1	yes	characteristic
496	#496	C₂²×C₇₃	1	2	yes	complemented
497	#490	C₂²×C₇₃	1	1	yes	characteristic, complemented
498	#489	C₂²×C₇₃	1	4	yes	—
499	#489	C₂²×C₇₃	1	1	yes	characteristic
500	#489	C₂²×C₇₃	1	2	yes	—
501	#489	C₂²×C₇₃	1	4	yes	complemented
502	#489	C₂²×C₇₃	1	2	yes	complemented
503	#489	C₂²×C₇₃	1	2	yes	complemented
504	#489	C₂²×C₇₃	1	2	yes	complemented
505	#487	C₂²×C₇₃	1	2	yes	complemented
506	#486	C₂²×C₇₃	1	2	yes	—
507	#484	C₂²×C₇₃	1	2	yes	complemented
508	#483	C₂²×C₇₃	1	4	yes	complemented
509	#481	C₂²×C₇₃	1	2	yes	—
510	#480	C₂²×C₇₃	1	4	yes	—
511	#477	C₂²×C₇₃	1	4	yes	complemented
512	#476	C₂²×C₇₃	1	4	yes	complemented
513	#475	C₂²×C₇₃	1	2	yes	complemented
514	#474	C₂²×C₇₃	1	2	yes	—
515	#469	C₂²×C₇₃	1	2	yes	—
516	#468	C₂²×C₇₃	1	2	yes	complemented
517	#466	C₂²×C₇₃	1	4	yes	—
518	#465	C₂²×C₇₃	1	4	yes	complemented
519	#463	C₂²×C₇₃	1	4	yes	—
520	#463	C₂²×C₇₃	1	4	yes	complemented
521	#461	C₂²×C₇₃	1	2	yes	complemented
522	#459	C₂²×C₇₃	1	2	yes	—
523	#449	C₂²×C₇₃	1	4	yes	complemented
524	#448	C₂²×C₇₃	1	4	yes	complemented
525	#447	C₂²×C₇₃	1	4	yes	—
526	#446	C₂²×C₇₃	1	2	yes	complemented
527	#442	C₂²×C₇₃	1	4	yes	complemented
528	#440	C₂²×C₇₃	1	4	yes	complemented
529	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
530	C₄×D₈	C₂²×C₇₃	1	2	yes	—
531	#435	C₂²×C₇₃	1	4	yes	complemented
532	C₈×D₄	C₂²×C₇₃	1	2	yes	—
533	#432	C₂²×C₇₃	1	2	yes	complemented
534	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
535	#417	C₂²×C₇₃	1	4	yes	complemented
536	C₂×#103	C₂²×C₇₃	1	4	yes	complemented
537	C₂×#102	C₂²×C₇₃	1	4	yes	—
538	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
539	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
540	2₋¹⁺⁴	—	4	8	no	—
541	C₂×#41	—	2	2	no	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	2	2	no	—
544	C₂×#41	—	2	1	no	—
545	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
546	C₂×#41	C₂³×C₇₃	1	2	yes	—
547	C₂²×Q₈	—	2	2	no	—
548	C₂²×Q₈	—	2	2	no	—
549	C₂²×Q₈	—	2	1	no	—
550	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
554	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
555	C₂×D₈	C₂³×C₇₃	1	2	yes	—
556	C₂×D₈	C₂³×C₇₃	1	4	yes	—
557	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
558	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	2	no	—
564	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	—
569	#127	C₂³×C₇₃	1	1	yes	characteristic
570	#127	C₂³×C₇₃	1	1	yes	characteristic
571	#126	—	2	2	no	—
572	#126	—	2	2	no	—
573	#126	—	2	1	no	—
574	#125	C₂³×C₇₃	1	1	yes	characteristic
575	#124	—	2	1	no	—
576	#124	—	2	2	no	—
577	#124	—	2	2	no	—
578	#124	—	2	2	no	—
579	#124	—	2	2	no	—
580	#124	—	2	1	no	—
581	#124	C₂³×C₇₃	1	1	yes	characteristic
582	#124	C₂³×C₇₃	1	2	yes	—
583	#124	C₂³×C₇₃	1	2	yes	—
584	#124	C₂³×C₇₃	1	2	yes	—
585	#123	—	2	1	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	4	no	—
590	#123	—	2	4	no	—
591	#123	—	2	4	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	4	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
601	#121	—	2	2	no	—
602	#121	—	2	1	no	—
603	#121	—	2	1	no	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	2	no	—
608	#121	C₂³×C₇₃	1	2	yes	—
609	#121	C₂³×C₇₃	1	1	yes	characteristic
610	#121	C₂³×C₇₃	1	4	yes	—
611	#121	C₂³×C₇₃	1	2	yes	—
612	#120	—	2	2	no	—
613	#120	—	2	2	no	—
614	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
616	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
628	C₄×D₄	D₄×C₇₃	1	2	yes	—
