Subgroups — #33966695

Order 18688.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623756	C₂	1	2	yes	maximal, complemented
2	#22622883	C₂	1	2	yes	maximal, complemented
3	#22622879	C₂	1	2	yes	maximal, complemented
4	#22622874	C₂	1	2	yes	maximal, complemented
5	#22622870	C₂	1	2	yes	maximal, complemented
6	#22622822	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622822	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622820	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622800	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622799	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622795	C₂	1	1	yes	maximal, characteristic, complemented
12	#22622795	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620468	C₂	1	1	yes	maximal, characteristic, complemented
14	#22620464	C₂	1	1	yes	maximal, characteristic, complemented
15	#499×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619796	C₂	1	2	yes	maximal, complemented
17	#22619790	C₂	1	2	yes	maximal, complemented
18	#22619750	C₂	1	2	yes	maximal, complemented
19	#22618860	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618806	C₂	1	1	yes	maximal, characteristic
21	#22618806	C₂	1	1	yes	maximal, characteristic
22	C₄×#14556614	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556614	C₂²	1	1	yes	characteristic
25	#17989316	C₂²	1	2	yes	—
26	#17989313	C₂²	1	2	yes	—
27	#17989313	C₂²	1	2	yes	—
28	#17989298	—	2	2	no	—
29	#17989298	C₂²	1	2	yes	—
30	#17989297	—	2	2	no	—
31	#17989297	C₂²	1	2	yes	—
32	#17989293	—	2	2	no	—
33	#17989293	—	2	2	no	—
34	#17989293	C₂²	1	2	yes	—
35	#17989293	C₂²	1	2	yes	—
36	#17989217	—	2	2	no	—
37	#17989217	C₂²	1	2	yes	—
38	#17989214	—	2	2	no	—
39	#17989214	C₂²	1	2	yes	—
40	#17989141	—	2	2	no	—
41	#17989141	C₂²	1	1	yes	characteristic
42	#125×D₇₃	—	2	2	no	—
43	#125×D₇₃	C₂²	1	2	yes	—
44	#17989069	C₂²	1	2	yes	—
45	#17989069	C₂²	1	2	yes	—
46	C₄×#11924029	C₂²	1	2	yes	—
47	#17988997	C₂²	1	2	yes	—
48	#17988995	C₂²	1	2	yes	—
49	#17988994	C₂²	1	2	yes	—
50	#17988993	C₂²	1	2	yes	—
51	#17988992	C₂²	1	1	yes	characteristic
52	#17988991	C₂²	1	1	yes	characteristic
53	#17988991	C₂²	1	1	yes	characteristic
54	#17988989	C₂²	1	1	yes	characteristic
55	#17988989	C₂²	1	1	yes	characteristic
56	#17988988	C₂²	1	1	yes	characteristic
57	#17988988	C₂²	1	1	yes	characteristic
58	#17988988	C₂²	1	1	yes	characteristic
59	#17988988	C₂²	1	1	yes	characteristic
60	#17988987	C₂²	1	2	yes	—
61	#17988986	C₂²	1	2	yes	—
62	#17988896	C₂²	1	2	yes	—
63	#17988896	C₂²	1	2	yes	—
64	#17988894	C₂²	1	2	yes	—
65	#17988894	C₂²	1	2	yes	—
66	#17988892	C₂²	1	2	yes	—
67	#17988892	C₂²	1	2	yes	—
68	#17988890	C₂²	1	2	yes	—
69	#17988890	C₂²	1	2	yes	—
70	#17988888	C₂²	1	2	yes	—
71	#17988888	C₂²	1	2	yes	—
72	#17988886	C₂²	1	2	yes	—
73	#17988886	C₂²	1	2	yes	—
74	#17988884	C₂²	1	2	yes	—
75	#17988884	C₂²	1	2	yes	—
76	#17988878	C₂²	1	2	yes	—
77	#17988876	C₂²	1	2	yes	—
78	#17988876	C₂²	1	2	yes	—
79	#17988874	C₂²	1	2	yes	—
80	#17988872	C₂²	1	2	yes	—
81	#17988870	C₂²	1	2	yes	—
82	#17988870	C₂²	1	2	yes	—
83	#17988718	C₂²	1	1	yes	characteristic
84	#17988716	C₂²	1	1	yes	characteristic
85	#17988716	C₂²	1	1	yes	characteristic
86	#17988714	C₂²	1	1	yes	characteristic
87	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
88	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
89	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
90	#17988690	C₂²	1	2	yes	—
91	#17988690	C₂²	1	2	yes	—
92	#17988685	C₂²	1	2	yes	—
93	#17988685	C₂²	1	2	yes	—
94	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
95	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
96	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
97	C₄×#11924015	C₂²	1	2	yes	—
98	#17988672	C₂²	1	2	yes	—
