Subgroups — #86800

Order 384.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#5708	C₂	1	1	yes	maximal, characteristic, complemented
3	#5705	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
5	#5701	C₂	1	1	yes	maximal, characteristic, complemented
6	#5678	C₂	1	1	yes	maximal, characteristic, complemented
7	#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	1	yes	maximal, characteristic, complemented
9	#5661	C₂	1	1	yes	maximal, characteristic, complemented
10	#5660	C₂	1	1	yes	maximal, characteristic, complemented
11	#5659	C₂	1	1	yes	maximal, characteristic, complemented
12	#5655	C₂	1	1	yes	maximal, characteristic, complemented
13	#5649	C₂	1	1	yes	maximal, characteristic, complemented
14	#5640	C₂	1	1	yes	maximal, characteristic, complemented
15	#5639	C₂	1	1	yes	maximal, characteristic, complemented
16	#5636	C₂	1	1	yes	maximal, characteristic, complemented
17	#5624	C₂	1	1	yes	maximal, characteristic, complemented
18	#5593	C₂	1	1	yes	maximal, characteristic, complemented
19	#5591	C₂	1	1	yes	maximal, characteristic, complemented
20	#5558	C₂	1	1	yes	maximal, characteristic, complemented
21	#5540	C₂	1	1	yes	maximal, characteristic, complemented
22	#5538	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
24	#5533	C₂	1	1	yes	maximal, characteristic, complemented
25	#5531	C₂	1	1	yes	maximal, characteristic, complemented
26	#5528	C₂	1	1	yes	maximal, characteristic, complemented
27	#5523	C₂	1	1	yes	maximal, characteristic, complemented
28	#5495	C₂	1	1	yes	maximal, characteristic, complemented
29	#5490	C₂	1	1	yes	maximal, characteristic, complemented
30	#5486	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#879	C₂	1	1	yes	maximal, characteristic, complemented
32	#3521	—	3	1	no	maximal, Sylow
33	C₂²×#67	C₂²	1	1	yes	characteristic
34	C₂×#237	C₂²	1	1	yes	characteristic
35	C₂×#235	C₂²	1	1	yes	characteristic
36	C₃×#126	C₂²	1	1	yes	characteristic
37	C₃×#126	C₂²	1	1	yes	characteristic
38	C₃×#124	C₂²	1	1	yes	characteristic
39	C₃×#123	C₂²	1	1	yes	characteristic
40	C₃×#123	C₂²	1	1	yes	characteristic, complemented
41	C₃×#123	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₃×#120	C₂²	1	1	yes	characteristic
45	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
47	C₃×#117	C₂²	1	1	yes	characteristic, complemented
48	C₃×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	#953	C₂²	1	1	yes	characteristic
52	C₂×#217	C₂²	1	1	yes	characteristic
53	C₂×#217	C₂²	1	1	yes	characteristic
54	#947	C₂²	1	1	yes	characteristic, complemented
55	#946	C₂²	1	1	yes	characteristic, complemented
56	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
57	#944	C₂²	1	1	yes	characteristic, complemented
58	#939	C₂²	1	1	yes	characteristic
59	#939	C₂²	1	1	yes	characteristic
60	#939	C₂²	1	1	yes	characteristic
61	#939	C₂²	1	1	yes	characteristic, complemented
62	#938	C₂²	1	1	yes	characteristic
63	#938	C₂²	1	1	yes	characteristic, complemented
64	#937	C₂²	1	1	yes	characteristic
65	#936	C₂²	1	1	yes	characteristic
66	#935	C₂²	1	1	yes	characteristic, complemented
67	D₄×Dic₃	C₂²	1	1	yes	characteristic
68	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
69	#930	C₂²	1	1	yes	characteristic
70	#929	C₂²	1	1	yes	characteristic
