Subgroups — #33964233

Order 18688.

2200 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623842	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623709	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622271	C₂	1	2	yes	maximal, complemented
4	#22622260	C₂	1	2	yes	maximal, complemented
5	#22622175	C₂	1	2	yes	maximal, complemented
6	#22622164	C₂	1	2	yes	maximal, complemented
7	#22621883	C₂	1	2	yes	maximal, complemented
8	#22621872	C₂	1	2	yes	maximal, complemented
9	#22621757	C₂	1	2	yes	maximal, complemented
10	#22621746	C₂	1	2	yes	maximal, complemented
11	C₂×#17988934	C₂	1	1	yes	maximal, characteristic, complemented
12	#22619892	C₂	1	2	yes	maximal, complemented
13	#22619746	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619614	C₂	1	2	yes	maximal, complemented
15	#22619411	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619231	C₂	1	2	yes	maximal, complemented
17	#22618644	C₂	1	1	yes	maximal, characteristic, complemented
18	#22618453	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14556637	C₂²	1	2	yes	—
21	C₂×#14556616	C₂²	1	2	yes	complemented
22	C₂×#14556597	C₂²	1	2	yes	complemented
23	#17989310	C₂²	1	2	yes	complemented
24	#17989302	C₂²	1	2	yes	complemented
25	#17989297	C₂²	1	2	yes	complemented
26	#17989283	—	2	2	no	—
27	#17989259	C₂²	1	2	yes	—
28	#17989259	C₂²	1	2	yes	—
29	#17989246	—	2	2	no	—
30	#17989242	C₂²	1	2	yes	complemented
31	D₄×D₂₉₂	—	2	2	no	—
32	D₄×D₂₉₂	—	2	2	no	—
33	D₄×D₂₉₂	C₂²	1	2	yes	—
34	D₄×D₂₉₂	C₂²	1	2	yes	—
35	#17989208	—	2	2	no	—
36	#17989165	C₂²	1	2	yes	complemented
37	#17989156	—	2	2	no	—
38	#17989156	C₂²	1	2	yes	—
39	#17989144	—	2	1	no	—
40	#17989137	—	2	1	no	—
41	#17989137	—	2	1	no	—
42	#17989137	C₂²	1	1	yes	characteristic
43	C₂×#14556591	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14556588	—	2	1	no	—
45	C₂×#14556588	C₂²	1	1	yes	characteristic
46	#17989067	C₂²	1	2	yes	complemented
47	#17988934	C₂²	1	2	yes	complemented
48	#17988934	C₂²	1	2	yes	complemented
49	#17988934	C₂²	1	2	yes	complemented
50	#17988934	C₂²	1	2	yes	complemented
51	#17988914	C₂²	1	4	yes	complemented
52	#17988913	C₂²	1	4	yes	complemented
53	#17988907	C₂²	1	4	yes	complemented
54	#17988902	C₂²	1	4	yes	complemented
55	#17988882	C₂²	1	2	yes	complemented
56	#17988877	C₂²	1	2	yes	complemented
57	#17988872	C₂²	1	2	yes	complemented
58	#17988867	C₂²	1	2	yes	complemented
59	#17988839	C₂²	1	4	yes	complemented
60	#17988836	C₂²	1	4	yes	complemented
61	#17988822	C₂²	1	4	yes	complemented
62	#17988819	C₂²	1	4	yes	complemented
63	#17988787	C₂²	1	2	yes	complemented
64	#17988787	C₂²	1	2	yes	complemented
65	#17988782	C₂²	1	2	yes	complemented
66	#17988782	C₂²	1	2	yes	complemented
67	#17988748	C₂²	1	4	yes	complemented
68	#17988736	C₂²	1	4	yes	complemented
69	#17988731	C₂²	1	4	yes	complemented
70	#17988719	C₂²	1	4	yes	complemented
71	#17988666	C₂²	1	2	yes	complemented
72	#17988666	C₂²	1	2	yes	complemented
73	C₈×D₂₉₂	C₂²	1	2	yes	complemented
74	C₈×D₂₉₂	C₂²	1	2	yes	complemented
75	#17988630	C₂²	1	2	yes	complemented
76	#17988611	C₂²	1	1	yes	characteristic, complemented
77	#17988591	C₂²	1	2	yes	complemented
78	#17988590	C₂²	1	4	yes	complemented
79	#17988588	C₂²	1	2	yes	—
80	#17988587	C₂²	1	4	yes	complemented
81	#17988582	C₂²	1	4	yes	complemented
82	C₂×#14556513	C₂²	1	2	yes	complemented
83	C₂×#14556513	C₂²	1	2	yes	complemented
84	#102×D₇₃	C₂²	1	4	yes	complemented
85	#17988553	C₂²	1	2	yes	complemented
86	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
87	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
88	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
89	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
