Subgroups — C₇₃×#62559 #32971963

Order 18688.

1666 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3561	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3327	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3314	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3312	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3223	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₇₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×#488×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
20	#564×C₇₃	—	2	1	no	—
21	#563×C₇₃	—	2	1	no	—
22	#563×C₇₃	—	2	1	no	—
23	#562×C₇₃	—	2	1	no	—
24	#557×C₇₃	C₂²	1	2	yes	complemented
25	#556×C₇₃	C₂²	1	2	yes	—
26	#554×C₇₃	C₂²	1	2	yes	—
27	#552×C₇₃	—	2	2	no	—
28	#552×C₇₃	C₂²	1	2	yes	—
29	#552×C₇₃	C₂²	1	2	yes	complemented
30	#551×C₇₃	—	2	2	no	—
31	D₄×Q₈×C₇₃	C₂²	1	2	yes	—
32	#548×C₇₃	C₂²	1	2	yes	—
33	#546×C₇₃	C₂²	1	2	yes	—
34	#544×C₇₃	—	2	1	no	—
35	#544×C₇₃	C₂²	1	2	yes	complemented
36	#543×C₇₃	—	2	1	no	—
37	#542×C₇₃	—	2	2	no	—
38	#542×C₇₃	C₂²	1	2	yes	—
39	#541×C₇₃	—	2	2	no	—
40	#541×C₇₃	C₂²	1	2	yes	complemented
41	#539×C₇₃	—	2	1	no	—
42	#538×C₇₃	—	2	1	no	—
43	#536×C₇₃	C₂²	1	2	yes	—
44	#533×C₇₃	C₂²	1	1	yes	characteristic
45	#533×C₇₃	C₂²	1	1	yes	characteristic
46	#529×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
49	#501×C₇₃	C₂²	1	2	yes	complemented
50	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	#497×C₇₃	C₂²	1	2	yes	—
52	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	#491×C₇₃	C₂²	1	2	yes	complemented
54	#491×C₇₃	C₂²	1	2	yes	complemented
55	#489×C₇₃	C₂²	1	2	yes	—
56	#489×C₇₃	C₂²	1	2	yes	—
57	#488×C₇₃	C₂²	1	2	yes	—
58	#488×C₇₃	C₂²	1	2	yes	—
59	#488×C₇₃	C₂²	1	2	yes	—
60	#488×C₇₃	C₂²	1	2	yes	—
61	#488×C₇₃	C₂²	1	2	yes	—
62	#487×C₇₃	C₂²	1	2	yes	complemented
63	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	#485×C₇₃	C₂²	1	2	yes	complemented
66	#484×C₇₃	C₂²	1	2	yes	—
67	#484×C₇₃	C₂²	1	2	yes	complemented
68	#483×C₇₃	C₂²	1	2	yes	—
69	#482×C₇₃	C₂²	1	2	yes	—
70	#480×C₇₃	C₂²	1	2	yes	—
71	#479×C₇₃	C₂²	1	2	yes	complemented
72	#479×C₇₃	C₂²	1	2	yes	complemented
73	#479×C₇₃	C₂²	1	2	yes	complemented
74	#478×C₇₃	C₂²	1	2	yes	—
75	#477×C₇₃	C₂²	1	2	yes	complemented
76	#474×C₇₃	C₂²	1	2	yes	—
77	#470×C₇₃	C₂²	1	2	yes	complemented
78	#468×C₇₃	C₂²	1	2	yes	—
79	#467×C₇₃	C₂²	1	2	yes	—
80	#467×C₇₃	C₂²	1	2	yes	—
81	#467×C₇₃	C₂²	1	2	yes	complemented
82	#465×C₇₃	C₂²	1	2	yes	—
83	#464×C₇₃	C₂²	1	2	yes	—
84	#464×C₇₃	C₂²	1	2	yes	—
85	#464×C₇₃	C₂²	1	2	yes	—
86	#464×C₇₃	C₂²	1	2	yes	—
87	#462×C₇₃	C₂²	1	2	yes	complemented
88	#462×C₇₃	C₂²	1	2	yes	complemented
89	#452×C₇₃	C₂²	1	2	yes	—
90	#452×C₇₃	C₂²	1	2	yes	—
91	#451×C₇₃	C₂²	1	2	yes	—
92	#451×C₇₃	C₂²	1	2	yes	complemented
93	#451×C₇₃	C₂²	1	2	yes	complemented
94	#450×C₇₃	C₂²	1	2	yes	—
95	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
96	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
97	#441×C₇₃	C₂²	1	2	yes	complemented
98	#440×C₇₃	C₂²	1	2	yes	—
99	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
103	#436×C₇₃	C₂²	1	1	yes	characteristic, complemented
104	#435×C₇₃	C₂²	1	2	yes	—
105	C₈×D₄×C₇₃	C₂²	1	2	yes	—
106	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
107	#433×C₇₃	C₂²	1	2	yes	complemented
108	#432×C₇₃	C₂²	1	1	yes	characteristic
109	#419×C₇₃	C₂²	1	2	yes	complemented
110	#417×C₇₃	C₂²	1	2	yes	—
111	#416×C₇₃	C₂²	1	2	yes	—
112	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