99	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
100	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
101	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
102	#17988669	C₂²	1	1	yes	characteristic
103	#17988669	C₂²	1	1	yes	characteristic
104	#17988669	C₂²	1	1	yes	characteristic
105	#17988628	C₂²	1	2	yes	—
106	#17988626	C₂²	1	2	yes	—
107	#17988624	C₂²	1	1	yes	characteristic
108	#107×D₇₃	C₂²	1	1	yes	characteristic
109	#107×D₇₃	C₂²	1	1	yes	characteristic
110	#106×D₇₃	C₂²	1	2	yes	—
111	#17988612	C₂²	1	1	yes	characteristic
112	#17988612	C₂²	1	1	yes	characteristic
113	#17988609	C₂²	1	1	yes	characteristic
114	#17988587	C₂²	1	2	yes	—
115	#17988587	C₂²	1	2	yes	—
116	#17988582	C₂²	1	2	yes	—
117	#17988541	C₂²	1	1	yes	characteristic
118	#17988541	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
120	#557×C₇₃	C₂²	1	2	yes	—
121	#500×C₇₃	C₂²	1	1	yes	characteristic
122	#499×C₇₃	C₂²	1	1	yes	characteristic
123	#499×C₇₃	C₂²	1	1	yes	characteristic
124	#479×C₇₃	C₂²	1	2	yes	—
125	#479×C₇₃	C₂²	1	2	yes	—
126	#475×C₇₃	C₂²	1	2	yes	—
127	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
128	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
129	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
131	C₂×#11924029	C₂³	1	2	yes	—
132	#14556614	Q₈	1	8	yes	complemented
133	C₂×#11924015	C₂³	1	2	yes	—
134	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
135	C₂×#11924011	C₂³	1	1	yes	characteristic
136	C₂×#11924011	C₂³	1	1	yes	characteristic
137	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
139	#14556591	—	2	2	no	—
140	#14556591	C₂³	1	2	yes	—
141	#14556590	—	2	2	no	—
142	#14556590	—	2	2	no	—
143	#14556590	—	2	2	no	—
144	#14556590	D₄	1	1	yes	characteristic
145	#14556590	C₂³	1	2	yes	—
146	#14556590	C₂³	1	2	yes	—
147	#14556589	—	2	2	no	—
148	#14556589	D₄	1	1	yes	characteristic
149	#14556583	—	2	2	no	—
150	#14556583	—	2	2	no	—
151	#14556583	C₂³	1	2	yes	—
152	#14556583	C₂³	1	2	yes	—
153	#14556582	—	2	2	no	—
154	#14556582	—	2	2	no	—
155	#14556582	—	2	2	no	—
156	#14556582	—	2	2	no	—
157	#14556582	C₂³	1	2	yes	—
158	#14556582	C₂³	1	2	yes	—
159	#14556582	C₂³	1	2	yes	—
160	#14556582	C₂³	1	2	yes	—
161	#14556581	—	2	2	no	—
162	#14556581	—	2	2	no	—
163	#14556581	—	2	2	no	—
164	#14556581	—	2	2	no	—
165	#14556581	D₄	1	1	yes	characteristic
166	#14556581	D₄	1	1	yes	characteristic
167	#14556571	—	2	2	no	—
168	#14556571	—	2	2	no	—
169	#14556571	—	2	2	no	—
170	#14556571	—	2	2	no	—
171	#14556571	D₄	1	1	yes	characteristic
172	#14556569	—	2	2	no	—
173	#14556569	—	2	2	no	—
174	#14556569	—	2	2	no	—
175	#14556569	—	2	2	no	—
176	#14556569	—	2	2	no	—
177	#14556569	—	2	2	no	—
178	#14556569	—	2	2	no	—
179	#14556569	—	2	2	no	—
180	#14556569	D₄	1	1	yes	characteristic
181	#14556569	D₄	1	1	yes	characteristic
182	#14556567	—	2	2	no	—
183	#14556567	—	2	2	no	—
184	#14556567	—	2	2	no	—
185	#14556567	—	2	2	no	—
186	#14556567	D₄	1	1	yes	characteristic
187	Q₈×Dic₇₃	C₂³	1	2	yes	—
188	Q₈×Dic₇₃	C₂³	1	2	yes	—
189	Q₈×Dic₇₃	C₂³	1	2	yes	—
190	C₄×Dic₁₄₆	—	2	2	no	—
191	C₄×Dic₁₄₆	—	2	2	no	—
192	C₄×Dic₁₄₆	—	2	2	no	—
193	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
196	C₄×D₂₉₂	—	2	2	no	—
197	C₄×D₂₉₂	—	2	2	no	—
198	C₄×D₂₉₂	—	2	2	no	—
199	C₄×D₂₉₂	C₂³	1	2	yes	—
200	C₄×D₂₉₂	C₂³	1	2	yes	—
201	C₄×D₂₉₂	C₂³	1	2	yes	—
202	#14556553	—	2	2	no	—
203	#14556553	—	2	2	no	—
204	#14556553	—	2	2	no	—
205	#14556553	C₂³	1	2	yes	—
206	#14556553	C₂³	1	2	yes	—
207	#14556553	C₂³	1	2	yes	—
208	#14556549	—	2	2	no	—
209	#14556549	C₂³	1	2	yes	—
210	#14556548	—	2	2	no	—
211	#14556548	—	2	2	no	—
212	#14556548	C₂³	1	1	yes	characteristic
213	#14556548	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×D₇₃	—	2	2	no	—
215	C₄⋊C₄×D₇₃	—	2	2	no	—
216	C₄⋊C₄×D₇₃	—	2	2	no	—
217	C₄⋊C₄×D₇₃	—	2	2	no	—