92	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
93	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
97	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
98	#416×C₇₃	C₂²	1	1	yes	characteristic
99	#416×C₇₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
101	#14556637	—	2	8	no	—
102	#14556637	—	4	4	no	—
103	C₂×#11924029	C₂³	1	4	yes	—
104	C₂×#11924028	—	2	2	no	—
105	C₂×#11924028	—	2	2	no	—
106	C₂×#11924028	C₂³	1	2	yes	—
107	C₂²×Dic₁₄₆	—	2	1	no	—
108	C₂²×D₂₉₂	—	2	2	no	—
109	C₂²×D₂₉₂	—	2	2	no	—
110	C₂²×D₂₉₂	—	2	2	no	—
111	C₂²×D₂₉₂	—	2	1	no	—
112	C₂²×D₂₉₂	—	2	1	no	—
113	C₂²×D₂₉₂	C₂³	1	2	yes	—
114	C₂×D₄×D₇₃	—	2	4	no	—
115	C₂×D₄×D₇₃	C₂³	1	4	yes	—
116	#14556616	—	4	4	no	—
117	C₂×#11924015	C₂³	1	4	yes	—
118	C₂×#11924013	C₂³	1	4	yes	—
119	#14556597	—	4	4	no	—
120	C₂×#11924012	C₂³	1	2	yes	—
121	C₂×#11924011	C₂³	1	4	yes	—
122	C₂×C₈×D₇₃	C₂³	1	4	yes	—
123	#14556591	—	2	1	no	—
124	#14556591	—	2	1	no	—
125	#14556591	D₄	1	1	yes	characteristic
126	#14556591	C₂³	1	2	yes	—
127	#14556591	C₂³	1	2	yes	—
128	#14556588	—	2	2	no	—
129	#14556588	—	2	2	no	—
130	#14556588	—	2	2	no	—
131	#14556588	—	2	1	no	—
132	#14556588	—	2	1	no	—
133	#14556588	D₄	1	1	yes	characteristic
134	#14556588	C₂³	1	2	yes	—
135	#14556588	C₂³	1	2	yes	—
136	#14556586	—	2	4	no	—
137	#14556583	—	2	2	no	—
138	#14556579	—	2	2	no	—
139	#14556579	—	2	2	no	—
140	#14556579	D₄	1	2	yes	—
141	#14556577	—	2	4	no	—
142	#14556573	—	2	4	no	—
143	#14556570	—	2	2	no	—
144	#14556570	—	2	2	no	—
145	#14556569	—	2	4	no	—
146	#14556567	C₂³	1	4	yes	—
147	#14556566	—	2	4	no	—
148	#14556566	—	2	4	no	—
149	#14556566	C₂³	1	4	yes	—
150	#14556566	C₂³	1	4	yes	—
151	#14556565	—	2	2	no	—
152	#14556565	—	2	2	no	—
153	#14556565	—	2	2	no	—
154	#14556565	—	2	2	no	—
155	#14556565	D₄	1	2	yes	—
156	#14556565	D₄	1	2	yes	—
157	#14556563	—	2	4	no	—
158	#14556562	C₂³	1	4	yes	—
159	#14556561	—	2	4	no	—
160	#14556561	—	2	4	no	—
161	#14556561	—	2	4	no	—
162	C₄×Dic₁₄₆	—	2	2	no	—
163	C₄×Dic₁₄₆	—	2	2	no	—
164	C₄×D₂₉₂	—	2	2	no	—
165	C₄×D₂₉₂	—	2	2	no	—
166	C₄×D₂₉₂	—	2	2	no	—
167	C₄×D₂₉₂	—	2	2	no	—
168	C₄×D₂₉₂	C₂³	1	2	yes	—
169	C₄×D₂₉₂	C₂³	1	2	yes	—
170	#14556551	—	2	4	no	—
171	#14556550	—	2	2	no	—
172	#14556549	C₂³	1	4	yes	—
173	C₂×C₄⋊Dic₇₃	—	2	1	no	—
174	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
175	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
176	#14556524	C₂³	1	4	yes	—
177	#14556522	C₂³	1	4	yes	—
178	C₄⋊#10596831	C₂³	1	2	yes	—
179	C₄⋊#10596831	C₂³	1	2	yes	—
180	#14556515	C₂³	1	4	yes	—
181	#14556513	C₂³	1	4	yes	—
182	#14556513	C₂³	1	4	yes	—
183	#14556513	C₂³	1	4	yes	—
184	#14556513	C₂³	1	4	yes	—
185	#14556512	C₂³	1	4	yes	—
186	#14556511	C₂³	1	4	yes	—
187	#14556511	C₂³	1	4	yes	—
188	#14556503	C₂³	1	4	yes	—
189	#14556503	C₂³	1	4	yes	—
190	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
191	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
192	#135×C₇₃	—	2	4	no	—
193	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
195	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
196	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
197	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
198	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
199	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
203	C₄×D₄×C₇₃	—	2	1	no	—
204	C₄×D₄×C₇₃	—	2	1	no	—
205	C₄×D₄×C₇₃	—	2	1	no	—
206	C₄×D₄×C₇₃	—	2	1	no	—
207	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
211	#117×C₇₃	—	2	1	no	—
212	#117×C₇₃	—	2	1	no	—
213	#117×C₇₃	C₂³	1	1	yes	characteristic
214	#117×C₇₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇₃	—	2	1	no	—
216	C₂×C₄²×C₇₃	—	2	1	no	—