71	#929	C₂²	1	1	yes	characteristic, complemented
72	#929	C₂²	1	1	yes	characteristic, complemented
73	C₄×#67	C₂²	1	1	yes	characteristic
74	C₄×#67	C₂²	1	1	yes	characteristic
75	C₄×#67	C₂²	1	1	yes	characteristic
76	C₄×#67	C₂²	1	1	yes	characteristic
77	C₄×#67	C₂²	1	1	yes	characteristic
78	C₄×#67	C₂²	1	1	yes	characteristic, complemented
79	C₄×#67	C₂²	1	1	yes	characteristic, complemented
80	C₄×#67	C₂²	1	1	yes	characteristic, complemented
81	#926	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
83	#924	C₂²	1	1	yes	characteristic, complemented
84	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
88	#898	C₂²	1	1	yes	characteristic, complemented
89	#898	C₂²	1	1	yes	characteristic, complemented
90	#898	C₂²	1	1	yes	characteristic, complemented
91	#898	C₂²	1	1	yes	characteristic, complemented
92	#897	C₂²	1	1	yes	characteristic, complemented
93	#896	C₂²	1	1	yes	characteristic, complemented
94	#896	C₂²	1	1	yes	characteristic, complemented
95	#896	C₂²	1	1	yes	characteristic, complemented
96	#896	C₂²	1	1	yes	characteristic, complemented
97	#894	C₂²	1	1	yes	characteristic, complemented
98	#894	C₂²	1	1	yes	characteristic, complemented
99	#893	C₂²	1	1	yes	characteristic, complemented
100	#892	C₂²	1	1	yes	characteristic, complemented
101	#892	C₂²	1	1	yes	characteristic, complemented
102	#892	C₂²	1	1	yes	characteristic, complemented
103	#892	C₂²	1	1	yes	characteristic, complemented
104	#892	C₂²	1	1	yes	characteristic, complemented
105	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	#890	C₂²	1	1	yes	characteristic, complemented
110	#890	C₂²	1	1	yes	characteristic, complemented
111	#889	C₂²	1	1	yes	characteristic, complemented
112	#889	C₂²	1	1	yes	characteristic, complemented
113	#889	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	#887	C₂²	1	1	yes	characteristic, complemented
119	#887	C₂²	1	1	yes	characteristic, complemented
120	#886	C₂²	1	1	yes	characteristic
121	#886	C₂²	1	1	yes	characteristic, complemented
122	#886	C₂²	1	1	yes	characteristic, complemented
123	#885	C₂²	1	1	yes	characteristic
124	#885	C₂²	1	1	yes	characteristic
125	#885	C₂²	1	1	yes	characteristic
126	#885	C₂²	1	1	yes	characteristic, complemented
127	#884	C₂²	1	1	yes	characteristic
128	#884	C₂²	1	1	yes	characteristic
129	#884	C₂²	1	1	yes	characteristic, complemented
130	#884	C₂²	1	1	yes	characteristic, complemented
131	#883	C₂²	1	1	yes	characteristic
132	#883	C₂²	1	1	yes	characteristic
133	#883	C₂²	1	1	yes	characteristic
134	#883	C₂²	1	1	yes	characteristic
135	#883	C₂²	1	1	yes	characteristic, complemented
136	#883	C₂²	1	1	yes	characteristic, complemented
137	#882	C₂²	1	1	yes	characteristic
138	#67⋊C₄	C₂²	1	1	yes	characteristic
139	#67⋊C₄	C₂²	1	1	yes	characteristic
140	#67⋊C₄	C₂²	1	1	yes	characteristic
141	#67⋊C₄	C₂²	1	1	yes	characteristic
142	#67⋊C₄	C₂²	1	1	yes	characteristic
143	#67⋊C₄	C₂²	1	1	yes	characteristic
144	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
145	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
148	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
149	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
150	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