113	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
114	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
115	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
116	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
117	#405×C₇₃	C₂²	1	2	yes	complemented
118	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₃	C₂³	1	2	yes	—
120	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₇₃	—	2	2	no	—
134	C₄⋊Q₈×C₇₃	—	2	2	no	—
135	C₄⋊Q₈×C₇₃	—	2	2	no	—
136	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
141	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
142	#126×C₇₃	—	2	2	no	—
143	#126×C₇₃	—	2	2	no	—
144	#126×C₇₃	—	2	2	no	—
145	#126×C₇₃	—	2	2	no	—
146	#126×C₇₃	—	2	2	no	—
147	#126×C₇₃	—	2	2	no	—
148	#126×C₇₃	—	2	2	no	—
149	#126×C₇₃	D₄	1	2	yes	—
150	#125×C₇₃	—	2	2	no	—
151	#125×C₇₃	—	2	2	no	—
152	#125×C₇₃	—	2	2	no	—
153	#125×C₇₃	—	2	2	no	—
154	#125×C₇₃	—	2	2	no	—
155	#125×C₇₃	—	2	2	no	—
156	#125×C₇₃	—	2	2	no	—
157	#125×C₇₃	—	2	2	no	—
158	#125×C₇₃	—	2	1	no	—
159	#125×C₇₃	—	2	1	no	—
160	#125×C₇₃	—	2	1	no	—
161	#125×C₇₃	—	2	1	no	—
162	#125×C₇₃	D₄	1	1	yes	characteristic
163	#125×C₇₃	C₂³	1	2	yes	—
164	#125×C₇₃	C₂³	1	2	yes	—
165	#125×C₇₃	C₂³	1	2	yes	—
166	#124×C₇₃	—	2	2	no	—
167	#124×C₇₃	—	2	2	no	—
168	#124×C₇₃	—	2	1	no	—
169	#124×C₇₃	—	2	1	no	—
170	#124×C₇₃	D₄	1	1	yes	characteristic
171	#124×C₇₃	C₂³	1	2	yes	—
172	#124×C₇₃	C₂³	1	2	yes	—
173	#124×C₇₃	C₂³	1	2	yes	—
174	#123×C₇₃	—	2	2	no	—
175	#123×C₇₃	—	2	2	no	—
176	#123×C₇₃	—	2	2	no	—
177	#123×C₇₃	—	2	2	no	—
178	#123×C₇₃	—	2	2	no	—
179	#123×C₇₃	—	2	2	no	—
180	#123×C₇₃	D₄	1	2	yes	—
181	C₂²⋊Q₈×C₇₃	—	2	2	no	—
182	C₂²⋊Q₈×C₇₃	—	2	1	no	—
183	C₂²⋊Q₈×C₇₃	—	2	1	no	—
184	C₂²⋊Q₈×C₇₃	—	2	2	no	—
185	C₂²⋊Q₈×C₇₃	—	2	2	no	—
186	C₂²⋊Q₈×C₇₃	—	2	2	no	—
187	C₂²⋊Q₈×C₇₃	—	2	2	no	—
188	C₂²⋊Q₈×C₇₃	—	2	2	no	—
189	C₂²⋊Q₈×C₇₃	—	2	2	no	—
190	C₂²⋊Q₈×C₇₃	—	2	2	no	—
191	C₂²⋊Q₈×C₇₃	—	2	2	no	—
192	C₂²⋊Q₈×C₇₃	—	2	2	no	—
193	C₂²⋊Q₈×C₇₃	—	2	2	no	—
194	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
195	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
200	#121×C₇₃	—	2	2	no	—
201	#121×C₇₃	—	2	2	no	—
202	#121×C₇₃	D₄	1	1	yes	characteristic
203	#121×C₇₃	C₂³	1	2	yes	—
204	#120×C₇₃	—	2	2	no	—
205	C₄×Q₈×C₇₃	—	2	2	no	—
206	C₄×Q₈×C₇₃	—	2	1	no	—
207	C₄×Q₈×C₇₃	—	2	1	no	—
208	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₇₃	—	2	2	no	—
215	C₄×D₄×C₇₃	—	2	2	no	—
216	C₄×D₄×C₇₃	—	2	2	no	—
217	C₄×D₄×C₇₃	C₂³	1	2	yes	—
218	C₄×D₄×C₇₃	C₂³	1	2	yes	—
219	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
220	#117×C₇₃	—	2	1	no	—
221	#117×C₇₃	—	2	1	no	—
222	#117×C₇₃	—	2	2	no	—
223	#117×C₇₃	—	2	2	no	—
224	#117×C₇₃	—	2	2	no	—
225	#117×C₇₃	C₂³	1	2	yes	—
226	#117×C₇₃	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
228	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
234	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
235	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
236	#107×C₇₃	C₂³	1	2	yes	—
237	#107×C₇₃	C₂³	1	2	yes	—
238	#107×C₇₃	C₂³	1	2	yes	—
239	#107×C₇₃	C₂³	1	2	yes	—
240	#106×C₇₃	C₂³	1	2	yes	—
241	#106×C₇₃	C₂³	1	2	yes	—
242	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
243	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
244	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
245	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
246	#103×C₇₃	C₂³	1	2	yes	—
247	#103×C₇₃	C₂³	1	2	yes	—
248	#103×C₇₃	C₂³	1	2	yes	—
249	#103×C₇₃	C₂³	1	2	yes	—
250	#103×C₇₃	C₂³	1	2	yes	—
