Subgroups — #86540

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#5735	C₂	1	1	yes	maximal, characteristic, complemented
3	#5727	C₂	1	1	yes	maximal, characteristic, complemented
4	#5710	C₂	1	1	yes	maximal, characteristic, complemented
5	#5706	C₂	1	1	yes	maximal, characteristic, complemented
6	#5705	C₂	1	1	yes	maximal, characteristic, complemented
7	#5702	C₂	1	1	yes	maximal, characteristic, complemented
8	#5679	C₂	1	1	yes	maximal, characteristic, complemented
9	#5678	C₂	1	1	yes	maximal, characteristic, complemented
10	#5677	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	#5669	C₂	1	1	yes	maximal, characteristic, complemented
13	#5669	C₂	1	1	yes	maximal, characteristic, complemented
14	#5657	C₂	1	1	yes	maximal, characteristic, complemented
15	#5654	C₂	1	1	yes	maximal, characteristic, complemented
16	#5651	C₂	1	1	yes	maximal, characteristic, complemented
17	#5648	C₂	1	1	yes	maximal, characteristic, complemented
18	#5647	C₂	1	1	yes	maximal, characteristic, complemented
19	#5640	C₂	1	1	yes	maximal, characteristic, complemented
20	#5634	C₂	1	1	yes	maximal, characteristic, complemented
21	#5634	C₂	1	1	yes	maximal, characteristic, complemented
22	#5632	C₂	1	1	yes	maximal, characteristic, complemented
23	#5628	C₂	1	1	yes	maximal, characteristic, complemented
24	#5621	C₂	1	1	yes	maximal, characteristic, complemented
25	#5610	C₂	1	1	yes	maximal, characteristic, complemented
26	#5582	C₂	1	1	yes	maximal, characteristic, complemented
27	#5578	C₂	1	1	yes	maximal, characteristic, complemented
28	#5556	C₂	1	1	yes	maximal, characteristic, complemented
29	#5552	C₂	1	1	yes	maximal, characteristic, complemented
30	#5533	C₂	1	1	yes	maximal, characteristic, complemented
31	#5527	C₂	1	1	yes	maximal, characteristic, complemented
32	#3561	—	3	1	no	maximal, Sylow
33	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
34	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×#237	C₂²	1	1	yes	characteristic
36	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
37	C₂×#235	C₂²	1	1	yes	characteristic
38	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×#126	C₂²	1	1	yes	characteristic, complemented
41	C₃×#126	C₂²	1	1	yes	characteristic, complemented
42	C₃×#124	C₂²	1	1	yes	characteristic
43	C₃×#124	C₂²	1	1	yes	characteristic, complemented
44	C₃×#124	C₂²	1	1	yes	characteristic, complemented
45	C₃×#123	C₂²	1	1	yes	characteristic
46	C₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₃×#121	C₂²	1	1	yes	characteristic
51	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₃×#117	C₂²	1	1	yes	characteristic, complemented
54	#947	C₂²	1	1	yes	characteristic
55	#947	C₂²	1	1	yes	characteristic, complemented
56	#946	C₂²	1	1	yes	characteristic
57	#946	C₂²	1	1	yes	characteristic
58	#946	C₂²	1	1	yes	characteristic, complemented
59	#946	C₂²	1	1	yes	characteristic, complemented
60	#946	C₂²	1	1	yes	characteristic, complemented
61	#946	C₂²	1	1	yes	characteristic, complemented
62	#944	C₂²	1	1	yes	characteristic, complemented
63	#944	C₂²	1	1	yes	characteristic, complemented
64	#939	C₂²	1	1	yes	characteristic
65	#939	C₂²	1	1	yes	characteristic
66	#939	C₂²	1	1	yes	characteristic, complemented
67	#938	C₂²	1	1	yes	characteristic, complemented
68	#937	C₂²	1	1	yes	characteristic
69	#937	C₂²	1	1	yes	characteristic
70	#936	C₂²	1	1	yes	characteristic
71	#935	C₂²	1	1	yes	characteristic
72	#935	C₂²	1	1	yes	characteristic, complemented
73	#935	C₂²	1	1	yes	characteristic, complemented
74	#930	C₂²	1	1	yes	characteristic, complemented
75	#929	C₂²	1	1	yes	characteristic, complemented
76	#929	C₂²	1	1	yes	characteristic, complemented
77	C₄×#67	C₂²	1	1	yes	characteristic
78	C₄×#67	C₂²	1	1	yes	characteristic
79	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
81	#924	C₂²	1	1	yes	characteristic, complemented
82	#924	C₂²	1	1	yes	characteristic, complemented