151	D₃×C₂²⋊C₄	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	#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	#879	C₂²	1	1	yes	characteristic, complemented
164	#879	C₂²	1	1	yes	characteristic, complemented
165	#879	C₂²	1	1	yes	characteristic, complemented
166	#878	C₂²	1	1	yes	characteristic
167	#878	C₂²	1	1	yes	characteristic
168	#878	C₂²	1	1	yes	characteristic, complemented
169	#878	C₂²	1	1	yes	characteristic, complemented
170	#878	C₂²	1	1	yes	characteristic, complemented
171	#878	C₂²	1	1	yes	characteristic, complemented
172	#877	C₂²	1	1	yes	characteristic
173	#877	C₂²	1	1	yes	characteristic
174	#877	C₂²	1	1	yes	characteristic, complemented
175	#877	C₂²	1	1	yes	characteristic, complemented
176	#876	C₂²	1	1	yes	characteristic, complemented
177	#876	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
180	#872	C₂²	1	1	yes	characteristic, complemented
181	#872	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
183	#870	C₂²	1	1	yes	characteristic, complemented
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	#556	—	3	1	no	—
189	#556	—	3	1	no	—
190	#554	—	3	1	no	—
191	#553	—	3	1	no	—
192	#553	—	3	1	no	—
193	#553	—	3	1	no	—
194	#552	—	3	1	no	—
195	#552	—	3	1	no	—
196	#552	—	3	1	no	—
197	#551	—	3	1	no	—
198	#551	—	3	1	no	—
199	#551	—	3	1	no	—
200	#551	D₃	1	1	yes	characteristic, complemented
201	#547	—	3	1	no	—
202	#546	—	3	1	no	—
203	#546	—	3	1	no	—
204	#542	—	3	1	no	—
205	#541	—	3	1	no	—
206	#539	—	3	1	no	—
207	#539	—	3	1	no	—
208	#538	—	3	1	no	—
209	#538	—	3	1	no	—
210	#529	—	3	1	no	—
211	#529	—	3	1	no	—
212	#529	—	3	1	no	—
213	#529	—	3	1	no	—
214	C₂×#126	—	3	1	no	—
215	C₂×#126	—	3	1	no	—
216	#520	—	3	1	no	—
217	#518	—	3	1	no	—
218	C₄×#41	—	3	1	no	—
219	C₂⁴×C₃	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×D₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
226	C₂²×C₃×C₄	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	—	2	4	no	—
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	C₂×#67	C₂³	1	1	yes	characteristic
239	C₂×#67	C₂³	1	1	yes	characteristic
240	C₂×#67	C₂³	1	1	yes	characteristic
241	C₂²×Dic₃	C₂³	1	1	yes	characteristic
242	C₂²×Dic₃	C₂³	1	1	yes	characteristic
243	C₂²×Dic₃	C₂³	1	1	yes	characteristic
244	C₂²×Dic₃	C₂³	1	1	yes	characteristic
245	C₂²×Dic₃	C₂³	1	1	yes	characteristic
246	C₂²×Dic₃	C₂³	1	1	yes	characteristic
247	C₂²×Dic₃	C₂³	1	1	yes	characteristic
248	#237	—	2	4	no	—
249	#235	—	2	4	no	—
250	C₂×D₁₂	C₂³	1	1	yes	characteristic
251	C₂×D₁₂	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	C₂³	1	1	yes	characteristic
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	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₃×C₂²⋊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×C₄²	C₂³	1	1	yes	characteristic
290	C₃×C₄²	C₂³	1	1	yes	characteristic
291	C₃×C₄²	C₂³	1	1	yes	characteristic
292	#217	C₂³	1	1	yes	characteristic
293	#217	C₂³	1	1	yes	characteristic
294	#217	C₂³	1	1	yes	characteristic
295	#217	C₂³	1	1	yes	characteristic
296	#217	C₂³	1	1	yes	characteristic
297	#217	C₂³	1	1	yes	characteristic
298	#217	C₂³	1	1	yes	characteristic
299	#217	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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
331	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