251	#103×C₇₃	C₂³	1	2	yes	—
252	#103×C₇₃	C₂³	1	2	yes	—
253	#103×C₇₃	C₂³	1	2	yes	—
254	#103×C₇₃	C₂³	1	2	yes	—
255	#103×C₇₃	C₂³	1	2	yes	—
256	#103×C₇₃	C₂³	1	2	yes	—
257	#103×C₇₃	C₂³	1	2	yes	—
258	#103×C₇₃	C₂³	1	2	yes	—
259	#103×C₇₃	C₂³	1	2	yes	—
260	#102×C₇₃	C₂³	1	2	yes	—
261	#102×C₇₃	C₂³	1	2	yes	—
262	#102×C₇₃	C₂³	1	2	yes	—
263	#102×C₇₃	C₂³	1	2	yes	—
264	#102×C₇₃	C₂³	1	2	yes	—
265	#102×C₇₃	C₂³	1	2	yes	—
266	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
267	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
268	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
269	#97×C₇₃	C₂³	1	2	yes	—
270	#97×C₇₃	C₂³	1	2	yes	—
271	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
273	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
274	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₄×C₈×C₇₃	C₂³	1	2	yes	—
276	C₂⁴×C₇₃	—	2	1	no	—
277	#41×C₇₃	—	4	2	no	—
278	#41×C₇₃	—	4	2	no	—
279	C₂×Q₈×C₇₃	—	2	1	no	—
280	C₂×Q₈×C₇₃	—	2	1	no	—
281	C₂×Q₈×C₇₃	—	2	2	no	—
282	C₂×Q₈×C₇₃	—	2	2	no	—
283	C₂×Q₈×C₇₃	—	2	1	no	—
284	C₂×Q₈×C₇₃	—	4	1	no	—
285	C₂×Q₈×C₇₃	—	4	1	no	—
286	C₂×Q₈×C₇₃	—	4	2	no	—
287	C₂×Q₈×C₇₃	—	4	2	no	—
288	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
289	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₇₃	—	2	2	no	—
293	C₂×D₄×C₇₃	—	2	2	no	—
294	C₂×D₄×C₇₃	—	2	1	no	—
295	C₂×D₄×C₇₃	—	4	1	no	—
296	C₂×D₄×C₇₃	—	4	1	no	—
297	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
298	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
299	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇₃	—	2	1	no	—
301	C₂²×C₄×C₇₃	—	2	1	no	—
302	C₂²×C₄×C₇₃	—	2	1	no	—
303	C₂²×C₄×C₇₃	—	2	2	no	—
304	C₂²×C₄×C₇₃	—	2	2	no	—
305	C₂²×C₄×C₇₃	—	2	2	no	—
306	C₂²×C₄×C₇₃	—	2	2	no	—
307	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
311	Q₁₆×C₇₃	—	4	2	no	—
312	Q₁₆×C₇₃	—	4	2	no	—
313	Q₁₆×C₇₃	—	4	2	no	—
314	Q₁₆×C₇₃	—	4	2	no	—
315	SD₁₆×C₇₃	—	4	2	no	—
316	SD₁₆×C₇₃	—	4	2	no	—
317	M₁₆×C₇₃	—	4	2	no	—
318	C₂×C₈×C₇₃	—	4	2	no	—
319	C₂×C₈×C₇₃	—	4	1	no	—
320	C₂×C₈×C₇₃	—	4	1	no	—
321	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
323	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₇₃	—	2	2	no	—
328	C₄⋊C₄×C₇₃	—	2	2	no	—
329	C₄⋊C₄×C₇₃	—	2	2	no	—
330	C₄⋊C₄×C₇₃	—	2	2	no	—
331	C₄⋊C₄×C₇₃	—	2	1	no	—
332	C₄⋊C₄×C₇₃	—	2	2	no	—
333	C₄⋊C₄×C₇₃	—	2	1	no	—
334	C₄⋊C₄×C₇₃	—	2	2	no	—
335	C₄⋊C₄×C₇₃	—	2	1	no	—
336	C₄⋊C₄×C₇₃	—	2	1	no	—
337	C₄⋊C₄×C₇₃	—	2	2	no	—
338	C₄⋊C₄×C₇₃	—	2	2	no	—
339	C₄⋊C₄×C₇₃	—	2	2	no	—
340	C₄⋊C₄×C₇₃	—	2	1	no	—
341	C₄⋊C₄×C₇₃	—	2	1	no	—
342	C₄⋊C₄×C₇₃	—	2	2	no	—
343	C₄⋊C₄×C₇₃	—	2	2	no	—
344	C₄⋊C₄×C₇₃	—	2	2	no	—
345	C₄⋊C₄×C₇₃	—	2	2	no	—
346	C₄⋊C₄×C₇₃	—	2	1	no	—
347	C₄⋊C₄×C₇₃	—	2	2	no	—
348	C₄⋊C₄×C₇₃	—	2	2	no	—
349	C₄⋊C₄×C₇₃	—	2	1	no	—
350	C₄⋊C₄×C₇₃	—	2	2	no	—
351	C₄⋊C₄×C₇₃	—	2	2	no	—
352	C₄⋊C₄×C₇₃	—	2	2	no	—
353	C₄⋊C₄×C₇₃	—	2	2	no	—
354	C₄⋊C₄×C₇₃	—	2	2	no	—
355	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
365	C₂²⋊C₄×C₇₃	—	2	2	no	—
366	C₂²⋊C₄×C₇₃	—	2	2	no	—
367	C₂²⋊C₄×C₇₃	—	2	2	no	—
368	C₂²⋊C₄×C₇₃	—	2	2	no	—
369	C₂²⋊C₄×C₇₃	—	2	2	no	—
370	C₂²⋊C₄×C₇₃	—	2	2	no	—
371	C₂²⋊C₄×C₇₃	—	2	2	no	—
372	C₂²⋊C₄×C₇₃	—	2	2	no	—
373	C₂²⋊C₄×C₇₃	—	2	2	no	—
374	C₂²⋊C₄×C₇₃	—	2	2	no	—
375	C₂²⋊C₄×C₇₃	—	2	2	no	—
376	C₂²⋊C₄×C₇₃	—	2	2	no	—
377	C₂²⋊C₄×C₇₃	—	2	2	no	—
378	C₂²⋊C₄×C₇₃	—	2	2	no	—
379	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
384	C₄²×C₇₃	—	2	2	no	—
385	C₄²×C₇₃	—	2	2	no	—
386	C₄²×C₇₃	—	2	2	no	—
387	C₄²×C₇₃	—	2	2	no	—
