Subgroups — #11660800

Order 768.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#85840	C₂	1	1	yes	maximal, characteristic
2	C₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
3	#82515	C₂	1	1	yes	maximal, characteristic, complemented
4	#79374	C₂	1	2	yes	maximal, complemented
5	#79371	C₂	1	2	yes	maximal, complemented
6	#79369	C₂	1	2	yes	maximal, complemented
7	#79367	C₂	1	2	yes	maximal, complemented
8	#79296	C₂	1	1	yes	maximal, characteristic, complemented
9	#79295	C₂	1	1	yes	maximal, characteristic, complemented
10	#79294	C₂	1	1	yes	maximal, characteristic, complemented
11	#79292	C₂	1	1	yes	maximal, characteristic, complemented
12	#79288	C₂	1	1	yes	maximal, characteristic, complemented
13	#79287	C₂	1	1	yes	maximal, characteristic, complemented
14	#79267	C₂	1	1	yes	maximal, characteristic, complemented
15	#79266	C₂	1	1	yes	maximal, characteristic, complemented
16	#79085	C₂	1	2	yes	maximal, complemented
17	#79083	C₂	1	2	yes	maximal, complemented
18	#78666	C₂	1	2	yes	maximal, complemented
19	#78664	C₂	1	2	yes	maximal, complemented
20	#78512	C₂	1	1	yes	maximal, characteristic, complemented
21	#78511	C₂	1	1	yes	maximal, characteristic, complemented
22	#78448	C₂	1	1	yes	maximal, characteristic, complemented
23	#78447	C₂	1	1	yes	maximal, characteristic, complemented
24	#60300	—	3	1	no	maximal, Sylow
25	C₃×C₄×#41	C₂²	1	1	yes	characteristic
26	#5828	C₂²	1	2	yes	—
27	#5584	C₄	1	1	yes	characteristic
28	#5581	C₄	1	2	yes	—
29	#5579	C₄	1	1	yes	characteristic
30	#5563	C₄	1	1	yes	characteristic
31	#5558	C₄	1	2	yes	—
32	#5556	C₄	1	2	yes	—
33	#5556	C₄	1	2	yes	—
34	#5551	C₄	1	1	yes	characteristic
35	#5550	C₄	1	1	yes	characteristic
36	#5550	C₄	1	1	yes	characteristic
37	#5541	C₄	1	1	yes	characteristic
38	#5541	C₄	1	1	yes	characteristic
39	#5528	C₂²	1	2	yes	—
40	#5528	C₂²	1	2	yes	—
41	D₃×#117	C₂²	1	2	yes	—
42	#5479	C₂²	1	1	yes	characteristic
43	#5479	C₂²	1	1	yes	characteristic
44	C₄×#235	C₂²	1	1	yes	characteristic
45	C₄×#235	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₁₂	C₂²	1	1	yes	characteristic
47	#5470	C₂²	1	1	yes	characteristic
48	C₃×#433	C₂²	1	1	yes	characteristic
49	C₃×#433	C₂²	1	1	yes	characteristic
50	C₃×#433	C₂²	1	1	yes	characteristic, complemented
51	C₃×#433	C₂²	1	1	yes	characteristic, complemented
52	C₃×#431	C₂²	1	1	yes	characteristic
53	C₃×#431	C₂²	1	1	yes	characteristic
54	C₃×#431	C₂²	1	1	yes	characteristic, complemented
55	C₃×#431	C₂²	1	1	yes	characteristic, complemented
56	C₃×#424	C₂²	1	1	yes	characteristic, complemented
57	C₃×#424	C₂²	1	1	yes	characteristic, complemented
58	C₃×#408	C₂²	1	1	yes	characteristic
59	C₃×#408	C₂²	1	1	yes	characteristic
60	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
62	#5234	C₂²	1	2	yes	—
63	#5128	C₂²	1	2	yes	complemented
64	#5128	C₂²	1	2	yes	complemented
65	#5128	C₂²	1	2	yes	complemented
66	#5127	C₂²	1	2	yes	complemented
67	#5111	C₂²	1	2	yes	complemented
68	#5111	C₂²	1	2	yes	complemented
69	#5111	C₂²	1	2	yes	complemented
70	C₈×#67	C₂²	1	2	yes	complemented
71	#5000	C₂²	1	2	yes	—
72	#5000	C₂²	1	2	yes	complemented
73	#4997	C₂²	1	2	yes	complemented
74	#4926	C₂²	1	1	yes	characteristic
75	#4926	C₂²	1	1	yes	characteristic, complemented
76	#4925	C₂²	1	1	yes	characteristic
77	#4925	C₂²	1	1	yes	characteristic, complemented
78	#4924	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
80	#4840	C₂²	1	2	yes	complemented
81	#4840	C₂²	1	2	yes	complemented
82	#4839	C₂²	1	2	yes	complemented
83	#4839	C₂²	1	2	yes	complemented
84	#4838	C₂²	1	2	yes	—
85	#4838	C₂²	1	2	yes	—
86	#4837	C₂²	1	2	yes	complemented
87	#4837	C₂²	1	2	yes	complemented
88	#4836	C₂²	1	2	yes	—
89	#4836	C₂²	1	2	yes	—
90	#4835	C₂²	1	2	yes	complemented
91	#4833	C₂²	1	2	yes	complemented
92	#4831	C₂²	1	2	yes	complemented
93	#4830	C₂²	1	2	yes	complemented
94	#4828	C₂²	1	2	yes	complemented
95	#4828	C₂²	1	2	yes	complemented
96	#4730	C₂²	1	2	yes	complemented
97	#4730	C₂²	1	2	yes	complemented
98	#4730	C₂²	1	2	yes	complemented
99	#4729	C₂²	1	2	yes	complemented
100	#4729	C₂²	1	2	yes	complemented
101	#4729	C₂²	1	2	yes	complemented
102	#4728	C₂²	1	2	yes	complemented
103	#4726	C₂²	1	2	yes	—
104	#4726	C₂²	1	2	yes	—
105	#4726	C₂²	1	2	yes	—
106	#67⋊C₈	C₂²	1	2	yes	complemented
107	D₃×C₂²⋊C₈	C₂²	1	2	yes	—
108	#4720	C₂²	1	2	yes	—
109	#4720	C₂²	1	2	yes	—
110	#4720	C₂²	1	2	yes	—
111	#4720	C₂²	1	2	yes	—
112	#4709	C₂²	1	2	yes	complemented
113	#4708	C₂²	1	2	yes	complemented
114	#4707	C₂²	1	2	yes	complemented
115	#4705	C₂²	1	2	yes	complemented
116	#4690	C₂²	1	2	yes	complemented
117	#4689	C₂²	1	2	yes	complemented
118	#4688	C₂²	1	1	yes	characteristic
119	#4688	C₂²	1	1	yes	characteristic
120	#4688	C₂²	1	1	yes	characteristic
121	#4688	C₂²	1	1	yes	characteristic
122	#4688	C₂²	1	1	yes	characteristic
123	#4688	C₂²	1	1	yes	characteristic
