Subgroups — #87121

Order 384.

910 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	#5731	C₂	1	1	yes	maximal, characteristic, complemented
3	#5729	C₂	1	1	yes	maximal, characteristic, complemented
4	#5722	C₂	1	1	yes	maximal, characteristic, complemented
5	#5721	C₂	1	1	yes	maximal, characteristic, complemented
6	#5708	C₂	1	1	yes	maximal, characteristic, complemented
7	#5702	C₂	1	1	yes	maximal, characteristic, complemented
8	#5702	C₂	1	1	yes	maximal, characteristic, complemented
9	#5702	C₂	1	1	yes	maximal, characteristic, complemented
10	#5701	C₂	1	1	yes	maximal, characteristic, complemented
11	#5701	C₂	1	1	yes	maximal, characteristic, complemented
12	#5701	C₂	1	1	yes	maximal, characteristic, complemented
13	#5701	C₂	1	1	yes	maximal, characteristic, complemented
14	#5696	C₂	1	1	yes	maximal, characteristic, complemented
15	#5696	C₂	1	1	yes	maximal, characteristic, complemented
16	#5685	C₂	1	1	yes	maximal, characteristic, complemented
17	#5685	C₂	1	1	yes	maximal, characteristic, complemented
18	#5671	C₂	1	1	yes	maximal, characteristic, complemented
19	#5669	C₂	1	1	yes	maximal, characteristic
20	#5662	C₂	1	1	yes	maximal, characteristic
21	#5651	C₂	1	1	yes	maximal, characteristic, complemented
22	#5650	C₂	1	1	yes	maximal, characteristic, complemented
23	#5649	C₂	1	1	yes	maximal, characteristic
24	#5646	C₂	1	1	yes	maximal, characteristic, complemented
25	#5646	C₂	1	1	yes	maximal, characteristic, complemented
26	#5641	C₂	1	1	yes	maximal, characteristic, complemented
27	#5636	C₂	1	1	yes	maximal, characteristic, complemented
28	#5625	C₂	1	1	yes	maximal, characteristic, complemented
29	#5623	C₂	1	1	yes	maximal, characteristic, complemented
30	#5622	C₂	1	1	yes	maximal, characteristic, complemented
31	#5622	C₂	1	1	yes	maximal, characteristic, complemented
32	#3555	—	3	1	no	maximal, Sylow
33	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×#126	C₂²	1	1	yes	characteristic
36	C₃×#126	C₂²	1	1	yes	characteristic
37	C₃×#126	C₂²	1	1	yes	characteristic
38	C₃×#126	C₂²	1	1	yes	characteristic
39	C₃×#125	C₂²	1	1	yes	characteristic
40	C₃×#125	C₂²	1	1	yes	characteristic
41	C₃×#124	C₂²	1	1	yes	characteristic
42	C₃×#123	C₂²	1	1	yes	characteristic
43	C₃×#123	C₂²	1	1	yes	characteristic
44	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	#946	C₂²	1	1	yes	characteristic
49	#946	C₂²	1	1	yes	characteristic
50	#946	C₂²	1	1	yes	characteristic
51	Q₈×Dic₃	C₂²	1	1	yes	characteristic
52	Q₈×Dic₃	C₂²	1	1	yes	characteristic
53	Q₈×Dic₃	C₂²	1	1	yes	characteristic
54	#944	C₂²	1	1	yes	characteristic
55	#944	C₂²	1	1	yes	characteristic
56	#944	C₂²	1	1	yes	characteristic
57	#944	C₂²	1	1	yes	characteristic
58	#944	C₂²	1	1	yes	characteristic
59	#944	C₂²	1	1	yes	characteristic
60	#939	C₂²	1	1	yes	characteristic
61	#936	C₂²	1	1	yes	characteristic
62	#935	C₂²	1	1	yes	characteristic
63	D₄×Dic₃	C₂²	1	1	yes	characteristic
64	#929	C₂²	1	1	yes	characteristic
65	C₄×#67	C₂²	1	1	yes	characteristic
66	#926	C₂²	1	1	yes	characteristic
67	#924	C₂²	1	1	yes	characteristic
68	#924	C₂²	1	1	yes	characteristic
69	#924	C₂²	1	1	yes	characteristic
70	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
72	#898	C₂²	1	1	yes	characteristic
