Subgroups — #11660738

Order 768.

1772 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×#2925	C₂	1	1	yes	maximal, characteristic, complemented
3	#82513	C₂	1	1	yes	maximal, characteristic, complemented
4	#79381	C₂	1	2	yes	maximal, complemented
5	#79379	C₂	1	2	yes	maximal, complemented
6	#79374	C₂	1	2	yes	maximal, complemented
7	D₃×#433	C₂	1	2	yes	maximal, complemented
8	#79336	C₂	1	1	yes	maximal, characteristic, complemented
9	#79328	C₂	1	1	yes	maximal, characteristic, complemented
10	#79325	C₂	1	1	yes	maximal, characteristic, complemented
11	#79316	C₂	1	1	yes	maximal, characteristic, complemented
12	#79286	C₂	1	1	yes	maximal, characteristic, complemented
13	#79280	C₂	1	1	yes	maximal, characteristic, complemented
14	#79276	C₂	1	1	yes	maximal, characteristic, complemented
15	#79267	C₂	1	1	yes	maximal, characteristic, complemented
16	#79053	C₂	1	1	yes	maximal, characteristic, complemented
17	#79051	C₂	1	1	yes	maximal, characteristic, complemented
18	#79017	C₂	1	1	yes	maximal, characteristic, complemented
19	#79013	C₂	1	1	yes	maximal, characteristic, complemented
20	#78665	C₂	1	2	yes	maximal, complemented
21	#78664	C₂	1	2	yes	maximal, complemented
22	#78558	C₂	1	2	yes	maximal, complemented
23	#78556	C₂	1	2	yes	maximal, complemented
24	#60298	—	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	2	yes	—
49	C₃×#433	C₂²	1	2	yes	complemented
50	C₃×#432	C₂²	1	1	yes	characteristic
51	C₃×#432	C₂²	1	1	yes	characteristic, complemented
52	C₃×#431	C₂²	1	1	yes	characteristic
53	C₃×#431	C₂²	1	1	yes	characteristic, complemented
54	C₃×#423	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₃×#408	C₂²	1	2	yes	—
57	C₃×#405	C₂²	1	2	yes	complemented
58	#5234	C₂²	1	1	yes	characteristic
59	#5234	C₂²	1	1	yes	characteristic
60	#5128	C₂²	1	2	yes	complemented
61	#5127	C₂²	1	2	yes	complemented
62	#5127	C₂²	1	2	yes	complemented
63	#5127	C₂²	1	2	yes	complemented
64	#5111	C₂²	1	2	yes	complemented
65	C₈×#67	C₂²	1	2	yes	complemented
66	C₈×#67	C₂²	1	2	yes	complemented
67	C₈×#67	C₂²	1	2	yes	complemented
68	#5000	C₂²	1	1	yes	characteristic
69	#5000	C₂²	1	1	yes	characteristic
70	#5000	C₂²	1	1	yes	characteristic, complemented
71	#5000	C₂²	1	1	yes	characteristic, complemented
72	#4999	C₂²	1	1	yes	characteristic, complemented
73	#4999	C₂²	1	1	yes	characteristic, complemented
74	#4925	C₂²	1	1	yes	characteristic
75	#4925	C₂²	1	1	yes	characteristic
76	#4925	C₂²	1	1	yes	characteristic, complemented
77	#4925	C₂²	1	1	yes	characteristic, complemented
78	C₄×#208	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	1	yes	characteristic
85	#4838	C₂²	1	1	yes	characteristic
86	#4835	C₂²	1	2	yes	complemented
87	#4834	C₂²	1	1	yes	characteristic
88	#4834	C₂²	1	1	yes	characteristic
89	#4834	C₂²	1	1	yes	characteristic
90	#4834	C₂²	1	1	yes	characteristic
91	#4834	C₂²	1	1	yes	characteristic
92	#4834	C₂²	1	1	yes	characteristic
93	#4833	C₂²	1	2	yes	complemented
94	D₃×C₄⋊C₈	C₂²	1	2	yes	complemented
95	D₃×C₄⋊C₈	C₂²	1	2	yes	complemented
96	#4831	C₂²	1	1	yes	characteristic, complemented
97	#4831	C₂²	1	1	yes	characteristic, complemented
98	#4831	C₂²	1	1	yes	characteristic, complemented
99	#4831	C₂²	1	1	yes	characteristic, complemented