218	C₄⋊C₄×D₇₃	—	2	2	no	—
219	C₄⋊C₄×D₇₃	—	2	2	no	—
220	C₄⋊C₄×D₇₃	—	2	2	no	—
221	C₄⋊C₄×D₇₃	—	2	2	no	—
222	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
223	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
224	C₄²×D₇₃	—	2	2	no	—
225	C₄²×D₇₃	C₂³	1	1	yes	characteristic
226	#14556525	C₂³	1	1	yes	characteristic
227	#14556525	C₂³	1	1	yes	characteristic
228	#14556525	C₂³	1	1	yes	characteristic
229	#14556525	C₂³	1	2	yes	—
230	#14556524	C₂³	1	2	yes	—
231	#14556524	C₂³	1	2	yes	—
232	#14556524	C₂³	1	2	yes	—
233	#14556524	C₂³	1	2	yes	—
234	#14556523	C₂³	1	2	yes	—
235	#14556523	C₂³	1	2	yes	—
236	#14556522	C₂³	1	2	yes	—
237	#14556522	C₂³	1	2	yes	—
238	#14556522	C₂³	1	2	yes	—
239	#14556522	C₂³	1	2	yes	—
240	#14556522	C₂³	1	2	yes	—
241	C₄⋊#10596831	C₂³	1	1	yes	characteristic
242	C₄⋊#10596831	C₂³	1	1	yes	characteristic
243	C₄⋊#10596831	C₂³	1	1	yes	characteristic
244	#14556520	C₂³	1	1	yes	characteristic
245	#14556520	C₂³	1	1	yes	characteristic
246	#14556520	C₂³	1	1	yes	characteristic
247	#14556520	C₂³	1	1	yes	characteristic
248	#14556520	C₂³	1	1	yes	characteristic
249	#14556520	C₂³	1	1	yes	characteristic
250	#14556515	C₂³	1	2	yes	—
251	#14556515	C₂³	1	2	yes	—
252	#14556515	C₂³	1	2	yes	—
253	#14556513	C₂³	1	2	yes	—
254	#14556513	C₂³	1	2	yes	—
255	#14556513	C₂³	1	2	yes	—
256	#14556511	C₂³	1	2	yes	—
257	#14556511	C₂³	1	2	yes	—
258	#14556511	C₂³	1	2	yes	—
259	#14556502	C₂³	1	1	yes	characteristic
260	#14556502	C₂³	1	1	yes	characteristic
261	#14556501	C₂³	1	1	yes	characteristic
262	#14556501	C₂³	1	1	yes	characteristic
263	C₄×#10596831	C₂³	1	1	yes	characteristic
264	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
268	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₇₃	—	2	2	no	—
270	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
271	#125×C₇₃	—	2	2	no	—
272	#125×C₇₃	—	2	2	no	—
273	#125×C₇₃	C₂³	1	2	yes	—
274	#125×C₇₃	C₂³	1	2	yes	—
275	C₄×Q₈×C₇₃	—	2	2	no	—
276	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
277	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
278	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
280	#107×C₇₃	C₂³	1	1	yes	characteristic
281	#107×C₇₃	C₂³	1	1	yes	characteristic
282	#107×C₇₃	C₂³	1	1	yes	characteristic
283	#107×C₇₃	C₂³	1	2	yes	—
284	#106×C₇₃	C₂³	1	2	yes	—
285	#106×C₇₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
289	#103×C₇₃	C₂³	1	2	yes	—
290	#103×C₇₃	C₂³	1	2	yes	—
291	#103×C₇₃	C₂³	1	2	yes	—
292	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
295	#11924029	—	2	4	no	—
296	#11924029	C₂×Q₈	1	8	yes	—
297	C₂×Dic₁₄₆	—	2	2	no	—
298	C₂×Dic₁₄₆	—	2	2	no	—
299	C₂×Dic₁₄₆	—	2	2	no	—
300	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
301	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
302	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
303	C₂×D₂₉₂	—	2	2	no	—
304	C₂×D₂₉₂	C₂⁴	1	2	yes	—
305	C₂×C₄×D₇₃	—	2	2	no	—
306	C₂×C₄×D₇₃	—	2	2	no	—
307	C₂×C₄×D₇₃	—	2	2	no	—
308	C₂×C₄×D₇₃	—	2	2	no	—
309	C₂×C₄×D₇₃	—	2	2	no	—
310	C₂×C₄×D₇₃	—	2	2	no	—
311	C₂×C₄×D₇₃	—	2	2	no	—
312	C₂×C₄×D₇₃	—	2	2	no	—
313	C₂×C₄×D₇₃	—	2	2	no	—
314	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
315	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
316	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
317	#11924015	C₂×Q₈	1	8	yes	—
318	D₅₈₄	C₂×Q₈	1	4	yes	—
319	#11924011	—	2	2	no	—
320	#11924011	—	2	2	no	—
321	C₂×#10596831	C₂⁴	1	1	yes	characteristic
322	C₂×#10596831	C₂⁴	1	1	yes	characteristic
323	C₂×#10596831	C₂⁴	1	1	yes	characteristic
324	C₂×#10596831	C₂⁴	1	1	yes	characteristic
325	C₈×D₇₃	—	2	2	no	—
326	C₈×D₇₃	C₂×Q₈	1	4	yes	—
327	C₄⋊Dic₇₃	—	2	2	no	—
328	C₄⋊Dic₇₃	—	2	2	no	—
329	C₄⋊Dic₇₃	—	2	2	no	—
330	C₄⋊Dic₇₃	—	2	2	no	—
331	C₄⋊Dic₇₃	—	2	2	no	—