73	#898	C₂²	1	1	yes	characteristic
74	#898	C₂²	1	1	yes	characteristic
75	#898	C₂²	1	1	yes	characteristic
76	#898	C₂²	1	1	yes	characteristic
77	#898	C₂²	1	1	yes	characteristic
78	#898	C₂²	1	1	yes	characteristic
79	#898	C₂²	1	1	yes	characteristic
80	#896	C₂²	1	1	yes	characteristic
81	#896	C₂²	1	1	yes	characteristic
82	#896	C₂²	1	1	yes	characteristic
83	#896	C₂²	1	1	yes	characteristic
84	#896	C₂²	1	1	yes	characteristic
85	#892	C₂²	1	1	yes	characteristic
86	#892	C₂²	1	1	yes	characteristic
87	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
88	#890	C₂²	1	1	yes	characteristic
89	#890	C₂²	1	1	yes	characteristic
90	#890	C₂²	1	1	yes	characteristic
91	#890	C₂²	1	1	yes	characteristic
92	#890	C₂²	1	1	yes	characteristic
93	#890	C₂²	1	1	yes	characteristic
94	#889	C₂²	1	1	yes	characteristic
95	#889	C₂²	1	1	yes	characteristic
96	#889	C₂²	1	1	yes	characteristic
97	#889	C₂²	1	1	yes	characteristic
98	#889	C₂²	1	1	yes	characteristic
99	#889	C₂²	1	1	yes	characteristic
100	#889	C₂²	1	1	yes	characteristic
101	#889	C₂²	1	1	yes	characteristic
102	#889	C₂²	1	1	yes	characteristic
103	#889	C₂²	1	1	yes	characteristic
104	#889	C₂²	1	1	yes	characteristic
105	#889	C₂²	1	1	yes	characteristic
106	#889	C₂²	1	1	yes	characteristic
107	#889	C₂²	1	1	yes	characteristic
108	#889	C₂²	1	1	yes	characteristic
109	#889	C₂²	1	1	yes	characteristic
110	#889	C₂²	1	1	yes	characteristic
111	#889	C₂²	1	1	yes	characteristic
112	#889	C₂²	1	1	yes	characteristic
113	#888	C₂²	1	1	yes	characteristic
114	#888	C₂²	1	1	yes	characteristic
115	#888	C₂²	1	1	yes	characteristic
116	#888	C₂²	1	1	yes	characteristic
117	#888	C₂²	1	1	yes	characteristic
118	#888	C₂²	1	1	yes	characteristic
119	#888	C₂²	1	1	yes	characteristic
120	#888	C₂²	1	1	yes	characteristic
121	#888	C₂²	1	1	yes	characteristic
122	#888	C₂²	1	1	yes	characteristic
123	#887	C₂²	1	1	yes	characteristic
124	#887	C₂²	1	1	yes	characteristic
125	#887	C₂²	1	1	yes	characteristic
126	#887	C₂²	1	1	yes	characteristic
127	#887	C₂²	1	1	yes	characteristic
128	#887	C₂²	1	1	yes	characteristic
129	#887	C₂²	1	1	yes	characteristic
130	#887	C₂²	1	1	yes	characteristic
131	#887	C₂²	1	1	yes	characteristic
132	#887	C₂²	1	1	yes	characteristic
133	#887	C₂²	1	1	yes	characteristic
134	#887	C₂²	1	1	yes	characteristic
135	#887	C₂²	1	1	yes	characteristic
136	#885	C₂²	1	1	yes	characteristic
137	#885	C₂²	1	1	yes	characteristic
138	#885	C₂²	1	1	yes	characteristic
139	#885	C₂²	1	1	yes	characteristic
140	#885	C₂²	1	1	yes	characteristic
141	#883	C₂²	1	1	yes	characteristic
142	#883	C₂²	1	1	yes	characteristic
143	#67⋊C₄	C₂²	1	1	yes	characteristic
144	#67⋊C₄	C₂²	1	1	yes	characteristic
145	#67⋊C₄	C₂²	1	1	yes	characteristic
146	#879	C₂²	1	1	yes	characteristic
147	#879	C₂²	1	1	yes	characteristic
148	#879	C₂²	1	1	yes	characteristic
149	#879	C₂²	1	1	yes	characteristic
150	#879	C₂²	1	1	yes	characteristic
151	#879	C₂²	1	1	yes	characteristic
152	#879	C₂²	1	1	yes	characteristic
153	#879	C₂²	1	1	yes	characteristic
154	#879	C₂²	1	1	yes	characteristic
155	#879	C₂²	1	1	yes	characteristic
156	#879	C₂²	1	1	yes	characteristic
157	#879	C₂²	1	1	yes	characteristic
158	#879	C₂²	1	1	yes	characteristic
159	#878	C₂²	1	1	yes	characteristic