83	#924	C₂²	1	1	yes	characteristic, complemented
84	#898	C₂²	1	1	yes	characteristic, complemented
85	#898	C₂²	1	1	yes	characteristic, complemented
86	#898	C₂²	1	1	yes	characteristic, complemented
87	#897	C₂²	1	1	yes	characteristic
88	#897	C₂²	1	1	yes	characteristic
89	#897	C₂²	1	1	yes	characteristic, complemented
90	#897	C₂²	1	1	yes	characteristic, complemented
91	#896	C₂²	1	1	yes	characteristic
92	#896	C₂²	1	1	yes	characteristic
93	#896	C₂²	1	1	yes	characteristic
94	#896	C₂²	1	1	yes	characteristic
95	#896	C₂²	1	1	yes	characteristic
96	#896	C₂²	1	1	yes	characteristic, complemented
97	#896	C₂²	1	1	yes	characteristic, complemented
98	#896	C₂²	1	1	yes	characteristic, complemented
99	#896	C₂²	1	1	yes	characteristic, complemented
100	#896	C₂²	1	1	yes	characteristic, complemented
101	#896	C₂²	1	1	yes	characteristic, complemented
102	#896	C₂²	1	1	yes	characteristic, complemented
103	#895	C₂²	1	1	yes	characteristic
104	#894	C₂²	1	1	yes	characteristic
105	#894	C₂²	1	1	yes	characteristic
106	#894	C₂²	1	1	yes	characteristic
107	#894	C₂²	1	1	yes	characteristic, complemented
108	#894	C₂²	1	1	yes	characteristic, complemented
109	#894	C₂²	1	1	yes	characteristic, complemented
110	#893	C₂²	1	1	yes	characteristic
111	#893	C₂²	1	1	yes	characteristic
112	#892	C₂²	1	1	yes	characteristic, complemented
113	#892	C₂²	1	1	yes	characteristic, complemented
114	#889	C₂²	1	1	yes	characteristic, complemented
115	#889	C₂²	1	1	yes	characteristic, complemented
116	#889	C₂²	1	1	yes	characteristic, complemented
117	#888	C₂²	1	1	yes	characteristic, complemented
118	#888	C₂²	1	1	yes	characteristic, complemented
119	#888	C₂²	1	1	yes	characteristic, complemented
120	#888	C₂²	1	1	yes	characteristic, complemented
121	#888	C₂²	1	1	yes	characteristic, complemented
122	#887	C₂²	1	1	yes	characteristic, complemented
123	#887	C₂²	1	1	yes	characteristic, complemented
124	#886	C₂²	1	1	yes	characteristic, complemented
125	#885	C₂²	1	1	yes	characteristic
126	#885	C₂²	1	1	yes	characteristic
127	#885	C₂²	1	1	yes	characteristic
128	#885	C₂²	1	1	yes	characteristic
129	#885	C₂²	1	1	yes	characteristic
130	#885	C₂²	1	1	yes	characteristic
131	#885	C₂²	1	1	yes	characteristic, complemented
132	#885	C₂²	1	1	yes	characteristic, complemented
133	#885	C₂²	1	1	yes	characteristic, complemented
134	#885	C₂²	1	1	yes	characteristic, complemented
135	#885	C₂²	1	1	yes	characteristic, complemented
136	#884	C₂²	1	1	yes	characteristic
137	#884	C₂²	1	1	yes	characteristic
138	#884	C₂²	1	1	yes	characteristic
139	#884	C₂²	1	1	yes	characteristic, complemented
140	#883	C₂²	1	1	yes	characteristic
141	#883	C₂²	1	1	yes	characteristic, complemented
142	#883	C₂²	1	1	yes	characteristic, complemented
143	#883	C₂²	1	1	yes	characteristic, complemented
144	#882	C₂²	1	1	yes	characteristic
145	#882	C₂²	1	1	yes	characteristic
146	#67⋊C₄	C₂²	1	1	yes	characteristic
147	#67⋊C₄	C₂²	1	1	yes	characteristic
148	#67⋊C₄	C₂²	1	1	yes	characteristic
149	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
153	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
155	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
156	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
157	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
158	#879	C₂²	1	1	yes	characteristic, complemented
159	#879	C₂²	1	1	yes	characteristic, complemented
160	#879	C₂²	1	1	yes	characteristic, complemented
161	#879	C₂²	1	1	yes	characteristic, complemented
162	#879	C₂²	1	1	yes	characteristic, complemented
163	#878	C₂²	1	1	yes	characteristic, complemented
164	#878	C₂²	1	1	yes	characteristic, complemented
165	#878	C₂²	1	1	yes	characteristic, complemented
166	#878	C₂²	1	1	yes	characteristic, complemented
167	#878	C₂²	1	1	yes	characteristic, complemented
168	#878	C₂²	1	1	yes	characteristic, complemented
