Subgroups — #33958477

Order 18688.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623685	C₂	1	1	yes	maximal, characteristic
2	#22623336	C₂	1	1	yes	maximal, characteristic, complemented
3	#22621225	C₂	1	2	yes	maximal, complemented
4	#22621210	C₂	1	2	yes	maximal, complemented
5	#22621203	C₂	1	2	yes	maximal, complemented
6	#22621195	C₂	1	2	yes	maximal, complemented
7	#22621169	C₂	1	2	yes	maximal, complemented
8	#22621142	C₂	1	2	yes	maximal, complemented
9	#22621107	C₂	1	2	yes	maximal, complemented
10	#22621088	C₂	1	2	yes	maximal, complemented
11	#22620471	C₂	1	1	yes	maximal, characteristic, complemented
12	#22620463	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620300	C₂	1	1	yes	maximal, characteristic, complemented
14	#22620300	C₂	1	1	yes	maximal, characteristic, complemented
15	#22619879	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619860	C₂	1	1	yes	maximal, characteristic
17	C₂×#17988929	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619791	C₂	1	1	yes	maximal, characteristic, complemented
19	#22619780	C₂	1	1	yes	maximal, characteristic, complemented
20	#22619776	C₂	1	1	yes	maximal, characteristic, complemented
21	#22619776	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618585	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3091	C₂	1	1	yes	maximal, characteristic
24	#17989307	—	2	1	no	—
25	#17989294	—	2	1	no	—
26	#17989277	—	2	1	no	—
27	#17989277	—	2	1	no	—
28	#17989274	—	2	2	no	—
29	#17989268	—	2	2	no	—
30	#17989218	C₂²	1	2	yes	—
31	#17989218	C₂²	1	2	yes	—
32	#17989215	—	2	1	no	—
33	#17989215	—	2	1	no	—
34	#17989215	C₂²	1	1	yes	characteristic
35	#17989215	C₂²	1	1	yes	characteristic
36	#17989215	C₂²	1	1	yes	characteristic
37	#17989215	C₂²	1	1	yes	characteristic
38	#17989215	C₂²	1	1	yes	characteristic
39	#17989213	—	2	2	no	—
40	#17989204	C₂²	1	2	yes	—
41	#17989197	C₂²	1	2	yes	—
42	#17989158	C₂²	1	1	yes	characteristic
43	#17989144	—	2	1	no	—
44	#17989144	—	2	1	no	—
45	#17989140	—	2	2	no	—
46	#17989140	C₂²	1	2	yes	—
47	#17989140	C₂²	1	2	yes	—
48	#17989139	C₂²	1	2	yes	—
49	#17989118	C₂²	1	2	yes	—
50	C₂×#14556570	C₂²	1	1	yes	characteristic
51	#17989070	C₂²	1	1	yes	characteristic
52	#17989064	C₂²	1	1	yes	characteristic
53	C₂×#14556550	C₂²	1	1	yes	characteristic
54	C₂×#14556550	C₂²	1	1	yes	characteristic
55	#17988995	C₂²	1	2	yes	complemented
56	#17988995	C₂²	1	2	yes	complemented
57	#17988994	C₂²	1	2	yes	complemented
58	#17988994	C₂²	1	2	yes	complemented
59	#17988991	C₂²	1	2	yes	complemented
60	#17988988	C₂²	1	2	yes	complemented
61	#17988987	C₂²	1	2	yes	complemented
62	#17988984	C₂²	1	2	yes	complemented
63	#17988954	C₂²	1	2	yes	complemented
64	#17988954	C₂²	1	2	yes	complemented
65	#17988945	C₂²	1	2	yes	complemented
66	#17988945	C₂²	1	2	yes	complemented
67	#17988940	C₂²	1	2	yes	complemented
68	#17988940	C₂²	1	2	yes	complemented
69	#17988936	C₂²	1	2	yes	complemented
70	#17988936	C₂²	1	2	yes	complemented
71	#17988929	C₂²	1	2	yes	—
72	#17988929	C₂²	1	2	yes	—
73	#17988929	C₂²	1	2	yes	—
74	#17988929	C₂²	1	2	yes	—
75	#17988928	C₂²	1	2	yes	—
76	#17988928	C₂²	1	2	yes	—
77	#17988925	C₂²	1	2	yes	—
78	#17988925	C₂²	1	2	yes	—
79	#17988922	C₂²	1	2	yes	—
80	#17988917	C₂²	1	2	yes	—
81	#17988908	C₂²	1	2	yes	—
82	#17988908	C₂²	1	2	yes	—
83	#17988897	C₂²	1	2	yes	complemented
84	#17988897	C₂²	1	2	yes	complemented
85	#17988896	C₂²	1	2	yes	complemented
86	#17988893	C₂²	1	2	yes	complemented
87	#17988893	C₂²	1	2	yes	complemented
88	#17988892	C₂²	1	2	yes	complemented
89	#17988889	C₂²	1	2	yes	complemented
90	#17988885	C₂²	1	2	yes	complemented
91	#17988881	C₂²	1	2	yes	complemented
92	#17988881	C₂²	1	2	yes	complemented
93	#17988880	C₂²	1	2	yes	complemented
94	#17988875	C₂²	1	2	yes	complemented
95	#17988871	C₂²	1	2	yes	complemented
96	#17988871	C₂²	1	2	yes	complemented
97	#17988870	C₂²	1	2	yes	complemented
98	#17988865	C₂²	1	2	yes	complemented
99	#17988645	C₂²	1	2	yes	—
100	#17988645	C₂²	1	2	yes	—