388	C₄²×C₇₃	—	2	2	no	—
389	C₄²×C₇₃	—	2	2	no	—
390	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
393	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₇₃	C₂⁴	1	2	yes	—
395	C₂³×C₇₃	—	2	2	no	—
396	C₂³×C₇₃	—	4	2	no	—
397	C₂³×C₇₃	—	8	1	no	—
398	C₂³×C₇₃	—	8	1	no	—
399	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
400	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
401	Q₈×C₇₃	—	2	2	no	—
402	Q₈×C₇₃	—	2	2	no	—
403	Q₈×C₇₃	—	2	2	no	—
404	Q₈×C₇₃	—	2	2	no	—
405	Q₈×C₇₃	—	2	2	no	—
406	Q₈×C₇₃	—	2	2	no	—
407	Q₈×C₇₃	—	4	1	no	—
408	Q₈×C₇₃	—	8	1	no	—
409	Q₈×C₇₃	—	8	1	no	—
410	Q₈×C₇₃	—	8	2	no	—
411	Q₈×C₇₃	—	8	2	no	—
412	Q₈×C₇₃	—	8	1	no	—
413	D₄×C₇₃	—	2	4	no	—
414	D₄×C₇₃	—	2	2	no	—
415	D₄×C₇₃	—	2	2	no	—
416	D₄×C₇₃	—	4	1	no	—
417	D₄×C₇₃	—	8	1	no	—
418	D₄×C₇₃	—	8	2	no	—
419	D₄×C₇₃	—	8	2	no	—
420	C₂×C₄×C₇₃	—	2	2	no	—
421	C₂×C₄×C₇₃	—	2	1	no	—
422	C₂×C₄×C₇₃	—	2	1	no	—
423	C₂×C₄×C₇₃	—	2	2	no	—
424	C₂×C₄×C₇₃	—	2	2	no	—
425	C₂×C₄×C₇₃	—	2	2	no	—
426	C₂×C₄×C₇₃	—	2	2	no	—
427	C₂×C₄×C₇₃	—	2	2	no	—
428	C₂×C₄×C₇₃	—	2	2	no	—
429	C₂×C₄×C₇₃	—	2	2	no	—
430	C₂×C₄×C₇₃	—	2	2	no	—
431	C₂×C₄×C₇₃	—	2	2	no	—
432	C₂×C₄×C₇₃	—	4	1	no	—
433	C₂×C₄×C₇₃	—	4	2	no	—
434	C₂×C₄×C₇₃	—	8	2	no	—
435	C₂×C₄×C₇₃	—	8	2	no	—
436	C₂×C₄×C₇₃	—	8	1	no	—
437	C₂×C₄×C₇₃	—	8	2	no	—
438	C₂×C₄×C₇₃	—	8	2	no	—
439	C₂×C₄×C₇₃	—	8	1	no	—
440	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
449	C₈×C₇₃	—	2	1	no	—
450	C₈×C₇₃	—	2	1	no	—
451	C₈×C₇₃	—	2	2	no	—
452	C₈×C₇₃	—	2	1	no	—
453	C₈×C₇₃	—	2	1	no	—
454	C₈×C₇₃	—	2	2	no	—
455	C₂²×C₇₃	—	2	1	no	—
456	C₂²×C₇₃	—	2	1	no	—
457	C₂²×C₇₃	—	2	2	no	—
458	C₂²×C₇₃	—	2	2	no	—
459	C₂²×C₇₃	—	2	2	no	—
460	C₂²×C₇₃	—	4	2	no	—
461	C₂²×C₇₃	—	4	2	no	—
462	C₂²×C₇₃	—	4	2	no	—
463	C₂²×C₇₃	—	16	2	no	—
464	C₂²×C₇₃	#578	1	2	yes	—
465	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₇₃	—	2	1	no	—
467	C₄×C₇₃	—	2	1	no	—
468	C₄×C₇₃	—	2	2	no	—
469	C₄×C₇₃	—	2	2	no	—
470	C₄×C₇₃	—	2	1	no	—
471	C₄×C₇₃	—	2	1	no	—
472	C₄×C₇₃	—	2	1	no	—
473	C₄×C₇₃	—	2	2	no	—
474	C₄×C₇₃	—	4	2	no	—
475	C₄×C₇₃	—	4	2	no	—
476	C₄×C₇₃	—	4	2	no	—
477	C₄×C₇₃	—	4	2	no	—
478	C₄×C₇₃	—	4	2	no	—
479	C₄×C₇₃	—	4	2	no	—
480	C₄×C₇₃	—	4	2	no	—
481	C₄×C₇₃	#585	1	1	yes	characteristic
482	C₄×C₇₃	#585	1	1	yes	characteristic
483	#62559	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂×C₇₃	—	2	2	no	—
485	C₂×C₇₃	—	4	2	no	—
486	C₂×C₇₃	—	8	2	no	—
487	C₂×C₇₃	#3500	1	1	yes	characteristic
488	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
489	C₂×C₇₃	#3584	1	1	yes	characteristic
490	#3563	C₂×C₇₃	1	1	yes	characteristic, complemented
491	#3561	C₂×C₇₃	1	1	yes	characteristic
492	#3377	C₂×C₇₃	1	2	yes	complemented
493	#3364	C₂×C₇₃	1	2	yes	complemented
494	#3327	C₂×C₇₃	1	2	yes	complemented
495	#3314	C₂×C₇₃	1	2	yes	complemented
496	#3312	C₂×C₇₃	1	2	yes	complemented
497	#3300	C₂×C₇₃	1	2	yes	complemented
498	#3299	C₂×C₇₃	1	2	yes	complemented
499	#3296	C₂×C₇₃	1	2	yes	complemented
500	#3243	C₂×C₇₃	1	2	yes	complemented
501	#3236	C₂×C₇₃	1	1	yes	characteristic, complemented
502	#3223	C₂×C₇₃	1	2	yes	complemented
503	#3215	C₂×C₇₃	1	1	yes	characteristic, complemented
504	#3178	C₂×C₇₃	1	2	yes	complemented
505	#3170	C₂×C₇₃	1	1	yes	characteristic, complemented
506	#3137	C₂×C₇₃	1	2	yes	complemented
507	C₂×#488	C₂×C₇₃	1	1	yes	characteristic, complemented
508	#2966	C₂×C₇₃	1	1	yes	characteristic, complemented
509	C₇₃	#62559	1	1	yes	characteristic, direct product factor, Sylow
510	#564	—	2	1	no	—