332	C₄⋊Dic₇₃	—	2	2	no	—
333	C₄⋊Dic₇₃	—	2	2	no	—
334	C₄⋊Dic₇₃	—	2	2	no	—
335	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
336	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
337	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
338	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
339	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
340	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
341	#11924007	—	2	2	no	—
342	#11924007	—	2	2	no	—
343	#11924007	—	2	2	no	—
344	#11924007	—	2	2	no	—
345	#11924007	—	2	2	no	—
346	#11924007	—	2	2	no	—
347	#11924007	—	2	2	no	—
348	#11924007	—	2	2	no	—
349	#11924007	—	2	2	no	—
350	#11924007	—	2	2	no	—
351	#11924007	—	2	2	no	—
352	#11924007	—	2	2	no	—
353	#11924007	C₂×D₄	1	1	yes	characteristic
354	#11924007	C₂×D₄	1	1	yes	characteristic
355	#11924007	C₂×D₄	1	1	yes	characteristic
356	#11924007	C₂×D₄	1	1	yes	characteristic
357	#11924007	C₂×D₄	1	1	yes	characteristic
358	#11924007	C₂×D₄	1	1	yes	characteristic
359	#11924007	C₂×D₄	1	1	yes	characteristic
360	#11924007	C₂×D₄	1	1	yes	characteristic
361	#11924007	C₂×D₄	1	1	yes	characteristic
362	#11924007	C₂×D₄	1	1	yes	characteristic
363	#11924005	—	2	2	no	—
364	#11924005	—	2	2	no	—
365	#11924005	—	2	2	no	—
366	#11924005	—	2	2	no	—
367	#11924005	—	2	2	no	—
368	#11924005	—	2	2	no	—
369	#11924005	—	2	2	no	—
370	#11924005	C₂×D₄	1	1	yes	characteristic
371	#11924005	C₂×D₄	1	1	yes	characteristic
372	#11924005	C₂×D₄	1	1	yes	characteristic
373	#11924005	C₂×D₄	1	1	yes	characteristic
374	C₄×Dic₇₃	—	2	2	no	—
375	C₄×Dic₇₃	—	2	2	no	—
376	C₄×Dic₇₃	—	2	2	no	—
377	C₄×Dic₇₃	—	2	2	no	—
378	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
379	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
380	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
381	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
382	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈×C₇₃	—	2	2	no	—
384	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
385	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
386	Q₁₆×C₇₃	C₂×Q₈	1	4	yes	—
387	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₇₃	—	2	2	no	—
392	C₄⋊C₄×C₇₃	—	2	2	no	—
393	C₄⋊C₄×C₇₃	—	2	2	no	—
394	C₄⋊C₄×C₇₃	—	2	2	no	—
395	C₄⋊C₄×C₇₃	—	2	2	no	—
396	C₄⋊C₄×C₇₃	—	2	2	no	—
397	C₄⋊C₄×C₇₃	—	2	2	no	—
398	C₄⋊C₄×C₇₃	—	2	2	no	—
399	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
405	C₄²×C₇₃	—	2	2	no	—
406	C₄²×C₇₃	—	2	2	no	—
407	C₄²×C₇₃	—	2	2	no	—
408	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
410	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
411	C₂²×D₇₃	—	2	2	no	—
412	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
413	Q₈×C₇₃	—	2	2	no	—
414	Q₈×C₇₃	—	4	1	no	—
415	Q₈×C₇₃	—	8	2	no	—
416	Q₈×C₇₃	C₂²×Q₈	1	4	yes	—
417	C₂×C₄×C₇₃	—	2	2	no	—
418	C₂×C₄×C₇₃	—	2	2	no	—
419	C₂×C₄×C₇₃	—	2	2	no	—
420	C₂×C₄×C₇₃	—	2	2	no	—
421	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
428	C₂×Dic₇₃	—	2	2	no	—
429	C₂×Dic₇₃	—	2	2	no	—
430	C₂×Dic₇₃	—	2	2	no	—
431	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
438	D₂₉₂	—	2	8	no	—
439	D₂₉₂	—	2	2	no	—
440	D₂₉₂	C₂²×Q₈	1	4	yes	—
441	C₄×D₇₃	—	2	8	no	—
442	C₄×D₇₃	—	4	1	no	—
443	C₄×D₇₃	—	4	1	no	—
444	C₄×D₇₃	—	8	2	no	—
445	C₄×D₇₃	—	8	2	no	—
446	C₄×D₇₃	—	8	2	no	—
447	C₄×D₇₃	—	8	2	no	—
448	C₄×D₇₃	—	8	2	no	—
449	C₄×D₇₃	—	8	2	no	—
450	C₄×D₇₃	—	8	2	no	—
451	C₄×D₇₃	—	8	2	no	—
452	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
453	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
454	Dic₁₄₆	—	4	1	no	—
455	Dic₁₄₆	—	4	1	no	—
456	Dic₁₄₆	—	4	1	no	—
457	Dic₁₄₆	—	8	2	no	—
458	Dic₁₄₆	—	8	2	no	—
459	Dic₁₄₆	—	8	2	no	—
460	C₈×C₇₃	—	2	1	no	—
461	C₈×C₇₃	—	2	1	no	—
462	C₈×C₇₃	—	2	1	no	—
463	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