124	C₄×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
125	C₈×D₁₂	C₂²	1	1	yes	characteristic
126	C₈×D₁₂	C₂²	1	1	yes	characteristic
127	#4685	C₂²	1	2	yes	complemented
128	#4679	C₂²	1	1	yes	characteristic, complemented
129	#4679	C₂²	1	1	yes	characteristic, complemented
130	#4679	C₂²	1	1	yes	characteristic, complemented
131	#4679	C₂²	1	1	yes	characteristic, complemented
132	C₈×Dic₆	C₂²	1	1	yes	characteristic, complemented
133	C₈×Dic₆	C₂²	1	1	yes	characteristic, complemented
134	C₈×Dic₆	C₂²	1	1	yes	characteristic, complemented
135	C₈×Dic₆	C₂²	1	1	yes	characteristic, complemented
136	#3475	—	3	1	no	—
137	#2995	—	3	2	no	—
138	#2994	—	3	1	no	—
139	#2993	—	3	1	no	—
140	#2993	—	3	2	no	—
141	#2991	—	3	1	no	—
142	#2989	—	3	1	no	—
143	#2986	—	3	1	no	—
144	#2985	—	3	1	no	—
145	#2978	—	3	2	no	—
146	#2976	—	3	2	no	—
147	#2975	—	3	1	no	—
148	#2974	—	3	1	no	—
149	#2971	—	3	1	no	—
150	#2969	—	3	2	no	—
151	#2969	—	3	1	no	—
152	#2967	—	3	2	no	—
153	#2966	—	3	1	no	—
154	#2965	—	3	1	no	—
155	#2925	—	3	1	no	—
156	#2924	—	3	2	no	—
157	#2922	D₃	1	1	yes	characteristic, complemented
158	#2921	—	3	2	no	—
159	C₂×C₃×#41	C₂³	1	1	yes	characteristic
160	C₂×#235	C₂×C₄	1	1	yes	characteristic
161	C₂×#235	C₂×C₄	1	1	yes	characteristic
162	C₂²×D₁₂	C₂×C₄	1	1	yes	characteristic
163	C₂²×C₄×D₃	C₂³	1	2	yes	—
164	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
166	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
167	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
168	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
169	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
170	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
171	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
173	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
174	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
175	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
176	C₃×#117	C₂³	1	1	yes	characteristic
177	C₃×#117	C₂³	1	1	yes	characteristic
178	C₃×#117	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
182	#946	C₂×C₄	1	2	yes	—
183	#946	C₂×C₄	1	2	yes	—
184	#938	C₂×C₄	1	2	yes	—
185	#938	C₂×C₄	1	2	yes	—
186	#937	C₂×C₄	1	2	yes	—
187	#937	C₂×C₄	1	2	yes	—
188	#935	C₂×C₄	1	2	yes	—
189	#935	C₂×C₄	1	2	yes	—
190	#930	C₂×C₄	1	1	yes	characteristic
191	#930	C₂×C₄	1	1	yes	characteristic
192	#929	C₂×C₄	1	2	yes	—
193	#929	C₂×C₄	1	2	yes	—
194	C₄×#67	C₂×C₄	1	2	yes	—
195	C₄×#67	C₂×C₄	1	2	yes	—
196	C₄×#67	C₂³	1	2	yes	—
197	C₄×#67	C₂³	1	2	yes	—
198	C₄×#67	C₂³	1	2	yes	—
199	C₄×#67	C₂³	1	2	yes	—
200	C₂×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
201	#926	C₂×C₄	1	1	yes	characteristic
202	#926	C₂×C₄	1	1	yes	characteristic
203	#926	C₂³	1	2	yes	—
204	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
205	#924	C₂×C₄	1	1	yes	characteristic
206	#924	C₂×C₄	1	1	yes	characteristic
207	#924	C₂×C₄	1	2	yes	—
208	#924	C₂×C₄	1	1	yes	characteristic
209	#924	C₂×C₄	1	1	yes	characteristic
210	C₂×#208	C₂³	1	2	yes	—
211	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
212	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
213	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
214	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
215	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
216	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
217	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
218	C₂×D₃×C₈	C₂³	1	2	yes	—
219	C₂×D₃×C₈	C₂³	1	2	yes	—
220	#898	C₂×C₄	1	2	yes	—
221	#898	C₂×C₄	1	2	yes	—
222	#896	C₂×C₄	1	2	yes	—
223	#896	C₂×C₄	1	2	yes	—
224	#894	C₂×C₄	1	2	yes	—
225	#894	C₂×C₄	1	2	yes	—
226	#892	C₂×C₄	1	2	yes	—
227	#892	C₂×C₄	1	2	yes	—
228	D₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
229	D₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
230	#889	C₂×C₄	1	2	yes	—
231	#889	C₂×C₄	1	2	yes	—
232	#885	C₂×C₄	1	2	yes	—
233	#885	C₂×C₄	1	2	yes	—
234	#884	C₂×C₄	1	2	yes	—
235	#884	C₂×C₄	1	2	yes	—
236	#883	C₂×C₄	1	2	yes	—
237	#883	C₂×C₄	1	2	yes	—
238	D₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
239	D₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
240	#879	C₂×C₄	1	2	yes	—
241	#879	C₂×C₄	1	2	yes	—
242	#877	C₂×C₄	1	2	yes	—
243	#877	C₂×C₄	1	2	yes	—
244	#876	C₂×C₄	1	2	yes	—
245	#876	C₂×C₄	1	2	yes	—
246	#875	C₂×C₄	1	1	yes	characteristic
247	#875	C₂×C₄	1	1	yes	characteristic
248	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
249	C₄×D₁₂	C₂×C₄	1	2	yes	—
250	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
251	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
252	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
253	C₄×D₁₂	C₂³	1	1	yes	characteristic
254	C₄×D₁₂	C₂³	1	1	yes	characteristic
255	C₄×D₁₂	C₂³	1	2	yes	—
256	#872	C₂×C₄	1	2	yes	—
257	#872	C₂×C₄	1	2	yes	—
258	#872	C₂³	1	2	yes	—
259	#872	C₂³	1	2	yes	—
260	C₄²×D₃	C₂³	1	2	yes	—
261	C₄²×D₃	C₂³	1	2	yes	—