511	#563	—	2	1	no	—
512	#563	—	2	1	no	—
513	#562	—	2	1	no	—
514	#557	C₂²×C₇₃	1	2	yes	complemented
515	#556	C₂²×C₇₃	1	2	yes	—
516	#554	C₂²×C₇₃	1	2	yes	—
517	#552	—	2	2	no	—
518	#552	C₂²×C₇₃	1	2	yes	—
519	#552	C₂²×C₇₃	1	2	yes	complemented
520	#551	—	2	2	no	—
521	D₄×Q₈	C₂²×C₇₃	1	2	yes	—
522	#548	C₂²×C₇₃	1	2	yes	—
523	#546	C₂²×C₇₃	1	2	yes	—
524	#544	—	2	1	no	—
525	#544	C₂²×C₇₃	1	2	yes	complemented
526	#543	—	2	1	no	—
527	#542	—	2	2	no	—
528	#542	C₂²×C₇₃	1	2	yes	—
529	#541	—	2	2	no	—
530	#541	C₂²×C₇₃	1	2	yes	complemented
531	#539	—	2	1	no	—
532	#538	—	2	1	no	—
533	#536	C₂²×C₇₃	1	2	yes	—
534	#533	C₂²×C₇₃	1	1	yes	characteristic
535	#533	C₂²×C₇₃	1	1	yes	characteristic
536	#529	C₂²×C₇₃	1	1	yes	characteristic
537	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
538	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
539	#501	C₂²×C₇₃	1	2	yes	complemented
540	#500	C₂²×C₇₃	1	1	yes	characteristic, complemented
541	#497	C₂²×C₇₃	1	2	yes	—
542	#494	C₂²×C₇₃	1	1	yes	characteristic, complemented
543	#491	C₂²×C₇₃	1	2	yes	complemented
544	#491	C₂²×C₇₃	1	2	yes	complemented
545	#489	C₂²×C₇₃	1	2	yes	—
546	#489	C₂²×C₇₃	1	2	yes	—
547	#488	C₂²×C₇₃	1	2	yes	—
548	#488	C₂²×C₇₃	1	2	yes	—
549	#488	C₂²×C₇₃	1	2	yes	—
550	#488	C₂²×C₇₃	1	2	yes	—
551	#488	C₂²×C₇₃	1	2	yes	—
552	#487	C₂²×C₇₃	1	2	yes	complemented
553	#487	C₂²×C₇₃	1	1	yes	characteristic, complemented
554	#487	C₂²×C₇₃	1	1	yes	characteristic, complemented
555	#485	C₂²×C₇₃	1	2	yes	complemented
556	#484	C₂²×C₇₃	1	2	yes	—
557	#484	C₂²×C₇₃	1	2	yes	complemented
558	#483	C₂²×C₇₃	1	2	yes	—
559	#482	C₂²×C₇₃	1	2	yes	—
560	#480	C₂²×C₇₃	1	2	yes	—
561	#479	C₂²×C₇₃	1	2	yes	complemented
562	#479	C₂²×C₇₃	1	2	yes	complemented
563	#479	C₂²×C₇₃	1	2	yes	complemented
564	#478	C₂²×C₇₃	1	2	yes	—
565	#477	C₂²×C₇₃	1	2	yes	complemented
566	#474	C₂²×C₇₃	1	2	yes	—
567	#470	C₂²×C₇₃	1	2	yes	complemented
568	#468	C₂²×C₇₃	1	2	yes	—
569	#467	C₂²×C₇₃	1	2	yes	—
570	#467	C₂²×C₇₃	1	2	yes	—
571	#467	C₂²×C₇₃	1	2	yes	complemented
572	#465	C₂²×C₇₃	1	2	yes	—
573	#464	C₂²×C₇₃	1	2	yes	—
574	#464	C₂²×C₇₃	1	2	yes	—
575	#464	C₂²×C₇₃	1	2	yes	—
576	#464	C₂²×C₇₃	1	2	yes	—
577	#462	C₂²×C₇₃	1	2	yes	complemented
578	#462	C₂²×C₇₃	1	2	yes	complemented
579	#452	C₂²×C₇₃	1	2	yes	—
580	#452	C₂²×C₇₃	1	2	yes	—
581	#451	C₂²×C₇₃	1	2	yes	—
582	#451	C₂²×C₇₃	1	2	yes	complemented
583	#451	C₂²×C₇₃	1	2	yes	complemented
584	#450	C₂²×C₇₃	1	2	yes	—
585	#446	C₂²×C₇₃	1	1	yes	characteristic, complemented
586	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
587	#441	C₂²×C₇₃	1	2	yes	complemented
588	#440	C₂²×C₇₃	1	2	yes	—
589	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
590	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
591	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
592	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
593	#436	C₂²×C₇₃	1	1	yes	characteristic, complemented
594	#435	C₂²×C₇₃	1	2	yes	—
595	C₈×D₄	C₂²×C₇₃	1	2	yes	—
596	C₈×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
597	#433	C₂²×C₇₃	1	2	yes	complemented
598	#432	C₂²×C₇₃	1	1	yes	characteristic
599	#419	C₂²×C₇₃	1	2	yes	complemented
600	#417	C₂²×C₇₃	1	2	yes	—
601	#416	C₂²×C₇₃	1	2	yes	—
602	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
603	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
604	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
605	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
606	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