332	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
333	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
334	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
335	C₄⋊Dic₃	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	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	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×Dic₃	C₂³	1	1	yes	characteristic
375	C₄×Dic₃	C₂³	1	1	yes	characteristic
376	C₄×Dic₃	C₂³	1	1	yes	characteristic
377	C₂×#41	—	3	1	no	—
378	C₂×#41	—	3	1	no	—
379	C₂²×D₄	—	3	1	no	—
380	C₄⋊Q₈	—	3	1	no	—
381	C₄⋊Q₈	—	3	1	no	—
382	#126	—	3	1	no	—
383	#126	—	3	1	no	—
384	#126	—	3	1	no	—
385	#126	—	3	1	no	—
386	#126	—	3	1	no	—
387	#126	—	3	1	no	—
388	#126	—	3	1	no	—
389	#126	—	3	1	no	—
390	#126	—	3	1	no	—
391	#126	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
403	#126	C₂×D₃	1	1	yes	characteristic
404	#125	—	3	1	no	—
405	#125	—	3	1	no	—
406	#125	—	3	1	no	—
407	#125	—	3	1	no	—
408	#125	—	3	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	#125	—	3	1	no	—
412	#125	—	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	C₂×D₃	1	1	yes	characteristic
420	#123	—	3	1	no	—
421	#123	—	3	1	no	—
422	#123	—	3	1	no	—
423	#123	—	3	1	no	—
424	#123	—	3	1	no	—
425	#123	—	3	1	no	—
426	#123	—	3	1	no	—
427	#123	—	3	1	no	—
428	#123	—	3	1	no	—
429	#123	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
436	#123	C₂×D₃	1	1	yes	characteristic, complemented
437	#123	C₂×D₃	1	1	yes	characteristic, complemented
438	C₂²⋊Q₈	—	3	1	no	—
439	C₂²⋊Q₈	—	3	1	no	—
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	C₂²⋊Q₈	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
444	C₂²⋊Q₈	—	3	1	no	—
445	C₂²⋊Q₈	—	3	1	no	—
446	C₂²⋊Q₈	—	3	1	no	—
447	C₂²⋊Q₈	—	3	1	no	—
448	C₂²⋊Q₈	—	3	1	no	—
449	C₂²⋊Q₈	—	3	1	no	—
450	C₂²⋊Q₈	—	3	1	no	—
451	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
452	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
453	#121	—	3	1	no	—
454	#121	—	3	1	no	—
455	#121	—	3	1	no	—
456	#121	—	3	1	no	—
457	#121	—	3	1	no	—
458	#121	—	3	1	no	—
459	#121	—	3	1	no	—
460	#121	—	3	1	no	—
461	#121	—	3	1	no	—
462	#121	—	3	1	no	—
463	#121	—	3	1	no	—
464	#120	—	3	1	no	—
465	#120	—	3	1	no	—
466	#120	—	3	1	no	—
467	#120	C₂×D₃	1	1	yes	characteristic
468	C₄×Q₈	—	3	1	no	—
469	C₄×Q₈	—	3	1	no	—
470	C₄×Q₈	—	3	1	no	—
471	C₄×Q₈	—	3	1	no	—
472	C₄×Q₈	—	3	1	no	—
473	C₄×Q₈	—	3	1	no	—
474	C₄×Q₈	—	3	1	no	—
475	C₄×D₄	—	3	1	no	—
476	C₄×D₄	—	3	1	no	—
477	C₄×D₄	—	3	1	no	—
478	C₄×D₄	—	3	1	no	—
479	C₄×D₄	—	3	1	no	—
480	C₄×D₄	—	3	1	no	—
481	C₄×D₄	—	3	1	no	—
482	C₄×D₄	—	3	1	no	—
483	C₄×D₄	—	3	1	no	—
484	C₄×D₄	—	3	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₄×D₄	—	3	1	no	—
487	C₄×D₄	—	3	1	no	—
488	C₄×D₄	—	3	1	no	—
489	C₄×D₄	—	3	1	no	—
490	C₄×D₄	—	3	1	no	—
491	C₄×D₄	—	3	1	no	—
492	C₄×D₄	—	3	1	no	—
493	C₄×D₄	—	3	1	no	—
494	C₄×D₄	—	3	1	no	—
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
499	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
500	#117	—	3	1	no	—
501	#117	—	3	1	no	—
502	#117	—	3	1	no	—
503	#117	—	3	1	no	—
504	#117	—	3	1	no	—
505	#117	—	3	1	no	—
506	#117	—	3	1	no	—
507	#117	—	3	1	no	—
508	#117	—	3	1	no	—
509	#117	—	3	1	no	—
510	#117	—	3	1	no	—
511	#117	—	3	1	no	—
512	#117	C₂×D₃	1	1	yes	characteristic, complemented