169	#878	C₂²	1	1	yes	characteristic, complemented
170	#877	C₂²	1	1	yes	characteristic, complemented
171	#877	C₂²	1	1	yes	characteristic, complemented
172	#876	C₂²	1	1	yes	characteristic, complemented
173	#876	C₂²	1	1	yes	characteristic, complemented
174	#876	C₂²	1	1	yes	characteristic, complemented
175	#876	C₂²	1	1	yes	characteristic, complemented
176	#875	C₂²	1	1	yes	characteristic
177	#875	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₁₂	C₂²	1	1	yes	characteristic
179	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
180	#872	C₂²	1	1	yes	characteristic
181	#872	C₂²	1	1	yes	characteristic
182	#872	C₂²	1	1	yes	characteristic, complemented
183	C₄²×D₃	C₂²	1	1	yes	characteristic
184	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#563	—	3	1	no	—
189	#563	—	3	1	no	—
190	#562	—	3	1	no	—
191	#562	—	3	1	no	—
192	#556	—	3	1	no	—
193	#556	—	3	1	no	—
194	#551	—	3	1	no	—
195	#551	—	3	1	no	—
196	#551	—	3	1	no	—
197	#551	—	3	1	no	—
198	D₄×Q₈	—	3	1	no	—
199	D₄×Q₈	—	3	1	no	—
200	#548	—	3	1	no	—
201	#548	—	3	1	no	—
202	#546	—	3	1	no	—
203	#546	—	3	1	no	—
204	#543	—	3	1	no	—
205	#543	—	3	1	no	—
206	#542	—	3	1	no	—
207	#542	—	3	1	no	—
208	#542	—	3	1	no	—
209	#542	—	3	1	no	—
210	#542	—	3	1	no	—
211	#542	D₃	1	1	yes	characteristic, complemented
212	#538	—	3	1	no	—
213	#538	—	3	1	no	—
214	#536	—	3	1	no	—
215	#536	—	3	1	no	—
216	#533	—	3	1	no	—
217	#529	—	3	1	no	—
218	C₂×#124	—	3	1	no	—
219	C₂³×D₃	C₂³	1	1	yes	characteristic
220	C₂³×D₃	C₂³	1	1	yes	characteristic
221	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
230	C₂×#67	C₂³	1	1	yes	characteristic
231	C₂×#67	C₂³	1	1	yes	characteristic
232	C₂×#67	C₂³	1	1	yes	characteristic
233	C₂×#67	C₂³	1	1	yes	characteristic
234	C₂×#67	C₂³	1	1	yes	characteristic
235	C₂×#67	C₂³	1	1	yes	characteristic
236	C₂×#67	C₂³	1	1	yes	characteristic
237	C₂×#67	C₂³	1	1	yes	characteristic
238	C₂²×Dic₃	C₂³	1	1	yes	characteristic
239	C₂²×Dic₃	C₂³	1	1	yes	characteristic
240	C₂²×Dic₃	C₂³	1	1	yes	characteristic
241	C₂²×Dic₃	C₂³	1	1	yes	characteristic
242	D₃×Q₈	—	4	2	no	—
243	D₃×Q₈	—	4	2	no	—
244	#237	—	4	2	no	—
245	D₃×D₄	—	4	2	no	—
246	#235	—	4	2	no	—
247	C₂×D₁₂	C₂³	1	1	yes	characteristic
248	C₂×D₁₂	C₂³	1	1	yes	characteristic
249	C₂×D₁₂	C₂³	1	1	yes	characteristic
250	C₂×D₁₂	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
263	C₂×Dic₆	—	4	2	no	—
264	C₂×Dic₆	C₂³	1	1	yes	characteristic
265	C₂×Dic₆	C₂³	1	1	yes	characteristic
266	C₂×Dic₆	C₂³	1	1	yes	characteristic
267	C₂×Dic₆	C₂³	1	1	yes	characteristic
268	C₂×Dic₆	C₂³	1	1	yes	characteristic
269	C₂×Dic₆	C₂³	1	1	yes	characteristic
270	C₂×Dic₆	C₂³	1	1	yes	characteristic
271	C₂×Dic₆	C₂³	1	1	yes	characteristic
272	C₂×Dic₆	C₂³	1	1	yes	characteristic
273	C₂×Dic₆	C₂³	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₃×C₄²	C₂³	1	1	yes	characteristic
297	C₃×C₄²	C₂³	1	1	yes	characteristic
298	C₃×C₄²	C₂³	1	1	yes	characteristic
299	C₃×C₄²	C₂³	1	1	yes	characteristic
300	#217	C₂³	1	1	yes	characteristic
301	#217	C₂³	1	1	yes	characteristic
302	#217	C₂³	1	1	yes	characteristic
303	#217	C₂³	1	1	yes	characteristic
304	#217	C₂³	1	1	yes	characteristic
305	#217	C₂³	1	1	yes	characteristic
306	#217	C₂³	1	1	yes	characteristic
307	#217	C₂³	1	1	yes	characteristic
308	#217	C₂³	1	1	yes	characteristic
309	#217	C₂³	1	1	yes	characteristic
310	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
313	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
314	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
315	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
316	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
317	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
318	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
319	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
320	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