217	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
218	#107×C₇₃	C₂³	1	1	yes	characteristic
219	#107×C₇₃	C₂³	1	1	yes	characteristic
220	#106×C₇₃	C₂³	1	1	yes	characteristic
221	#106×C₇₃	C₂³	1	1	yes	characteristic
222	#103×C₇₃	C₂³	1	1	yes	characteristic
223	#103×C₇₃	C₂³	1	1	yes	characteristic
224	#103×C₇₃	C₂³	1	1	yes	characteristic
225	#103×C₇₃	C₂³	1	1	yes	characteristic
226	#102×C₇₃	C₂³	1	1	yes	characteristic
227	#102×C₇₃	C₂³	1	1	yes	characteristic
228	#102×C₇₃	C₂³	1	1	yes	characteristic
229	#102×C₇₃	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
231	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
232	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
233	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
234	C₂³×D₇₃	—	2	2	no	—
235	C₂³×D₇₃	—	2	4	no	—
236	#11924029	—	2	8	no	—
237	#11924029	—	4	4	no	—
238	#11924028	—	2	4	no	—
239	#11924028	—	2	4	no	—
240	#11924028	—	4	8	no	—
241	#11924028	—	8	4	no	—
242	C₂×Dic₁₄₆	—	2	2	no	—
243	C₂×Dic₁₄₆	—	2	2	no	—
244	C₂×Dic₁₄₆	—	8	2	no	—
245	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
246	C₂×D₂₉₂	—	2	4	no	—
247	C₂×D₂₉₂	—	2	4	no	—
248	C₂×D₂₉₂	—	2	4	no	—
249	C₂×D₂₉₂	—	2	2	no	—
250	C₂×D₂₉₂	—	2	2	no	—
251	C₂×D₂₉₂	—	2	2	no	—
252	C₂×D₂₉₂	—	2	4	no	—
253	C₂×D₂₉₂	—	2	4	no	—
254	C₂×D₂₉₂	—	2	2	no	—
255	C₂×D₂₉₂	—	2	2	no	—
256	C₂×D₂₉₂	—	4	8	no	—
257	C₂×D₂₉₂	—	8	4	no	—
258	C₂×D₂₉₂	—	8	4	no	—
259	C₂×D₂₉₂	—	8	2	no	—
260	C₂×D₂₉₂	—	8	2	no	—
261	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
262	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
263	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
264	C₂×D₂₉₂	C₂⁴	1	4	yes	—
265	C₂×C₂²⋊D₇₃	—	2	4	no	—
266	C₂×C₂²⋊D₇₃	—	2	4	no	—
267	C₂×C₂²⋊D₇₃	C₂×D₄	1	4	yes	—
268	D₄×D₇₃	—	2	8	no	—
269	D₄×D₇₃	—	4	4	no	—
270	D₄×D₇₃	—	4	16	no	—
271	C₂²×Dic₇₃	—	2	2	no	—
272	C₂×C₄×D₇₃	—	2	4	no	—
273	C₂×C₄×D₇₃	—	2	4	no	—
274	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
275	#11924015	—	4	4	no	—
276	#11924013	—	4	4	no	—
277	#11924012	—	2	4	no	—
278	#11924011	—	4	4	no	—
279	C₂×#10596831	C₂⁴	1	4	yes	—
280	C₈×D₇₃	—	4	4	no	—
281	C₄⋊Dic₇₃	—	2	2	no	—
282	C₄⋊Dic₇₃	—	2	2	no	—
283	C₄⋊Dic₇₃	—	2	2	no	—
284	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
285	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
286	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
287	#11924007	—	2	4	no	—
288	#11924007	—	2	4	no	—
289	C₂²⋊Dic₇₃	—	2	4	no	—
290	#11924005	—	2	4	no	—
291	#11924005	—	2	4	no	—
292	#11924005	—	2	4	no	—
293	#11924005	—	2	4	no	—
294	#11924005	C₂×D₄	1	4	yes	—
295	#11924005	C₂×D₄	1	4	yes	—
296	C₄×Dic₇₃	—	2	4	no	—
297	#41×C₇₃	—	2	2	no	—
298	#41×C₇₃	—	2	2	no	—
299	#41×C₇₃	—	2	2	no	—
300	#41×C₇₃	#41	1	4	yes	complemented
301	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
302	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
303	C₂×D₄×C₇₃	—	2	1	no	—
304	C₂×D₄×C₇₃	—	2	1	no	—
305	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇₃	—	2	1	no	—
308	C₂²×C₄×C₇₃	—	2	1	no	—
309	C₂²×C₄×C₇₃	—	2	1	no	—
310	C₂²×C₄×C₇₃	—	2	1	no	—
311	C₂²×C₄×C₇₃	—	2	1	no	—
312	C₂²×C₄×C₇₃	—	2	1	no	—
313	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
316	Q₁₆×C₇₃	—	2	2	no	—
317	SD₁₆×C₇₃	—	2	2	no	—
318	SD₁₆×C₇₃	—	2	2	no	—
319	D₈×C₇₃	—	2	2	no	—
320	C₂×C₈×C₇₃	—	2	2	no	—
321	C₂×C₈×C₇₃	—	2	2	no	—
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	1	yes	characteristic
326	C₄⋊C₄×C₇₃	—	2	1	no	—
327	C₄⋊C₄×C₇₃	—	2	1	no	—
328	C₄⋊C₄×C₇₃	—	2	1	no	—
329	C₄⋊C₄×C₇₃	—	2	1	no	—
330	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
334	C₂²⋊C₄×C₇₃	—	2	1	no	—
335	C₂²⋊C₄×C₇₃	—	2	1	no	—
336	C₂²⋊C₄×C₇₃	—	2	1	no	—
337	C₂²⋊C₄×C₇₃	—	2	1	no	—
338	C₂²⋊C₄×C₇₃	—	2	1	no	—