160	#878	C₂²	1	1	yes	characteristic
161	#878	C₂²	1	1	yes	characteristic
162	#878	C₂²	1	1	yes	characteristic
163	#878	C₂²	1	1	yes	characteristic
164	#878	C₂²	1	1	yes	characteristic
165	#878	C₂²	1	1	yes	characteristic
166	#878	C₂²	1	1	yes	characteristic
167	#878	C₂²	1	1	yes	characteristic
168	#878	C₂²	1	1	yes	characteristic
169	#877	C₂²	1	1	yes	characteristic
170	#877	C₂²	1	1	yes	characteristic
171	#877	C₂²	1	1	yes	characteristic
172	#877	C₂²	1	1	yes	characteristic
173	#877	C₂²	1	1	yes	characteristic
174	#877	C₂²	1	1	yes	characteristic
175	#877	C₂²	1	1	yes	characteristic
176	#876	C₂²	1	1	yes	characteristic
177	#872	C₂²	1	1	yes	characteristic
178	#872	C₂²	1	1	yes	characteristic
179	#870	C₂²	1	1	yes	characteristic
180	#870	C₂²	1	1	yes	characteristic
181	C₄×Dic₆	C₂²	1	1	yes	characteristic
182	C₄×Dic₆	C₂²	1	1	yes	characteristic
183	C₄×Dic₆	C₂²	1	1	yes	characteristic
184	C₄×Dic₆	C₂²	1	1	yes	characteristic
185	C₄×Dic₆	C₂²	1	1	yes	characteristic
186	C₄×Dic₆	C₂²	1	1	yes	characteristic
187	C₄×Dic₆	C₂²	1	1	yes	characteristic
188	#563	—	3	1	no	—
189	#563	—	3	1	no	—
190	#563	—	3	1	no	—
191	#563	D₃	1	1	yes	characteristic, complemented
192	Q₈²	—	3	1	no	—
193	#557	—	3	1	no	—
194	#557	—	3	1	no	—
195	#557	—	3	1	no	—
196	#556	—	3	1	no	—
197	#556	—	3	1	no	—
198	#556	—	3	1	no	—
199	#556	—	3	1	no	—
200	#556	—	3	1	no	—
201	#554	—	3	1	no	—
202	#552	—	3	1	no	—
203	#552	—	3	1	no	—
204	#544	—	3	1	no	—
205	#544	—	3	1	no	—
206	#542	—	3	1	no	—
207	#542	—	3	1	no	—
208	#541	—	3	1	no	—
209	#541	—	3	1	no	—
210	#541	—	3	1	no	—
211	#541	—	3	1	no	—
212	#541	—	3	1	no	—
213	#541	—	3	1	no	—
214	#541	—	3	1	no	—
215	#541	—	3	1	no	—
216	#533	—	3	1	no	—
217	#533	—	3	1	no	—
218	#529	—	3	1	no	—
219	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
225	C₂×#67	C₂³	1	1	yes	characteristic
226	C₂×#67	C₂³	1	1	yes	characteristic
227	C₂²×Dic₃	C₂³	1	1	yes	characteristic
228	C₂²×Dic₃	C₂³	1	1	yes	characteristic
229	C₂²×Dic₃	C₂³	1	1	yes	characteristic
230	C₂²×Dic₃	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
234	C₂×Dic₆	C₂³	1	1	yes	characteristic
235	C₂×Dic₆	C₂³	1	1	yes	characteristic
236	C₂×Dic₆	C₂³	1	1	yes	characteristic
237	C₂×Dic₆	C₂³	1	1	yes	characteristic
238	C₂×Dic₆	C₂³	1	1	yes	characteristic
239	C₂×Dic₆	C₂³	1	1	yes	characteristic
240	C₂×Dic₆	C₂³	1	1	yes	characteristic
241	C₂×Dic₆	C₂³	1	1	yes	characteristic
242	C₂×Dic₆	C₂³	1	1	yes	characteristic
243	C₂×Dic₆	C₂³	1	1	yes	characteristic
244	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₃×C₄²	C₂³	1	1	yes	characteristic
271	C₃×C₄²	C₂³	1	1	yes	characteristic
272	C₃×C₄²	C₂³	1	1	yes	characteristic
273	#217	C₂³	1	1	yes	characteristic
274	#217	C₂³	1	1	yes	characteristic
275	#217	C₂³	1	1	yes	characteristic
276	#217	C₂³	1	1	yes	characteristic
277	#217	C₂³	1	1	yes	characteristic
278	#217	C₂³	1	1	yes	characteristic
279	#217	C₂³	1	1	yes	characteristic
280	#217	C₂³	1	1	yes	characteristic
281	#217	C₂³	1	1	yes	characteristic
282	#217	C₂³	1	1	yes	characteristic
283	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
309	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
310	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
313	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