321	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
322	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
323	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
324	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
325	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
326	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
327	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
328	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
329	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
330	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
331	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
332	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
333	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
334	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
335	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
339	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
340	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
341	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
342	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
343	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
344	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
345	C₄⋊Dic₃	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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
352	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
353	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
354	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
355	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
369	Dic₃⋊C₄	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×Dic₃	C₂³	1	1	yes	characteristic
375	C₄×Dic₃	C₂³	1	1	yes	characteristic
376	C₄×Dic₃	C₂³	1	1	yes	characteristic
377	C₄×Dic₃	C₂³	1	1	yes	characteristic
378	C₄×Dic₃	C₂³	1	1	yes	characteristic
379	C₄×Dic₃	C₂³	1	1	yes	characteristic
380	C₂×#41	—	3	1	no	—
381	C₂×#41	—	3	1	no	—
382	C₂²×Q₈	—	3	1	no	—
383	C₂²×Q₈	—	3	1	no	—
384	C₂²×Q₈	—	3	1	no	—
385	C₂²×D₄	—	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	—	3	1	no	—
391	C₄⋊Q₈	—	3	1	no	—
392	C₄⋊Q₈	—	3	1	no	—
393	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
407	#126	C₂×D₃	1	1	yes	characteristic, complemented
408	#125	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	#124	—	3	1	no	—
412	#124	—	3	1	no	—
413	#124	—	3	1	no	—
414	#124	—	3	1	no	—
415	#124	—	3	1	no	—
416	#124	—	3	1	no	—
417	#124	—	3	1	no	—
418	#124	—	3	1	no	—
419	#124	—	3	1	no	—
420	#124	—	3	1	no	—
421	#124	—	3	1	no	—
422	#124	—	3	1	no	—
423	#124	—	3	1	no	—
424	#124	—	3	1	no	—
425	#124	—	3	1	no	—
426	#124	—	3	1	no	—
427	#124	C₂×D₃	1	1	yes	characteristic
428	#124	C₂×D₃	1	1	yes	characteristic, complemented
429	#124	C₂×D₃	1	1	yes	characteristic, complemented
430	#123	—	3	1	no	—
431	#123	—	3	1	no	—
432	#123	—	3	1	no	—
433	#123	—	3	1	no	—
434	#123	—	3	1	no	—
435	#123	—	3	1	no	—
436	#123	—	3	1	no	—
437	#123	—	3	1	no	—
438	#123	—	3	1	no	—
439	#123	—	3	1	no	—
440	#123	—	3	1	no	—
441	#123	—	3	1	no	—
442	#123	—	3	1	no	—
443	#123	—	3	1	no	—
444	#123	—	3	1	no	—
445	#123	—	3	1	no	—
446	#123	C₂×D₃	1	1	yes	characteristic
447	#123	C₂×D₃	1	1	yes	characteristic, complemented
448	C₂²⋊Q₈	—	3	1	no	—
449	C₂²⋊Q₈	—	3	1	no	—
450	C₂²⋊Q₈	—	3	1	no	—
451	C₂²⋊Q₈	—	3	1	no	—
452	C₂²⋊Q₈	—	3	1	no	—
453	C₂²⋊Q₈	—	3	1	no	—
454	C₂²⋊Q₈	—	3	1	no	—
455	C₂²⋊Q₈	—	3	1	no	—
456	C₂²⋊Q₈	—	3	1	no	—
457	C₂²⋊Q₈	—	3	1	no	—
458	C₂²⋊Q₈	—	3	1	no	—
459	C₂²⋊Q₈	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
481	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
482	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
483	#121	—	3	1	no	—
484	#121	—	3	1	no	—
485	#121	—	3	1	no	—
486	#121	—	3	1	no	—
487	#121	—	3	1	no	—
488	#121	—	3	1	no	—
489	#121	—	3	1	no	—
490	#121	—	3	1	no	—
491	#121	—	3	1	no	—
492	#121	—	3	1	no	—
493	#121	C₂×D₃	1	1	yes	characteristic