262	#870	C₂×C₄	1	2	yes	—
263	#870	C₂×C₄	1	1	yes	characteristic
264	#870	C₂×C₄	1	1	yes	characteristic
265	#869	C₂×C₄	1	1	yes	characteristic
266	#869	C₂×C₄	1	1	yes	characteristic
267	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
268	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
269	C₄×Dic₆	C₂³	1	1	yes	characteristic
270	C₄×Dic₆	C₂³	1	1	yes	characteristic
271	C₄×Dic₆	C₂³	1	2	yes	—
272	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₃×#97	C₂³	1	1	yes	characteristic
289	C₃×#97	C₂³	1	1	yes	characteristic
290	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
291	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
292	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
293	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
294	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
295	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
296	#830	C₂³	1	2	yes	—
297	#830	C₂³	1	2	yes	—
298	#830	C₂³	1	2	yes	—
299	#830	C₂³	1	2	yes	—
300	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
301	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
302	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
303	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
304	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
305	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
306	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
307	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
308	#815	C₂³	1	2	yes	—
309	#815	C₂³	1	2	yes	—
310	#815	C₂³	1	2	yes	—
311	#815	C₂³	1	2	yes	—
312	Dic₃⋊C₈	C₂³	1	2	yes	—
313	Dic₃⋊C₈	C₂³	1	2	yes	—
314	Dic₃⋊C₈	C₂³	1	2	yes	—
315	Dic₃⋊C₈	C₂³	1	2	yes	—
316	Dic₃⋊C₈	C₂³	1	2	yes	—
317	Dic₃⋊C₈	C₂³	1	2	yes	—
318	Dic₃⋊C₈	C₂³	1	2	yes	—
319	Dic₃⋊C₈	C₂³	1	2	yes	—
320	C₈×Dic₃	C₂³	1	2	yes	—
321	C₈×Dic₃	C₂³	1	2	yes	—
322	C₈×Dic₃	C₂³	1	2	yes	—
323	C₈×Dic₃	C₂³	1	2	yes	—
324	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
325	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
326	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
327	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
328	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
329	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
330	#803	C₂³	1	2	yes	—
331	#803	C₂³	1	2	yes	—
332	C₄×C₃⋊C₈	C₂³	1	2	yes	—
333	C₄×C₃⋊C₈	C₂³	1	2	yes	—
334	#556	—	3	1	no	—
335	#555	—	3	1	no	—
336	#554	—	3	1	no	—
337	#553	—	3	2	no	—
338	#552	—	3	2	no	—
339	#552	—	3	1	no	—
340	#552	—	3	1	no	—
341	#551	—	3	2	no	—
342	#551	—	3	2	no	—
343	#547	—	3	1	no	—
344	#546	—	3	1	no	—
345	#546	—	3	1	no	—
346	#533	—	3	1	no	—
347	#529	—	3	2	no	—
348	#529	—	3	2	no	—
349	#529	—	3	1	no	—
350	#529	—	3	1	no	—
351	#525	—	3	2	no	—
352	C₄×#41	—	3	1	no	—
353	C₄×#41	—	3	1	no	—
354	C₄×#41	C₂×D₃	1	1	yes	characteristic
355	C₂×C₄×D₄	—	3	1	no	—
356	C₂×#117	—	3	2	no	—
357	#446	—	3	2	no	—
358	#446	—	3	2	no	—
359	#446	—	3	2	no	—
360	#446	—	3	1	no	—
361	#446	—	3	1	no	—
362	#446	—	3	1	no	—
363	#446	—	3	1	no	—
364	C₈×Q₈	—	3	2	no	—
365	C₈×Q₈	—	3	1	no	—
366	C₈×Q₈	—	3	1	no	—
367	C₈×Q₈	—	3	1	no	—
368	C₈×Q₈	—	3	1	no	—
369	#436	—	3	2	no	—
370	#436	—	3	2	no	—
371	#436	—	3	2	no	—
372	#436	—	3	2	no	—
373	#436	—	3	2	no	—
374	#436	—	3	2	no	—
375	#436	—	3	2	no	—
376	#436	—	3	2	no	—
377	#436	—	3	1	no	—
378	#436	—	3	1	no	—
379	#436	—	3	1	no	—
380	#436	—	3	1	no	—
381	#436	—	3	1	no	—
382	#436	—	3	1	no	—
383	#435	—	3	2	no	—
384	#435	—	3	2	no	—
385	#435	—	3	2	no	—
386	#435	—	3	2	no	—
387	#435	—	3	2	no	—
388	#435	—	3	2	no	—
389	#435	—	3	2	no	—
390	#435	—	3	2	no	—
391	#435	—	3	2	no	—
392	#435	—	3	2	no	—
393	C₈×D₄	—	3	2	no	—
394	C₈×D₄	—	3	2	no	—
395	C₈×D₄	—	3	1	no	—
396	C₈×D₄	—	3	1	no	—
397	#433	—	3	2	no	—
398	#433	—	3	2	no	—
399	#433	—	3	2	no	—
400	#433	—	3	2	no	—
401	#433	—	3	2	no	—
402	#433	—	3	2	no	—
403	#433	—	3	2	no	—
404	#433	—	3	2	no	—
405	#433	—	3	2	no	—
406	#433	—	3	2	no	—
407	#433	C₂×D₃	1	1	yes	characteristic
408	#433	C₂×D₃	1	1	yes	characteristic
409	#433	C₂×D₃	1	1	yes	characteristic, complemented
410	#433	C₂×D₃	1	1	yes	characteristic, complemented
411	#432	—	3	1	no	—
412	#432	—	3	1	no	—
413	#432	—	3	2	no	—
414	#432	—	3	2	no	—
415	#431	—	3	1	no	—
416	#431	—	3	1	no	—
417	#431	—	3	2	no	—
418	#431	—	3	2	no	—
419	#431	C₂×D₃	1	1	yes	characteristic
420	#431	C₂×D₃	1	1	yes	characteristic
421	#431	C₂×D₃	1	1	yes	characteristic, complemented
422	#431	C₂×D₃	1	1	yes	characteristic, complemented
423	#424	—	3	2	no	—
424	#424	—	3	2	no	—
425	#424	C₂×D₃	1	1	yes	characteristic, complemented
426	#424	C₂×D₃	1	1	yes	characteristic, complemented
427	#423	—	3	1	no	—
428	#423	—	3	2	no	—
429	#423	—	3	2	no	—
430	C₂×C₄⋊C₈	—	3	1	no	—
431	#408	—	3	2	no	—
432	#408	C₂×D₃	1	1	yes	characteristic
433	#408	C₂×D₃	1	1	yes	characteristic
434	#407	—	3	2	no	—
435	#407	—	3	2	no	—
436	#407	—	3	2	no	—
437	C₂×C₂²⋊C₈	—	3	2	no	—