101	#17988641	C₂²	1	2	yes	—
102	#17988637	C₂²	1	2	yes	—
103	#17988630	C₂²	1	1	yes	characteristic
104	#17988630	C₂²	1	1	yes	characteristic
105	#17988630	C₂²	1	1	yes	characteristic
106	#17988630	C₂²	1	1	yes	characteristic
107	C₂×#14556525	C₂²	1	1	yes	characteristic
108	C₂×#14556523	C₂²	1	1	yes	characteristic
109	#17988613	C₂²	1	1	yes	characteristic
110	#17988613	C₂²	1	1	yes	characteristic
111	#17988595	C₂²	1	1	yes	characteristic
112	#17988595	C₂²	1	1	yes	characteristic
113	#17988588	C₂²	1	1	yes	characteristic
114	#17988588	C₂²	1	1	yes	characteristic
115	C₂×#14556516	C₂²	1	1	yes	characteristic
116	C₂×#14556516	C₂²	1	1	yes	characteristic
117	#17988551	C₂²	1	1	yes	characteristic
118	#17988542	C₂²	1	1	yes	characteristic
119	#17988542	C₂²	1	1	yes	characteristic
120	#525×C₇₃	C₂²	1	1	yes	characteristic
121	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
122	#485×C₇₃	C₂²	1	1	yes	characteristic
123	#485×C₇₃	C₂²	1	1	yes	characteristic
124	#484×C₇₃	C₂²	1	1	yes	characteristic
125	#483×C₇₃	C₂²	1	1	yes	characteristic
126	#482×C₇₃	C₂²	1	1	yes	characteristic
127	#482×C₇₃	C₂²	1	1	yes	characteristic
128	#481×C₇₃	C₂²	1	1	yes	characteristic
129	#480×C₇₃	C₂²	1	1	yes	characteristic
130	#427×C₇₃	C₂²	1	1	yes	characteristic
131	#427×C₇₃	C₂²	1	1	yes	characteristic
132	#416×C₇₃	C₂²	1	1	yes	characteristic
133	#416×C₇₃	C₂²	1	1	yes	characteristic
134	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
135	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
136	C₂×#11924012	C₂³	1	1	yes	characteristic
137	C₂×#11924012	C₂³	1	1	yes	characteristic
138	#14556591	—	2	1	no	—
139	#14556591	—	2	1	no	—
140	#14556591	—	2	1	no	—
141	#14556591	—	2	1	no	—
142	#14556591	—	2	1	no	—
143	#14556590	—	2	2	no	—
144	#14556590	—	2	2	no	—
145	#14556590	C₂³	1	2	yes	—
146	#14556590	C₂³	1	2	yes	—
147	#14556590	C₂³	1	2	yes	—
148	#14556590	C₂³	1	2	yes	—
149	#14556590	C₂³	1	2	yes	—
150	#14556589	C₂³	1	2	yes	—
151	#14556584	—	2	2	no	—
152	#14556584	—	2	2	no	—
153	#14556584	—	2	2	no	—
154	#14556584	—	2	2	no	—
155	#14556583	—	2	1	no	—
156	#14556583	—	2	1	no	—
157	#14556583	—	2	1	no	—
158	#14556583	—	2	1	no	—
159	#14556583	—	2	1	no	—
160	#14556582	—	2	2	no	—
161	#14556582	—	2	2	no	—
162	#14556582	—	2	2	no	—
163	#14556582	C₂³	1	2	yes	—
164	#14556582	C₂³	1	2	yes	—
165	#14556582	C₂³	1	2	yes	—
166	#14556582	C₂³	1	2	yes	—
167	#14556582	C₂³	1	2	yes	—
168	#14556581	—	2	2	no	—
169	#14556581	—	2	2	no	—
170	#14556578	—	2	2	no	—
171	#14556578	C₂³	1	2	yes	—
172	#14556572	—	2	2	no	—
173	#14556572	—	2	2	no	—
174	#14556572	—	2	2	no	—
175	#14556570	—	2	1	no	—
176	#14556570	—	2	1	no	—
177	#14556570	—	2	2	no	—
178	#14556570	—	2	2	no	—
179	#14556570	—	2	2	no	—
180	#14556570	—	2	2	no	—
181	#14556570	—	2	1	no	—
182	#14556570	—	2	1	no	—
183	#14556570	C₂³	1	2	yes	—
184	#14556570	C₂³	1	2	yes	—
185	#14556568	—	2	2	no	—
186	#14556568	—	2	2	no	—
187	#14556568	—	2	2	no	—
188	#14556568	—	2	2	no	—
189	#14556568	—	2	2	no	—
190	#14556568	—	2	2	no	—
191	#14556568	—	2	2	no	—
192	#14556568	—	2	2	no	—
193	#14556568	—	2	2	no	—
194	#14556568	—	2	2	no	—
195	#14556568	—	2	2	no	—
196	Q₈×Dic₇₃	C₂³	1	2	yes	—
197	C₄×Dic₁₄₆	—	2	1	no	—
198	C₄×Dic₁₄₆	—	2	1	no	—
199	C₄×Dic₁₄₆	—	2	2	no	—
200	C₄×Dic₁₄₆	—	2	2	no	—
201	C₄×Dic₁₄₆	—	2	2	no	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	#14556556	—	2	2	no	—
204	#14556556	C₂³	1	2	yes	—
205	#14556556	C₂³	1	2	yes	—
206	D₄×Dic₇₃	—	2	2	no	—
207	D₄×Dic₇₃	—	2	2	no	—
208	D₄×Dic₇₃	C₂³	1	2	yes	—
209	#14556550	—	2	1	no	—
210	#14556550	—	2	1	no	—
211	#14556550	—	2	1	no	—
212	#14556550	D₄	1	2	yes	—
213	#14556550	D₄	1	1	yes	characteristic
214	#14556550	D₄	1	1	yes	characteristic
215	#14556550	C₂³	1	2	yes	—
216	#14556550	C₂³	1	2	yes	—
217	#14556550	C₂³	1	1	yes	characteristic
218	#14556550	C₂³	1	2	yes	—
219	#14556550	C₂³	1	1	yes	characteristic
220	#14556547	—	2	2	no	—
221	#14556547	—	2	2	no	—
222	#14556547	—	2	2	no	—
223	C₂×C₄⋊Dic₇₃	—	2	1	no	—