494	#120	—	3	1	no	—
495	#120	—	3	1	no	—
496	#120	—	3	1	no	—
497	#120	—	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	C₂×D₃	1	1	yes	characteristic, complemented
505	C₄×D₄	—	3	1	no	—
506	C₄×D₄	—	3	1	no	—
507	C₄×D₄	—	3	1	no	—
508	C₄×D₄	—	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	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	3	1	no	—
517	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
526	C₂×C₂²⋊C₄	—	3	1	no	—
527	C₂×C₂²⋊C₄	—	3	1	no	—
528	C₂×C₂²⋊C₄	—	3	1	no	—
529	C₂×C₂²⋊C₄	—	3	1	no	—
530	C₂×C₂²⋊C₄	—	3	1	no	—
531	C₂×C₂²⋊C₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₄²	—	3	1	no	—
535	C₂³×C₃	C₂⁴	1	1	yes	characteristic
536	C₂³×C₃	C₂⁴	1	1	yes	characteristic
537	C₂³×C₃	C₂⁴	1	1	yes	characteristic
538	C₂²×D₃	—	2	2	no	—
539	C₂²×D₃	—	2	2	no	—
540	C₂²×D₃	—	4	1	no	—
541	C₂²×D₃	—	4	1	no	—
542	C₂²×D₃	—	4	1	no	—
543	C₂²×D₃	—	4	1	no	—
544	C₂²×D₃	C₂⁴	1	1	yes	characteristic
545	C₂²×D₃	C₂⁴	1	1	yes	characteristic
546	C₂²×D₃	C₂⁴	1	1	yes	characteristic
547	C₂²×D₃	C₂⁴	1	1	yes	characteristic
548	C₃×Q₈	—	4	1	no	—
549	C₃×Q₈	—	4	1	no	—
550	C₃×Q₈	—	4	1	no	—
551	C₃×D₄	—	4	1	no	—
552	C₃×D₄	—	4	1	no	—
553	C₃×D₄	—	4	1	no	—
554	C₂×C₃×C₄	—	4	1	no	—
555	C₂×C₃×C₄	—	4	1	no	—
556	C₂×C₃×C₄	—	4	1	no	—
557	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
558	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
559	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
569	#67	—	2	2	no	—
570	#67	—	2	2	no	—
571	#67	—	2	2	no	—
572	#67	—	4	1	no	—
573	#67	—	4	1	no	—
574	#67	—	4	1	no	—
575	#67	—	4	1	no	—
576	#67	—	4	1	no	—
577	C₂×Dic₃	—	2	2	no	—
578	C₂×Dic₃	—	4	1	no	—
579	C₂×Dic₃	—	4	1	no	—
580	C₂×Dic₃	—	4	1	no	—
581	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
582	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
583	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
584	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
585	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
586	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
587	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
588	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
589	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
590	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
591	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
592	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
593	D₁₂	—	2	2	no	—
594	D₁₂	—	4	1	no	—
595	D₁₂	—	4	1	no	—
596	D₁₂	—	4	1	no	—
597	C₄×D₃	—	2	2	no	—
598	C₄×D₃	—	2	2	no	—
599	C₄×D₃	—	2	2	no	—
600	C₄×D₃	—	4	1	no	—
601	C₄×D₃	—	4	1	no	—
602	C₄×D₃	—	4	1	no	—
603	C₄×D₃	—	4	1	no	—
604	C₄×D₃	—	4	1	no	—
605	C₄×D₃	—	4	1	no	—
606	C₄×D₃	—	4	1	no	—
607	C₄×D₃	—	4	1	no	—
608	C₄×D₃	—	4	1	no	—
609	Dic₆	—	2	2	no	—
610	Dic₆	—	2	2	no	—
611	Dic₆	—	2	2	no	—
612	Dic₆	—	2	2	no	—
613	Dic₆	—	4	1	no	—
614	Dic₆	—	4	1	no	—
615	Dic₆	—	4	1	no	—
616	Dic₆	—	4	1	no	—
617	Dic₆	—	4	1	no	—
618	Dic₆	—	4	1	no	—
619	C₂⁴	—	3	1	no	—
620	C₂⁴	—	3	1	no	—
621	#41	—	12	2	no	—
622	#41	—	12	2	no	—
623	C₂×Q₈	—	3	1	no	—
624	C₂×Q₈	—	3	1	no	—
625	C₂×Q₈	—	3	1	no	—
626	C₂×Q₈	—	3	1	no	—
627	C₂×Q₈	—	3	1	no	—
628	C₂×Q₈	—	3	1	no	—
629	C₂×Q₈	—	3	1	no	—
630	C₂×Q₈	—	3	1	no	—
631	C₂×Q₈	—	3	1	no	—
632	C₂×Q₈	—	3	1	no	—
633	C₂×Q₈	—	12	2	no	—
634	C₂×Q₈	—	12	2	no	—
635	C₂×Q₈	—	12	2	no	—
636	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
637	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
638	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
639	C₂×D₄	—	3	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	3	1	no	—
642	C₂×D₄	—	3	1	no	—
643	C₂×D₄	—	3	1	no	—
644	C₂×D₄	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	3	1	no	—
649	C₂×D₄	—	3	1	no	—
650	C₂×D₄	—	3	1	no	—
651	C₂×D₄	—	12	2	no	—
652	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
653	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