607	#405	C₂²×C₇₃	1	2	yes	complemented
608	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
609	C₂×#41	C₂³×C₇₃	1	2	yes	—
610	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
611	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
612	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
613	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
614	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
615	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
616	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
619	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
620	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
623	C₄⋊Q₈	—	2	2	no	—
624	C₄⋊Q₈	—	2	2	no	—
625	C₄⋊Q₈	—	2	2	no	—
626	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
627	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
628	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	D₄×C₇₃	1	2	yes	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	D₄×C₇₃	1	1	yes	characteristic
653	#125	C₂³×C₇₃	1	2	yes	—
654	#125	C₂³×C₇₃	1	2	yes	—
655	#125	C₂³×C₇₃	1	2	yes	—
656	#124	—	2	2	no	—
657	#124	—	2	2	no	—
658	#124	—	2	1	no	—
659	#124	—	2	1	no	—
660	#124	D₄×C₇₃	1	1	yes	characteristic
661	#124	C₂³×C₇₃	1	2	yes	—
662	#124	C₂³×C₇₃	1	2	yes	—
663	#124	C₂³×C₇₃	1	2	yes	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	D₄×C₇₃	1	2	yes	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	1	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	D₄×C₇₃	1	1	yes	characteristic
693	#121	C₂³×C₇₃	1	2	yes	—
694	#120	—	2	2	no	—
695	C₄×Q₈	—	2	2	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
699	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
700	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
701	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
702	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
703	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	C₂³×C₇₃	1	2	yes	—
708	C₄×D₄	C₂³×C₇₃	1	2	yes	—
709	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
710	#117	—	2	1	no	—
711	#117	—	2	1	no	—
712	#117	—	2	2	no	—
713	#117	—	2	2	no	—
714	#117	—	2	2	no	—
715	#117	C₂³×C₇₃	1	2	yes	—
716	#117	C₂³×C₇₃	1	2	yes	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	—	2	1	no	—
719	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
722	C₂×C₂²⋊C₄	—	2	1	no	—
723	C₂×C₂²⋊C₄	—	2	1	no	—
724	C₂×C₂²⋊C₄	—	2	2	no	—
725	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
726	#107	C₂³×C₇₃	1	2	yes	—
727	#107	C₂³×C₇₃	1	2	yes	—
728	#107	C₂³×C₇₃	1	2	yes	—
729	#107	C₂³×C₇₃	1	2	yes	—
730	#106	C₂³×C₇₃	1	2	yes	—
731	#106	C₂³×C₇₃	1	2	yes	—
732	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
733	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
734	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
735	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
736	#103	C₂³×C₇₃	1	2	yes	—
737	#103	C₂³×C₇₃	1	2	yes	—
738	#103	C₂³×C₇₃	1	2	yes	—
739	#103	C₂³×C₇₃	1	2	yes	—
740	#103	C₂³×C₇₃	1	2	yes	—
741	#103	C₂³×C₇₃	1	2	yes	—
742	#103	C₂³×C₇₃	1	2	yes	—
743	#103	C₂³×C₇₃	1	2	yes	—
744	#103	C₂³×C₇₃	1	2	yes	—
745	#103	C₂³×C₇₃	1	2	yes	—
746	#103	C₂³×C₇₃	1	2	yes	—
747	#103	C₂³×C₇₃	1	2	yes	—
748	#103	C₂³×C₇₃	1	2	yes	—
749	#103	C₂³×C₇₃	1	2	yes	—
750	#102	C₂³×C₇₃	1	2	yes	—
751	#102	C₂³×C₇₃	1	2	yes	—
752	#102	C₂³×C₇₃	1	2	yes	—
753	#102	C₂³×C₇₃	1	2	yes	—
754	#102	C₂³×C₇₃	1	2	yes	—
755	#102	C₂³×C₇₃	1	2	yes	—