100	#4830	C₂²	1	1	yes	characteristic, complemented
101	#4830	C₂²	1	1	yes	characteristic, complemented
102	#4830	C₂²	1	1	yes	characteristic, complemented
103	#4830	C₂²	1	1	yes	characteristic, complemented
104	#4730	C₂²	1	2	yes	complemented
105	#4729	C₂²	1	2	yes	complemented
106	#4728	C₂²	1	2	yes	complemented
107	#4728	C₂²	1	2	yes	complemented
108	#4728	C₂²	1	2	yes	complemented
109	#4726	C₂²	1	2	yes	—
110	#67⋊C₈	C₂²	1	2	yes	complemented
111	#67⋊C₈	C₂²	1	2	yes	complemented
112	#67⋊C₈	C₂²	1	2	yes	complemented
113	D₃×C₂²⋊C₈	C₂²	1	2	yes	—
114	D₃×C₂²⋊C₈	C₂²	1	2	yes	—
115	D₃×C₂²⋊C₈	C₂²	1	2	yes	—
116	#4720	C₂²	1	2	yes	—
117	#4720	C₂²	1	2	yes	—
118	#4720	C₂²	1	2	yes	—
119	#4720	C₂²	1	2	yes	—
120	#4709	C₂²	1	2	yes	complemented
121	#4708	C₂²	1	2	yes	complemented
122	#4706	C₂²	1	2	yes	—
123	#4706	C₂²	1	2	yes	—
124	#4705	C₂²	1	2	yes	complemented
125	D₃×#97	C₂²	1	2	yes	complemented
126	#4701	C₂²	1	2	yes	complemented
127	#4701	C₂²	1	2	yes	complemented
128	#4690	C₂²	1	2	yes	complemented
129	#4689	C₂²	1	2	yes	complemented
130	C₈×D₁₂	C₂²	1	2	yes	—
131	C₈×D₁₂	C₂²	1	2	yes	—
132	#4685	C₂²	1	2	yes	complemented
133	C₄×D₃×C₈	C₂²	1	2	yes	complemented
134	#4679	C₂²	1	2	yes	complemented
135	C₈×Dic₆	C₂²	1	2	yes	complemented
136	#3475	—	3	1	no	—
137	#2994	—	3	2	no	—
138	#2994	—	3	1	no	—
139	#2993	—	3	1	no	—
140	#2992	—	3	2	no	—
141	#2990	—	3	1	no	—
142	#2988	—	3	1	no	—
143	#2986	—	3	1	no	—
144	#2985	—	3	1	no	—
145	#2977	—	3	2	no	—
146	#2976	—	3	2	no	—
147	#2974	—	3	1	no	—
148	#2972	—	3	1	no	—
149	#2970	—	3	1	no	—
150	#2969	—	3	1	no	—
151	#2968	—	3	2	no	—
152	#2966	—	3	1	no	—
153	#2966	—	3	2	no	—
154	C₈×#41	—	3	1	no	—
155	#2925	D₃	1	1	yes	characteristic, complemented
156	#2924	—	3	2	no	—
157	#2922	—	3	1	no	—
158	C₂×#433	—	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	2	yes	—
165	C₂²×C₃×C₈	C₂³	1	2	yes	—
166	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
167	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
168	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
169	C₃×C₄×D₄	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×#117	C₂³	1	1	yes	characteristic
175	C₃×#117	C₂³	1	1	yes	characteristic
176	C₃×#117	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	#946	C₂×C₄	1	2	yes	—
181	#946	C₂×C₄	1	2	yes	—
182	#938	C₂×C₄	1	2	yes	—
183	#938	C₂×C₄	1	2	yes	—
184	#937	C₂×C₄	1	2	yes	—
185	#937	C₂×C₄	1	2	yes	—
186	#935	C₂×C₄	1	2	yes	—
187	#935	C₂×C₄	1	2	yes	—
188	#930	C₂×C₄	1	1	yes	characteristic
189	#930	C₂×C₄	1	1	yes	characteristic
190	#929	C₂×C₄	1	2	yes	—
191	#929	C₂×C₄	1	2	yes	—
192	C₄×#67	C₂×C₄	1	2	yes	—
193	C₄×#67	C₂×C₄	1	2	yes	—
194	C₄×#67	C₂³	1	2	yes	—
195	C₄×#67	C₂³	1	2	yes	—
196	C₄×#67	C₂³	1	2	yes	—
197	C₄×#67	C₂³	1	2	yes	—
198	C₂×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
199	#926	C₂×C₄	1	1	yes	characteristic
200	#926	C₂×C₄	1	1	yes	characteristic
201	#926	C₂³	1	2	yes	—
202	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
203	#924	C₂×C₄	1	1	yes	characteristic
204	#924	C₂×C₄	1	1	yes	characteristic
205	#924	C₂×C₄	1	2	yes	—
206	#924	C₂×C₄	1	1	yes	characteristic
207	#924	C₂×C₄	1	1	yes	characteristic
208	C₂×#208	C₂³	1	1	yes	characteristic
209	C₂×#208	C₂³	1	1	yes	characteristic