654	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	3	1	no	—
657	C₂²×C₄	—	3	1	no	—
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	1	no	—
662	C₂²×C₄	—	3	1	no	—
663	C₂²×C₄	—	3	1	no	—
664	C₂²×C₄	—	3	1	no	—
665	C₂²×C₄	—	3	1	no	—
666	C₂²×C₄	—	3	1	no	—
667	C₂²×C₄	—	3	1	no	—
668	C₂²×C₄	—	3	1	no	—
669	C₂²×C₄	—	3	1	no	—
670	C₂²×C₄	—	3	1	no	—
671	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
672	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
673	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
674	C₄⋊C₄	—	3	1	no	—
675	C₄⋊C₄	—	3	1	no	—
676	C₄⋊C₄	—	3	1	no	—
677	C₄⋊C₄	—	3	1	no	—
678	C₄⋊C₄	—	3	1	no	—
679	C₄⋊C₄	—	3	1	no	—
680	C₄⋊C₄	—	3	1	no	—
681	C₄⋊C₄	—	3	1	no	—
682	C₄⋊C₄	—	3	1	no	—
683	C₄⋊C₄	—	3	1	no	—
684	C₄⋊C₄	—	3	1	no	—
685	C₄⋊C₄	—	3	1	no	—
686	C₄⋊C₄	—	3	1	no	—
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	3	1	no	—
689	C₄⋊C₄	—	3	1	no	—
690	C₄⋊C₄	—	3	1	no	—
691	C₄⋊C₄	—	3	1	no	—
692	C₄⋊C₄	—	3	1	no	—
693	C₄⋊C₄	—	3	1	no	—
694	C₄⋊C₄	—	3	1	no	—
695	C₄⋊C₄	—	3	1	no	—
696	C₄⋊C₄	—	3	1	no	—
697	C₄⋊C₄	—	3	1	no	—
698	C₄⋊C₄	—	3	1	no	—
699	C₄⋊C₄	—	3	1	no	—
700	C₄⋊C₄	—	3	1	no	—
701	C₄⋊C₄	—	3	1	no	—
702	C₄⋊C₄	—	3	1	no	—
703	C₄⋊C₄	—	3	1	no	—
704	C₄⋊C₄	—	3	1	no	—
705	C₄⋊C₄	—	3	1	no	—
706	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
708	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
709	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
710	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
711	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
714	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
715	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
716	C₂²⋊C₄	—	3	1	no	—
717	C₂²⋊C₄	—	3	1	no	—
718	C₂²⋊C₄	—	3	1	no	—
719	C₂²⋊C₄	—	3	1	no	—
720	C₂²⋊C₄	—	3	1	no	—
721	C₂²⋊C₄	—	3	1	no	—
722	C₂²⋊C₄	—	3	1	no	—
723	C₂²⋊C₄	—	3	1	no	—
724	C₂²⋊C₄	—	3	1	no	—
725	C₂²⋊C₄	—	3	1	no	—
726	C₂²⋊C₄	—	3	1	no	—
727	C₂²⋊C₄	—	3	1	no	—
728	C₂²⋊C₄	—	3	1	no	—
729	C₂²⋊C₄	—	3	1	no	—
730	C₂²⋊C₄	—	3	1	no	—
731	C₂²⋊C₄	—	3	1	no	—
732	C₂²⋊C₄	—	3	1	no	—
733	C₂²⋊C₄	—	3	1	no	—
734	C₂²⋊C₄	—	3	1	no	—
735	C₂²⋊C₄	—	3	1	no	—
736	C₂²⋊C₄	—	3	1	no	—
737	C₂²⋊C₄	—	3	1	no	—
738	C₂²⋊C₄	—	3	1	no	—
739	C₂²⋊C₄	—	3	1	no	—
740	C₂²⋊C₄	—	3	1	no	—
741	C₂²⋊C₄	—	3	1	no	—
742	C₂²⋊C₄	—	3	1	no	—
743	C₂²⋊C₄	—	3	1	no	—
744	C₂²⋊C₄	—	3	1	no	—
745	C₂²⋊C₄	—	3	1	no	—
746	C₂²⋊C₄	—	3	1	no	—
747	C₂²⋊C₄	—	3	1	no	—
748	C₂²⋊C₄	—	3	1	no	—
749	C₂²⋊C₄	—	3	1	no	—
750	C₂²⋊C₄	—	3	1	no	—
751	C₂²⋊C₄	—	3	1	no	—
752	C₂²⋊C₄	—	3	1	no	—
753	C₂²⋊C₄	—	3	1	no	—
754	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
755	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
756	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
757	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
758	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
759	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
760	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
761	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
762	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
763	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
764	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
765	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
766	C₄²	—	3	1	no	—
767	C₄²	—	3	1	no	—
768	C₄²	—	3	1	no	—
769	C₄²	—	3	1	no	—
770	C₄²	—	3	1	no	—
771	C₄²	—	3	1	no	—
772	C₄²	—	3	1	no	—
773	C₄²	—	3	1	no	—
774	C₄²	—	3	1	no	—
775	C₄²	—	3	1	no	—
776	C₄²	C₂²×D₃	1	1	yes	characteristic
777	C₄²	C₂²×D₃	1	1	yes	characteristic
778	C₄²	C₂²×D₃	1	1	yes	characteristic
779	C₄²	C₂²×D₃	1	1	yes	characteristic
780	C₂²×C₃	—	2	1	no	—
781	C₂²×C₃	—	2	1	no	—
782	C₂²×C₃	—	2	1	no	—
783	C₂²×C₃	—	2	1	no	—
784	C₂²×C₃	—	2	1	no	—
785	C₂²×C₃	—	2	1	no	—
786	C₂²×C₃	—	2	1	no	—
787	C₂²×C₃	—	2	1	no	—
788	C₂²×C₃	—	2	1	no	—
789	C₂²×C₃	C₂⁵	1	1	yes	characteristic
790	C₂×D₃	—	2	1	no	—