339	C₂²⋊C₄×C₇₃	—	2	1	no	—
340	C₄²×C₇₃	—	2	1	no	—
341	C₄²×C₇₃	—	2	1	no	—
342	C₄²×C₇₃	—	2	1	no	—
343	C₄²×C₇₃	—	2	1	no	—
344	C₄²×C₇₃	—	2	1	no	—
345	C₄²×C₇₃	—	2	1	no	—
346	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₇₃	—	2	1	no	—
351	C₂³×C₇₃	—	2	1	no	—
352	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
353	C₂²×D₇₃	—	2	4	no	—
354	C₂²×D₇₃	—	4	8	no	—
355	C₂²×D₇₃	—	4	4	no	—
356	C₂²×D₇₃	—	8	4	no	—
357	C₂²×D₇₃	—	8	4	no	—
358	C₂²×D₇₃	—	8	2	no	—
359	C₂²×D₇₃	—	8	2	no	—
360	C₂²×D₇₃	C₂²×D₄	1	4	yes	—
361	Q₈×C₇₃	—	2	1	no	—
362	Q₈×C₇₃	—	2	1	no	—
363	Q₈×C₇₃	—	2	1	no	—
364	Q₈×C₇₃	C₂×#41	1	2	yes	—
365	D₄×C₇₃	—	2	4	no	—
366	D₄×C₇₃	—	2	1	no	—
367	D₄×C₇₃	—	2	1	no	—
368	D₄×C₇₃	—	2	1	no	—
369	D₄×C₇₃	—	4	2	no	—
370	D₄×C₇₃	C₂×#41	1	2	yes	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	4	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	2	no	—
375	C₂×C₄×C₇₃	—	2	1	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	1	no	—
380	C₂×C₄×C₇₃	—	4	2	no	—
381	C₂×C₄×C₇₃	—	4	2	no	—
382	C₂×C₄×C₇₃	—	4	2	no	—
383	C₂×C₄×C₇₃	—	4	2	no	—
384	C₂×C₄×C₇₃	—	4	2	no	—
385	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
391	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
392	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
393	C₂²⋊D₇₃	—	2	8	no	—
394	C₂²⋊D₇₃	—	4	8	no	—
395	C₂²⋊D₇₃	—	8	4	no	—
396	C₂×Dic₇₃	—	2	4	no	—
397	C₂×Dic₇₃	—	8	2	no	—
398	C₂×Dic₇₃	C₂²×D₄	1	4	yes	—
399	D₂₉₂	—	2	4	no	—
400	D₂₉₂	—	2	4	no	—
401	D₂₉₂	—	2	4	no	—
402	D₂₉₂	—	2	4	no	—
403	D₂₉₂	—	2	4	no	—
404	D₂₉₂	—	4	8	no	—
405	D₂₉₂	—	4	4	no	—
406	D₂₉₂	—	4	4	no	—
407	D₂₉₂	—	4	4	no	—
408	D₂₉₂	—	8	2	no	—
409	D₂₉₂	—	8	2	no	—
410	D₂₉₂	—	8	4	no	—
411	D₂₉₂	—	8	4	no	—
412	C₄×D₇₃	—	2	4	no	—
413	C₄×D₇₃	—	2	4	no	—
414	C₄×D₇₃	—	4	8	no	—
415	C₄×D₇₃	—	8	4	no	—
416	Dic₁₄₆	—	2	4	no	—
417	Dic₁₄₆	—	4	4	no	—
418	Dic₁₄₆	—	8	2	no	—
419	C₈×C₇₃	—	2	1	no	—
420	C₈×C₇₃	—	2	1	no	—
421	C₈×C₇₃	—	2	1	no	—
422	C₈×C₇₃	—	2	1	no	—
423	#10596831	—	2	4	no	—
424	C₂²×C₇₃	—	2	1	no	—
425	C₂²×C₇₃	—	2	1	no	—
426	C₂²×C₇₃	—	2	2	no	—
427	C₂²×C₇₃	—	4	1	no	—
428	C₂²×C₇₃	—	4	1	no	—
429	C₂²×C₇₃	—	4	1	no	—
430	C₂²×C₇₃	—	4	1	no	—
431	C₂²×C₇₃	—	4	1	no	—
432	C₂²×C₇₃	#546	1	2	yes	—
433	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
434	C₂×D₇₃	—	2	4	no	—
435	C₂×D₇₃	—	2	4	no	—
436	C₂×D₇₃	—	2	4	no	—
437	C₂×D₇₃	—	4	4	no	—
438	C₂×D₇₃	—	4	4	no	—
439	C₂×D₇₃	—	4	4	no	—
440	C₂×D₇₃	—	16	8	no	—
441	C₂×D₇₃	—	16	4	no	—
442	C₄×C₇₃	—	2	2	no	—
443	C₄×C₇₃	—	2	1	no	—
444	C₄×C₇₃	—	2	1	no	—
445	C₄×C₇₃	—	4	1	no	—
446	C₄×C₇₃	—	4	1	no	—
447	C₄×C₇₃	—	4	1	no	—
448	C₄×C₇₃	—	4	1	no	—
449	C₄×C₇₃	—	4	1	no	—
450	C₄×C₇₃	#546	1	2	yes	—
451	C₄×C₇₃	#576	1	2	yes	—
452	C₄×C₇₃	#577	1	2	yes	—
453	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
454	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	Dic₇₃	—	2	4	no	—
456	Dic₇₃	—	4	4	no	—
457	#61215	—	73	1	no	maximal, Sylow
458	C₂×C₇₃	—	2	2	no	—
459	C₂×C₇₃	—	4	2	no	—
460	C₂×C₇₃	—	8	1	no	—
461	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
462	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
463	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
464	D₇₃	—	4	4	no	—
465	D₇₃	—	8	4	no	—
466	#3511	—	73	1	no	—
467	#3498	—	73	1	no	—
468	#3333	—	73	2	no	—
469	#3332	—	73	2	no	—
470	#3325	—	73	2	no	—
471	#3324	—	73	2	no	—
472	#3305	—	73	2	no	—
473	#3304	—	73	2	no	—
474	#3295	—	73	2	no	—
475	#3294	—	73	2	no	—
476	C₂×#486	—	73	1	no	—
477	#3096	—	73	2	no	—
478	#3079	—	73	1	no	—
479	#3062	—	73	2	no	—
480	#3038	—	73	1	no	—
481	#3012	—	73	2	no	—
482	C₄×#135	D₇₃	1	1	yes	characteristic, complemented
483	#2931	—	73	1	no	—
484	#2897	—	73	2	no	—
485	C₇₃	#61215	1	1	yes	characteristic, complemented, Sylow