438	#405	—	3	2	no	—
439	#405	—	3	2	no	—
440	#405	—	3	2	no	—
441	C₄×M₁₆	—	3	2	no	—
442	C₄×M₁₆	—	3	2	no	—
443	C₄×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
444	C₂×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
445	C₂³×D₃	C₂²×C₄	1	2	yes	—
446	C₃×#41	—	4	1	no	—
447	C₃×#41	—	4	1	no	—
448	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
449	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
450	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
451	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
455	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
457	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
461	C₂×#67	C₂²×C₄	1	2	yes	—
462	C₂×#67	C₂²×C₄	1	2	yes	—
463	C₂×#67	C₂²×C₄	1	2	yes	—
464	C₂×#67	C₂²×C₄	1	2	yes	—
465	C₂²×Dic₃	C₂²×C₄	1	2	yes	—
466	#235	—	4	2	no	—
467	#235	—	4	2	no	—
468	C₂×D₁₂	—	4	2	no	—
469	C₂×D₁₂	C₂²×C₄	1	1	yes	characteristic
470	C₂×D₁₂	C₂²×C₄	1	1	yes	characteristic
471	C₂×D₁₂	C₂²×C₄	1	2	yes	—
472	C₂×C₄×D₃	—	4	2	no	—
473	C₂×C₄×D₃	—	4	2	no	—
474	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
475	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
476	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
477	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
478	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
479	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
480	C₂×C₄×D₃	C₂⁴	1	2	yes	—
481	C₂×C₄×D₃	C₂⁴	1	2	yes	—
482	C₂×Dic₆	C₂²×C₄	1	1	yes	characteristic
483	C₂×Dic₆	C₂²×C₄	1	1	yes	characteristic
484	C₂×Dic₆	C₂²×C₄	1	2	yes	—
485	C₃×M₁₆	—	4	1	no	—
486	C₃×M₁₆	—	4	1	no	—
487	C₂×C₃×C₈	—	4	1	no	—
488	C₂×C₃×C₈	—	4	1	no	—
489	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
490	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
491	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
492	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
493	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
494	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
495	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
496	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
497	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
498	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
499	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
500	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
501	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
502	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
503	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
504	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
505	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
506	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
507	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
508	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
509	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
510	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
511	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
512	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
513	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
514	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
515	C₃×C₄²	C₂⁴	1	1	yes	characteristic
516	C₃×C₄²	C₂⁴	1	1	yes	characteristic
517	C₃×C₄²	C₂⁴	1	1	yes	characteristic
518	C₃×C₄²	C₂⁴	1	1	yes	characteristic
519	#217	C₂²×C₄	1	2	yes	—
520	#217	C₂²×C₄	1	2	yes	—
521	#217	C₂²×C₄	1	2	yes	—
522	#217	C₂²×C₄	1	2	yes	—
523	#217	C₂²×C₄	1	2	yes	—
524	#217	C₂²×C₄	1	2	yes	—
525	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
526	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
527	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
528	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
529	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
530	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
531	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
532	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
533	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
534	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
535	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
536	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
537	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
538	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
539	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
540	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
541	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
542	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
543	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
544	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
545	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
546	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