224	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
225	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
226	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
229	C₂×#11924007	—	2	1	no	—
230	C₂×C₂²⋊Dic₇₃	—	2	1	no	—
231	C₂×C₂²⋊Dic₇₃	—	2	1	no	—
232	C₂×C₂²⋊Dic₇₃	D₄	1	2	yes	—
233	C₂×C₄×Dic₇₃	—	2	1	no	—
234	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
235	#14556525	C₂³	1	2	yes	—
236	#14556525	C₂³	1	2	yes	—
237	#14556524	C₂³	1	2	yes	—
238	#14556524	C₂³	1	2	yes	—
239	#14556524	C₂³	1	2	yes	—
240	#14556524	C₂³	1	2	yes	—
241	#14556523	C₂³	1	2	yes	—
242	#14556523	C₂³	1	2	yes	—
243	#14556522	C₂³	1	2	yes	—
244	#14556522	C₂³	1	2	yes	—
245	#14556522	C₂³	1	2	yes	—
246	#14556522	C₂³	1	2	yes	—
247	#14556520	C₂³	1	2	yes	—
248	#14556520	C₂³	1	2	yes	—
249	#14556520	C₂³	1	2	yes	—
250	#14556520	C₂³	1	2	yes	—
251	#14556516	C₂³	1	2	yes	—
252	#14556516	C₂³	1	2	yes	—
253	#14556516	C₂³	1	2	yes	—
254	#14556516	C₂³	1	2	yes	—
255	#14556515	C₂³	1	2	yes	—
256	#14556515	C₂³	1	2	yes	—
257	#14556514	C₂³	1	2	yes	—
258	#14556514	C₂³	1	2	yes	—
259	#14556514	C₂³	1	2	yes	—
260	#14556514	C₂³	1	2	yes	—
261	#14556512	C₂³	1	2	yes	—
262	#14556512	C₂³	1	2	yes	—
263	C₂²⋊#10596831	C₂³	1	2	yes	—
264	C₂²⋊#10596831	C₂³	1	2	yes	—
265	#14556501	C₂³	1	2	yes	—
266	#14556501	C₂³	1	2	yes	—
267	C₈×Dic₇₃	C₂³	1	2	yes	—
268	C₈×Dic₇₃	C₂³	1	2	yes	—
269	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
270	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
273	#123×C₇₃	—	2	1	no	—
274	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
276	#121×C₇₃	C₂³	1	1	yes	characteristic
277	#121×C₇₃	C₂³	1	1	yes	characteristic
278	#120×C₇₃	—	2	1	no	—
279	C₄×D₄×C₇₃	—	2	1	no	—
280	C₄×D₄×C₇₃	—	2	1	no	—
281	#117×C₇₃	—	2	1	no	—
282	#117×C₇₃	—	2	1	no	—
283	#117×C₇₃	C₂³	1	1	yes	characteristic
284	#117×C₇₃	C₂³	1	1	yes	characteristic
285	#117×C₇₃	C₂³	1	1	yes	characteristic
286	#117×C₇₃	C₂³	1	1	yes	characteristic
287	#117×C₇₃	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
291	C₂×C₄²×C₇₃	—	2	1	no	—
292	#107×C₇₃	C₂³	1	1	yes	characteristic
293	#107×C₇₃	C₂³	1	1	yes	characteristic
294	#107×C₇₃	C₂³	1	1	yes	characteristic
295	#107×C₇₃	C₂³	1	1	yes	characteristic
296	#106×C₇₃	C₂³	1	1	yes	characteristic
297	#106×C₇₃	C₂³	1	1	yes	characteristic
298	#106×C₇₃	C₂³	1	1	yes	characteristic
299	#106×C₇₃	C₂³	1	1	yes	characteristic
300	#103×C₇₃	C₂³	1	1	yes	characteristic
301	#103×C₇₃	C₂³	1	1	yes	characteristic
302	#103×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#102×C₇₃	C₂³	1	1	yes	characteristic
305	#102×C₇₃	C₂³	1	1	yes	characteristic
306	#102×C₇₃	C₂³	1	1	yes	characteristic
307	#102×C₇₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
312	C₂×Dic₁₄₆	—	2	2	no	—
313	C₂×Dic₁₄₆	—	2	2	no	—
314	C₂×Dic₁₄₆	—	2	1	no	—
315	C₂×Dic₁₄₆	—	2	2	no	—
316	C₂×Dic₁₄₆	—	2	2	no	—
317	C₂×Dic₁₄₆	—	2	2	no	—
318	C₂×Dic₁₄₆	—	2	2	no	—
319	C₂×Dic₁₄₆	—	2	2	no	—
320	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
321	C₂²×Dic₇₃	—	2	1	no	—
322	C₂²×Dic₇₃	—	2	1	no	—
323	C₂²×Dic₇₃	—	2	1	no	—
324	C₂²×Dic₇₃	—	2	1	no	—
325	C₂²×Dic₇₃	—	2	2	no	—
326	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
327	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
328	#11924012	—	2	2	no	—
329	#11924012	—	2	2	no	—
330	C₂×#10596831	C₂⁴	1	2	yes	—
331	C₂×#10596831	C₂⁴	1	2	yes	—
332	C₄⋊Dic₇₃	—	2	1	no	—
333	C₄⋊Dic₇₃	—	2	1	no	—
334	C₄⋊Dic₇₃	—	2	1	no	—
335	C₄⋊Dic₇₃	—	2	2	no	—
336	C₄⋊Dic₇₃	—	2	2	no	—
337	C₄⋊Dic₇₃	—	2	2	no	—
338	C₄⋊Dic₇₃	—	2	2	no	—
339	C₄⋊Dic₇₃	—	2	2	no	—
340	C₄⋊Dic₇₃	—	2	2	no	—
341	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
342	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
344	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
345	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
346	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
347	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
348	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