513	#117	C₂×D₃	1	1	yes	characteristic, complemented
514	C₂×C₄⋊C₄	—	3	1	no	—
515	C₂×C₄⋊C₄	—	3	1	no	—
516	C₂×C₄⋊C₄	—	3	1	no	—
517	C₂×C₄⋊C₄	—	3	1	no	—
518	C₂×C₄⋊C₄	—	3	1	no	—
519	C₂×C₄⋊C₄	—	3	1	no	—
520	C₂×C₄⋊C₄	—	3	1	no	—
521	C₂×C₂²⋊C₄	—	3	1	no	—
522	C₂×C₂²⋊C₄	—	3	1	no	—
523	C₂×C₂²⋊C₄	—	3	1	no	—
524	C₂×C₂²⋊C₄	—	3	1	no	—
525	C₂×C₂²⋊C₄	—	3	1	no	—
526	C₂×C₂²⋊C₄	—	3	1	no	—
527	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
529	C₂×C₄²	—	3	1	no	—
530	C₂×C₄²	—	3	1	no	—
531	C₂×C₄²	—	3	1	no	—
532	C₂³×C₃	—	2	2	no	—
533	C₂³×C₃	—	4	1	no	—
534	C₂³×C₃	—	4	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	C₂³×C₃	C₂⁴	1	1	yes	characteristic
539	C₂²×D₃	—	2	2	no	—
540	C₂²×D₃	—	4	1	no	—
541	C₂²×D₃	—	4	1	no	—
542	C₂²×D₃	C₂⁴	1	1	yes	characteristic
543	C₂²×D₃	C₂⁴	1	1	yes	characteristic
544	C₂²×D₃	C₂⁴	1	1	yes	characteristic
545	C₃×Q₈	—	4	1	no	—
546	C₃×D₄	—	2	2	no	—
547	C₃×D₄	—	4	1	no	—
548	C₃×D₄	—	4	1	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	4	1	no	—
551	C₂×C₃×C₄	—	4	1	no	—
552	C₂×C₃×C₄	—	4	1	no	—
553	C₂×C₃×C₄	—	4	1	no	—
554	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
555	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
556	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	2	no	—
566	#67	—	2	2	no	—
567	#67	—	2	2	no	—
568	#67	—	2	2	no	—
569	#67	—	2	2	no	—
570	#67	—	4	1	no	—
571	#67	—	4	1	no	—
572	#67	—	4	1	no	—
573	#67	—	4	1	no	—
574	#67	#41	1	4	yes	—
575	C₂×Dic₃	—	2	2	no	—
576	C₂×Dic₃	—	2	2	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	—	4	1	no	—
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	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
594	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
595	D₁₂	—	2	2	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	Dic₆	—	2	2	no	—
609	Dic₆	—	2	2	no	—
610	Dic₆	—	4	1	no	—
611	Dic₆	—	4	1	no	—
612	C₂⁴	—	3	1	no	—
613	C₂⁴	C₂²×D₃	1	1	yes	characteristic
614	#41	—	6	4	no	—
615	#41	—	6	4	no	—
616	C₂×Q₈	—	3	1	no	—
617	C₂×Q₈	—	3	1	no	—
618	C₂×Q₈	—	3	1	no	—
619	C₂×Q₈	—	3	1	no	—
620	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
621	C₂×D₄	—	3	1	no	—
622	C₂×D₄	—	3	1	no	—
623	C₂×D₄	—	3	1	no	—
624	C₂×D₄	—	3	1	no	—
625	C₂×D₄	—	3	1	no	—
626	C₂×D₄	—	3	1	no	—
627	C₂×D₄	—	3	1	no	—
628	C₂×D₄	—	3	1	no	—
629	C₂×D₄	—	3	1	no	—
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	3	1	no	—
632	C₂×D₄	—	3	1	no	—
633	C₂×D₄	—	6	4	no	—
634	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
635	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
636	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
637	C₂²×C₄	—	3	1	no	—
638	C₂²×C₄	—	3	1	no	—
639	C₂²×C₄	—	3	1	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	3	1	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	3	1	no	—
647	C₂²×C₄	—	3	1	no	—
648	C₂²×C₄	—	3	1	no	—
649	C₂²×C₄	—	3	1	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
656	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
657	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
658	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
659	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
669	C₄⋊C₄	—	3	1	no	—
670	C₄⋊C₄	—	3	1	no	—
671	C₄⋊C₄	—	3	1	no	—
672	C₄⋊C₄	—	3	1	no	—