464	#10596831	—	2	1	no	—
465	#10596831	—	2	1	no	—
466	#10596831	—	2	1	no	—
467	#10596831	C₂²×Q₈	1	2	yes	—
468	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
469	C₂×D₇₃	—	2	1	no	—
470	C₂×D₇₃	—	2	1	no	—
471	C₂×D₇₃	—	2	4	no	—
472	C₂×D₇₃	—	4	2	no	—
473	C₂×D₇₃	—	4	2	no	—
474	C₂×D₇₃	D₄×Q₈	1	2	yes	—
475	C₄×C₇₃	—	2	1	no	—
476	C₄×C₇₃	—	2	1	no	—
477	C₄×C₇₃	—	2	1	no	—
478	C₄×C₇₃	—	2	1	no	—
479	C₄×C₇₃	—	2	1	no	—
480	C₄×C₇₃	—	2	1	no	—
481	C₄×C₇₃	—	2	4	no	—
482	C₄×C₇₃	—	4	2	no	—
483	C₄×C₇₃	—	4	2	no	—
484	C₄×C₇₃	—	4	2	no	—
485	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
486	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
487	Dic₇₃	—	2	1	no	—
488	Dic₇₃	—	2	1	no	—
489	Dic₇₃	—	2	1	no	—
490	Dic₇₃	—	2	1	no	—
491	Dic₇₃	—	2	1	no	—
492	Dic₇₃	—	2	1	no	—
493	Dic₇₃	—	4	2	no	—
494	Dic₇₃	—	4	2	no	—
495	Dic₇₃	—	4	2	no	—
496	Dic₇₃	D₄×Q₈	1	2	yes	—
497	#61376	—	73	1	no	maximal, Sylow
498	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
499	C₂×C₇₃	#3584	1	1	yes	characteristic
500	C₂×C₇₃	#3584	1	1	yes	characteristic
501	D₇₃	—	2	2	no	—
502	D₇₃	—	4	4	no	—
503	#3504	—	73	2	no	—
504	#3388	—	73	2	no	—
505	#3388	—	73	2	no	—
506	#3388	—	73	2	no	—
507	#3388	—	73	2	no	—
508	#3383	—	73	1	no	—
509	#3383	—	73	1	no	—
510	#3383	—	73	1	no	—
511	#3383	D₇₃	1	1	yes	characteristic, complemented
512	#3380	—	73	1	no	—
513	#3380	—	73	1	no	—
514	#3380	—	73	1	no	—
515	#3380	—	73	1	no	—
516	#3164	—	73	1	no	—
517	#3164	—	73	1	no	—
518	C₂×#499	—	73	1	no	—
519	#3084	—	73	2	no	—
520	#3084	—	73	2	no	—
521	#3080	—	73	2	no	—
522	#2960	—	73	1	no	—
523	#2951	—	73	1	no	—
524	#2951	—	73	1	no	—
525	C₄×#135	—	73	1	no	—
526	C₇₃	#61376	1	1	yes	characteristic, complemented, Sylow
527	C₂×#135	—	73	1	no	—
528	#557	—	73	2	no	—
529	#557	—	73	2	no	—
530	#557	—	73	2	no	—
531	#557	C₂×D₇₃	1	2	yes	—
532	#554	—	73	2	no	—
533	#554	—	73	2	no	—
534	#554	—	73	2	no	—
535	#554	—	73	2	no	—
536	#554	—	146	2	no	—
537	#554	—	146	2	no	—
538	#554	—	146	2	no	—
539	#554	—	146	2	no	—
540	#544	—	73	2	no	—
541	#544	—	73	2	no	—
542	#544	—	146	2	no	—
543	#544	—	146	2	no	—
544	#533	—	73	1	no	—
545	#533	—	146	2	no	—
546	C₂×#125	—	73	2	no	—
547	C₂×#125	—	146	2	no	—
548	#520	—	73	2	no	—
549	#520	—	73	2	no	—
550	C₄×#41	—	73	2	no	—
551	#501	—	73	2	no	—
552	#501	—	73	2	no	—
553	#501	—	73	2	no	—
554	#501	—	73	2	no	—
555	#500	—	73	1	no	—
556	#500	—	73	1	no	—
557	#500	—	73	1	no	—
558	#500	C₂×D₇₃	1	1	yes	characteristic
559	#499	—	73	2	no	—
560	#499	—	73	1	no	—
561	#499	—	73	1	no	—
562	#499	—	73	1	no	—
563	#499	—	73	1	no	—
564	#499	—	73	2	no	—
565	#499	—	73	1	no	—
566	#499	—	73	1	no	—
567	#499	C₂×D₇₃	1	1	yes	characteristic
568	#499	C₂×D₇₃	1	1	yes	characteristic
569	#479	—	73	2	no	—
570	#479	—	73	2	no	—
571	#479	—	73	2	no	—
572	#479	—	73	2	no	—
573	#479	—	73	2	no	—
574	#479	—	73	2	no	—
575	#479	C₂×D₇₃	1	2	yes	—
576	#479	C₂×D₇₃	1	2	yes	—
577	#478	—	73	2	no	—
578	#478	—	73	2	no	—
579	#478	—	73	2	no	—
580	#478	—	73	2	no	—
581	#478	—	73	2	no	—
582	#478	—	73	2	no	—
583	#478	—	73	2	no	—
584	#478	—	73	2	no	—
585	#476	—	73	2	no	—
586	#476	—	73	2	no	—
587	#476	—	73	2	no	—
588	#476	—	73	2	no	—
589	#475	—	73	2	no	—
590	#475	—	73	2	no	—
591	#475	—	73	2	no	—
592	#475	C₂×D₇₃	1	2	yes	—
593	#446	—	73	1	no	—
594	#446	—	73	1	no	—
595	#446	—	73	1	no	—
596	#446	—	73	1	no	—
597	C₈×Q₈	—	73	1	no	—
598	C₈×Q₈	—	73	1	no	—
599	C₈×Q₈	—	73	1	no	—
600	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic
601	#440	—	73	2	no	—
602	#440	—	73	2	no	—
603	#440	—	73	2	no	—
604	#440	—	73	2	no	—
605	C₄×Q₁₆	—	73	1	no	—
606	C₄×Q₁₆	—	73	1	no	—
607	C₄×Q₁₆	—	73	1	no	—
608	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
609	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
610	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