486	C₂×H(5,𝔽₂)	—	73	2	no	—
487	C₂×AGL(1,ℤ/8)	—	73	2	no	—
488	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
489	C₂×#131	—	73	2	no	—
490	#556	—	73	2	no	—
491	#555	—	73	2	no	—
492	#554	—	73	2	no	—
493	#553	—	146	2	no	—
494	#550	—	73	2	no	—
495	#550	—	73	2	no	—
496	#548	—	146	2	no	—
497	#547	—	73	2	no	—
498	D₄²	—	73	2	no	—
499	D₄²	—	73	2	no	—
500	D₄²	—	146	2	no	—
501	D₄²	—	146	2	no	—
502	#542	—	146	2	no	—
503	#537	—	73	2	no	—
504	#535	—	73	2	no	—
505	#535	—	146	2	no	—
506	#533	—	146	1	no	—
507	#532	—	73	1	no	—
508	#532	—	146	1	no	—
509	#532	—	146	1	no	—
510	C₂×C₄⋊Q₈	—	73	1	no	—
511	C₂×#127	—	73	1	no	—
512	C₂×#127	—	146	1	no	—
513	#520	—	73	2	no	—
514	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
515	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
516	#486	—	73	2	no	—
517	#486	—	73	2	no	—
518	#486	—	73	2	no	—
519	#486	—	73	2	no	—
520	#482	—	73	4	no	—
521	#482	—	73	4	no	—
522	#481	—	73	4	no	—
523	#480	—	73	4	no	—
524	#477	—	73	2	no	—
525	#476	—	73	2	no	—
526	#475	—	73	2	no	—
527	#474	—	73	2	no	—
528	#469	—	73	4	no	—
529	#468	—	73	4	no	—
530	#466	—	73	4	no	—
531	#465	—	73	4	no	—
532	#460	—	73	2	no	—
533	#460	—	73	2	no	—
534	#459	—	73	2	no	—
535	#459	—	73	2	no	—
536	#452	—	73	4	no	—
537	#450	—	73	4	no	—
538	#449	—	73	4	no	—
539	#447	—	73	4	no	—
540	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
541	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
542	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
543	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
544	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
545	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
546	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
547	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
548	#436	—	73	2	no	—
549	#436	—	73	2	no	—
550	C₈×D₄	—	73	2	no	—
551	C₈×D₄	—	73	2	no	—
552	#428	—	73	2	no	—
553	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
554	#423	—	73	1	no	—
555	#418	—	73	2	no	—
556	#418	—	73	4	no	—
557	#417	—	73	2	no	—
558	#417	—	73	4	no	—
559	#416	—	73	4	no	—
560	#416	C₂×D₇₃	1	1	yes	characteristic
561	#416	C₂×D₇₃	1	1	yes	characteristic, complemented
562	C₂×#102	—	73	2	no	—
563	C₂×#102	—	73	2	no	—
564	C₂×#102	—	73	4	no	—
565	#408	—	73	2	no	—
566	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
567	H(5,𝔽₂)	—	292	4	no	—
568	H(5,𝔽₂)	—	146	8	no	—
569	C₂×#41	—	73	2	no	—
570	C₂×#41	—	73	4	no	—
571	C₂×#41	—	146	2	no	—
572	C₂×#41	—	146	2	no	—
573	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
574	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
575	C₂²×Q₈	—	146	1	no	—
576	C₂²×D₄	—	73	4	no	—
577	C₂²×D₄	—	73	2	no	—
578	C₂²×D₄	—	146	2	no	—
579	C₂²×D₄	—	146	2	no	—
580	C₂²×D₄	—	146	2	no	—
581	C₂²×D₄	—	146	4	no	—
582	C₂²×D₄	—	146	1	no	—
583	C₂²×D₄	—	146	1	no	—
584	AGL(1,ℤ/8)	—	292	4	no	—
585	#135	—	2	4	no	—
586	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
587	C₂×SD₁₆	—	73	4	no	—
588	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
589	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
590	C₂×D₈	—	73	4	no	—
591	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
592	#131	—	292	4	no	—
593	C₂×M₁₆	—	73	2	no	—
594	C₂×M₁₆	—	73	4	no	—
595	C₂²×C₈	—	73	4	no	—
596	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
597	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
598	C₄⋊Q₈	—	73	1	no	—
599	C₄⋊Q₈	—	73	2	no	—
600	C₄⋊Q₈	—	73	2	no	—
601	C₄⋊Q₈	—	146	1	no	—
602	C₄⋊Q₈	—	146	1	no	—
603	#127	—	73	1	no	—
604	#127	—	73	2	no	—
605	#127	—	73	2	no	—
606	#127	—	146	2	no	—
607	#127	—	146	2	no	—
608	#127	—	146	2	no	—
609	#127	—	146	1	no	—
610	#127	—	146	1	no	—
611	#126	—	146	4	no	—