210	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
211	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
212	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
213	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
214	C₂×D₃×C₈	C₂³	1	2	yes	—
215	C₂×D₃×C₈	C₂³	1	2	yes	—
216	C₂×D₃×C₈	C₂³	1	2	yes	—
217	C₂×D₃×C₈	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	2	yes	—
254	C₄×D₁₂	C₂³	1	1	yes	characteristic
255	C₄×D₁₂	C₂³	1	1	yes	characteristic
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	2	yes	—
270	C₄×Dic₆	C₂³	1	1	yes	characteristic
271	C₄×Dic₆	C₂³	1	1	yes	characteristic
272	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₃×C₄⋊C₈	C₂³	1	2	yes	—
275	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₃×#97	C₂³	1	2	yes	—
283	C₃×#97	C₂³	1	2	yes	—
284	C₃×C₄×C₈	C₂³	1	2	yes	—
285	C₃×C₄×C₈	C₂³	1	2	yes	—
286	#830	C₂³	1	1	yes	characteristic
287	#830	C₂³	1	1	yes	characteristic
288	#830	C₂³	1	1	yes	characteristic
289	#830	C₂³	1	1	yes	characteristic
290	#830	C₂³	1	1	yes	characteristic
291	#830	C₂³	1	1	yes	characteristic
292	#830	C₂³	1	1	yes	characteristic
293	#830	C₂³	1	1	yes	characteristic
294	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
295	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
296	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
297	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
298	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
299	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
300	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
301	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
302	#815	C₂³	1	2	yes	—
303	#815	C₂³	1	2	yes	—
304	#815	C₂³	1	2	yes	—
305	#815	C₂³	1	2	yes	—
306	Dic₃⋊C₈	C₂³	1	2	yes	—
307	Dic₃⋊C₈	C₂³	1	2	yes	—
308	Dic₃⋊C₈	C₂³	1	2	yes	—
309	Dic₃⋊C₈	C₂³	1	2	yes	—
310	Dic₃⋊C₈	C₂³	1	2	yes	—
311	Dic₃⋊C₈	C₂³	1	2	yes	—
312	Dic₃⋊C₈	C₂³	1	2	yes	—
313	Dic₃⋊C₈	C₂³	1	2	yes	—
314	C₈×Dic₃	C₂³	1	2	yes	—
315	C₈×Dic₃	C₂³	1	2	yes	—
316	C₈×Dic₃	C₂³	1	2	yes	—
317	C₈×Dic₃	C₂³	1	2	yes	—
318	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
319	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
320	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
321	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
322	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
323	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
324	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
325	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
326	#803	C₂³	1	1	yes	characteristic
327	#803	C₂³	1	1	yes	characteristic
328	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
329	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
330	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
331	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
332	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
333	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
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	1	no	—
358	#446	—	3	1	no	—
359	#446	—	3	1	no	—
360	#446	—	3	1	no	—
361	#446	—	3	2	no	—
362	#446	—	3	2	no	—
363	#446	—	3	2	no	—
364	C₈×Q₈	—	3	1	no	—
365	C₈×Q₈	—	3	1	no	—
366	C₈×Q₈	—	3	1	no	—
367	C₈×Q₈	—	3	1	no	—