611	C₄×SD₁₆	—	73	2	no	—
612	C₄×SD₁₆	—	73	2	no	—
613	C₄×D₈	—	73	1	no	—
614	C₄×D₈	—	73	1	no	—
615	C₄×D₈	—	73	1	no	—
616	C₄×D₈	—	73	1	no	—
617	C₄×D₈	—	73	1	no	—
618	C₄×D₈	—	73	1	no	—
619	#428	—	73	2	no	—
620	#428	—	73	2	no	—
621	#427	—	73	1	no	—
622	C₂×#107	—	73	1	no	—
623	C₂×#107	—	73	1	no	—
624	C₂×#106	—	73	2	no	—
625	#424	—	73	1	no	—
626	#424	—	73	1	no	—
627	#423	—	73	1	no	—
628	#417	—	73	2	no	—
629	#417	—	73	2	no	—
630	#416	—	73	2	no	—
631	#405	—	73	1	no	—
632	#405	—	73	1	no	—
633	C₂×C₄×C₈	—	73	1	no	—
634	C₂×#41	—	73	2	no	—
635	#135	—	73	8	no	—
636	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
637	C₂×SD₁₆	—	73	2	no	—
638	C₂×D₈	—	73	1	no	—
639	C₂×M₁₆	—	73	1	no	—
640	C₂×M₁₆	—	73	1	no	—
641	C₂²×C₈	—	73	1	no	—
642	C₂²×C₈	—	73	1	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	73	1	no	—
645	C₄⋊Q₈	—	73	1	no	—
646	C₄⋊Q₈	—	73	2	no	—
647	C₄⋊Q₈	—	73	2	no	—
648	C₄⋊Q₈	—	73	2	no	—
649	C₄⋊Q₈	—	146	2	no	—
650	C₄⋊Q₈	—	146	2	no	—
651	C₄⋊Q₈	—	146	2	no	—
652	C₄⋊Q₈	—	146	2	no	—
653	C₄⋊Q₈	—	146	2	no	—
654	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	73	1	no	—
658	#125	—	73	1	no	—
659	#125	—	73	2	no	—
660	#125	—	73	2	no	—
661	#125	—	73	2	no	—
662	#125	—	73	2	no	—
663	#125	—	73	2	no	—
664	#125	—	73	2	no	—
665	#125	—	146	2	no	—
666	#125	—	146	2	no	—
667	#125	—	146	2	no	—
668	#125	—	146	2	no	—
669	#125	—	146	2	no	—
670	#125	—	146	2	no	—
671	#125	—	146	2	no	—
672	#125	—	146	2	no	—
673	#125	—	146	2	no	—
674	#125	—	146	2	no	—
675	#125	C₂²×D₇₃	1	2	yes	—
676	#125	C₂²×D₇₃	1	2	yes	—
677	C₂²⋊Q₈	—	73	1	no	—
678	C₂²⋊Q₈	—	73	1	no	—
679	C₂²⋊Q₈	—	73	1	no	—
680	C₂²⋊Q₈	—	73	1	no	—
681	C₂²⋊Q₈	—	146	2	no	—
682	C₂²⋊Q₈	—	146	2	no	—
683	C₂²⋊Q₈	—	146	2	no	—
684	C₂²⋊Q₈	—	146	2	no	—
685	C₂²⋊Q₈	—	146	2	no	—
686	C₂²⋊Q₈	—	146	2	no	—
687	C₂²⋊Q₈	—	146	2	no	—
688	C₂²⋊Q₈	—	146	2	no	—
689	C₂²⋊Q₈	—	146	2	no	—
690	C₂²⋊Q₈	—	146	2	no	—
691	C₂²⋊Q₈	—	146	2	no	—
692	C₂²⋊Q₈	—	146	2	no	—
693	C₂²⋊Q₈	—	146	2	no	—
694	C₂²⋊Q₈	—	146	2	no	—
695	C₂²⋊Q₈	—	146	2	no	—
696	C₂²⋊Q₈	—	146	2	no	—
697	C₄×Q₈	—	2	2	no	—
698	C₄×Q₈	—	73	1	no	—
699	C₄×Q₈	—	73	1	no	—
700	C₄×Q₈	—	73	1	no	—
701	C₄×Q₈	—	73	2	no	—
702	C₄×Q₈	—	73	2	no	—
703	C₄×Q₈	—	73	2	no	—
704	C₄×Q₈	—	146	2	no	—
705	C₄×Q₈	—	146	2	no	—
706	C₄×Q₈	—	146	2	no	—
707	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
708	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
709	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
710	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
711	C₄×D₄	—	73	2	no	—
712	C₄×D₄	—	73	2	no	—
713	C₄×D₄	—	73	2	no	—
714	C₄×D₄	—	73	2	no	—
715	C₄×D₄	—	73	2	no	—
716	C₄×D₄	—	73	2	no	—
717	C₄×D₄	—	146	2	no	—
718	C₄×D₄	—	146	2	no	—
719	C₄×D₄	—	146	2	no	—
720	C₄×D₄	—	146	2	no	—
721	C₄×D₄	—	146	2	no	—
722	C₄×D₄	—	146	2	no	—
723	#117	—	73	1	no	—
724	#117	—	73	1	no	—
725	#117	—	73	2	no	—
726	#117	—	146	2	no	—
727	#117	—	146	2	no	—
728	#117	—	146	2	no	—
729	C₂×C₄⋊C₄	—	73	2	no	—
730	C₂×C₄⋊C₄	—	73	2	no	—
731	C₂×C₄⋊C₄	—	146	2	no	—
732	C₂×C₄⋊C₄	—	146	2	no	—
733	C₂×C₄⋊C₄	—	146	2	no	—
734	C₂×C₄⋊C₄	—	146	2	no	—
735	C₂×C₄⋊C₄	—	146	2	no	—
736	C₂×C₄⋊C₄	—	146	2	no	—
737	C₂×C₄⋊C₄	—	146	2	no	—
738	C₂×C₄⋊C₄	—	146	2	no	—
739	C₂×C₄²	—	73	1	no	—
740	C₂×C₄²	—	146	2	no	—
741	#107	—	73	1	no	—
742	#107	—	73	1	no	—
743	#107	—	73	1	no	—
744	#107	—	73	2	no	—
745	#107	—	73	2	no	—
746	#107	—	73	2	no	—
747	#107	—	73	2	no	—
748	#107	—	73	2	no	—
749	#107	C₂²×D₇₃	1	1	yes	characteristic
750	#107	C₂²×D₇₃	1	1	yes	characteristic
751	#107	C₂²×D₇₃	1	1	yes	characteristic
752	#107	C₂²×D₇₃	1	2	yes	—
753	#106	—	73	2	no	—
754	#106	—	73	2	no	—
755	#106	—	73	2	no	—
756	#106	—	73	2	no	—
757	#106	—	73	2	no	—
758	#106	—	73	2	no	—
759	#106	—	73	2	no	—
760	#106	C₂²×D₇₃	1	2	yes	—
761	#106	C₂²×D₇₃	1	2	yes	—