612	#125	—	146	2	no	—
613	#124	—	73	2	no	—
614	#124	—	146	2	no	—
615	#124	—	146	2	no	—
616	#124	—	146	4	no	—
617	#123	—	146	4	no	—
618	C₂²⋊Q₈	—	73	4	no	—
619	C₂²⋊Q₈	—	146	4	no	—
620	C₂²⋊Q₈	—	146	2	no	—
621	C₂²⋊Q₈	—	146	2	no	—
622	#121	—	73	2	no	—
623	#121	—	73	2	no	—
624	#121	—	73	4	no	—
625	#121	—	73	4	no	—
626	#121	—	73	4	no	—
627	#121	—	146	4	no	—
628	#121	—	146	4	no	—
629	#121	—	146	2	no	—
630	#121	—	146	2	no	—
631	#121	—	146	2	no	—
632	#121	—	146	2	no	—
633	#121	—	146	4	no	—
634	#120	—	146	4	no	—
635	#120	—	146	4	no	—
636	#120	—	146	4	no	—
637	C₄×Q₈	—	146	2	no	—
638	C₄×Q₈	—	146	2	no	—
639	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
640	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
641	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
642	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	73	2	no	—
648	C₄×D₄	—	73	2	no	—
649	C₄×D₄	—	146	2	no	—
650	C₄×D₄	—	146	2	no	—
651	C₄×D₄	—	146	2	no	—
652	C₄×D₄	—	146	2	no	—
653	C₄×D₄	—	146	4	no	—
654	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
655	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
656	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
657	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
658	#117	—	2	1	no	—
659	#117	—	2	1	no	—
660	#117	—	73	4	no	—
661	#117	—	146	2	no	—
662	#117	C₂²×D₇₃	1	1	yes	characteristic
663	#117	C₂²×D₇₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	—	73	2	no	—
665	C₂×C₄⋊C₄	—	73	4	no	—
666	C₂×C₄⋊C₄	—	146	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
670	#107	—	73	4	no	—
671	#107	C₂²×D₇₃	1	1	yes	characteristic
672	#107	C₂²×D₇₃	1	1	yes	characteristic
673	#106	—	73	4	no	—
674	#106	C₂²×D₇₃	1	1	yes	characteristic
675	#106	C₂²×D₇₃	1	1	yes	characteristic
676	C₄⋊C₈	—	73	2	no	—
677	C₄⋊C₈	—	73	2	no	—
678	#103	—	73	4	no	—
679	#103	C₂²×D₇₃	1	1	yes	characteristic
680	#103	C₂²×D₇₃	1	1	yes	characteristic
681	#103	C₂²×D₇₃	1	1	yes	characteristic
682	#103	C₂²×D₇₃	1	1	yes	characteristic
683	#102	—	73	4	no	—
684	#102	—	73	4	no	—
685	#102	—	73	4	no	—
686	#102	—	73	4	no	—
687	#102	—	73	4	no	—
688	#102	—	73	4	no	—
689	#102	—	73	4	no	—
690	#102	C₂²×D₇₃	1	1	yes	characteristic
691	#102	C₂²×D₇₃	1	1	yes	characteristic
692	#102	C₂²×D₇₃	1	1	yes	characteristic
693	#102	C₂²×D₇₃	1	1	yes	characteristic
694	C₂²⋊C₈	—	73	4	no	—
695	C₂²⋊C₈	—	73	4	no	—
696	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
697	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
698	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
699	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
700	C₂⁴	—	146	4	no	—
701	C₂⁴	—	146	2	no	—
702	#41	—	2	2	no	—
703	#41	—	2	2	no	—
704	#41	—	2	2	no	—
705	#41	—	292	8	no	—
706	#41	—	292	4	no	—
707	#41	—	584	4	no	—
708	#41	—	146	8	no	—
709	#41	—	146	4	no	—
710	#41	—	146	4	no	—
711	#41	#11924028	1	4	yes	complemented
712	C₂×Q₈	—	584	2	no	—
713	C₂×Q₈	—	73	2	no	—
714	C₂×Q₈	—	146	2	no	—
715	C₂×Q₈	—	146	2	no	—
716	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
717	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	292	8	no	—
721	C₂×D₄	—	292	16	no	—
722	C₂×D₄	—	292	4	no	—
723	C₂×D₄	—	584	2	no	—
724	C₂×D₄	—	584	2	no	—
725	C₂×D₄	—	584	4	no	—
726	C₂×D₄	—	584	4	no	—
727	C₂×D₄	—	73	4	no	—
728	C₂×D₄	—	73	2	no	—
729	C₂×D₄	—	73	2	no	—
730	C₂×D₄	—	73	2	no	—
731	C₂×D₄	—	73	4	no	—
732	C₂×D₄	—	146	4	no	—
733	C₂×D₄	—	146	4	no	—
734	C₂×D₄	—	146	4	no	—
735	C₂×D₄	—	146	4	no	—
736	C₂×D₄	—	146	8	no	—
737	C₂×D₄	—	146	4	no	—
738	C₂×D₄	—	146	2	no	—
739	C₂×D₄	—	146	2	no	—
740	C₂×D₄	—	146	2	no	—
741	C₂×D₄	—	146	2	no	—
742	C₂×D₄	—	146	2	no	—
743	C₂×D₄	—	146	4	no	—
744	C₂×D₄	—	146	4	no	—