339	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
341	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
342	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
343	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
344	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
345	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
346	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
347	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
348	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
349	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
350	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
351	C₄×Dic₃	C₂³	1	1	yes	characteristic
352	C₄×Dic₃	C₂³	1	1	yes	characteristic
353	C₄×Dic₃	C₂³	1	1	yes	characteristic
354	C₄×Dic₃	C₂³	1	1	yes	characteristic
355	C₄×Dic₃	C₂³	1	1	yes	characteristic
356	C₄×Dic₃	C₂³	1	1	yes	characteristic
357	C₄×Dic₃	C₂³	1	1	yes	characteristic
358	C₄×Dic₃	C₂³	1	1	yes	characteristic
359	C₄×Dic₃	C₂³	1	1	yes	characteristic
360	C₄×Dic₃	C₂³	1	1	yes	characteristic
361	C₄×Dic₃	C₂³	1	1	yes	characteristic
362	C₄×Dic₃	C₂³	1	1	yes	characteristic
363	C₄×Dic₃	C₂³	1	1	yes	characteristic
364	C₄×Dic₃	C₂³	1	1	yes	characteristic
365	C₄×Dic₃	C₂³	1	1	yes	characteristic
366	C₄×Dic₃	C₂³	1	1	yes	characteristic
367	C₄×Dic₃	C₂³	1	1	yes	characteristic
368	C₄×Dic₃	C₂³	1	1	yes	characteristic
369	C₄×Dic₃	C₂³	1	1	yes	characteristic
370	C₄×Dic₃	C₂³	1	1	yes	characteristic
371	C₄×Dic₃	C₂³	1	1	yes	characteristic
372	C₄×Dic₃	C₂³	1	1	yes	characteristic
373	C₄×Dic₃	C₂³	1	1	yes	characteristic
374	C₄⋊Q₈	—	3	1	no	—
375	C₄⋊Q₈	—	3	1	no	—
376	C₄⋊Q₈	—	3	1	no	—
377	C₄⋊Q₈	—	3	1	no	—
378	C₄⋊Q₈	—	3	1	no	—
379	C₄⋊Q₈	—	3	1	no	—
380	C₄⋊Q₈	—	3	1	no	—
381	C₄⋊Q₈	—	3	1	no	—
382	C₄⋊Q₈	—	3	1	no	—
383	C₄⋊Q₈	—	3	1	no	—
384	C₄⋊Q₈	—	3	1	no	—
385	C₄⋊Q₈	—	3	1	no	—
386	C₄⋊Q₈	—	3	1	no	—
387	C₄⋊Q₈	—	3	1	no	—
388	C₄⋊Q₈	—	3	1	no	—
389	C₄⋊Q₈	—	3	1	no	—
390	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
391	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
392	#126	—	3	1	no	—
393	#126	—	3	1	no	—
394	#126	—	3	1	no	—
395	#126	—	3	1	no	—
396	#126	—	3	1	no	—
397	#126	—	3	1	no	—
398	#126	—	3	1	no	—
399	#126	—	3	1	no	—
400	#126	—	3	1	no	—
401	#126	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#126	—	3	1	no	—
405	#126	—	3	1	no	—
406	#126	—	3	1	no	—
407	#126	—	3	1	no	—
408	#126	—	3	1	no	—
409	#126	—	3	1	no	—
410	#126	—	3	1	no	—
411	#126	—	3	1	no	—
412	#126	—	3	1	no	—
413	#126	—	3	1	no	—
414	#126	C₂×D₃	1	1	yes	characteristic
415	#126	C₂×D₃	1	1	yes	characteristic
416	#126	C₂×D₃	1	1	yes	characteristic
417	#126	C₂×D₃	1	1	yes	characteristic
418	#125	—	3	1	no	—
419	#125	—	3	1	no	—
420	#125	—	3	1	no	—
421	#125	—	3	1	no	—
422	#125	—	3	1	no	—
423	#125	—	3	1	no	—
424	#125	—	3	1	no	—
425	#125	—	3	1	no	—
426	#125	—	3	1	no	—
427	#125	—	3	1	no	—
428	#125	—	3	1	no	—
429	#125	—	3	1	no	—
430	#125	—	3	1	no	—
431	#125	—	3	1	no	—
432	#125	—	3	1	no	—
433	#125	—	3	1	no	—
434	#125	—	3	1	no	—
435	#125	—	3	1	no	—
436	#125	—	3	1	no	—
437	#125	—	3	1	no	—
438	#125	—	3	1	no	—
439	#125	—	3	1	no	—
440	#125	—	3	1	no	—
441	#125	—	3	1	no	—
442	#125	—	3	1	no	—
443	#125	—	3	1	no	—
444	#125	—	3	1	no	—
445	#125	C₂×D₃	1	1	yes	characteristic