762	C₄⋊C₈	—	73	1	no	—
763	C₄⋊C₈	—	73	1	no	—
764	C₄⋊C₈	—	73	1	no	—
765	C₄⋊C₈	—	73	1	no	—
766	C₄⋊C₈	—	73	1	no	—
767	C₄⋊C₈	—	73	1	no	—
768	C₄⋊C₈	—	73	1	no	—
769	C₄⋊C₈	—	73	1	no	—
770	C₄⋊C₈	—	73	1	no	—
771	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
772	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
773	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
774	#103	—	73	2	no	—
775	#103	—	73	2	no	—
776	#103	—	73	2	no	—
777	#103	C₂²×D₇₃	1	2	yes	—
778	#103	C₂²×D₇₃	1	2	yes	—
779	#103	C₂²×D₇₃	1	2	yes	—
780	#102	—	73	2	no	—
781	#102	—	73	2	no	—
782	#102	—	73	2	no	—
783	#102	—	73	2	no	—
784	#102	—	73	2	no	—
785	#102	—	73	2	no	—
786	#97	—	73	1	no	—
787	#97	—	73	1	no	—
788	#97	—	73	1	no	—
789	#97	—	73	1	no	—
790	C₄×C₈	—	73	1	no	—
791	C₄×C₈	—	73	1	no	—
792	C₄×C₈	—	73	1	no	—
793	C₄×C₈	—	73	1	no	—
794	C₄×C₈	—	73	1	no	—
795	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
796	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
797	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
798	#41	—	73	8	no	—
799	#41	—	146	4	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	73	1	no	—
802	C₂×Q₈	—	73	1	no	—
803	C₂×Q₈	—	73	1	no	—
804	C₂×Q₈	—	146	2	no	—
805	C₂×Q₈	—	146	2	no	—
806	C₂×Q₈	—	146	2	no	—
807	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
808	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
809	C₂×D₄	—	73	2	no	—
810	C₂×D₄	—	146	2	no	—
811	C₂²×C₄	—	73	1	no	—
812	C₂²×C₄	—	73	1	no	—
813	C₂²×C₄	—	73	1	no	—
814	C₂²×C₄	—	146	2	no	—
815	C₂²×C₄	—	146	2	no	—
816	C₂²×C₄	—	146	2	no	—
817	C₂²×C₄	—	146	2	no	—
818	C₂²×C₄	—	146	2	no	—
819	C₂²×C₄	—	146	2	no	—
820	C₂²×C₄	—	146	2	no	—
821	C₂²×C₄	—	146	2	no	—
822	C₂²×C₄	—	146	2	no	—
823	Q₁₆	Q₈×D₇₃	1	4	yes	—
824	SD₁₆	—	73	8	no	—
825	D₈	—	73	4	no	—
826	M₁₆	—	146	2	no	—
827	M₁₆	—	146	2	no	—
828	C₂×C₈	—	73	1	no	—
829	C₂×C₈	—	73	4	no	—
830	C₂×C₈	—	73	1	no	—
831	C₂×C₈	—	73	1	no	—
832	C₂×C₈	—	73	1	no	—
833	C₂×C₈	—	146	2	no	—
834	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
835	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
836	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
837	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	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	—	2	2	no	—
846	C₄⋊C₄	—	73	1	no	—
847	C₄⋊C₄	—	73	1	no	—
848	C₄⋊C₄	—	73	1	no	—
849	C₄⋊C₄	—	73	1	no	—
850	C₄⋊C₄	—	73	1	no	—
851	C₄⋊C₄	—	73	1	no	—
852	C₄⋊C₄	—	73	1	no	—
853	C₄⋊C₄	—	73	1	no	—
854	C₄⋊C₄	—	73	1	no	—
855	C₄⋊C₄	—	73	1	no	—
856	C₄⋊C₄	—	73	1	no	—
857	C₄⋊C₄	—	73	1	no	—
858	C₄⋊C₄	—	73	1	no	—
859	C₄⋊C₄	—	73	2	no	—
860	C₄⋊C₄	—	73	2	no	—
861	C₄⋊C₄	—	73	2	no	—
862	C₄⋊C₄	—	146	2	no	—
863	C₄⋊C₄	—	146	2	no	—
864	C₄⋊C₄	—	146	2	no	—
865	C₄⋊C₄	—	146	2	no	—
866	C₄⋊C₄	—	146	2	no	—
867	C₄⋊C₄	—	146	2	no	—
868	C₄⋊C₄	—	146	2	no	—
869	C₄⋊C₄	—	146	2	no	—
870	C₄⋊C₄	—	146	2	no	—
871	C₄⋊C₄	—	146	2	no	—
872	C₄⋊C₄	—	146	2	no	—
873	C₄⋊C₄	—	146	2	no	—
874	C₄⋊C₄	—	146	2	no	—
875	C₄⋊C₄	—	146	2	no	—
876	C₄⋊C₄	—	146	2	no	—
877	C₄⋊C₄	—	146	2	no	—
878	C₄⋊C₄	—	146	2	no	—
879	C₄⋊C₄	—	146	2	no	—
880	C₄⋊C₄	—	146	2	no	—
881	C₄⋊C₄	—	146	2	no	—
882	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
883	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
884	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
886	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
887	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
888	C₂²⋊C₄	—	73	1	no	—
889	C₂²⋊C₄	—	73	1	no	—
890	C₂²⋊C₄	—	73	1	no	—
891	C₂²⋊C₄	—	73	1	no	—
892	C₂²⋊C₄	—	146	2	no	—
893	C₂²⋊C₄	—	146	2	no	—
894	C₂²⋊C₄	—	146	2	no	—
895	C₂²⋊C₄	—	146	2	no	—
896	C₂²⋊C₄	—	146	2	no	—
897	C₂²⋊C₄	—	146	2	no	—
898	C₂²⋊C₄	—	146	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	73	1	no	—
903	C₄²	—	73	1	no	—
904	C₄²	—	73	1	no	—