629	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₇₃	1	2	yes	—
631	C₄×D₄	C₂³×C₇₃	1	2	yes	—
632	C₄×D₄	C₂³×C₇₃	1	4	yes	—
633	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₇₃	1	2	yes	—
635	#117	—	2	1	no	—
636	#117	—	2	1	no	—
637	#117	—	2	2	no	—
638	#117	D₄×C₇₃	1	2	yes	—
639	#117	D₄×C₇₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	—	2	2	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
644	C₂×C₂²⋊C₄	—	2	2	no	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₂²⋊C₄	—	2	2	no	—
647	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
649	#107	C₂³×C₇₃	1	2	yes	—
650	#107	C₂³×C₇₃	1	4	yes	—
651	#106	C₂³×C₇₃	1	2	yes	—
652	#106	C₂³×C₇₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
654	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
655	#103	C₂³×C₇₃	1	2	yes	—
656	#103	C₂³×C₇₃	1	4	yes	—
657	#103	C₂³×C₇₃	1	4	yes	—
658	#103	C₂³×C₇₃	1	4	yes	—
659	#103	C₂³×C₇₃	1	4	yes	—
660	#102	C₂³×C₇₃	1	2	yes	—
661	#102	C₂³×C₇₃	1	4	yes	—
662	#102	C₂³×C₇₃	1	4	yes	—
663	#102	C₂³×C₇₃	1	4	yes	—
664	#102	C₂³×C₇₃	1	4	yes	—
665	#102	C₂³×C₇₃	1	2	yes	—
666	#102	C₂³×C₇₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
669	#97	C₂³×C₇₃	1	1	yes	characteristic
670	#97	C₂³×C₇₃	1	2	yes	—
671	#97	C₂³×C₇₃	1	4	yes	—
672	#97	C₂³×C₇₃	1	1	yes	characteristic
673	C₄×C₈	C₂³×C₇₃	1	2	yes	—
674	C₂⁴	—	2	2	no	—
675	#41	—	2	4	no	—
676	#41	—	4	8	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	4	16	no	—
680	#41	—	4	8	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	4	8	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	—	4	8	no	—
690	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
709	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	2	no	—
726	D₈	—	4	4	no	—
727	D₈	—	4	2	no	—
728	M₁₆	—	4	2	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
732	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
774	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
775	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	C₂×D₄×C₇₃	1	2	yes	—
779	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₇₃	1	2	yes	—
782	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
784	C₄²	C₂⁴×C₇₃	1	2	yes	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	8	2	no	—
790	C₂³	—	8	2	no	—
791	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
792	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	8	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	8	2	no	—
801	D₄	—	2	4	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	1	no	—
814	D₄	—	8	2	no	—
815	D₄	—	8	1	no	—
816	D₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
845	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	4	no	—
848	C₈	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	16	4	no	—
864	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	4	yes	—
865	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	4	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
880	C₄	#585×C₇₃	1	2	yes	—
881	C₂	—	2	4	no	—
882	C₂	—	4	1	no	—
883	C₂	—	8	1	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₇₃×#3500	1	1	yes	characteristic
887	C₂	C₂²×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
888	C₂	C₇₃×#3586	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×#3514	C₂	semidirect
2. C₇₃×#3499	C₂	semidirect
3. C₇₃×#3373	C₂	semidirect
4. C₇₃×#3367	C₂	semidirect
5. C₇₃×#3308	C₂	semidirect
6. C₇₃×#3306	C₂	semidirect
7. C₇₃×#3298	C₂	semidirect
8. C₇₃×#3294	C₂	semidirect
9. C₇₃×#3239	C₂	semidirect