791	C₂×D₃	—	2	1	no	—
792	C₂×D₃	—	2	1	no	—
793	C₂×D₃	—	2	1	no	—
794	C₂×D₃	—	2	1	no	—
795	C₂×D₃	—	2	1	no	—
796	C₂×D₃	—	2	1	no	—
797	C₂×D₃	—	2	1	no	—
798	C₂×D₃	—	2	1	no	—
799	C₂×D₃	—	2	1	no	—
800	C₂×D₃	—	2	1	no	—
801	C₂×D₃	—	8	2	no	—
802	C₂×D₃	—	8	2	no	—
803	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
804	C₃×C₄	—	2	1	no	—
805	C₃×C₄	—	2	1	no	—
806	C₃×C₄	—	2	1	no	—
807	C₃×C₄	—	2	1	no	—
808	C₃×C₄	—	2	1	no	—
809	C₃×C₄	—	2	1	no	—
810	C₃×C₄	—	2	1	no	—
811	C₃×C₄	—	2	1	no	—
812	C₃×C₄	—	2	1	no	—
813	C₃×C₄	—	2	1	no	—
814	C₃×C₄	—	2	1	no	—
815	C₃×C₄	—	2	1	no	—
816	Dic₃	—	2	1	no	—
817	Dic₃	—	2	1	no	—
818	Dic₃	—	2	1	no	—
819	Dic₃	—	2	1	no	—
820	Dic₃	—	2	1	no	—
821	Dic₃	—	2	1	no	—
822	Dic₃	—	2	1	no	—
823	Dic₃	—	2	1	no	—
824	Dic₃	—	2	1	no	—
825	Dic₃	—	2	1	no	—
826	Dic₃	—	2	1	no	—
827	Dic₃	H(5,𝔽₂)	1	2	yes	—
828	C₂³	—	3	1	no	—
829	C₂³	—	3	1	no	—
830	C₂³	—	3	1	no	—
831	C₂³	—	3	1	no	—
832	C₂³	—	6	2	no	—
833	C₂³	—	6	2	no	—
834	C₂³	—	12	1	no	—
835	C₂³	—	12	1	no	—
836	C₂³	—	12	1	no	—
837	C₂³	—	12	1	no	—
838	C₂³	C₂³×D₃	1	1	yes	characteristic
839	C₂³	C₂³×D₃	1	1	yes	characteristic
840	C₂³	C₂³×D₃	1	1	yes	characteristic
841	Q₈	—	4	1	no	—
842	Q₈	—	4	1	no	—
843	Q₈	—	4	1	no	—
844	Q₈	—	6	2	no	—
845	Q₈	—	6	2	no	—
846	Q₈	—	6	2	no	—
847	Q₈	—	6	2	no	—
848	Q₈	—	12	1	no	—
849	Q₈	—	12	1	no	—
850	Q₈	—	12	1	no	—
851	Q₈	—	12	1	no	—
852	Q₈	—	12	1	no	—
853	Q₈	—	12	1	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	1	no	—
856	D₄	—	4	1	no	—
857	D₄	—	6	2	no	—
858	D₄	—	6	2	no	—
859	D₄	—	6	2	no	—
860	D₄	—	6	2	no	—
861	D₄	—	12	1	no	—
862	D₄	—	12	1	no	—
863	D₄	—	12	1	no	—
864	D₄	—	12	1	no	—
865	D₄	—	12	1	no	—
866	D₄	—	12	1	no	—
867	D₄	—	12	1	no	—
868	D₄	—	12	1	no	—
869	C₂×C₄	—	3	1	no	—
870	C₂×C₄	—	3	1	no	—
871	C₂×C₄	—	3	1	no	—
872	C₂×C₄	—	3	1	no	—
873	C₂×C₄	—	3	1	no	—
874	C₂×C₄	—	3	1	no	—
875	C₂×C₄	—	3	1	no	—
876	C₂×C₄	—	3	1	no	—
877	C₂×C₄	—	3	1	no	—
878	C₂×C₄	—	3	1	no	—
879	C₂×C₄	—	3	1	no	—
880	C₂×C₄	—	3	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	6	2	no	—
885	C₂×C₄	—	6	2	no	—
886	C₂×C₄	—	6	2	no	—
887	C₂×C₄	—	6	2	no	—
888	C₂×C₄	—	12	1	no	—
889	C₂×C₄	—	12	1	no	—
890	C₂×C₄	—	12	1	no	—
891	C₂×C₄	—	12	1	no	—
892	C₂×C₄	—	12	1	no	—
893	C₂×C₄	—	12	1	no	—
894	C₂×C₄	—	12	1	no	—
895	C₂×C₄	—	12	1	no	—
896	C₂×C₄	—	12	1	no	—
897	C₂×C₄	—	12	1	no	—
898	C₂×C₄	—	12	1	no	—
899	C₂×C₄	—	12	1	no	—
900	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
909	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
912	C₂×C₃	—	4	1	no	—
913	C₂×C₃	—	4	1	no	—
914	C₂×C₃	—	4	1	no	—
915	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
917	C₂×C₃	#585	1	1	yes	characteristic
918	D₃	—	2	2	no	—
919	D₃	—	4	1	no	—
920	D₃	—	4	1	no	—
921	D₃	—	4	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	3	2	no	—
932	C₂²	—	6	1	no	—
933	C₂²	—	6	1	no	—
934	C₂²	—	6	1	no	—
935	C₂²	—	6	1	no	—
936	C₂²	—	6	1	no	—
937	C₂²	—	6	1	no	—
938	C₂²	—	6	1	no	—
939	C₂²	—	6	1	no	—
940	C₂²	—	6	1	no	—
941	C₂²	—	6	1	no	—
942	C₂²	—	6	1	no	—
943	C₂²	—	24	2	no	—
944	C₂²	—	24	2	no	—
945	C₂²	C₂⁴×D₃	1	1	yes	characteristic
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	3	2	no	—
959	C₄	—	6	1	no	—
960	C₄	—	6	1	no	—
961	C₄	—	6	1	no	—
962	C₄	—	6	1	no	—
963	C₄	—	6	1	no	—
964	C₄	—	6	1	no	—
965	C₄	—	6	1	no	—
966	C₄	—	6	1	no	—
967	C₄	—	6	1	no	—
968	C₄	—	6	1	no	—
969	C₄	—	6	1	no	—
970	C₃	#3561	1	1	yes	characteristic, complemented, Sylow
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	6	2	no	—
975	C₂	—	12	1	no	—
976	C₂	—	12	1	no	—
977	C₂	—	12	1	no	—
978	C₂	#5964	1	1	yes	characteristic
979	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
980	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×#542	C₂
hypercenter	#542	D₃
hypocenter	C₃	#3561
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₃×#542	C₂	semidirect
2. #5735	C₂	semidirect
3. #5727	C₂	semidirect
4. #5710	C₂	semidirect