349	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
350	#11924007	—	2	2	no	—
351	#11924007	—	2	2	no	—
352	#11924007	—	2	2	no	—
353	#11924007	—	2	2	no	—
354	#11924007	—	2	2	no	—
355	#11924007	—	2	2	no	—
356	#11924007	—	2	2	no	—
357	#11924007	—	2	2	no	—
358	#11924007	—	2	2	no	—
359	#11924007	—	2	2	no	—
360	#11924007	—	2	2	no	—
361	#11924007	—	2	2	no	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
365	#11924007	—	2	2	no	—
366	C₂²⋊Dic₇₃	—	2	2	no	—
367	C₂²⋊Dic₇₃	—	2	2	no	—
368	C₂²⋊Dic₇₃	—	2	2	no	—
369	C₂²⋊Dic₇₃	—	2	2	no	—
370	C₂²⋊Dic₇₃	—	2	2	no	—
371	C₂²⋊Dic₇₃	—	2	2	no	—
372	C₂²⋊Dic₇₃	—	2	2	no	—
373	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
374	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
375	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
376	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
377	C₄×Dic₇₃	—	2	2	no	—
378	C₄×Dic₇₃	—	2	2	no	—
379	C₄×Dic₇₃	—	2	2	no	—
380	C₄×Dic₇₃	—	2	2	no	—
381	C₄×Dic₇₃	—	2	2	no	—
382	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
383	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
384	C₄×Dic₇₃	C₂⁴	1	2	yes	—
385	C₄×Dic₇₃	C₂⁴	1	2	yes	—
386	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
387	#41×C₇₃	—	2	2	no	—
388	#41×C₇₃	—	2	2	no	—
389	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₇₃	—	2	1	no	—
391	C₂×D₄×C₇₃	—	2	1	no	—
392	C₂×D₄×C₇₃	—	2	1	no	—
393	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₇₃	—	2	2	no	—
395	C₂²×C₄×C₇₃	—	2	2	no	—
396	C₂²×C₄×C₇₃	—	2	1	no	—
397	C₂²×C₄×C₇₃	—	2	1	no	—
398	C₂²×C₄×C₇₃	—	2	1	no	—
399	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₇₃	—	2	2	no	—
406	C₂×C₈×C₇₃	—	2	2	no	—
407	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₇₃	—	2	1	no	—
412	C₄⋊C₄×C₇₃	—	2	1	no	—
413	C₄⋊C₄×C₇₃	—	2	1	no	—
414	C₄⋊C₄×C₇₃	—	2	1	no	—
415	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₇₃	—	2	1	no	—
422	C₂²⋊C₄×C₇₃	—	2	1	no	—
423	C₂²⋊C₄×C₇₃	—	2	1	no	—
424	C₂²⋊C₄×C₇₃	—	2	1	no	—
425	C₂²⋊C₄×C₇₃	—	2	1	no	—
426	C₂²⋊C₄×C₇₃	—	2	1	no	—
427	C₂²⋊C₄×C₇₃	—	2	1	no	—
428	C₂²⋊C₄×C₇₃	—	2	1	no	—
429	C₂²⋊C₄×C₇₃	—	2	1	no	—
430	C₄²×C₇₃	—	2	1	no	—
431	C₄²×C₇₃	—	2	1	no	—
432	C₄²×C₇₃	—	2	1	no	—
433	C₄²×C₇₃	—	2	1	no	—
434	C₄²×C₇₃	—	2	1	no	—
435	C₂³×C₇₃	—	2	2	no	—
436	C₂³×C₇₃	—	2	1	no	—
437	C₂³×C₇₃	—	4	1	no	—
438	C₂³×C₇₃	—	4	1	no	—
439	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
440	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₇₃	—	2	1	no	—
443	Q₈×C₇₃	—	2	1	no	—
444	D₄×C₇₃	—	2	1	no	—
445	D₄×C₇₃	—	2	1	no	—
446	D₄×C₇₃	—	4	2	no	—
447	D₄×C₇₃	—	4	2	no	—
448	D₄×C₇₃	—	8	1	no	—
449	C₂×C₄×C₇₃	—	2	2	no	—
450	C₂×C₄×C₇₃	—	2	2	no	—
451	C₂×C₄×C₇₃	—	2	2	no	—
452	C₂×C₄×C₇₃	—	2	1	no	—
453	C₂×C₄×C₇₃	—	2	1	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	—	2	1	no	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	2	1	no	—
459	C₂×C₄×C₇₃	—	2	1	no	—
460	C₂×C₄×C₇₃	—	2	1	no	—
461	C₂×C₄×C₇₃	—	2	1	no	—
462	C₂×C₄×C₇₃	—	2	1	no	—
463	C₂×C₄×C₇₃	—	4	2	no	—
464	C₂×C₄×C₇₃	—	8	1	no	—
465	C₂×C₄×C₇₃	—	8	1	no	—
466	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
471	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
472	C₂×Dic₇₃	—	2	2	no	—
473	C₂×Dic₇₃	—	2	2	no	—
474	C₂×Dic₇₃	—	2	2	no	—
475	C₂×Dic₇₃	—	2	2	no	—
476	C₂×Dic₇₃	—	4	2	no	—
477	C₂×Dic₇₃	—	4	2	no	—
478	C₂×Dic₇₃	—	4	2	no	—
479	C₂×Dic₇₃	—	8	2	no	—
480	C₂×Dic₇₃	—	8	1	no	—
481	C₂×Dic₇₃	—	8	1	no	—
482	C₂×Dic₇₃	—	8	1	no	—
483	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
484	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
485	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
486	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
487	Dic₁₄₆	—	2	2	no	—
488	Dic₁₄₆	—	2	2	no	—
489	Dic₁₄₆	—	4	2	no	—
490	Dic₁₄₆	—	8	2	no	—
491	Dic₁₄₆	—	8	2	no	—
492	Dic₁₄₆	—	8	2	no	—
493	Dic₁₄₆	—	8	2	no	—
494	Dic₁₄₆	—	8	2	no	—
495	C₈×C₇₃	—	2	1	no	—
496	C₈×C₇₃	—	2	1	no	—
497	C₈×C₇₃	—	2	1	no	—
498	C₈×C₇₃	—	2	1	no	—
499	#10596831	—	2	2	no	—