756	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
759	#97	C₂³×C₇₃	1	2	yes	—
760	#97	C₂³×C₇₃	1	2	yes	—
761	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
762	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
763	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
764	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
765	C₄×C₈	C₂³×C₇₃	1	2	yes	—
766	C₂⁴	—	2	1	no	—
767	#41	—	4	2	no	—
768	#41	—	4	2	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	4	1	no	—
775	C₂×Q₈	—	4	1	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
788	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
789	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
801	Q₁₆	—	4	2	no	—
802	Q₁₆	—	4	2	no	—
803	Q₁₆	—	4	2	no	—
804	Q₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	SD₁₆	—	4	2	no	—
807	M₁₆	—	4	2	no	—
808	C₂×C₈	—	4	2	no	—
809	C₂×C₈	—	4	1	no	—
810	C₂×C₈	—	4	1	no	—
811	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
812	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
813	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
814	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
815	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
846	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
848	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
849	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
850	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
851	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
870	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
871	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
872	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
873	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
881	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
882	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
883	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
884	C₄²	C₂⁴×C₇₃	1	2	yes	—
885	C₂³	—	2	2	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	8	1	no	—
888	C₂³	—	8	1	no	—
889	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
890	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	4	1	no	—
898	Q₈	—	8	2	no	—
899	Q₈	—	8	1	no	—
900	Q₈	—	8	1	no	—
901	Q₈	—	8	1	no	—
902	Q₈	—	8	2	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	2	no	—
906	D₄	—	4	1	no	—
907	D₄	—	8	1	no	—
908	D₄	—	8	2	no	—
909	D₄	—	8	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	1	no	—
928	C₂×C₄	—	8	1	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
934	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
938	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
939	C₈	—	2	1	no	—
940	C₈	—	2	1	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	—	2	1	no	—
944	C₈	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	16	2	no	—
954	C₂²	#578×C₇₃	1	2	yes	—
955	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	#585×C₇₃	1	1	yes	characteristic
972	C₄	#585×C₇₃	1	1	yes	characteristic
973	C₂	—	2	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₇₃×#3500	1	1	yes	characteristic
977	C₂	C₂×#578×C₇₃	1	1	yes	characteristic
978	C₂	C₇₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₇₃×#3561	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #529×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3563	C₂	semidirect
3. C₇₃×#3377	C₂	semidirect
4. C₇₃×#3364	C₂	semidirect
5. C₇₃×#3327	C₂	semidirect
6. C₇₃×#3314	C₂	semidirect
7. C₇₃×#3312	C₂	semidirect