368	C₈×Q₈	—	3	2	no	—
369	#436	—	3	2	no	—
370	#436	—	3	1	no	—
371	#436	—	3	1	no	—
372	#436	—	3	2	no	—
373	#435	—	3	2	no	—
374	#435	—	3	2	no	—
375	#435	—	3	2	no	—
376	#435	—	3	2	no	—
377	#435	—	3	2	no	—
378	#435	—	3	2	no	—
379	#435	—	3	2	no	—
380	#435	—	3	2	no	—
381	#435	—	3	2	no	—
382	#435	—	3	2	no	—
383	C₈×D₄	—	3	2	no	—
384	C₈×D₄	—	3	2	no	—
385	C₈×D₄	—	3	2	no	—
386	C₈×D₄	—	3	1	no	—
387	C₈×D₄	—	3	1	no	—
388	C₈×D₄	—	3	1	no	—
389	C₈×D₄	—	3	1	no	—
390	C₈×D₄	—	3	1	no	—
391	C₈×D₄	—	3	1	no	—
392	C₈×D₄	—	3	2	no	—
393	C₈×D₄	—	3	2	no	—
394	C₈×D₄	—	3	2	no	—
395	C₈×D₄	—	3	2	no	—
396	C₈×D₄	—	3	2	no	—
397	#433	—	3	1	no	—
398	#433	—	3	1	no	—
399	#433	—	3	1	no	—
400	#433	—	3	1	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	—	3	2	no	—
408	#433	—	3	2	no	—
409	#433	C₂×D₃	1	2	yes	—
410	#433	C₂×D₃	1	2	yes	complemented
411	#432	—	3	2	no	—
412	#432	—	3	2	no	—
413	#432	C₂×D₃	1	1	yes	characteristic
414	#432	C₂×D₃	1	1	yes	characteristic, complemented
415	#431	—	3	1	no	—
416	#431	—	3	1	no	—
417	#431	—	3	1	no	—
418	#431	—	3	1	no	—
419	#431	—	3	2	no	—
420	#431	—	3	2	no	—
421	#431	C₂×D₃	1	1	yes	characteristic
422	#431	C₂×D₃	1	1	yes	characteristic, complemented
423	#424	—	3	1	no	—
424	#424	—	3	1	no	—
425	#424	—	3	2	no	—
426	#424	—	3	2	no	—
427	#423	C₂×D₃	1	1	yes	characteristic, complemented
428	C₂×C₄⋊C₈	—	3	2	no	—
429	C₂×C₄⋊C₈	—	3	2	no	—
430	C₂×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
431	#408	—	3	1	no	—
432	#408	—	3	1	no	—
433	#408	C₂×D₃	1	2	yes	—
434	#407	—	3	2	no	—
435	C₂×C₂²⋊C₈	—	3	2	no	—
436	C₂×C₂²⋊C₈	—	3	2	no	—
437	C₂×C₂²⋊C₈	—	3	2	no	—
438	#405	—	3	2	no	—
439	#405	—	3	2	no	—
440	#405	C₂×D₃	1	2	yes	complemented
441	C₄×M₁₆	—	3	1	no	—
442	C₂×#97	—	3	2	no	—
443	C₂×C₄×C₈	—	3	1	no	—
444	C₂×C₄×C₈	—	3	2	no	—
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	—	2	4	no	—
467	#235	—	2	4	no	—
468	C₂×D₁₂	—	2	4	no	—
469	C₂×D₁₂	C₂²×C₄	1	1	yes	characteristic
470	C₂×D₁₂	C₂²×C₄	1	2	yes	—
471	C₂×D₁₂	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
486	C₂×C₃×C₈	—	4	2	no	—
487	C₂×C₃×C₈	C₂⁴	1	2	yes	—
488	C₂×C₃×C₈	C₂⁴	1	2	yes	—
489	C₂×C₃×C₈	C₂⁴	1	2	yes	—
490	C₂×C₃×C₈	C₂⁴	1	2	yes	—
491	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
492	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
493	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
494	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
495	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
496	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
497	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
498	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
499	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
500	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
501	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
502	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
503	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
504	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
505	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
506	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
507	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
508	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