446	#125	C₂×D₃	1	1	yes	characteristic
447	#124	—	3	1	no	—
448	#124	—	3	1	no	—
449	#124	—	3	1	no	—
450	#124	—	3	1	no	—
451	#124	—	3	1	no	—
452	#124	—	3	1	no	—
453	#124	C₂×D₃	1	1	yes	characteristic
454	#123	—	3	1	no	—
455	#123	—	3	1	no	—
456	#123	—	3	1	no	—
457	#123	—	3	1	no	—
458	#123	C₂×D₃	1	1	yes	characteristic
459	#123	C₂×D₃	1	1	yes	characteristic
460	C₂²⋊Q₈	—	3	1	no	—
461	C₂²⋊Q₈	—	3	1	no	—
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	C₂²⋊Q₈	—	3	1	no	—
465	C₂²⋊Q₈	—	3	1	no	—
466	C₂²⋊Q₈	—	3	1	no	—
467	C₂²⋊Q₈	—	3	1	no	—
468	C₂²⋊Q₈	—	3	1	no	—
469	C₂²⋊Q₈	—	3	1	no	—
470	C₂²⋊Q₈	—	3	1	no	—
471	C₂²⋊Q₈	—	3	1	no	—
472	C₂²⋊Q₈	—	3	1	no	—
473	C₂²⋊Q₈	—	3	1	no	—
474	C₂²⋊Q₈	—	3	1	no	—
475	C₂²⋊Q₈	—	3	1	no	—
476	C₂²⋊Q₈	—	3	1	no	—
477	C₂²⋊Q₈	—	3	1	no	—
478	C₂²⋊Q₈	—	3	1	no	—
479	C₂²⋊Q₈	—	3	1	no	—
480	C₂²⋊Q₈	—	3	1	no	—
481	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
482	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
483	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
484	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
485	#121	—	3	1	no	—
486	C₄×Q₈	—	3	1	no	—
487	C₄×Q₈	—	3	1	no	—
488	C₄×Q₈	—	3	1	no	—
489	C₄×Q₈	—	3	1	no	—
490	C₄×Q₈	—	3	1	no	—
491	C₄×Q₈	—	3	1	no	—
492	C₄×Q₈	—	3	1	no	—
493	C₄×Q₈	—	3	1	no	—
494	C₄×Q₈	—	3	1	no	—
495	C₄×Q₈	—	3	1	no	—
496	C₄×Q₈	—	3	1	no	—
497	C₄×Q₈	—	3	1	no	—
498	C₄×Q₈	—	3	1	no	—
499	C₄×Q₈	—	3	1	no	—
500	C₄×Q₈	—	3	1	no	—
501	C₄×Q₈	—	3	1	no	—
502	C₄×Q₈	—	3	1	no	—
503	C₄×Q₈	—	3	1	no	—
504	C₄×Q₈	—	3	1	no	—
505	C₄×Q₈	—	3	1	no	—
506	C₄×Q₈	—	3	1	no	—
507	C₄×Q₈	—	3	1	no	—
508	C₄×Q₈	—	3	1	no	—
509	C₄×D₄	—	3	1	no	—
510	C₄×D₄	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₄×D₄	—	3	1	no	—
513	C₄×D₄	—	3	1	no	—
514	#117	—	3	1	no	—
515	#117	—	3	1	no	—
516	#117	—	3	1	no	—
517	#117	—	3	1	no	—
518	#117	—	3	1	no	—
519	#117	—	3	1	no	—
520	#117	—	3	1	no	—
521	#117	—	3	1	no	—
522	#117	—	3	1	no	—
523	#117	—	3	1	no	—
524	#117	—	3	1	no	—
525	#117	—	3	1	no	—
526	C₂×C₄⋊C₄	—	3	1	no	—
527	C₂×C₄⋊C₄	—	3	1	no	—
528	C₂×C₄²	—	3	1	no	—
529	C₂³×C₃	C₂⁴	1	1	yes	characteristic
530	C₂³×C₃	C₂⁴	1	1	yes	characteristic
531	C₂²×D₃	C₂⁴	1	1	yes	characteristic
532	C₃×Q₈	—	4	1	no	—
533	C₃×Q₈	—	4	1	no	—
534	C₃×Q₈	—	4	1	no	—
535	C₃×D₄	—	4	1	no	—
536	C₂×C₃×C₄	—	4	1	no	—
537	C₂×C₃×C₄	—	4	1	no	—
538	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
544	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
545	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
546	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
547	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
548	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
551	#67	—	2	2	no	—
552	#67	—	4	1	no	—
553	C₂×Dic₃	—	2	2	no	—
554	C₂×Dic₃	—	2	2	no	—
555	C₂×Dic₃	—	2	2	no	—
556	C₂×Dic₃	—	4	1	no	—
557	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
558	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
559	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
560	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
561	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
562	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
563	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