547	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
548	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
549	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
550	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
551	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
552	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
553	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
554	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
555	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
556	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
557	C₄×Dic₃	C₂²×C₄	1	2	yes	—
558	C₄×Dic₃	C₂²×C₄	1	2	yes	—
559	C₄×Dic₃	C₂²×C₄	1	2	yes	—
560	C₄×Dic₃	C₂²×C₄	1	2	yes	—
561	C₄×Dic₃	C₂⁴	1	2	yes	—
562	C₄×Dic₃	C₂⁴	1	2	yes	—
563	#208	—	4	2	no	—
564	C₂×C₃⋊C₈	—	4	2	no	—
565	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
566	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
567	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
568	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
569	ΓL(1,𝔽₂₅)	—	4	2	no	—
570	ΓL(1,𝔽₂₅)	—	4	2	no	—
571	ΓL(1,𝔽₂₅)	—	4	2	no	—
572	ΓL(1,𝔽₂₅)	—	4	2	no	—
573	ΓL(1,𝔽₂₅)	—	4	2	no	—
574	ΓL(1,𝔽₂₅)	—	4	2	no	—
575	D₃×C₈	—	4	2	no	—
576	D₃×C₈	—	4	2	no	—
577	C₂×#41	—	3	1	no	—
578	C₂×#41	—	3	1	no	—
579	C₂×#41	C₂²×D₃	1	1	yes	characteristic
580	C₂²×D₄	—	3	1	no	—
581	C₂³×C₄	—	3	2	no	—
582	C₂×M₁₆	—	3	2	no	—
583	C₂×M₁₆	—	3	2	no	—
584	C₂×M₁₆	—	3	2	no	—
585	C₂×M₁₆	—	3	2	no	—
586	C₂×M₁₆	—	3	2	no	—
587	C₂×M₁₆	—	3	2	no	—
588	C₂×M₁₆	—	3	2	no	—
589	C₂×M₁₆	C₂²×D₃	1	1	yes	characteristic
590	C₂×M₁₆	C₂²×D₃	1	1	yes	characteristic
591	C₂²×C₈	—	3	2	no	—
592	C₂²×C₈	—	3	2	no	—
593	C₂²×C₈	—	3	2	no	—
594	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
595	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
596	C₄⋊Q₈	—	3	1	no	—
597	C₄⋊Q₈	—	3	1	no	—
598	#126	—	3	2	no	—
599	#126	—	3	2	no	—
600	#126	—	3	2	no	—
601	#126	—	3	2	no	—
602	#126	—	3	2	no	—
603	#126	—	3	2	no	—
604	#125	—	3	2	no	—
605	#125	—	3	2	no	—
606	#125	—	3	1	no	—
607	#125	—	3	1	no	—
608	#125	—	3	2	no	—
609	#124	—	3	2	no	—
610	#124	—	3	2	no	—
611	#124	—	3	1	no	—
612	#124	—	3	1	no	—
613	#123	—	3	2	no	—
614	#123	—	3	2	no	—
615	#123	—	3	2	no	—
616	#123	—	3	2	no	—
617	#123	—	3	2	no	—
618	#123	—	3	2	no	—
619	#123	—	3	2	no	—
620	#123	—	3	2	no	—
621	C₂²⋊Q₈	—	3	2	no	—
622	C₂²⋊Q₈	—	3	2	no	—
623	C₂²⋊Q₈	—	3	1	no	—
624	C₂²⋊Q₈	—	3	1	no	—
625	C₂²⋊Q₈	—	3	1	no	—
626	C₂²⋊Q₈	—	3	1	no	—
627	C₂²⋊Q₈	—	3	2	no	—
628	C₂²⋊Q₈	—	3	2	no	—
629	C₂²⋊Q₈	—	3	2	no	—
630	#121	—	3	2	no	—
631	#121	—	3	2	no	—
632	#121	—	3	1	no	—
633	#121	—	3	1	no	—
634	#121	—	3	2	no	—
635	#121	—	3	2	no	—
636	#120	—	3	2	no	—
637	#120	—	3	2	no	—
638	C₄×Q₈	—	3	1	no	—
639	C₄×Q₈	—	3	1	no	—
640	C₄×Q₈	—	3	1	no	—
641	C₄×Q₈	—	3	1	no	—
642	C₄×Q₈	—	3	2	no	—
643	C₄×Q₈	C₄×D₃	1	1	yes	characteristic
644	C₄×Q₈	C₄×D₃	1	1	yes	characteristic
645	C₄×D₄	—	3	2	no	—
646	C₄×D₄	—	3	2	no	—
647	C₄×D₄	—	3	2	no	—
648	C₄×D₄	—	3	2	no	—
649	C₄×D₄	—	3	2	no	—
650	C₄×D₄	—	3	2	no	—
651	C₄×D₄	—	3	1	no	—
652	C₄×D₄	—	3	2	no	—
653	C₄×D₄	—	3	1	no	—
654	C₄×D₄	—	3	1	no	—
655	C₄×D₄	—	3	1	no	—
656	C₄×D₄	—	3	1	no	—
657	C₄×D₄	—	3	1	no	—
658	C₄×D₄	—	3	2	no	—
659	C₄×D₄	C₄×D₃	1	1	yes	characteristic
660	C₄×D₄	C₄×D₃	1	1	yes	characteristic
661	C₄×D₄	C₄×D₃	1	1	yes	characteristic
662	C₄×D₄	C₄×D₃	1	1	yes	characteristic
663	C₄×D₄	C₄×D₃	1	1	yes	characteristic
664	C₄×D₄	C₄×D₃	1	1	yes	characteristic
665	#117	—	3	1	no	—
666	#117	—	3	1	no	—
667	#117	—	3	2	no	—
668	#117	—	3	2	no	—
669	#117	—	3	2	no	—
670	#117	—	3	2	no	—
671	#117	—	3	2	no	—
672	#117	—	3	2	no	—
673	#117	—	3	2	no	—
674	#117	—	3	2	no	—
675	#117	—	3	2	no	—
676	#117	C₂²×D₃	1	1	yes	characteristic
677	#117	C₂²×D₃	1	1	yes	characteristic
678	#117	C₂²×D₃	1	1	yes	characteristic
679	C₂×C₄⋊C₄	—	3	1	no	—
680	C₂×C₄⋊C₄	—	3	2	no	—
681	C₂×C₄⋊C₄	—	3	2	no	—
682	C₂×C₂²⋊C₄	—	3	2	no	—
683	C₂×C₂²⋊C₄	—	3	2	no	—
684	C₂×C₂²⋊C₄	—	3	2	no	—
685	C₂×C₄²	—	3	2	no	—
686	C₂×C₄²	—	3	2	no	—
687	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
688	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
689	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
690	C₄⋊C₈	—	3	2	no	—
691	C₄⋊C₈	—	3	2	no	—
692	C₄⋊C₈	—	3	2	no	—
693	C₄⋊C₈	—	3	2	no	—
694	C₄⋊C₈	—	3	2	no	—
695	C₄⋊C₈	—	3	2	no	—
696	C₄⋊C₈	—	3	2	no	—
697	C₄⋊C₈	—	3	2	no	—
698	C₄⋊C₈	—	3	2	no	—
699	C₄⋊C₈	—	3	1	no	—
700	C₄⋊C₈	—	3	1	no	—
701	C₄⋊C₈	—	3	2	no	—
702	C₄⋊C₈	—	3	1	no	—
703	C₄⋊C₈	—	3	1	no	—
704	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
705	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
706	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
707	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
708	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
709	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
710	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