509	C₃×C₄²	C₂⁴	1	1	yes	characteristic
510	C₃×C₄²	C₂⁴	1	1	yes	characteristic
511	C₃×C₄²	C₂⁴	1	1	yes	characteristic
512	C₃×C₄²	C₂⁴	1	1	yes	characteristic
513	#217	C₂²×C₄	1	2	yes	—
514	#217	C₂²×C₄	1	2	yes	—
515	#217	C₂²×C₄	1	2	yes	—
516	#217	C₂²×C₄	1	2	yes	—
517	#217	C₂²×C₄	1	2	yes	—
518	#217	C₂²×C₄	1	2	yes	—
519	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
520	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
521	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
522	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
523	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
524	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
532	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
533	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
534	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
535	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
536	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
537	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
538	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
539	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
540	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
541	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
542	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
543	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
544	Dic₃⋊C₄	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	C₄×Dic₃	C₂²×C₄	1	2	yes	—
552	C₄×Dic₃	C₂²×C₄	1	2	yes	—
553	C₄×Dic₃	C₂²×C₄	1	2	yes	—
554	C₄×Dic₃	C₂²×C₄	1	2	yes	—
555	C₄×Dic₃	C₂⁴	1	2	yes	—
556	C₄×Dic₃	C₂⁴	1	2	yes	—
557	#208	—	4	1	no	—
558	#208	—	4	1	no	—
559	C₂×C₃⋊C₈	—	4	1	no	—
560	C₂×C₃⋊C₈	—	4	1	no	—
561	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
562	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
563	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
564	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
565	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
566	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
567	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
568	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
569	ΓL(1,𝔽₂₅)	—	4	2	no	—
570	ΓL(1,𝔽₂₅)	—	4	2	no	—
571	D₃×C₈	—	4	2	no	—
572	D₃×C₈	—	4	2	no	—
573	D₃×C₈	—	4	2	no	—
574	D₃×C₈	—	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	1	no	—
583	C₂×M₁₆	—	3	1	no	—
584	C₂×M₁₆	—	3	2	no	—
585	C₂×M₁₆	—	3	2	no	—
586	C₂×M₁₆	C₂²×D₃	1	2	yes	—
587	C₂²×C₈	—	3	1	no	—
588	C₂²×C₈	—	3	1	no	—
589	C₂²×C₈	—	3	2	no	—
590	C₂²×C₈	—	3	2	no	—
591	C₂²×C₈	—	3	2	no	—
592	C₂²×C₈	—	3	2	no	—
593	C₂²×C₈	—	3	2	no	—
594	C₂²×C₈	—	3	2	no	—
595	C₂²×C₈	C₂²×D₃	1	2	yes	—
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	2	no	—
658	C₄×D₄	—	3	1	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	1	no	—
699	C₄⋊C₈	—	3	1	no	—
700	C₄⋊C₈	—	3	1	no	—
701	C₄⋊C₈	—	3	1	no	—
702	C₄⋊C₈	—	3	1	no	—
703	C₄⋊C₈	—	3	1	no	—
704	C₄⋊C₈	—	3	1	no	—
705	C₄⋊C₈	—	3	1	no	—
706	C₄⋊C₈	C₂²×D₃	1	2	yes	—
707	C₄⋊C₈	C₂²×D₃	1	2	yes	—
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	1	no	—
713	C₂²⋊C₈	—	3	1	no	—
714	C₂²⋊C₈	—	3	1	no	—
715	C₂²⋊C₈	—	3	1	no	—
716	C₂²⋊C₈	—	3	1	no	—
717	C₂²⋊C₈	—	3	1	no	—
718	C₂²⋊C₈	—	3	1	no	—