500	#10596831	—	2	2	no	—
501	C₂²×C₇₃	—	2	1	no	—
502	C₂²×C₇₃	—	2	1	no	—
503	C₂²×C₇₃	—	2	1	no	—
504	C₂²×C₇₃	—	2	1	no	—
505	C₂²×C₇₃	—	2	1	no	—
506	C₂²×C₇₃	—	2	1	no	—
507	C₂²×C₇₃	—	2	1	no	—
508	C₂²×C₇₃	—	2	1	no	—
509	C₂²×C₇₃	—	4	1	no	—
510	C₂²×C₇₃	—	4	1	no	—
511	C₂²×C₇₃	—	4	1	no	—
512	C₂²×C₇₃	—	8	2	no	—
513	C₂²×C₇₃	#536	1	2	yes	—
514	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₇₃	—	2	1	no	—
516	C₄×C₇₃	—	2	1	no	—
517	C₄×C₇₃	—	4	1	no	—
518	C₄×C₇₃	—	4	1	no	—
519	C₄×C₇₃	—	4	1	no	—
520	C₄×C₇₃	—	4	1	no	—
521	C₄×C₇₃	—	4	1	no	—
522	C₄×C₇₃	—	4	1	no	—
523	C₄×C₇₃	—	4	1	no	—
524	C₄×C₇₃	#536	1	2	yes	—
525	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	Dic₇₃	—	2	2	no	—
528	Dic₇₃	—	2	2	no	—
529	Dic₇₃	—	2	2	no	—
530	Dic₇₃	—	2	2	no	—
531	Dic₇₃	—	4	2	no	—
532	Dic₇₃	—	4	2	no	—
533	Dic₇₃	—	4	2	no	—
534	Dic₇₃	—	4	2	no	—
535	#60876	—	73	1	no	maximal, Sylow
536	C₂×C₇₃	—	2	2	no	—
537	C₂×C₇₃	—	4	1	no	—
538	C₂×C₇₃	—	4	1	no	—
539	C₂×C₇₃	—	8	1	no	—
540	C₂×C₇₃	C₂×#536	1	1	yes	characteristic
541	C₂×C₇₃	#3584	1	1	yes	characteristic
542	C₂×C₇₃	#3586	1	1	yes	characteristic
543	#3495	—	73	1	no	—
544	#3458	—	73	1	no	—
545	#3244	—	73	2	no	—
546	#3243	—	73	2	no	—
547	#3242	—	73	2	no	—
548	#3242	—	73	2	no	—
549	#3240	—	73	2	no	—
550	#3237	—	73	2	no	—
551	#3233	—	73	2	no	—
552	#3231	—	73	2	no	—
553	#3164	—	73	1	no	—
554	#3163	—	73	1	no	—
555	#3137	—	73	1	no	—
556	#3137	—	73	1	no	—
557	#3095	—	73	1	no	—
558	#3093	—	73	1	no	—
559	#3091	D₇₃	1	1	yes	characteristic
560	C₂×#485	—	73	1	no	—
561	#3084	—	73	1	no	—
562	#3083	—	73	1	no	—
563	#3082	—	73	1	no	—
564	#3082	—	73	1	no	—
565	#2924	—	73	1	no	—
566	C₇₃	#60876	1	1	yes	characteristic, complemented, Sylow
567	#556	—	146	1	no	—
568	#554	—	146	1	no	—
569	#552	—	146	1	no	—
570	#552	—	146	1	no	—
571	#552	—	146	2	no	—
572	#551	—	146	2	no	—
573	#544	—	73	1	no	—
574	#544	—	73	1	no	—
575	#544	—	73	1	no	—
576	#544	—	73	1	no	—
577	#544	—	73	1	no	—
578	#544	—	73	2	no	—
579	#544	—	73	2	no	—
580	#544	—	146	1	no	—
581	#544	—	146	1	no	—
582	#543	—	146	2	no	—
583	#542	—	73	2	no	—
584	#541	—	73	2	no	—
585	#536	—	73	1	no	—
586	#533	—	73	2	no	—
587	#533	—	73	2	no	—
588	#533	—	73	2	no	—
589	#533	—	146	1	no	—
590	#533	—	146	1	no	—
591	#533	—	146	2	no	—
592	#529	—	73	2	no	—
593	#525	C₂×D₇₃	1	1	yes	characteristic
594	C₂×C₂²⋊Q₈	—	73	1	no	—
595	#520	—	73	1	no	—
596	#519	—	73	1	no	—
597	C₂×#117	—	73	1	no	—
598	C₂×#117	—	73	1	no	—
599	C₂×#117	C₂×D₇₃	1	1	yes	characteristic
600	#501	—	73	2	no	—
601	#501	—	73	2	no	—
602	#501	—	73	2	no	—
603	#501	—	73	2	no	—
604	#500	—	73	2	no	—
605	#499	—	73	2	no	—
606	#499	—	73	2	no	—
607	#498	—	73	2	no	—
608	#491	—	73	2	no	—
609	#491	—	73	2	no	—
610	#489	—	73	2	no	—
611	#489	—	73	2	no	—
612	#488	—	73	2	no	—
613	#488	—	73	2	no	—
614	#487	—	73	2	no	—
615	#487	—	73	2	no	—
616	#485	—	73	2	no	—
617	#485	—	73	2	no	—
618	#485	—	73	2	no	—
619	#485	—	73	2	no	—
620	#485	—	73	2	no	—
621	#485	—	73	2	no	—
622	#485	—	73	2	no	—
623	#485	—	73	2	no	—
624	#485	C₂×D₇₃	1	1	yes	characteristic
625	#485	C₂×D₇₃	1	1	yes	characteristic
626	#484	—	73	2	no	—
627	#484	C₂×D₇₃	1	1	yes	characteristic
628	#483	—	73	2	no	—
629	#483	C₂×D₇₃	1	1	yes	characteristic
630	#482	—	73	2	no	—
631	#482	—	73	2	no	—
632	#482	C₂×D₇₃	1	1	yes	characteristic
633	#482	C₂×D₇₃	1	1	yes	characteristic
634	#481	C₂×D₇₃	1	1	yes	characteristic
635	#480	C₂×D₇₃	1	1	yes	characteristic
636	#479	—	73	2	no	—
637	#479	—	73	2	no	—
638	#479	—	73	2	no	—
639	#479	—	73	2	no	—
640	#479	—	73	2	no	—
641	#479	—	73	2	no	—
642	#478	—	73	2	no	—
643	#478	—	73	2	no	—
644	#477	—	73	2	no	—
645	#477	—	73	2	no	—
646	#477	—	73	2	no	—
647	#476	—	73	2	no	—
648	#475	—	73	2	no	—
649	#475	—	73	2	no	—
650	#475	—	73	2	no	—
651	#474	—	73	2	no	—
652	#433	—	73	2	no	—
653	#433	—	73	2	no	—
654	#432	—	73	2	no	—
655	#431	—	73	2	no	—
656	#428	—	73	1	no	—
657	#428	—	73	1	no	—
658	#428	—	73	1	no	—
659	#428	—	73	1	no	—
660	#427	C₂×D₇₃	1	1	yes	characteristic