8. C₇₃×#3300	C₂	semidirect
9. C₇₃×#3299	C₂	semidirect
10. C₇₃×#3296	C₂	semidirect
11. C₇₃×#3243	C₂	semidirect
12. C₇₃×#3236	C₂	semidirect
13. C₇₃×#3223	C₂	semidirect
14. C₇₃×#3215	C₂	semidirect
15. C₇₃×#3178	C₂	semidirect
16. C₇₃×#3170	C₂	semidirect
17. C₇₃×#3137	C₂	semidirect
18. C₂×#488×C₇₃	C₂	semidirect
19. C₇₃×#2966	C₂	semidirect
24. #557×C₇₃	C₂²	semidirect
29. #552×C₇₃	C₂²	semidirect
35. #544×C₇₃	C₂²	semidirect
40. #541×C₇₃	C₂²	semidirect
49. #501×C₇₃	C₂²	semidirect
50. #500×C₇₃	C₂²	semidirect
52. #494×C₇₃	C₂²	semidirect
53. #491×C₇₃	C₂²	semidirect
54. #491×C₇₃	C₂²	semidirect
62. #487×C₇₃	C₂²	semidirect
63. #487×C₇₃	C₂²	semidirect
64. #487×C₇₃	C₂²	semidirect
65. #485×C₇₃	C₂²	semidirect
67. #484×C₇₃	C₂²	semidirect
71. #479×C₇₃	C₂²	semidirect
72. #479×C₇₃	C₂²	semidirect
73. #479×C₇₃	C₂²	semidirect
75. #477×C₇₃	C₂²	semidirect
77. #470×C₇₃	C₂²	semidirect
81. #467×C₇₃	C₂²	semidirect
87. #462×C₇₃	C₂²	semidirect
88. #462×C₇₃	C₂²	semidirect
92. #451×C₇₃	C₂²	semidirect
93. #451×C₇₃	C₂²	semidirect
95. #446×C₇₃	C₂²	semidirect
96. C₈×Q₈×C₇₃	C₂²	semidirect
97. #441×C₇₃	C₂²	semidirect
99. C₄×Q₁₆×C₇₃	C₂²	semidirect
100. C₄×Q₁₆×C₇₃	C₂²	semidirect
101. C₄×Q₁₆×C₇₃	C₂²	semidirect
103. #436×C₇₃	C₂²	semidirect
106. C₈×D₄×C₇₃	C₂²	semidirect
107. #433×C₇₃	C₂²	semidirect
109. #419×C₇₃	C₂²	semidirect
114. C₂×#103×C₇₃	C₂²	semidirect
117. #405×C₇₃	C₂²	semidirect
483. #62559	C₇₃	direct (N × H)
490. #3563	C₂×C₇₃	semidirect
492. #3377	C₂×C₇₃	semidirect
493. #3364	C₂×C₇₃	semidirect
494. #3327	C₂×C₇₃	semidirect
495. #3314	C₂×C₇₃	semidirect
496. #3312	C₂×C₇₃	semidirect
497. #3300	C₂×C₇₃	semidirect
498. #3299	C₂×C₇₃	semidirect
499. #3296	C₂×C₇₃	semidirect
500. #3243	C₂×C₇₃	semidirect
501. #3236	C₂×C₇₃	semidirect
502. #3223	C₂×C₇₃	semidirect
503. #3215	C₂×C₇₃	semidirect
504. #3178	C₂×C₇₃	semidirect
505. #3170	C₂×C₇₃	semidirect
506. #3137	C₂×C₇₃	semidirect
507. C₂×#488	C₂×C₇₃	semidirect
508. #2966	C₂×C₇₃	semidirect
509. C₇₃	#62559	direct (N × H)
514. #557	C₂²×C₇₃	semidirect
519. #552	C₂²×C₇₃	semidirect
525. #544	C₂²×C₇₃	semidirect
530. #541	C₂²×C₇₃	semidirect
539. #501	C₂²×C₇₃	semidirect
540. #500	C₂²×C₇₃	semidirect
542. #494	C₂²×C₇₃	semidirect
543. #491	C₂²×C₇₃	semidirect
544. #491	C₂²×C₇₃	semidirect
552. #487	C₂²×C₇₃	semidirect
553. #487	C₂²×C₇₃	semidirect
554. #487	C₂²×C₇₃	semidirect
555. #485	C₂²×C₇₃	semidirect
557. #484	C₂²×C₇₃	semidirect
561. #479	C₂²×C₇₃	semidirect
562. #479	C₂²×C₇₃	semidirect
563. #479	C₂²×C₇₃	semidirect
565. #477	C₂²×C₇₃	semidirect
567. #470	C₂²×C₇₃	semidirect
571. #467	C₂²×C₇₃	semidirect
577. #462	C₂²×C₇₃	semidirect
578. #462	C₂²×C₇₃	semidirect
582. #451	C₂²×C₇₃	semidirect
583. #451	C₂²×C₇₃	semidirect
585. #446	C₂²×C₇₃	semidirect
586. C₈×Q₈	C₂²×C₇₃	semidirect
587. #441	C₂²×C₇₃	semidirect
589. C₄×Q₁₆	C₂²×C₇₃	semidirect
590. C₄×Q₁₆	C₂²×C₇₃	semidirect
591. C₄×Q₁₆	C₂²×C₇₃	semidirect
593. #436	C₂²×C₇₃	semidirect
596. C₈×D₄	C₂²×C₇₃	semidirect
597. #433	C₂²×C₇₃	semidirect
599. #419	C₂²×C₇₃	semidirect
604. C₂×#103	C₂²×C₇₃	semidirect
607. #405	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×#3563	2
C₇₃×#3561	2
C₇₃×#3377	2
C₇₃×#3364	2
C₇₃×#3327	2
C₇₃×#3314	2
C₇₃×#3312	2
C₇₃×#3300	2
C₇₃×#3299	2
C₇₃×#3296	2
C₇₃×#3243	2
C₇₃×#3236	2
C₇₃×#3223	2
C₇₃×#3215	2
C₇₃×#3178	2
C₇₃×#3170	2
C₇₃×#3137	2
C₂×#488×C₇₃	2
C₇₃×#2966	2
#62559	73

Subgroups — C73×#62559 #32971963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62559 #32971963