711	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
712	C₂²⋊C₈	—	3	2	no	—
713	C₂²⋊C₈	—	3	2	no	—
714	C₂²⋊C₈	—	3	2	no	—
715	C₂²⋊C₈	—	3	2	no	—
716	C₂²⋊C₈	—	3	2	no	—
717	C₂²⋊C₈	—	3	2	no	—
718	C₂²⋊C₈	—	3	2	no	—
719	C₂²⋊C₈	—	3	2	no	—
720	C₂²⋊C₈	—	3	2	no	—
721	C₂²⋊C₈	—	3	2	no	—
722	C₂²⋊C₈	—	3	2	no	—
723	C₂²⋊C₈	—	3	2	no	—
724	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
725	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
726	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
727	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
728	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
729	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
730	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
731	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
732	#97	—	3	2	no	—
733	#97	—	3	2	no	—
734	#97	—	3	2	no	—
735	#97	—	3	2	no	—
736	#97	—	3	2	no	—
737	#97	—	3	2	no	—
738	#97	C₂²×D₃	1	1	yes	characteristic
739	#97	C₂²×D₃	1	1	yes	characteristic
740	C₄×C₈	—	3	2	no	—
741	C₄×C₈	—	3	2	no	—
742	C₄×C₈	—	3	2	no	—
743	C₄×C₈	—	3	2	no	—
744	C₄×C₈	—	3	2	no	—
745	C₄×C₈	—	3	2	no	—
746	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
747	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
748	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
749	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
750	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
751	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
752	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
753	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
754	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
755	C₂²×D₃	—	4	2	no	—
756	C₂²×D₃	—	4	2	no	—
757	C₂²×D₃	—	4	2	no	—
758	C₂²×D₃	C₂³×C₄	1	2	yes	—
759	C₂²×D₃	C₂³×C₄	1	2	yes	—
760	C₃×Q₈	—	4	1	no	—
761	C₃×D₄	—	4	1	no	—
762	C₃×D₄	—	4	1	no	—
763	C₃×D₄	—	4	1	no	—
764	C₂×C₃×C₄	—	2	2	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	2	2	no	—
767	C₂×C₃×C₄	—	2	1	no	—
768	C₂×C₃×C₄	—	2	1	no	—
769	C₂×C₃×C₄	—	2	1	no	—
770	C₂×C₃×C₄	—	2	1	no	—
771	C₂×C₃×C₄	—	2	1	no	—
772	C₂×C₃×C₄	—	2	1	no	—
773	C₂×C₃×C₄	—	4	1	no	—
774	C₂×C₃×C₄	—	4	1	no	—
775	C₂×C₃×C₄	—	4	1	no	—
776	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
777	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
778	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
779	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
780	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
781	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
782	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
783	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
784	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
785	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
786	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
787	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
788	#67	—	4	2	no	—
789	#67	—	4	2	no	—
790	#67	—	4	2	no	—
791	#67	—	4	2	no	—
792	C₂×Dic₃	—	4	2	no	—
793	C₂×Dic₃	C₂³×C₄	1	2	yes	—
794	C₂×Dic₃	C₂³×C₄	1	2	yes	—
795	C₂×Dic₃	C₂³×C₄	1	2	yes	—
796	C₂×Dic₃	C₂³×C₄	1	2	yes	—
797	C₂×Dic₃	C₂³×C₄	1	2	yes	—
798	C₂×Dic₃	C₂³×C₄	1	2	yes	—
799	D₁₂	—	2	2	no	—
800	D₁₂	—	2	2	no	—
801	D₁₂	—	4	2	no	—
802	C₄×D₃	—	2	2	no	—
803	C₄×D₃	—	2	2	no	—
804	C₄×D₃	—	2	2	no	—
805	C₄×D₃	—	2	2	no	—
806	C₄×D₃	—	4	2	no	—
807	C₄×D₃	—	4	2	no	—
808	C₄×D₃	—	4	2	no	—
809	C₄×D₃	—	4	2	no	—
810	C₄×D₃	—	4	2	no	—
811	C₄×D₃	—	4	2	no	—
812	Dic₆	—	2	2	no	—
813	Dic₆	—	2	2	no	—
814	Dic₆	—	4	2	no	—
815	C₃×C₈	—	2	1	no	—
816	C₃×C₈	—	2	1	no	—
817	C₃×C₈	—	2	1	no	—
818	C₃×C₈	—	2	1	no	—
819	C₃×C₈	—	2	1	no	—
820	C₃×C₈	—	2	1	no	—
821	C₃×C₈	—	2	1	no	—
822	C₃×C₈	—	2	1	no	—
823	C₃⋊C₈	—	2	2	no	—
824	C₃⋊C₈	—	2	2	no	—
825	C₃⋊C₈	—	2	2	no	—
826	C₃⋊C₈	—	2	2	no	—
827	C₂⁴	—	3	2	no	—
828	#41	—	4	1	no	—
829	#41	—	4	1	no	—
830	#41	—	12	2	no	—
831	#41	—	12	2	no	—
832	C₂×Q₈	—	3	1	no	—
833	C₂×Q₈	—	3	1	no	—
834	C₂×Q₈	—	3	2	no	—
835	C₂×Q₈	C₂×C₄×D₃	1	1	yes	characteristic
836	C₂×D₄	—	3	2	no	—
837	C₂×D₄	—	3	2	no	—
838	C₂×D₄	—	3	2	no	—
839	C₂×D₄	—	3	2	no	—
840	C₂×D₄	—	3	1	no	—
841	C₂×D₄	—	3	1	no	—
842	C₂×D₄	—	3	2	no	—
843	C₂×D₄	—	12	2	no	—
844	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
845	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
846	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
847	C₂²×C₄	—	3	2	no	—
848	C₂²×C₄	—	3	2	no	—
849	C₂²×C₄	—	3	2	no	—
850	C₂²×C₄	—	3	2	no	—
851	C₂²×C₄	—	3	2	no	—
852	C₂²×C₄	—	3	2	no	—
853	C₂²×C₄	—	3	2	no	—
854	C₂²×C₄	—	3	2	no	—
855	C₂²×C₄	—	3	2	no	—
856	C₂²×C₄	—	12	2	no	—
857	C₂²×C₄	—	12	2	no	—
858	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
859	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
860	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
861	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