719	C₂²⋊C₈	—	3	1	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	—	3	2	no	—
725	C₂²⋊C₈	—	3	2	no	—
726	C₂²⋊C₈	—	3	2	no	—
727	C₂²⋊C₈	—	3	2	no	—
728	C₂²⋊C₈	C₂²×D₃	1	2	yes	—
729	C₂²⋊C₈	C₂²×D₃	1	2	yes	—
730	C₂²⋊C₈	C₂²×D₃	1	2	yes	—
731	C₂²⋊C₈	C₂²×D₃	1	2	yes	—
732	#97	—	3	2	no	—
733	#97	—	3	2	no	—
734	#97	—	3	2	no	—
735	#97	—	3	2	no	—
736	#97	—	3	1	no	—
737	#97	—	3	1	no	—
738	#97	C₂²×D₃	1	2	yes	—
739	#97	C₂²×D₃	1	2	yes	—
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	1	no	—
745	C₄×C₈	—	3	1	no	—
746	C₄×C₈	—	3	1	no	—
747	C₄×C₈	—	3	1	no	—
748	C₄×C₈	—	3	1	no	—
749	C₄×C₈	—	3	1	no	—
750	C₄×C₈	C₂²×D₃	1	2	yes	—
751	C₄×C₈	C₂²×D₃	1	2	yes	—
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	—	2	4	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	—	2	4	no	—
789	#67	—	2	4	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	4	no	—
800	D₁₂	—	2	2	no	—
801	D₁₂	#131	1	4	yes	—
802	C₄×D₃	—	2	4	no	—
803	C₄×D₃	—	2	4	no	—
804	C₄×D₃	—	2	2	no	—
805	C₄×D₃	—	2	2	no	—
806	C₄×D₃	—	2	2	no	—
807	C₄×D₃	—	2	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	2	no	—
816	C₃×C₈	—	2	2	no	—
817	C₃×C₈	—	2	2	no	—
818	C₃×C₈	—	2	2	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	1	no	—
824	C₃⋊C₈	—	2	1	no	—
825	C₃⋊C₈	—	2	1	no	—
826	C₃⋊C₈	—	2	1	no	—
827	C₂⁴	—	3	2	no	—
828	#41	—	4	1	no	—
829	#41	—	4	1	no	—
830	#41	—	6	4	no	—
831	#41	—	6	4	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	2	no	—
842	C₂×D₄	—	3	1	no	—
843	C₂×D₄	—	6	4	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	2	no	—
868	M₁₆	—	12	2	no	—
869	M₁₆	—	12	2	no	—
870	M₁₆	—	12	1	no	—
871	M₁₆	—	12	1	no	—
872	C₂×C₈	—	3	1	no	—
873	C₂×C₈	—	3	1	no	—
874	C₂×C₈	—	3	1	no	—
875	C₂×C₈	—	3	1	no	—
876	C₂×C₈	—	3	1	no	—
877	C₂×C₈	—	3	1	no	—
878	C₂×C₈	—	3	1	no	—
879	C₂×C₈	—	3	1	no	—
880	C₂×C₈	—	4	2	no	—
881	C₂×C₈	—	12	2	no	—
882	C₂×C₈	—	12	2	no	—
883	C₂×C₈	—	12	2	no	—
884	C₂×C₈	—	12	2	no	—
885	C₂×C₈	—	12	2	no	—
886	C₂×C₈	—	12	2	no	—
887	C₂×C₈	—	12	1	no	—
888	C₂×C₈	—	12	1	no	—
889	C₂×C₈	C₂³×D₃	1	2	yes	—
890	C₂×C₈	C₂³×D₃	1	2	yes	—
891	C₂×C₈	C₂³×D₃	1	2	yes	—
892	C₂×C₈	C₂³×D₃	1	2	yes	—
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	—	8	4	no	—
975	C₂×D₃	C₂×#131	1	4	yes	—
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	C₂×#131	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	—	6	4	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	—	3	4	no	—
1008	D₄	—	4	1	no	—
1009	D₄	—	4	1	no	—
1010	D₄	—	4	1	no	—
1011	D₄	—	6	4	no	—
1012	D₄	—	6	4	no	—
1013	D₄	—	6	4	no	—
1014	D₄	—	6	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	4	no	—
1036	C₂×C₄	—	6	4	no	—
1037	C₂×C₄	—	6	2	no	—
1038	C₂×C₄	—	6	2	no	—
1039	C₂×C₄	—	6	2	no	—
1040	C₂×C₄	—	6	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	2	no	—
1059	C₈	—	2	2	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	2	no	—
1062	C₈	—	6	1	no	—
1063	C₈	—	6	1	no	—
1064	C₈	—	6	1	no	—
1065	C₈	—	6	1	no	—
1066	C₈	—	6	1	no	—
1067	C₈	—	6	1	no	—
1068	C₈	—	6	1	no	—
1069	C₈	—	6	1	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	C₂²×#131	1	1	yes	characteristic
1075	C₂×C₃	#3573	1	1	yes	characteristic
1076	D₃	—	2	4	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	—	3	4	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	D₃×#131	1	2	yes	—