661	#427	C₂×D₇₃	1	1	yes	characteristic
662	C₂×#107	—	73	1	no	—
663	C₂×#106	—	73	1	no	—
664	#424	—	73	1	no	—
665	#424	—	73	1	no	—
666	#419	—	73	1	no	—
667	#419	—	73	1	no	—
668	#417	—	73	1	no	—
669	#417	—	73	1	no	—
670	#416	C₂×D₇₃	1	1	yes	characteristic
671	#416	C₂×D₇₃	1	1	yes	characteristic
672	C₂×#103	—	73	1	no	—
673	C₂×#103	—	73	1	no	—
674	#407	—	73	1	no	—
675	C₂×C₂²⋊C₈	C₂×D₇₃	1	1	yes	characteristic
676	#405	—	73	1	no	—
677	#405	—	73	1	no	—
678	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
679	C₂²×Q₈	—	73	1	no	—
680	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
681	C₂×M₁₆	—	73	1	no	—
682	C₂×M₁₆	—	73	1	no	—
683	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
684	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
685	C₄⋊Q₈	—	73	2	no	—
686	C₄⋊Q₈	—	73	2	no	—
687	C₄⋊Q₈	—	73	2	no	—
688	C₄⋊Q₈	—	73	2	no	—
689	C₄⋊Q₈	—	73	2	no	—
690	C₄⋊Q₈	—	73	2	no	—
691	C₄⋊Q₈	—	146	1	no	—
692	C₄⋊Q₈	—	146	1	no	—
693	C₄⋊Q₈	—	146	1	no	—
694	C₄⋊Q₈	—	146	1	no	—
695	C₄⋊Q₈	—	146	1	no	—
696	C₄⋊Q₈	—	146	2	no	—
697	C₄⋊Q₈	—	146	2	no	—
698	#126	—	146	2	no	—
699	#126	—	146	2	no	—
700	#126	—	146	2	no	—
701	#126	—	146	2	no	—
702	#125	—	73	2	no	—
703	#125	—	73	2	no	—
704	#125	—	73	2	no	—
705	#125	—	73	2	no	—
706	#125	—	73	2	no	—
707	#125	—	146	1	no	—
708	#125	—	146	1	no	—
709	#125	—	146	1	no	—
710	#125	—	146	1	no	—
711	#125	—	146	1	no	—
712	#125	—	146	2	no	—
713	#125	—	146	2	no	—
714	#125	—	146	2	no	—
715	#125	—	146	2	no	—
716	#125	—	146	2	no	—
717	#124	—	73	2	no	—
718	#124	—	146	2	no	—
719	#123	—	2	1	no	—
720	#123	—	146	2	no	—
721	#123	—	146	2	no	—
722	#123	—	146	2	no	—
723	C₂²⋊Q₈	—	73	2	no	—
724	C₂²⋊Q₈	—	73	2	no	—
725	C₂²⋊Q₈	—	146	2	no	—
726	C₂²⋊Q₈	—	146	2	no	—
727	C₂²⋊Q₈	—	146	2	no	—
728	C₂²⋊Q₈	—	146	2	no	—
729	C₂²⋊Q₈	—	146	2	no	—
730	C₂²⋊Q₈	—	146	2	no	—
731	C₂²⋊Q₈	—	146	2	no	—
732	C₂²⋊Q₈	—	146	2	no	—
733	C₂²⋊Q₈	—	146	2	no	—
734	C₂²⋊Q₈	—	146	2	no	—
735	C₂²⋊Q₈	—	146	2	no	—
736	C₂²⋊Q₈	—	146	2	no	—
737	C₂²⋊Q₈	—	146	2	no	—
738	C₂²⋊Q₈	—	146	2	no	—
739	C₂²⋊Q₈	—	146	2	no	—
740	C₂²⋊Q₈	—	146	1	no	—
741	C₂²⋊Q₈	—	146	1	no	—
742	C₂²⋊Q₈	—	146	1	no	—
743	C₂²⋊Q₈	—	146	1	no	—
744	C₂²⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
745	C₂²⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
746	#121	C₂²×D₇₃	1	1	yes	characteristic
747	#121	C₂²×D₇₃	1	1	yes	characteristic
748	#120	—	2	1	no	—
749	C₄×Q₈	—	73	2	no	—
750	C₄×Q₈	—	73	2	no	—
751	C₄×Q₈	—	73	2	no	—
752	C₄×Q₈	—	146	2	no	—
753	C₄×Q₈	—	146	2	no	—
754	C₄×Q₈	—	146	2	no	—
755	C₄×Q₈	—	146	2	no	—
756	C₄×Q₈	—	146	1	no	—
757	C₄×Q₈	—	146	1	no	—
758	C₄×Q₈	—	146	2	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	73	2	no	—
762	C₄×D₄	—	146	2	no	—
763	C₄×D₄	—	146	2	no	—
764	#117	—	2	1	no	—
765	#117	—	2	1	no	—
766	#117	—	73	1	no	—
767	#117	—	73	2	no	—
768	#117	—	73	1	no	—
769	#117	—	73	1	no	—
770	#117	—	73	1	no	—
771	#117	—	73	2	no	—
772	#117	—	73	2	no	—
773	#117	—	73	2	no	—
774	#117	—	146	2	no	—
775	#117	—	146	2	no	—
776	#117	—	146	2	no	—
777	#117	—	146	1	no	—
778	#117	—	146	1	no	—
779	#117	—	146	1	no	—
780	#117	C₂²×D₇₃	1	1	yes	characteristic
781	#117	C₂²×D₇₃	1	1	yes	characteristic
782	#117	C₂²×D₇₃	1	1	yes	characteristic
783	#117	C₂²×D₇₃	1	1	yes	characteristic
784	#117	C₂²×D₇₃	1	1	yes	characteristic
785	C₂×C₄⋊C₄	—	73	1	no	—
786	C₂×C₄⋊C₄	—	73	1	no	—
787	C₂×C₄⋊C₄	—	73	1	no	—
788	C₂×C₄⋊C₄	—	73	1	no	—
789	C₂×C₄⋊C₄	—	73	1	no	—
790	C₂×C₄⋊C₄	—	146	1	no	—
791	C₂×C₄⋊C₄	—	146	1	no	—
792	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	—	2	1	no	—
795	C₂×C₂²⋊C₄	—	73	2	no	—
796	C₂×C₂²⋊C₄	—	146	1	no	—
797	C₂×C₂²⋊C₄	—	146	1	no	—
798	C₂×C₄²	—	2	1	no	—
799	C₂×C₄²	—	73	2	no	—
800	C₂×C₄²	—	146	1	no	—
801	#107	—	73	2	no	—
802	#107	—	73	2	no	—
803	#107	—	73	2	no	—
804	#107	—	73	2	no	—
805	#107	—	73	2	no	—
806	#107	—	73	2	no	—
807	#107	C₂²×D₇₃	1	1	yes	characteristic
808	#107	C₂²×D₇₃	1	1	yes	characteristic
809	#107	C₂²×D₇₃	1	1	yes	characteristic
810	#107	C₂²×D₇₃	1	1	yes	characteristic