673	C₄⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
699	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
700	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
701	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
702	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
703	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
706	C₂²⋊C₄	—	3	1	no	—
707	C₂²⋊C₄	—	3	1	no	—
708	C₂²⋊C₄	—	3	1	no	—
709	C₂²⋊C₄	—	3	1	no	—
710	C₂²⋊C₄	—	3	1	no	—
711	C₂²⋊C₄	—	3	1	no	—
712	C₂²⋊C₄	—	3	1	no	—
713	C₂²⋊C₄	—	3	1	no	—
714	C₂²⋊C₄	—	3	1	no	—
715	C₂²⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
739	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
740	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
741	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
742	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
743	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
744	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
745	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
746	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
747	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
748	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
749	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
750	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
751	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
752	C₄²	—	3	1	no	—
753	C₄²	—	3	1	no	—
754	C₄²	—	3	1	no	—
755	C₄²	—	3	1	no	—
756	C₄²	—	3	1	no	—
757	C₄²	—	3	1	no	—
758	C₄²	—	3	1	no	—
759	C₄²	—	3	1	no	—
760	C₄²	—	3	1	no	—
761	C₄²	—	3	1	no	—
762	C₄²	—	3	1	no	—
763	C₄²	—	3	1	no	—
764	C₄²	—	3	1	no	—
765	C₄²	—	3	1	no	—
766	C₄²	—	3	1	no	—
767	C₄²	C₂²×D₃	1	1	yes	characteristic
768	C₄²	C₂²×D₃	1	1	yes	characteristic
769	C₄²	C₂²×D₃	1	1	yes	characteristic
770	C₂²×C₃	—	2	1	no	—
771	C₂²×C₃	—	2	1	no	—
772	C₂²×C₃	—	2	1	no	—
773	C₂²×C₃	—	2	1	no	—
774	C₂²×C₃	—	2	1	no	—
775	C₂²×C₃	—	2	1	no	—
776	C₂²×C₃	—	2	1	no	—
777	C₂²×C₃	—	2	1	no	—
778	C₂²×C₃	—	2	1	no	—
779	C₂²×C₃	—	2	1	no	—
780	C₂²×C₃	—	2	1	no	—
781	C₂²×C₃	—	8	2	no	—
782	C₂²×C₃	C₂×#41	1	2	yes	—
783	C₂²×C₃	C₂⁵	1	1	yes	characteristic
784	C₂×D₃	—	2	1	no	—
785	C₂×D₃	—	2	1	no	—
786	C₂×D₃	—	2	1	no	—
787	C₂×D₃	—	2	1	no	—
788	C₂×D₃	—	2	1	no	—
789	C₂×D₃	—	2	1	no	—
790	C₂×D₃	—	2	1	no	—
791	C₂×D₃	—	2	1	no	—
792	C₂×D₃	—	8	2	no	—
793	C₂×D₃	C₂×#41	1	2	yes	—
794	C₃×C₄	—	2	1	no	—
795	C₃×C₄	—	2	1	no	—
796	C₃×C₄	—	2	1	no	—
797	C₃×C₄	—	2	1	no	—
798	C₃×C₄	—	2	1	no	—
799	C₃×C₄	—	2	1	no	—
800	C₃×C₄	—	2	1	no	—
801	C₃×C₄	—	2	1	no	—
802	C₃×C₄	—	2	1	no	—
803	C₃×C₄	—	2	1	no	—
804	C₃×C₄	—	2	1	no	—
805	Dic₃	—	2	1	no	—
806	Dic₃	—	2	1	no	—
807	Dic₃	—	2	1	no	—
808	Dic₃	—	2	1	no	—
809	Dic₃	—	2	1	no	—
810	Dic₃	—	2	1	no	—
811	Dic₃	—	2	1	no	—
812	Dic₃	—	2	1	no	—
813	Dic₃	—	2	1	no	—
814	Dic₃	—	2	1	no	—
815	Dic₃	—	2	1	no	—
816	Dic₃	—	2	1	no	—
817	Dic₃	C₂×#41	1	2	yes	—
818	C₂³	—	2	2	no	—
819	C₂³	—	3	1	no	—
820	C₂³	—	3	1	no	—
821	C₂³	—	3	1	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	6	2	no	—
825	C₂³	—	12	1	no	—
826	C₂³	—	12	1	no	—
827	C₂³	C₂³×D₃	1	1	yes	characteristic
828	C₂³	C₂³×D₃	1	1	yes	characteristic
829	C₂³	C₂³×D₃	1	1	yes	characteristic
830	C₂³	C₂³×D₃	1	1	yes	characteristic
831	Q₈	—	4	1	no	—
832	Q₈	—	6	2	no	—
833	Q₈	—	6	2	no	—