862	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
863	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
864	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
865	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
866	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
867	M₁₆	—	4	1	no	—
868	M₁₆	—	4	1	no	—
869	M₁₆	—	12	2	no	—
870	M₁₆	—	12	2	no	—
871	M₁₆	—	12	2	no	—
872	M₁₆	—	12	2	no	—
873	M₁₆	—	12	2	no	—
874	M₁₆	—	12	2	no	—
875	M₁₆	—	12	2	no	—
876	C₂×C₈	—	3	2	no	—
877	C₂×C₈	—	3	2	no	—
878	C₂×C₈	—	3	2	no	—
879	C₂×C₈	—	3	2	no	—
880	C₂×C₈	—	4	1	no	—
881	C₂×C₈	—	4	1	no	—
882	C₂×C₈	—	12	2	no	—
883	C₂×C₈	—	12	2	no	—
884	C₂×C₈	—	12	2	no	—
885	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
886	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
887	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
888	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
892	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
893	C₄⋊C₄	—	3	1	no	—
894	C₄⋊C₄	—	3	2	no	—
895	C₄⋊C₄	—	3	2	no	—
896	C₄⋊C₄	—	3	2	no	—
897	C₄⋊C₄	—	3	2	no	—
898	C₄⋊C₄	—	3	2	no	—
899	C₄⋊C₄	—	3	2	no	—
900	C₄⋊C₄	—	3	1	no	—
901	C₄⋊C₄	—	3	2	no	—
902	C₄⋊C₄	—	3	1	no	—
903	C₄⋊C₄	—	3	1	no	—
904	C₄⋊C₄	—	3	2	no	—
905	C₄⋊C₄	—	3	2	no	—
906	C₄⋊C₄	—	3	2	no	—
907	C₄⋊C₄	—	3	2	no	—
908	C₄⋊C₄	—	3	2	no	—
909	C₄⋊C₄	—	3	2	no	—
910	C₄⋊C₄	—	3	2	no	—
911	C₄⋊C₄	—	3	2	no	—
912	C₄⋊C₄	—	3	2	no	—
913	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
914	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
915	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
916	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
917	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
918	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
919	C₂²⋊C₄	—	3	2	no	—
920	C₂²⋊C₄	—	3	2	no	—
921	C₂²⋊C₄	—	3	2	no	—
922	C₂²⋊C₄	—	3	2	no	—
923	C₂²⋊C₄	—	3	2	no	—
924	C₂²⋊C₄	—	3	2	no	—
925	C₂²⋊C₄	—	3	2	no	—
926	C₂²⋊C₄	—	3	2	no	—
927	C₂²⋊C₄	—	3	2	no	—
928	C₂²⋊C₄	—	3	2	no	—
929	C₂²⋊C₄	—	3	2	no	—
930	C₂²⋊C₄	—	3	2	no	—
931	C₂²⋊C₄	—	3	2	no	—
932	C₂²⋊C₄	—	3	2	no	—
933	C₂²⋊C₄	—	3	2	no	—
934	C₂²⋊C₄	—	3	2	no	—
935	C₂²⋊C₄	—	3	2	no	—
936	C₂²⋊C₄	—	3	2	no	—
937	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
938	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
939	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
940	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
941	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
942	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
943	C₄²	—	3	2	no	—
944	C₄²	—	3	2	no	—
945	C₄²	—	3	2	no	—
946	C₄²	—	3	2	no	—
947	C₄²	—	3	2	no	—
948	C₄²	—	3	2	no	—
949	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
950	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
951	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
952	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
953	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
954	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
955	C₄²	C₂³×D₃	1	1	yes	characteristic
956	C₄²	C₂³×D₃	1	1	yes	characteristic
957	C₄²	C₂³×D₃	1	1	yes	characteristic
958	C₄²	C₂³×D₃	1	1	yes	characteristic
959	C₂²×C₃	—	2	1	no	—
960	C₂²×C₃	—	2	1	no	—
961	C₂²×C₃	—	2	1	no	—
962	C₂²×C₃	—	2	1	no	—
963	C₂²×C₃	—	2	1	no	—
964	C₂²×C₃	—	2	1	no	—
965	C₂²×C₃	—	2	1	no	—
966	C₂²×C₃	—	2	1	no	—
967	C₂²×C₃	—	2	1	no	—
968	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
969	C₂×D₃	—	2	2	no	—
970	C₂×D₃	—	2	2	no	—
971	C₂×D₃	—	2	2	no	—
972	C₂×D₃	—	2	2	no	—
973	C₂×D₃	—	2	2	no	—
974	C₂×D₃	—	2	2	no	—
975	C₂×D₃	—	8	4	no	—
976	C₃×C₄	—	2	1	no	—
977	C₃×C₄	—	2	1	no	—
978	C₃×C₄	—	2	1	no	—
979	C₃×C₄	—	2	1	no	—
980	C₃×C₄	—	2	1	no	—
981	C₃×C₄	—	2	1	no	—
982	C₃×C₄	—	2	1	no	—
983	C₃×C₄	—	2	1	no	—
984	C₃×C₄	—	2	1	no	—
985	C₃×C₄	—	2	1	no	—
986	C₃×C₄	#568	1	2	yes	—
987	C₃×C₄	#585	1	1	yes	characteristic
988	C₃×C₄	#585	1	1	yes	characteristic
989	Dic₃	—	2	2	no	—
990	Dic₃	—	2	2	no	—
991	Dic₃	—	2	2	no	—
992	Dic₃	—	2	2	no	—
993	Dic₃	—	2	2	no	—
994	Dic₃	—	2	2	no	—
995	C₂³	—	3	2	no	—
996	C₂³	—	3	2	no	—
997	C₂³	—	12	2	no	—
998	C₂³	—	12	2	no	—
999	C₂³	—	12	2	no	—
1000	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1001	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1002	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1003	Q₈	—	4	1	no	—
1004	Q₈	—	6	2	no	—
1005	Q₈	—	6	2	no	—
1006	Q₈	—	12	2	no	—
1007	D₄	—	4	1	no	—
1008	D₄	—	4	1	no	—
1009	D₄	—	4	1	no	—
1010	D₄	—	6	2	no	—
1011	D₄	—	6	2	no	—
1012	D₄	—	12	2	no	—
1013	D₄	—	12	2	no	—
1014	D₄	—	12	2	no	—
1015	D₄	—	12	2	no	—
1016	D₄	—	12	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	3	2	no	—
1027	C₂×C₄	—	3	2	no	—
1028	C₂×C₄	—	3	2	no	—
1029	C₂×C₄	—	3	2	no	—
1030	C₂×C₄	—	3	2	no	—
1031	C₂×C₄	—	3	2	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	6	2	no	—
1036	C₂×C₄	—	6	2	no	—
1037	C₂×C₄	—	6	2	no	—