811	#106	—	73	2	no	—
812	#106	—	73	2	no	—
813	#106	—	73	2	no	—
814	#106	—	73	2	no	—
815	#106	—	73	2	no	—
816	#106	—	73	2	no	—
817	#106	C₂²×D₇₃	1	1	yes	characteristic
818	#106	C₂²×D₇₃	1	1	yes	characteristic
819	#106	C₂²×D₇₃	1	1	yes	characteristic
820	#106	C₂²×D₇₃	1	1	yes	characteristic
821	C₄⋊C₈	—	73	2	no	—
822	C₄⋊C₈	—	73	2	no	—
823	C₄⋊C₈	—	73	2	no	—
824	C₄⋊C₈	—	73	2	no	—
825	#103	—	73	2	no	—
826	#103	—	73	2	no	—
827	#103	—	73	2	no	—
828	#103	—	73	2	no	—
829	#103	—	73	2	no	—
830	#103	—	73	2	no	—
831	#103	—	73	2	no	—
832	#103	—	73	2	no	—
833	#103	—	73	2	no	—
834	#103	—	73	2	no	—
835	#103	C₂²×D₇₃	1	1	yes	characteristic
836	#103	C₂²×D₇₃	1	1	yes	characteristic
837	#103	C₂²×D₇₃	1	1	yes	characteristic
838	#103	C₂²×D₇₃	1	1	yes	characteristic
839	#102	—	73	2	no	—
840	#102	—	73	2	no	—
841	#102	C₂²×D₇₃	1	1	yes	characteristic
842	#102	C₂²×D₇₃	1	1	yes	characteristic
843	#102	C₂²×D₇₃	1	1	yes	characteristic
844	#102	C₂²×D₇₃	1	1	yes	characteristic
845	C₂²⋊C₈	—	73	2	no	—
846	C₂²⋊C₈	—	73	2	no	—
847	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
848	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
849	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
850	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
851	#97	—	73	2	no	—
852	#97	—	73	2	no	—
853	C₄×C₈	—	73	2	no	—
854	C₄×C₈	—	73	2	no	—
855	C₂⁴	D₄×D₇₃	1	1	yes	characteristic
856	#41	—	2	2	no	—
857	#41	—	2	2	no	—
858	C₂×Q₈	—	73	2	no	—
859	C₂×Q₈	—	146	2	no	—
860	C₂×Q₈	—	146	2	no	—
861	C₂×Q₈	—	146	2	no	—
862	C₂×Q₈	—	146	2	no	—
863	C₂×Q₈	—	146	2	no	—
864	C₂×Q₈	—	146	2	no	—
865	C₂×Q₈	—	146	2	no	—
866	C₂×Q₈	—	146	1	no	—
867	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	73	2	no	—
878	C₂²×C₄	—	73	2	no	—
879	C₂²×C₄	—	146	1	no	—
880	C₂²×C₄	—	146	2	no	—
881	C₂²×C₄	—	146	1	no	—
882	C₂²×C₄	—	146	1	no	—
883	C₂²×C₄	—	146	1	no	—
884	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
885	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
886	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
887	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
888	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
889	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
890	M₁₆	—	146	2	no	—
891	M₁₆	—	146	2	no	—
892	C₂×C₈	—	2	2	no	—
893	C₂×C₈	—	2	2	no	—
894	C₂×C₈	—	73	2	no	—
895	C₂×C₈	—	73	2	no	—
896	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
897	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
898	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
899	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	73	1	no	—
905	C₄⋊C₄	—	73	1	no	—
906	C₄⋊C₄	—	73	2	no	—
907	C₄⋊C₄	—	73	1	no	—
908	C₄⋊C₄	—	73	1	no	—
909	C₄⋊C₄	—	73	2	no	—
910	C₄⋊C₄	—	73	2	no	—
911	C₄⋊C₄	—	73	2	no	—
912	C₄⋊C₄	—	73	2	no	—
913	C₄⋊C₄	—	146	2	no	—
914	C₄⋊C₄	—	146	2	no	—
915	C₄⋊C₄	—	146	2	no	—
916	C₄⋊C₄	—	146	2	no	—
917	C₄⋊C₄	—	146	2	no	—
918	C₄⋊C₄	—	146	2	no	—
919	C₄⋊C₄	—	146	2	no	—
920	C₄⋊C₄	—	146	2	no	—
921	C₄⋊C₄	—	146	2	no	—
922	C₄⋊C₄	—	146	2	no	—
923	C₄⋊C₄	—	146	2	no	—
924	C₄⋊C₄	—	146	2	no	—
925	C₄⋊C₄	—	146	2	no	—
926	C₄⋊C₄	—	146	2	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	2	no	—
929	C₄⋊C₄	—	146	2	no	—
930	C₄⋊C₄	—	146	2	no	—
931	C₄⋊C₄	—	146	2	no	—
932	C₄⋊C₄	—	146	2	no	—
933	C₄⋊C₄	—	146	2	no	—
934	C₄⋊C₄	—	146	2	no	—
935	C₄⋊C₄	—	146	1	no	—
936	C₄⋊C₄	—	146	1	no	—
937	C₄⋊C₄	—	146	1	no	—
938	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	73	2	no	—
954	C₂²⋊C₄	—	73	2	no	—
955	C₂²⋊C₄	—	73	2	no	—
956	C₂²⋊C₄	—	73	2	no	—
957	C₂²⋊C₄	—	146	2	no	—
958	C₂²⋊C₄	—	146	2	no	—
959	C₂²⋊C₄	—	146	2	no	—
960	C₂²⋊C₄	—	146	2	no	—
961	C₂²⋊C₄	—	146	2	no	—
962	C₂²⋊C₄	—	146	2	no	—
963	C₂²⋊C₄	—	146	2	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	73	2	no	—
970	C₄²	—	73	2	no	—
971	C₄²	—	73	2	no	—
972	C₄²	—	73	2	no	—
973	C₄²	—	146	2	no	—
974	C₄²	—	146	2	no	—
975	C₄²	—	146	2	no	—
976	C₄²	—	146	2	no	—
977	C₄²	—	146	2	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	1	no	—