5. #5706	C₂	semidirect
6. #5705	C₂	semidirect
7. #5702	C₂	semidirect
8. #5679	C₂	semidirect
9. #5678	C₂	semidirect
10. #5677	C₂	semidirect
11. D₃×#124	C₂	semidirect
12. #5669	C₂	semidirect
13. #5669	C₂	semidirect
14. #5657	C₂	semidirect
15. #5654	C₂	semidirect
16. #5651	C₂	semidirect
17. #5648	C₂	semidirect
18. #5647	C₂	semidirect
19. #5640	C₂	semidirect
20. #5634	C₂	semidirect
21. #5634	C₂	semidirect
22. #5632	C₂	semidirect
23. #5628	C₂	semidirect
24. #5621	C₂	semidirect
25. #5610	C₂	semidirect
26. #5582	C₂	semidirect
27. #5578	C₂	semidirect
28. #5556	C₂	semidirect
29. #5552	C₂	semidirect
30. #5533	C₂	semidirect
31. #5527	C₂	semidirect
34. C₂×D₃×Q₈	C₂²	semidirect
38. C₂²×Dic₆	C₂²	semidirect
39. C₃×C₄⋊Q₈	C₂²	semidirect
40. C₃×#126	C₂²	semidirect
41. C₃×#126	C₂²	semidirect
43. C₃×#124	C₂²	semidirect
44. C₃×#124	C₂²	semidirect
46. C₃×#123	C₂²	semidirect
47. C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×C₂²⋊Q₈	C₂²	semidirect
51. C₃×C₄×Q₈	C₂²	semidirect
52. C₃×C₄×D₄	C₂²	semidirect
53. C₃×#117	C₂²	semidirect
55. #947	C₂²	semidirect
58. #946	C₂²	semidirect
59. #946	C₂²	semidirect
60. #946	C₂²	semidirect
61. #946	C₂²	semidirect
62. #944	C₂²	semidirect
63. #944	C₂²	semidirect
66. #939	C₂²	semidirect
67. #938	C₂²	semidirect
72. #935	C₂²	semidirect
73. #935	C₂²	semidirect
74. #930	C₂²	semidirect
75. #929	C₂²	semidirect
76. #929	C₂²	semidirect
81. #924	C₂²	semidirect
82. #924	C₂²	semidirect
83. #924	C₂²	semidirect
84. #898	C₂²	semidirect
85. #898	C₂²	semidirect
86. #898	C₂²	semidirect
89. #897	C₂²	semidirect
90. #897	C₂²	semidirect
96. #896	C₂²	semidirect
97. #896	C₂²	semidirect
98. #896	C₂²	semidirect
99. #896	C₂²	semidirect
100. #896	C₂²	semidirect
101. #896	C₂²	semidirect
102. #896	C₂²	semidirect
107. #894	C₂²	semidirect
108. #894	C₂²	semidirect
109. #894	C₂²	semidirect
112. #892	C₂²	semidirect
113. #892	C₂²	semidirect
114. #889	C₂²	semidirect
115. #889	C₂²	semidirect
116. #889	C₂²	semidirect
117. #888	C₂²	semidirect
118. #888	C₂²	semidirect
119. #888	C₂²	semidirect
120. #888	C₂²	semidirect
121. #888	C₂²	semidirect
122. #887	C₂²	semidirect
123. #887	C₂²	semidirect
124. #886	C₂²	semidirect
131. #885	C₂²	semidirect
132. #885	C₂²	semidirect
133. #885	C₂²	semidirect
134. #885	C₂²	semidirect
135. #885	C₂²	semidirect
139. #884	C₂²	semidirect
141. #883	C₂²	semidirect
142. #883	C₂²	semidirect
143. #883	C₂²	semidirect
149. #67⋊C₄	C₂²	semidirect
150. #67⋊C₄	C₂²	semidirect
151. #67⋊C₄	C₂²	semidirect
158. #879	C₂²	semidirect
159. #879	C₂²	semidirect
160. #879	C₂²	semidirect
161. #879	C₂²	semidirect
162. #879	C₂²	semidirect
163. #878	C₂²	semidirect
164. #878	C₂²	semidirect
165. #878	C₂²	semidirect
166. #878	C₂²	semidirect
167. #878	C₂²	semidirect
168. #878	C₂²	semidirect
169. #878	C₂²	semidirect
170. #877	C₂²	semidirect
171. #877	C₂²	semidirect
172. #876	C₂²	semidirect
173. #876	C₂²	semidirect
174. #876	C₂²	semidirect
175. #876	C₂²	semidirect
177. #875	C₂²	semidirect
179. C₄×D₁₂	C₂²	semidirect
182. #872	C₂²	semidirect
184. C₄×Dic₆	C₂²	semidirect
185. C₄×Dic₆	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
211. #542	D₃	semidirect
393. C₄⋊Q₈	C₂×D₃	semidirect
406. #126	C₂×D₃	semidirect
407. #126	C₂×D₃	semidirect
428. #124	C₂×D₃	semidirect
429. #124	C₂×D₃	semidirect
447. #123	C₂×D₃	semidirect
480. C₂²⋊Q₈	C₂×D₃	semidirect
481. C₂²⋊Q₈	C₂×D₃	semidirect
482. C₂²⋊Q₈	C₂×D₃	semidirect
504. C₄×Q₈	C₂×D₃	semidirect
517. C₄×D₄	C₂×D₃	semidirect
525. #117	C₂×D₃	semidirect
970. C₃	#3561	semidirect

Maximal subgroups

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

subgroup	index
C₃×#542	2
#5735	2
#5727	2
#5710	2
#5706	2
#5705	2
#5702	2
#5679	2
#5678	2
#5677	2
D₃×#124	2
#5669	2
#5657	2
#5654	2
#5651	2
#5648	2
#5647	2
#5640	2
#5634	2
#5632	2
#5628	2
#5621	2
#5610	2
#5582	2
#5578	2
#5556	2
#5552	2
#5533	2
#5527	2
#3561	3