834	Q₈	—	12	1	no	—
835	Q₈	—	12	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	3	4	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	6	2	no	—
841	D₄	—	6	2	no	—
842	D₄	—	6	2	no	—
843	D₄	—	6	2	no	—
844	D₄	—	6	2	no	—
845	D₄	—	6	2	no	—
846	D₄	—	12	1	no	—
847	D₄	—	12	1	no	—
848	D₄	—	12	1	no	—
849	D₄	—	12	1	no	—
850	D₄	—	12	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	3	1	no	—
853	C₂×C₄	—	3	1	no	—
854	C₂×C₄	—	3	1	no	—
855	C₂×C₄	—	3	1	no	—
856	C₂×C₄	—	3	1	no	—
857	C₂×C₄	—	3	1	no	—
858	C₂×C₄	—	3	1	no	—
859	C₂×C₄	—	3	1	no	—
860	C₂×C₄	—	3	1	no	—
861	C₂×C₄	—	3	1	no	—
862	C₂×C₄	—	3	1	no	—
863	C₂×C₄	—	3	1	no	—
864	C₂×C₄	—	3	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	6	2	no	—
870	C₂×C₄	—	6	2	no	—
871	C₂×C₄	—	6	2	no	—
872	C₂×C₄	—	6	2	no	—
873	C₂×C₄	—	6	2	no	—
874	C₂×C₄	—	6	2	no	—
875	C₂×C₄	—	12	1	no	—
876	C₂×C₄	—	12	1	no	—
877	C₂×C₄	—	12	1	no	—
878	C₂×C₄	—	12	1	no	—
879	C₂×C₄	—	12	1	no	—
880	C₂×C₄	—	12	1	no	—
881	C₂×C₄	—	12	1	no	—
882	C₂×C₄	—	12	1	no	—
883	C₂×C₄	—	12	1	no	—
884	C₂×C₄	—	12	1	no	—
885	C₂×C₄	—	12	1	no	—
886	C₂×C₄	—	12	1	no	—
887	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
895	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
896	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
897	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
898	C₂×C₃	—	2	2	no	—
899	C₂×C₃	—	4	1	no	—
900	C₂×C₃	—	4	1	no	—
901	C₂×C₃	—	4	1	no	—
902	C₂×C₃	C₂²×#41	1	1	yes	characteristic
903	C₂×C₃	#585	1	1	yes	characteristic
904	C₂×C₃	#585	1	1	yes	characteristic
905	D₃	—	2	2	no	—
906	D₃	—	4	1	no	—
907	D₃	—	4	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	3	2	no	—
920	C₂²	—	6	1	no	—
921	C₂²	—	6	1	no	—
922	C₂²	—	6	1	no	—
923	C₂²	—	6	1	no	—
924	C₂²	—	6	1	no	—
925	C₂²	—	6	1	no	—
926	C₂²	—	6	1	no	—
927	C₂²	—	6	1	no	—
928	C₂²	—	8	2	no	—
929	C₂²	—	24	2	no	—
930	C₂²	D₃×#41	1	2	yes	—
931	C₂²	C₂⁴×D₃	1	1	yes	characteristic
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	3	2	no	—
944	C₄	—	6	1	no	—
945	C₄	—	6	1	no	—
946	C₄	—	6	1	no	—
947	C₄	—	6	1	no	—
948	C₄	—	6	1	no	—
949	C₄	—	6	1	no	—
950	C₄	—	6	1	no	—
951	C₄	—	6	1	no	—
952	C₄	—	6	1	no	—
953	C₄	—	6	1	no	—
954	C₄	—	6	1	no	—
955	C₄	—	6	1	no	—
956	C₃	#3521	1	1	yes	characteristic, complemented, Sylow
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	6	2	no	—
962	C₂	—	12	1	no	—
963	C₂	—	12	1	no	—
964	C₂	C₂×D₃×#41	1	1	yes	characteristic
965	C₂	#5964	1	1	yes	characteristic
966	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#551	C₂
hypercenter	#551	D₃
hypocenter	C₃	#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₃×#551	C₂	semidirect
2. #5708	C₂	semidirect
3. #5705	C₂	semidirect
4. D₃×#126	C₂	semidirect
5. #5701	C₂	semidirect
6. #5678	C₂	semidirect
7. #5671	C₂	semidirect
8. #5665	C₂	semidirect
9. #5661	C₂	semidirect
10. #5660	C₂	semidirect
11. #5659	C₂	semidirect
12. #5655	C₂	semidirect
13. #5649	C₂	semidirect
14. #5640	C₂	semidirect
15. #5639	C₂	semidirect
16. #5636	C₂	semidirect
17. #5624	C₂	semidirect
18. #5593	C₂	semidirect
19. #5591	C₂	semidirect
20. #5558	C₂	semidirect
21. #5540	C₂	semidirect
22. #5538	C₂	semidirect
23. C₄×#237	C₂	semidirect
24. #5533	C₂	semidirect
25. #5531	C₂	semidirect
26. #5528	C₂	semidirect
27. #5523	C₂	semidirect