982	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
983	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
984	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
985	Q₈	—	2	1	no	—
986	Q₈	—	2	1	no	—
987	Q₈	—	292	2	no	—
988	Q₈	—	584	2	no	—
989	Q₈	—	584	2	no	—
990	Q₈	—	584	2	no	—
991	Q₈	—	584	2	no	—
992	Q₈	—	584	2	no	—
993	Q₈	—	146	2	no	—
994	Q₈	—	146	2	no	—
995	D₄	—	2	1	no	—
996	D₄	—	2	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	D₄	—	8	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	1	no	—
1017	C₂×C₄	—	292	2	no	—
1018	C₂×C₄	—	292	2	no	—
1019	C₂×C₄	—	292	2	no	—
1020	C₂×C₄	—	584	1	no	—
1021	C₂×C₄	—	584	1	no	—
1022	C₂×C₄	—	584	1	no	—
1023	C₂×C₄	—	584	2	no	—
1024	C₂×C₄	—	73	2	no	—
1025	C₂×C₄	—	73	2	no	—
1026	C₂×C₄	—	73	2	no	—
1027	C₂×C₄	—	73	2	no	—
1028	C₂×C₄	—	146	2	no	—
1029	C₂×C₄	—	146	2	no	—
1030	C₂×C₄	—	146	2	no	—
1031	C₂×C₄	—	146	2	no	—
1032	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1033	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1035	C₂×C₄	#14556638	1	2	yes	—
1036	C₂×C₄	#14556638	1	2	yes	—
1037	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	146	2	no	—
1043	C₈	—	146	2	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	8	2	no	—
1056	C₂²	#17989159	1	2	yes	—
1057	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	292	2	no	—
1068	C₄	—	292	2	no	—
1069	C₄	—	292	2	no	—
1070	C₄	—	292	2	no	—
1071	C₄	—	146	2	no	—
1072	C₄	—	146	2	no	—
1073	C₄	—	146	2	no	—
1074	C₄	—	146	2	no	—
1075	C₄	#17989159	1	2	yes	—
1076	C₄	C₂×#14556638	1	1	yes	characteristic
1077	C₄	C₂×#14556638	1	1	yes	characteristic
1078	C₂	—	2	2	no	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	1	no	—
1081	C₂	—	8	1	no	—
1082	C₂	C₂×#17989159	1	1	yes	characteristic
1083	C₂	#22624700	1	1	yes	characteristic
1084	C₂	#22624715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3091	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#525×C₇₃	C₂²
hypercenter	#3091	D₇₃
hypocenter	C₇₃	#60876
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
2. #22623336	C₂	semidirect
3. #22621225	C₂	semidirect
4. #22621210	C₂	semidirect
5. #22621203	C₂	semidirect
6. #22621195	C₂	semidirect
7. #22621169	C₂	semidirect
8. #22621142	C₂	semidirect
9. #22621107	C₂	semidirect
10. #22621088	C₂	semidirect
11. #22620471	C₂	semidirect
12. #22620463	C₂	semidirect
13. #22620300	C₂	semidirect
14. #22620300	C₂	semidirect
15. #22619879	C₂	semidirect
17. C₂×#17988929	C₂	semidirect
18. #22619791	C₂	semidirect
19. #22619780	C₂	semidirect
20. #22619776	C₂	semidirect
21. #22619776	C₂	semidirect
22. #22618585	C₂	semidirect
55. #17988995	C₂²	semidirect
56. #17988995	C₂²	semidirect
57. #17988994	C₂²	semidirect
58. #17988994	C₂²	semidirect
59. #17988991	C₂²	semidirect
60. #17988988	C₂²	semidirect
61. #17988987	C₂²	semidirect
62. #17988984	C₂²	semidirect
63. #17988954	C₂²	semidirect
64. #17988954	C₂²	semidirect
65. #17988945	C₂²	semidirect
66. #17988945	C₂²	semidirect
67. #17988940	C₂²	semidirect
68. #17988940	C₂²	semidirect
69. #17988936	C₂²	semidirect
70. #17988936	C₂²	semidirect
83. #17988897	C₂²	semidirect
84. #17988897	C₂²	semidirect
85. #17988896	C₂²	semidirect
86. #17988893	C₂²	semidirect
87. #17988893	C₂²	semidirect
88. #17988892	C₂²	semidirect
89. #17988889	C₂²	semidirect
90. #17988885	C₂²	semidirect
91. #17988881	C₂²	semidirect
92. #17988881	C₂²	semidirect
93. #17988880	C₂²	semidirect
94. #17988875	C₂²	semidirect
95. #17988871	C₂²	semidirect
96. #17988871	C₂²	semidirect
97. #17988870	C₂²	semidirect
98. #17988865	C₂²	semidirect
566. C₇₃	#60876	semidirect

Maximal subgroups

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

subgroup	index
#22623685	2
#22623336	2
#22621225	2
#22621210	2
#22621203	2
#22621195	2
#22621169	2
#22621142	2
#22621107	2
#22621088	2
#22620471	2
#22620463	2
#22620300	2
#22619879	2
#22619860	2
C₂×#17988929	2
#22619791	2
#22619780	2
#22619776	2
#22618585	2
C₇₃×#3091	2
#60876	73