905	C₄²	—	73	1	no	—
906	C₄²	—	73	1	no	—
907	C₄²	—	146	2	no	—
908	C₄²	—	146	2	no	—
909	C₄²	—	146	2	no	—
910	C₄²	—	146	2	no	—
911	C₄²	C₂³×D₇₃	1	1	yes	characteristic
912	C₄²	C₂³×D₇₃	1	1	yes	characteristic
913	C₄²	C₂³×D₇₃	1	1	yes	characteristic
914	C₂³	—	73	1	no	—
915	C₂³	—	146	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	4	1	no	—
918	Q₈	—	8	2	no	—
919	Q₈	—	292	1	no	—
920	Q₈	—	292	1	no	—
921	Q₈	—	292	1	no	—
922	Q₈	—	584	2	no	—
923	Q₈	—	584	2	no	—
924	Q₈	—	584	2	no	—
925	Q₈	C₂×Q₈×D₇₃	1	4	yes	—
926	D₄	—	73	4	no	—
927	D₄	—	146	8	no	—
928	D₄	—	146	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	292	1	no	—
934	C₂×C₄	—	292	1	no	—
935	C₂×C₄	—	584	2	no	—
936	C₂×C₄	—	584	2	no	—
937	C₂×C₄	—	584	2	no	—
938	C₂×C₄	—	584	2	no	—
939	C₂×C₄	—	584	2	no	—
940	C₂×C₄	—	584	2	no	—
941	C₂×C₄	—	584	2	no	—
942	C₂×C₄	—	584	2	no	—
943	C₂×C₄	—	73	1	no	—
944	C₂×C₄	—	73	2	no	—
945	C₂×C₄	—	73	2	no	—
946	C₂×C₄	—	73	1	no	—
947	C₂×C₄	—	73	1	no	—
948	C₂×C₄	—	73	1	no	—
949	C₂×C₄	—	73	1	no	—
950	C₂×C₄	—	73	1	no	—
951	C₂×C₄	—	73	1	no	—
952	C₂×C₄	—	146	8	no	—
953	C₂×C₄	—	146	2	no	—
954	C₂×C₄	—	146	2	no	—
955	C₂×C₄	—	146	2	no	—
956	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
957	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
958	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
959	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
960	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
961	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
962	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
963	C₈	—	2	1	no	—
964	C₈	—	2	1	no	—
965	C₈	—	2	1	no	—
966	C₈	—	73	2	no	—
967	C₈	—	146	1	no	—
968	C₈	—	146	1	no	—
969	C₈	—	146	1	no	—
970	C₈	C₂×Q₈×D₇₃	1	2	yes	—
971	C₂²	—	292	2	no	—
972	C₂²	—	292	2	no	—
973	C₂²	—	73	2	no	—
974	C₂²	—	146	4	no	—
975	C₂²	—	146	1	no	—
976	C₂²	—	146	1	no	—
977	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
978	C₄	—	2	4	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	292	2	no	—
989	C₄	—	292	2	no	—
990	C₄	—	292	2	no	—
991	C₄	—	73	2	no	—
992	C₄	—	146	1	no	—
993	C₄	—	146	1	no	—
994	C₄	—	146	1	no	—
995	C₄	—	146	1	no	—
996	C₄	—	146	1	no	—
997	C₄	—	146	1	no	—
998	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
999	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1000	C₂	—	292	4	no	—
1001	C₂	—	146	2	no	—
1002	C₂	D₄×Q₈×D₇₃	1	1	yes	characteristic
1003	C₂	#22624700	1	1	yes	characteristic
1004	C₂	#22624701	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×#3383	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂×#14556614	C₂²
hypercenter	#3383	D₇₃
hypocenter	C₇₃	#61376
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3383

Complements

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

N	H ≅ G/N	type
1. #22623756	C₂	semidirect
2. #22622883	C₂	semidirect
3. #22622879	C₂	semidirect
4. #22622874	C₂	semidirect
5. #22622870	C₂	semidirect
6. #22622822	C₂	semidirect
7. #22622822	C₂	semidirect
8. #22622820	C₂	semidirect
9. #22622800	C₂	semidirect
10. #22622799	C₂	semidirect
11. #22622795	C₂	semidirect
12. #22622795	C₂	semidirect
13. #22620468	C₂	semidirect
14. #22620464	C₂	semidirect
15. #499×D₇₃	C₂	semidirect
16. #22619796	C₂	semidirect
17. #22619790	C₂	semidirect
18. #22619750	C₂	semidirect
19. #22618860	C₂	semidirect
23. C₇₃×#3383	C₂	semidirect
132. #14556614	Q₈	semidirect
511. #3383	D₇₃	semidirect
526. C₇₃	#61376	semidirect

Maximal subgroups

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

subgroup	index
#22623756	2
#22622883	2
#22622879	2
#22622874	2
#22622870	2
#22622822	2
#22622820	2
#22622800	2
#22622799	2
#22622795	2
#22620468	2
#22620464	2
#499×D₇₃	2
#22619796	2
#22619790	2
#22619750	2
#22618860	2
#22618806	2
C₄×#14556614	2
C₇₃×#3383	2
#61376	73