745	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
746	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	73	4	no	—
754	C₂²×C₄	—	146	4	no	—
755	C₂²×C₄	—	146	4	no	—
756	C₂²×C₄	—	146	2	no	—
757	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
758	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
759	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
760	Q₁₆	—	2	2	no	—
761	SD₁₆	—	2	2	no	—
762	SD₁₆	—	2	2	no	—
763	SD₁₆	—	292	4	no	—
764	D₈	—	2	2	no	—
765	D₈	—	292	4	no	—
766	M₁₆	—	292	4	no	—
767	M₁₆	—	146	4	no	—
768	C₂×C₈	—	2	2	no	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	292	4	no	—
771	C₂×C₈	—	73	4	no	—
772	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
773	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
774	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
775	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	73	2	no	—
781	C₄⋊C₄	—	73	2	no	—
782	C₄⋊C₄	—	73	4	no	—
783	C₄⋊C₄	—	146	4	no	—
784	C₄⋊C₄	—	146	4	no	—
785	C₄⋊C₄	—	146	2	no	—
786	C₄⋊C₄	—	146	2	no	—
787	C₄⋊C₄	—	146	2	no	—
788	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	73	4	no	—
799	C₂²⋊C₄	—	73	4	no	—
800	C₂²⋊C₄	—	146	4	no	—
801	C₂²⋊C₄	—	146	4	no	—
802	C₂²⋊C₄	—	146	4	no	—
803	C₂²⋊C₄	—	146	4	no	—
804	C₂²⋊C₄	—	146	4	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	1	no	—
807	C₄²	—	2	1	no	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	1	no	—
811	C₄²	—	146	4	no	—
812	C₄²	D₄×D₇₃	1	1	yes	characteristic
813	C₄²	D₄×D₇₃	1	1	yes	characteristic
814	C₄²	C₂³×D₇₃	1	1	yes	characteristic
815	C₄²	C₂³×D₇₃	1	1	yes	characteristic
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	292	8	no	—
819	C₂³	—	292	4	no	—
820	C₂³	—	584	2	no	—
821	C₂³	—	584	2	no	—
822	C₂³	—	584	4	no	—
823	C₂³	—	584	4	no	—
824	C₂³	—	73	4	no	—
825	C₂³	—	146	4	no	—
826	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
827	Q₈	—	2	1	no	—
828	Q₈	—	2	1	no	—
829	Q₈	—	2	1	no	—
830	Q₈	—	292	4	no	—
831	Q₈	—	584	2	no	—
832	Q₈	—	146	4	no	—
833	Q₈	C₂×#11924028	1	2	yes	—
834	D₄	—	2	4	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	1	no	—
837	D₄	—	2	1	no	—
838	D₄	—	4	2	no	—
839	D₄	—	292	8	no	—
840	D₄	—	292	8	no	—
841	D₄	—	292	4	no	—
842	D₄	—	292	4	no	—
843	D₄	—	292	4	no	—
844	D₄	—	584	2	no	—
845	D₄	—	584	2	no	—
846	D₄	—	584	4	no	—
847	D₄	—	584	4	no	—
848	D₄	—	584	4	no	—
849	D₄	—	146	8	no	—
850	D₄	—	146	4	no	—
851	D₄	—	146	4	no	—
852	D₄	—	146	4	no	—
853	D₄	—	146	4	no	—
854	D₄	—	146	4	no	—
855	D₄	C₂×#11924028	1	2	yes	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	292	8	no	—
871	C₂×C₄	—	584	4	no	—
872	C₂×C₄	—	584	2	no	—
873	C₂×C₄	—	73	4	no	—
874	C₂×C₄	—	146	4	no	—
875	C₂×C₄	—	146	4	no	—
876	C₂×C₄	—	146	4	no	—
877	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
878	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
879	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
880	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
881	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
882	C₂×C₄	C₂×#11924028	1	2	yes	—
883	C₂×C₄	#14556637	1	2	yes	—
884	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	2	1	no	—
888	C₈	—	2	1	no	—
889	C₈	—	146	4	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	292	4	no	—
899	C₂²	—	292	4	no	—
900	C₂²	—	292	4	no	—
901	C₂²	—	1168	4	no	—
902	C₂²	—	1168	8	no	—
903	C₂²	—	146	4	no	—
904	C₂²	—	146	4	no	—
905	C₂²	—	146	4	no	—
906	C₂²	#17989233	1	2	yes	—
907	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
908	C₄	—	2	2	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	1	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	1	no	—
916	C₄	—	292	4	no	—
917	C₄	—	146	4	no	—
918	C₄	#17989233	1	2	yes	—
919	C₄	#17989389	1	2	yes	—