1112	C₄	#5964	1	1	yes	characteristic
1113	C₄	#5964	1	1	yes	characteristic
1114	C₃	#60298	1	1	yes	characteristic, complemented, Sylow
1115	C₂	—	4	1	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	6	4	no	—
1119	C₂	—	12	2	no	—
1120	C₂	#85731	1	1	yes	characteristic
1121	C₂	C₂×D₃×#131	1	1	yes	characteristic
1122	C₂	#87166	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₃
commutator, socle	C₂²×C₃	C₂⁴×C₄
Fitting	C₃×#2925	C₂
prime radical	#85840	C₂
cosocle	C₂×C₃×C₄	C₂⁵
hypercenter	#2925	D₃
hypocenter	C₃	#60298
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #2925

Complements

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

N	H ≅ G/N	type
2. C₃×#2925	C₂	semidirect
3. #82513	C₂	semidirect
4. #79381	C₂	semidirect
5. #79379	C₂	semidirect
6. #79374	C₂	semidirect
7. D₃×#433	C₂	semidirect
8. #79336	C₂	semidirect
9. #79328	C₂	semidirect
10. #79325	C₂	semidirect
11. #79316	C₂	semidirect
12. #79286	C₂	semidirect
13. #79280	C₂	semidirect
14. #79276	C₂	semidirect
15. #79267	C₂	semidirect
16. #79053	C₂	semidirect
17. #79051	C₂	semidirect
18. #79017	C₂	semidirect
19. #79013	C₂	semidirect
20. #78665	C₂	semidirect
21. #78664	C₂	semidirect
22. #78558	C₂	semidirect
23. #78556	C₂	semidirect
49. C₃×#433	C₂²	semidirect
51. C₃×#432	C₂²	semidirect
53. C₃×#431	C₂²	semidirect
54. C₃×#423	C₂²	semidirect
55. C₂×C₃×C₄⋊C₈	C₂²	semidirect
57. C₃×#405	C₂²	semidirect
60. #5128	C₂²	semidirect
61. #5127	C₂²	semidirect
62. #5127	C₂²	semidirect
63. #5127	C₂²	semidirect
64. #5111	C₂²	semidirect
65. C₈×#67	C₂²	semidirect
66. C₈×#67	C₂²	semidirect
67. C₈×#67	C₂²	semidirect
70. #5000	C₂²	semidirect
71. #5000	C₂²	semidirect
72. #4999	C₂²	semidirect
73. #4999	C₂²	semidirect
76. #4925	C₂²	semidirect
77. #4925	C₂²	semidirect
78. C₄×#208	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. #4835	C₂²	semidirect
93. #4833	C₂²	semidirect
94. D₃×C₄⋊C₈	C₂²	semidirect
95. D₃×C₄⋊C₈	C₂²	semidirect
96. #4831	C₂²	semidirect
97. #4831	C₂²	semidirect
98. #4831	C₂²	semidirect
99. #4831	C₂²	semidirect
100. #4830	C₂²	semidirect
101. #4830	C₂²	semidirect
102. #4830	C₂²	semidirect
103. #4830	C₂²	semidirect
104. #4730	C₂²	semidirect
105. #4729	C₂²	semidirect
106. #4728	C₂²	semidirect
107. #4728	C₂²	semidirect
108. #4728	C₂²	semidirect
110. #67⋊C₈	C₂²	semidirect
111. #67⋊C₈	C₂²	semidirect
112. #67⋊C₈	C₂²	semidirect
120. #4709	C₂²	semidirect
121. #4708	C₂²	semidirect
124. #4705	C₂²	semidirect
125. D₃×#97	C₂²	semidirect
126. #4701	C₂²	semidirect
127. #4701	C₂²	semidirect
128. #4690	C₂²	semidirect
129. #4689	C₂²	semidirect
132. #4685	C₂²	semidirect
133. C₄×D₃×C₈	C₂²	semidirect
134. #4679	C₂²	semidirect
135. C₈×Dic₆	C₂²	semidirect
155. #2925	D₃	semidirect
410. #433	C₂×D₃	semidirect
414. #432	C₂×D₃	semidirect
422. #431	C₂×D₃	semidirect
427. #423	C₂×D₃	semidirect
430. C₂×C₄⋊C₈	C₂×D₃	semidirect
440. #405	C₂×D₃	semidirect
1114. C₃	#60298	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×#2925	2
#82513	2
#79381	2
#79379	2
#79374	2
D₃×#433	2
#79336	2
#79328	2
#79325	2
#79316	2
#79286	2
#79280	2
#79276	2
#79267	2
#79053	2
#79051	2
#79017	2
#79013	2
#78665	2
#78664	2
#78558	2
#78556	2
#60298	3