1038	C₂×C₄	—	6	2	no	—
1039	C₂×C₄	—	12	2	no	—
1040	C₂×C₄	—	12	2	no	—
1041	C₂×C₄	—	12	2	no	—
1042	C₂×C₄	—	12	2	no	—
1043	C₂×C₄	—	12	2	no	—
1044	C₂×C₄	—	12	2	no	—
1045	C₂×C₄	—	12	2	no	—
1046	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1048	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1051	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1052	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1053	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1054	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1056	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1057	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	1	no	—
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	6	2	no	—
1067	C₈	—	6	2	no	—
1068	C₈	—	6	2	no	—
1069	C₈	—	6	2	no	—
1070	C₂×C₃	—	4	1	no	—
1071	C₂×C₃	—	4	1	no	—
1072	C₂×C₃	—	4	1	no	—
1073	C₂×C₃	#3428	1	1	yes	characteristic
1074	C₂×C₃	C₂×#568	1	1	yes	characteristic
1075	C₂×C₃	#3573	1	1	yes	characteristic
1076	D₃	—	4	2	no	—
1077	D₃	—	4	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	6	2	no	—
1088	C₂²	—	6	2	no	—
1089	C₂²	—	6	2	no	—
1090	C₂²	—	6	2	no	—
1091	C₂²	—	6	2	no	—
1092	C₂²	—	6	2	no	—
1093	C₂²	—	24	4	no	—
1094	C₂²	C₂³×C₄×D₃	1	1	yes	characteristic
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	6	2	no	—
1106	C₄	—	6	2	no	—
1107	C₄	—	6	2	no	—
1108	C₄	—	6	2	no	—
1109	C₄	—	6	2	no	—
1110	C₄	—	6	2	no	—
1111	C₄	#5750	1	2	yes	—
1112	C₄	#5964	1	1	yes	characteristic
1113	C₄	#5964	1	1	yes	characteristic
1114	C₃	#60300	1	1	yes	characteristic, complemented, Sylow
1115	C₂	—	4	1	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	12	2	no	—
1119	C₂	—	12	2	no	—
1120	C₂	#85731	1	1	yes	characteristic
1121	C₂	C₂×#5750	1	1	yes	characteristic
1122	C₂	#87160	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₃
commutator, socle	C₂²×C₃	C₂⁴×C₄
Fitting	C₃×#2922	C₂
prime radical	#85840	C₂
cosocle	C₂×C₃×C₄	C₂⁵
hypercenter	#2922	D₃
hypocenter	C₃	#60300
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #2922

Complements

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

N	H ≅ G/N	type
2. C₃×#2922	C₂	semidirect
3. #82515	C₂	semidirect
4. #79374	C₂	semidirect
5. #79371	C₂	semidirect
6. #79369	C₂	semidirect
7. #79367	C₂	semidirect
8. #79296	C₂	semidirect
9. #79295	C₂	semidirect
10. #79294	C₂	semidirect
11. #79292	C₂	semidirect
12. #79288	C₂	semidirect
13. #79287	C₂	semidirect
14. #79267	C₂	semidirect
15. #79266	C₂	semidirect
16. #79085	C₂	semidirect
17. #79083	C₂	semidirect
18. #78666	C₂	semidirect
19. #78664	C₂	semidirect
20. #78512	C₂	semidirect
21. #78511	C₂	semidirect
22. #78448	C₂	semidirect
23. #78447	C₂	semidirect
50. C₃×#433	C₂²	semidirect
51. C₃×#433	C₂²	semidirect
54. C₃×#431	C₂²	semidirect
55. C₃×#431	C₂²	semidirect
56. C₃×#424	C₂²	semidirect
57. C₃×#424	C₂²	semidirect
60. C₃×C₄×M₁₆	C₂²	semidirect
61. C₂×C₃×C₄×C₈	C₂²	semidirect
63. #5128	C₂²	semidirect
64. #5128	C₂²	semidirect
65. #5128	C₂²	semidirect
66. #5127	C₂²	semidirect
67. #5111	C₂²	semidirect
68. #5111	C₂²	semidirect
69. #5111	C₂²	semidirect
70. C₈×#67	C₂²	semidirect
72. #5000	C₂²	semidirect
73. #4997	C₂²	semidirect
75. #4926	C₂²	semidirect
77. #4925	C₂²	semidirect
78. #4924	C₂²	semidirect
79. C₂×C₄⋊(C₃⋊C₈)	C₂²	semidirect
80. #4840	C₂²	semidirect
81. #4840	C₂²	semidirect
82. #4839	C₂²	semidirect
83. #4839	C₂²	semidirect
86. #4837	C₂²	semidirect
87. #4837	C₂²	semidirect
90. #4835	C₂²	semidirect
91. #4833	C₂²	semidirect
92. #4831	C₂²	semidirect
93. #4830	C₂²	semidirect
94. #4828	C₂²	semidirect
95. #4828	C₂²	semidirect
96. #4730	C₂²	semidirect
97. #4730	C₂²	semidirect
98. #4730	C₂²	semidirect
99. #4729	C₂²	semidirect
100. #4729	C₂²	semidirect
101. #4729	C₂²	semidirect
102. #4728	C₂²	semidirect
106. #67⋊C₈	C₂²	semidirect
112. #4709	C₂²	semidirect
113. #4708	C₂²	semidirect
114. #4707	C₂²	semidirect
115. #4705	C₂²	semidirect
116. #4690	C₂²	semidirect
117. #4689	C₂²	semidirect
124. C₄×ΓL(1,𝔽₂₅)	C₂²	semidirect
127. #4685	C₂²	semidirect
128. #4679	C₂²	semidirect
129. #4679	C₂²	semidirect
130. #4679	C₂²	semidirect
131. #4679	C₂²	semidirect
132. C₈×Dic₆	C₂²	semidirect
133. C₈×Dic₆	C₂²	semidirect
134. C₈×Dic₆	C₂²	semidirect
135. C₈×Dic₆	C₂²	semidirect
157. #2922	D₃	semidirect
409. #433	C₂×D₃	semidirect
410. #433	C₂×D₃	semidirect
421. #431	C₂×D₃	semidirect
422. #431	C₂×D₃	semidirect
425. #424	C₂×D₃	semidirect
426. #424	C₂×D₃	semidirect
443. C₄×M₁₆	C₂×D₃	semidirect
444. C₂×C₄×C₈	C₂×D₃	semidirect
1114. C₃	#60300	semidirect

Maximal subgroups

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

subgroup	index
#85840	2
C₃×#2922	2
#82515	2
#79374	2
#79371	2
#79369	2
#79367	2
#79296	2
#79295	2
#79294	2
#79292	2
#79288	2
#79287	2
#79267	2
#79266	2
#79085	2
#79083	2
#78666	2
#78664	2
#78512	2
#78511	2
#78448	2
#78447	2
#60300	3