564	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
565	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
566	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
567	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
568	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
569	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
570	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
571	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
572	C₄×D₃	—	2	2	no	—
573	C₄×D₃	—	4	1	no	—
574	C₄×D₃	—	4	1	no	—
575	Dic₆	—	2	2	no	—
576	Dic₆	—	2	2	no	—
577	Dic₆	—	2	2	no	—
578	Dic₆	—	2	2	no	—
579	Dic₆	—	2	2	no	—
580	Dic₆	—	4	1	no	—
581	Dic₆	—	4	1	no	—
582	Dic₆	—	4	1	no	—
583	Dic₆	—	4	1	no	—
584	Dic₆	—	4	1	no	—
585	C₂×Q₈	—	3	1	no	—
586	C₂×Q₈	—	3	1	no	—
587	C₂×Q₈	—	3	1	no	—
588	C₂×Q₈	—	3	1	no	—
589	C₂×Q₈	—	3	1	no	—
590	C₂×Q₈	—	3	1	no	—
591	C₂×Q₈	—	3	1	no	—
592	C₂×Q₈	—	3	1	no	—
593	C₂×Q₈	—	3	1	no	—
594	C₂×Q₈	—	3	1	no	—
595	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
596	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
597	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
598	C₂×D₄	—	3	1	no	—
599	C₂×D₄	—	3	1	no	—
600	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
601	C₂²×C₄	—	3	1	no	—
602	C₂²×C₄	—	3	1	no	—
603	C₂²×C₄	—	3	1	no	—
604	C₂²×C₄	—	3	1	no	—
605	C₂²×C₄	—	3	1	no	—
606	C₂²×C₄	—	3	1	no	—
607	C₂²×C₄	—	3	1	no	—
608	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
609	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
610	C₄⋊C₄	—	3	1	no	—
611	C₄⋊C₄	—	3	1	no	—
612	C₄⋊C₄	—	3	1	no	—
613	C₄⋊C₄	—	3	1	no	—
614	C₄⋊C₄	—	3	1	no	—
615	C₄⋊C₄	—	3	1	no	—
616	C₄⋊C₄	—	3	1	no	—
617	C₄⋊C₄	—	3	1	no	—
618	C₄⋊C₄	—	3	1	no	—
619	C₄⋊C₄	—	3	1	no	—
620	C₄⋊C₄	—	3	1	no	—
621	C₄⋊C₄	—	3	1	no	—
622	C₄⋊C₄	—	3	1	no	—
623	C₄⋊C₄	—	3	1	no	—
624	C₄⋊C₄	—	3	1	no	—
625	C₄⋊C₄	—	3	1	no	—
626	C₄⋊C₄	—	3	1	no	—
627	C₄⋊C₄	—	3	1	no	—
628	C₄⋊C₄	—	3	1	no	—
629	C₄⋊C₄	—	3	1	no	—
630	C₄⋊C₄	—	3	1	no	—
631	C₄⋊C₄	—	3	1	no	—
632	C₄⋊C₄	—	3	1	no	—
633	C₄⋊C₄	—	3	1	no	—
634	C₄⋊C₄	—	3	1	no	—
635	C₄⋊C₄	—	3	1	no	—
636	C₄⋊C₄	—	3	1	no	—
637	C₄⋊C₄	—	3	1	no	—
638	C₄⋊C₄	—	3	1	no	—
639	C₄⋊C₄	—	3	1	no	—
640	C₄⋊C₄	—	3	1	no	—
641	C₄⋊C₄	—	3	1	no	—
642	C₄⋊C₄	—	3	1	no	—
643	C₄⋊C₄	—	3	1	no	—
644	C₄⋊C₄	—	3	1	no	—
645	C₄⋊C₄	—	3	1	no	—
646	C₄⋊C₄	—	3	1	no	—
647	C₄⋊C₄	—	3	1	no	—
648	C₄⋊C₄	—	3	1	no	—
649	C₄⋊C₄	—	3	1	no	—
650	C₄⋊C₄	—	3	1	no	—
651	C₄⋊C₄	—	3	1	no	—
652	C₄⋊C₄	—	3	1	no	—
653	C₄⋊C₄	—	3	1	no	—
654	C₄⋊C₄	—	3	1	no	—
655	C₄⋊C₄	—	3	1	no	—
656	C₄⋊C₄	—	3	1	no	—
657	C₄⋊C₄	—	3	1	no	—
658	C₄⋊C₄	—	3	1	no	—
659	C₄⋊C₄	—	3	1	no	—
660	C₄⋊C₄	—	3	1	no	—
661	C₄⋊C₄	—	3	1	no	—
662	C₄⋊C₄	—	3	1	no	—
663	C₄⋊C₄	—	3	1	no	—
664	C₄⋊C₄	—	3	1	no	—
665	C₄⋊C₄	—	3	1	no	—
666	C₄⋊C₄	—	3	1	no	—
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
669	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
670	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
672	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
673	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
674	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
675	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
676	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
677	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