28. #5495	C₂	semidirect
29. #5490	C₂	semidirect
30. #5486	C₂	semidirect
31. C₂×#879	C₂	semidirect
40. C₃×#123	C₂²	semidirect
41. C₃×#123	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
43. C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₄×D₄	C₂²	semidirect
46. C₃×C₄×D₄	C₂²	semidirect
47. C₃×#117	C₂²	semidirect
48. C₃×#117	C₂²	semidirect
54. #947	C₂²	semidirect
55. #946	C₂²	semidirect
56. Q₈×Dic₃	C₂²	semidirect
57. #944	C₂²	semidirect
61. #939	C₂²	semidirect
63. #938	C₂²	semidirect
66. #935	C₂²	semidirect
68. D₄×Dic₃	C₂²	semidirect
71. #929	C₂²	semidirect
72. #929	C₂²	semidirect
78. C₄×#67	C₂²	semidirect
79. C₄×#67	C₂²	semidirect
80. C₄×#67	C₂²	semidirect
81. #926	C₂²	semidirect
82. C₂×C₄⋊Dic₃	C₂²	semidirect
83. #924	C₂²	semidirect
84. C₂×Dic₃⋊C₄	C₂²	semidirect
85. C₂×Dic₃⋊C₄	C₂²	semidirect
86. C₂×C₄×Dic₃	C₂²	semidirect
87. C₂×C₄×Dic₃	C₂²	semidirect
88. #898	C₂²	semidirect
89. #898	C₂²	semidirect
90. #898	C₂²	semidirect
91. #898	C₂²	semidirect
92. #897	C₂²	semidirect
93. #896	C₂²	semidirect
94. #896	C₂²	semidirect
95. #896	C₂²	semidirect
96. #896	C₂²	semidirect
97. #894	C₂²	semidirect
98. #894	C₂²	semidirect
99. #893	C₂²	semidirect
100. #892	C₂²	semidirect
101. #892	C₂²	semidirect
102. #892	C₂²	semidirect
103. #892	C₂²	semidirect
104. #892	C₂²	semidirect
105. D₃×C₄⋊C₄	C₂²	semidirect
106. D₃×C₄⋊C₄	C₂²	semidirect
107. D₃×C₄⋊C₄	C₂²	semidirect
108. D₃×C₄⋊C₄	C₂²	semidirect
109. #890	C₂²	semidirect
110. #890	C₂²	semidirect
111. #889	C₂²	semidirect
112. #889	C₂²	semidirect
113. #889	C₂²	semidirect
114. #889	C₂²	semidirect
115. #889	C₂²	semidirect
116. #889	C₂²	semidirect
117. #888	C₂²	semidirect
118. #887	C₂²	semidirect
119. #887	C₂²	semidirect
121. #886	C₂²	semidirect
122. #886	C₂²	semidirect
126. #885	C₂²	semidirect
129. #884	C₂²	semidirect
130. #884	C₂²	semidirect
135. #883	C₂²	semidirect
136. #883	C₂²	semidirect
144. #67⋊C₄	C₂²	semidirect
145. #67⋊C₄	C₂²	semidirect
146. #67⋊C₄	C₂²	semidirect
147. #67⋊C₄	C₂²	semidirect
159. #879	C₂²	semidirect
160. #879	C₂²	semidirect
161. #879	C₂²	semidirect
162. #879	C₂²	semidirect
163. #879	C₂²	semidirect
164. #879	C₂²	semidirect
165. #879	C₂²	semidirect
168. #878	C₂²	semidirect
169. #878	C₂²	semidirect
170. #878	C₂²	semidirect
171. #878	C₂²	semidirect
174. #877	C₂²	semidirect
175. #877	C₂²	semidirect
176. #876	C₂²	semidirect
177. #876	C₂²	semidirect
178. C₄×D₁₂	C₂²	semidirect
179. C₄×D₁₂	C₂²	semidirect
180. #872	C₂²	semidirect
181. #872	C₂²	semidirect
182. C₄²×D₃	C₂²	semidirect
183. #870	C₂²	semidirect
184. C₄×Dic₆	C₂²	semidirect
185. C₄×Dic₆	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
200. #551	D₃	semidirect
436. #123	C₂×D₃	semidirect
437. #123	C₂×D₃	semidirect
451. C₂²⋊Q₈	C₂×D₃	semidirect
452. C₂²⋊Q₈	C₂×D₃	semidirect
498. C₄×D₄	C₂×D₃	semidirect
499. C₄×D₄	C₂×D₃	semidirect
512. #117	C₂×D₃	semidirect
513. #117	C₂×D₃	semidirect
956. C₃	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₃×#551	2
#5708	2
#5705	2
D₃×#126	2
#5701	2
#5678	2
#5671	2
#5665	2
#5661	2
#5660	2
#5659	2
#5655	2
#5649	2
#5640	2
#5639	2
#5636	2
#5624	2
#5593	2
#5591	2
#5558	2
#5540	2
#5538	2
C₄×#237	2
#5533	2
#5531	2
#5528	2
#5523	2
#5495	2
#5490	2
#5486	2
C₂×#879	2
#3521	3