10. C₇₃×#3238	C₂	semidirect
11. C₇₃×#3214	C₂	semidirect
12. C₇₃×#3213	C₂	semidirect
13. C₇₃×#3180	C₂	semidirect
14. C₇₃×#3171	C₂	semidirect
15. C₇₃×#3141	C₂	semidirect
16. C₂×#489×C₇₃	C₂	semidirect
17. C₇₃×#2970	C₂	semidirect
25. D₄×Q₈×C₇₃	C₂²	semidirect
30. #547×C₇₃	C₂²	semidirect
39. #532×C₇₃	C₂²	semidirect
40. #532×C₇₃	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
42. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
48. #501×C₇₃	C₂²	semidirect
49. #501×C₇₃	C₂²	semidirect
51. #496×C₇₃	C₂²	semidirect
52. #490×C₇₃	C₂²	semidirect
56. #489×C₇₃	C₂²	semidirect
57. #489×C₇₃	C₂²	semidirect
58. #489×C₇₃	C₂²	semidirect
59. #489×C₇₃	C₂²	semidirect
60. #487×C₇₃	C₂²	semidirect
62. #484×C₇₃	C₂²	semidirect
63. #483×C₇₃	C₂²	semidirect
66. #477×C₇₃	C₂²	semidirect
67. #476×C₇₃	C₂²	semidirect
68. #475×C₇₃	C₂²	semidirect
71. #468×C₇₃	C₂²	semidirect
73. #465×C₇₃	C₂²	semidirect
75. #463×C₇₃	C₂²	semidirect
76. #461×C₇₃	C₂²	semidirect
78. #449×C₇₃	C₂²	semidirect
79. #448×C₇₃	C₂²	semidirect
81. #446×C₇₃	C₂²	semidirect
82. #442×C₇₃	C₂²	semidirect
83. #440×C₇₃	C₂²	semidirect
84. C₄×SD₁₆×C₇₃	C₂²	semidirect
86. #435×C₇₃	C₂²	semidirect
88. #432×C₇₃	C₂²	semidirect
89. #432×C₇₃	C₂²	semidirect
90. #417×C₇₃	C₂²	semidirect
91. C₂×#103×C₇₃	C₂²	semidirect
93. C₄×M₁₆×C₇₃	C₂²	semidirect
94. C₂×#97×C₇₃	C₂²	semidirect
436. #62583	C₇₃	direct (N × H)
445. #3514	C₂×C₇₃	semidirect
446. #3499	C₂×C₇₃	semidirect
447. #3373	C₂×C₇₃	semidirect
448. #3367	C₂×C₇₃	semidirect
449. #3308	C₂×C₇₃	semidirect
450. #3306	C₂×C₇₃	semidirect
451. #3298	C₂×C₇₃	semidirect
452. #3294	C₂×C₇₃	semidirect
453. #3239	C₂×C₇₃	semidirect
454. #3238	C₂×C₇₃	semidirect
455. #3214	C₂×C₇₃	semidirect
456. #3213	C₂×C₇₃	semidirect
457. #3180	C₂×C₇₃	semidirect
458. #3171	C₂×C₇₃	semidirect
459. #3141	C₂×C₇₃	semidirect
460. C₂×#489	C₂×C₇₃	semidirect
461. #2970	C₂×C₇₃	semidirect
462. C₇₃	#62583	direct (N × H)
470. D₄×Q₈	C₂²×C₇₃	semidirect
475. #547	C₂²×C₇₃	semidirect
484. #532	C₂²×C₇₃	semidirect
485. #532	C₂²×C₇₃	semidirect
486. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
487. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
493. #501	C₂²×C₇₃	semidirect
494. #501	C₂²×C₇₃	semidirect
496. #496	C₂²×C₇₃	semidirect
497. #490	C₂²×C₇₃	semidirect
501. #489	C₂²×C₇₃	semidirect
502. #489	C₂²×C₇₃	semidirect
503. #489	C₂²×C₇₃	semidirect
504. #489	C₂²×C₇₃	semidirect
505. #487	C₂²×C₇₃	semidirect
507. #484	C₂²×C₇₃	semidirect
508. #483	C₂²×C₇₃	semidirect
511. #477	C₂²×C₇₃	semidirect
512. #476	C₂²×C₇₃	semidirect
513. #475	C₂²×C₇₃	semidirect
516. #468	C₂²×C₇₃	semidirect
518. #465	C₂²×C₇₃	semidirect
520. #463	C₂²×C₇₃	semidirect
521. #461	C₂²×C₇₃	semidirect
523. #449	C₂²×C₇₃	semidirect
524. #448	C₂²×C₇₃	semidirect
526. #446	C₂²×C₇₃	semidirect
527. #442	C₂²×C₇₃	semidirect
528. #440	C₂²×C₇₃	semidirect
529. C₄×SD₁₆	C₂²×C₇₃	semidirect
531. #435	C₂²×C₇₃	semidirect
533. #432	C₂²×C₇₃	semidirect
534. #432	C₂²×C₇₃	semidirect
535. #417	C₂²×C₇₃	semidirect
536. C₂×#103	C₂²×C₇₃	semidirect
538. C₄×M₁₆	C₂²×C₇₃	semidirect
539. C₂×#97	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3514	2
C₇₃×#3499	2
C₇₃×#3373	2
C₇₃×#3367	2
C₇₃×#3308	2
C₇₃×#3306	2
C₇₃×#3298	2
C₇₃×#3294	2
C₇₃×#3239	2
C₇₃×#3238	2
C₇₃×#3214	2
C₇₃×#3213	2
C₇₃×#3180	2
C₇₃×#3171	2
C₇₃×#3141	2
C₂×#489×C₇₃	2
C₇₃×#2970	2
#62583	73

Subgroups — C73×#62583 #32971987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62583 #32971987