678	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
679	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
680	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
681	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
684	C₂²⋊C₄	—	3	1	no	—
685	C₂²⋊C₄	—	3	1	no	—
686	C₂²⋊C₄	—	3	1	no	—
687	C₂²⋊C₄	—	3	1	no	—
688	C₂²⋊C₄	—	3	1	no	—
689	C₂²⋊C₄	—	3	1	no	—
690	C₂²⋊C₄	—	3	1	no	—
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	3	1	no	—
694	C₂²⋊C₄	—	3	1	no	—
695	C₂²⋊C₄	—	3	1	no	—
696	C₂²⋊C₄	—	3	1	no	—
697	C₂²⋊C₄	—	3	1	no	—
698	C₂²⋊C₄	—	3	1	no	—
699	C₂²⋊C₄	—	3	1	no	—
700	C₂²⋊C₄	—	3	1	no	—
701	C₂²⋊C₄	—	3	1	no	—
702	C₂²⋊C₄	—	3	1	no	—
703	C₂²⋊C₄	—	3	1	no	—
704	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
705	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
706	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
707	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
708	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
709	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
710	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
711	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
712	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
713	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
714	C₄²	—	3	1	no	—
715	C₄²	—	3	1	no	—
716	C₄²	—	3	1	no	—
717	C₄²	—	3	1	no	—
718	C₄²	—	3	1	no	—
719	C₄²	—	3	1	no	—
720	C₄²	—	3	1	no	—
721	C₄²	—	3	1	no	—
722	C₄²	—	3	1	no	—
723	C₄²	—	3	1	no	—
724	C₄²	—	3	1	no	—
725	C₄²	—	3	1	no	—
726	C₄²	—	3	1	no	—
727	C₄²	—	3	1	no	—
728	C₄²	—	3	1	no	—
729	C₄²	—	3	1	no	—
730	C₄²	—	3	1	no	—
731	C₄²	—	3	1	no	—
732	C₄²	—	3	1	no	—
733	C₄²	—	3	1	no	—
734	C₄²	—	3	1	no	—
735	C₄²	—	3	1	no	—
736	C₄²	—	3	1	no	—
737	C₄²	C₂²×D₃	1	1	yes	characteristic
738	C₄²	C₂²×D₃	1	1	yes	characteristic
739	C₄²	C₂²×D₃	1	1	yes	characteristic
740	C₂²×C₃	—	2	1	no	—
741	C₂²×C₃	—	2	1	no	—
742	C₂²×C₃	—	2	1	no	—
743	C₂²×C₃	—	2	1	no	—
744	C₂²×C₃	—	2	1	no	—
745	C₂²×C₃	—	2	1	no	—
746	C₂²×C₃	C₂⁵	1	1	yes	characteristic
747	C₂×D₃	—	2	1	no	—
748	C₂×D₃	—	2	1	no	—
749	C₂×D₃	—	2	1	no	—
750	C₃×C₄	—	2	1	no	—
751	C₃×C₄	—	2	1	no	—
752	C₃×C₄	—	2	1	no	—
753	C₃×C₄	—	2	1	no	—
754	C₃×C₄	—	2	1	no	—
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	1	no	—
759	C₃×C₄	—	2	1	no	—
760	C₃×C₄	—	2	1	no	—
761	C₃×C₄	—	2	1	no	—
762	C₃×C₄	—	2	1	no	—
763	Dic₃	—	2	1	no	—
764	Dic₃	—	2	1	no	—
765	Dic₃	—	2	1	no	—
766	Dic₃	—	2	1	no	—
767	Dic₃	—	2	1	no	—
768	Dic₃	—	2	1	no	—
769	Dic₃	—	2	1	no	—
770	Dic₃	—	2	1	no	—
771	Dic₃	—	2	1	no	—
772	Dic₃	—	2	1	no	—
773	Dic₃	—	2	1	no	—
774	Dic₃	—	2	1	no	—
775	Dic₃	—	2	1	no	—
776	Dic₃	2₋¹⁺⁴	1	2	yes	—
777	Dic₃	2₋¹⁺⁴	1	2	yes	—
778	C₂³	—	3	1	no	—
779	C₂³	C₂³×D₃	1	1	yes	characteristic
780	C₂³	C₂³×D₃	1	1	yes	characteristic
781	Q₈	—	4	1	no	—
782	Q₈	—	4	1	no	—
783	Q₈	—	4	1	no	—
784	Q₈	—	6	2	no	—
785	Q₈	—	6	2	no	—
786	Q₈	—	6	2	no	—
787	Q₈	—	6	2	no	—
788	Q₈	—	6	2	no	—
789	Q₈	—	12	1	no	—
790	Q₈	—	12	1	no	—
791	Q₈	—	12	1	no	—
792	Q₈	—	12	1	no	—
793	Q₈	—	12	1	no	—
794	D₄	—	4	1	no	—
795	D₄	—	6	2	no	—
796	D₄	—	12	1	no	—
797	C₂×C₄	—	3	1	no	—
798	C₂×C₄	—	3	1	no	—
799	C₂×C₄	—	3	1	no	—
800	C₂×C₄	—	3	1	no	—
801	C₂×C₄	—	3	1	no	—
802	C₂×C₄	—	3	1	no	—