920	C₄	#17989394	1	2	yes	—
921	C₄	C₂²×#11924028	1	1	yes	characteristic
922	C₄	C₂×#14556637	1	1	yes	characteristic
923	C₂	—	2	2	no	—
924	C₂	—	4	2	no	—
925	C₂	—	8	1	no	—
926	C₂	—	292	4	no	—
927	C₂	—	584	4	no	—
928	C₂	C₂×#17989233	1	1	yes	characteristic
929	C₂	C₂×#17989389	1	1	yes	characteristic
930	C₂	C₂×#17989394	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₄×#135×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	C₄×#135	D₇₃
hypocenter	C₇₃	#61215
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22623842	C₂	semidirect
2. #22623709	C₂	semidirect
3. #22622271	C₂	semidirect
4. #22622260	C₂	semidirect
5. #22622175	C₂	semidirect
6. #22622164	C₂	semidirect
7. #22621883	C₂	semidirect
8. #22621872	C₂	semidirect
9. #22621757	C₂	semidirect
10. #22621746	C₂	semidirect
11. C₂×#17988934	C₂	semidirect
12. #22619892	C₂	semidirect
13. #22619746	C₂	semidirect
14. #22619614	C₂	semidirect
15. #22619411	C₂	semidirect
16. #22619231	C₂	semidirect
17. #22618644	C₂	semidirect
18. #22618453	C₂	semidirect
19. C₄×#135×C₇₃	C₂	semidirect
21. C₂×#14556616	C₂²	semidirect
22. C₂×#14556597	C₂²	semidirect
23. #17989310	C₂²	semidirect
24. #17989302	C₂²	semidirect
25. #17989297	C₂²	semidirect
30. #17989242	C₂²	semidirect
36. #17989165	C₂²	semidirect
43. C₂×#14556591	C₂²	semidirect
46. #17989067	C₂²	semidirect
47. #17988934	C₂²	semidirect
48. #17988934	C₂²	semidirect
49. #17988934	C₂²	semidirect
50. #17988934	C₂²	semidirect
51. #17988914	C₂²	semidirect
52. #17988913	C₂²	semidirect
53. #17988907	C₂²	semidirect
54. #17988902	C₂²	semidirect
55. #17988882	C₂²	semidirect
56. #17988877	C₂²	semidirect
57. #17988872	C₂²	semidirect
58. #17988867	C₂²	semidirect
59. #17988839	C₂²	semidirect
60. #17988836	C₂²	semidirect
61. #17988822	C₂²	semidirect
62. #17988819	C₂²	semidirect
63. #17988787	C₂²	semidirect
64. #17988787	C₂²	semidirect
65. #17988782	C₂²	semidirect
66. #17988782	C₂²	semidirect
67. #17988748	C₂²	semidirect
68. #17988736	C₂²	semidirect
69. #17988731	C₂²	semidirect
70. #17988719	C₂²	semidirect
71. #17988666	C₂²	semidirect
72. #17988666	C₂²	semidirect
73. C₈×D₂₉₂	C₂²	semidirect
74. C₈×D₂₉₂	C₂²	semidirect
75. #17988630	C₂²	semidirect
76. #17988611	C₂²	semidirect
77. #17988591	C₂²	semidirect
78. #17988590	C₂²	semidirect
80. #17988587	C₂²	semidirect
81. #17988582	C₂²	semidirect
82. C₂×#14556513	C₂²	semidirect
83. C₂×#14556513	C₂²	semidirect
84. #102×D₇₃	C₂²	semidirect
85. #17988553	C₂²	semidirect
88. C₄×#41×C₇₃	C₂²	semidirect
89. C₄×Q₁₆×C₇₃	C₂²	semidirect
90. C₄×Q₁₆×C₇₃	C₂²	semidirect
91. C₄×SD₁₆×C₇₃	C₂²	semidirect
92. C₄×SD₁₆×C₇₃	C₂²	semidirect
93. C₄×SD₁₆×C₇₃	C₂²	semidirect
94. C₄×SD₁₆×C₇₃	C₂²	semidirect
95. C₄×D₈×C₇₃	C₂²	semidirect
96. C₄×D₈×C₇₃	C₂²	semidirect
97. #427×C₇₃	C₂²	semidirect
99. #416×C₇₃	C₂²	semidirect
100. C₂×C₄×C₈×C₇₃	C₂²	semidirect
300. #41×C₇₃	#41	semidirect
482. C₄×#135	D₇₃	semidirect
485. C₇₃	#61215	semidirect
515. C₄×#41	C₂×D₇₃	semidirect
540. C₄×Q₁₆	C₂×D₇₃	semidirect
541. C₄×Q₁₆	C₂×D₇₃	semidirect
542. C₄×SD₁₆	C₂×D₇₃	semidirect
543. C₄×SD₁₆	C₂×D₇₃	semidirect
544. C₄×SD₁₆	C₂×D₇₃	semidirect
545. C₄×SD₁₆	C₂×D₇₃	semidirect
546. C₄×D₈	C₂×D₇₃	semidirect
547. C₄×D₈	C₂×D₇₃	semidirect
553. #427	C₂×D₇₃	semidirect
561. #416	C₂×D₇₃	semidirect
566. C₂×C₄×C₈	C₂×D₇₃	semidirect
711. #41	#11924028	semidirect

Maximal subgroups

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

subgroup	index
#22623842	2
#22623709	2
#22622271	2
#22622260	2
#22622175	2
#22622164	2
#22621883	2
#22621872	2
#22621757	2
#22621746	2
C₂×#17988934	2
#22619892	2
#22619746	2
#22619614	2
#22619411	2
#22619231	2
#22618644	2
#22618453	2
C₄×#135×C₇₃	2
#61215	73