803	C₂×C₄	—	3	1	no	—
804	C₂×C₄	—	3	1	no	—
805	C₂×C₄	—	3	1	no	—
806	C₂×C₄	—	3	1	no	—
807	C₂×C₄	—	3	1	no	—
808	C₂×C₄	—	3	1	no	—
809	C₂×C₄	—	3	1	no	—
810	C₂×C₄	—	3	1	no	—
811	C₂×C₄	—	3	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	6	2	no	—
815	C₂×C₄	—	6	2	no	—
816	C₂×C₄	—	6	2	no	—
817	C₂×C₄	—	6	2	no	—
818	C₂×C₄	—	12	1	no	—
819	C₂×C₄	—	12	1	no	—
820	C₂×C₄	—	12	1	no	—
821	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
822	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
823	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
824	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
825	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
826	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
827	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
828	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
829	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
830	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
831	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
832	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
833	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
834	C₂×C₃	—	4	1	no	—
835	C₂×C₃	—	4	1	no	—
836	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
837	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
838	C₂×C₃	#585	1	1	yes	characteristic
839	D₃	—	4	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	6	1	no	—
847	C₂²	—	6	1	no	—
848	C₂²	—	6	1	no	—
849	C₂²	C₂⁴×D₃	1	1	yes	characteristic
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	3	2	no	—
864	C₄	—	3	2	no	—
865	C₄	—	6	1	no	—
866	C₄	—	6	1	no	—
867	C₄	—	6	1	no	—
868	C₄	—	6	1	no	—
869	C₄	—	6	1	no	—
870	C₄	—	6	1	no	—
871	C₄	—	6	1	no	—
872	C₄	—	6	1	no	—
873	C₄	—	6	1	no	—
874	C₄	—	6	1	no	—
875	C₄	—	6	1	no	—
876	C₄	—	6	1	no	—
877	C₄	—	6	1	no	—
878	C₃	#3555	1	1	yes	characteristic, complemented, Sylow
879	C₂	—	4	1	no	—
880	C₂	—	4	1	no	—
881	C₂	—	12	1	no	—
882	C₂	#5966	1	1	yes	characteristic
883	C₂	D₃×2₋¹⁺⁴	1	1	yes	characteristic
884	C₂	D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#563	C₂
prime radical	#939	C₂²
hypercenter	#563	D₃
hypocenter	C₃	#3555
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. C₃×#563	C₂	semidirect
2. #5731	C₂	semidirect
3. #5729	C₂	semidirect
4. #5722	C₂	semidirect
5. #5721	C₂	semidirect
6. #5708	C₂	semidirect
7. #5702	C₂	semidirect
8. #5702	C₂	semidirect
9. #5702	C₂	semidirect
10. #5701	C₂	semidirect
11. #5701	C₂	semidirect
12. #5701	C₂	semidirect
13. #5701	C₂	semidirect
14. #5696	C₂	semidirect
15. #5696	C₂	semidirect
16. #5685	C₂	semidirect
17. #5685	C₂	semidirect
18. #5671	C₂	semidirect
21. #5651	C₂	semidirect
22. #5650	C₂	semidirect
24. #5646	C₂	semidirect
25. #5646	C₂	semidirect
26. #5641	C₂	semidirect
27. #5636	C₂	semidirect
28. #5625	C₂	semidirect
29. #5623	C₂	semidirect
30. #5622	C₂	semidirect
31. #5622	C₂	semidirect
191. #563	D₃	semidirect
878. C₃	#3555	semidirect

Maximal subgroups

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

subgroup	index
C₃×#563	2
#5731	2
#5729	2
#5722	2
#5721	2
#5708	2
#5702	2
#5701	2
#5696	2
#5685	2
#5671	2
#5669	2
#5662	2
#5651	2
#5650	2
#5649	2
#5646	2
#5641	2
#5636	2
#5625	2
#5623	2
#5622	2
#3555	3