Subgroups — #86829

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#5710	C₂	1	1	yes	maximal, characteristic, complemented
3	#5708	C₂	1	1	yes	maximal, characteristic, complemented
4	#5706	C₂	1	1	yes	maximal, characteristic, complemented
5	#5702	C₂	1	1	yes	maximal, characteristic, complemented
6	#5696	C₂	1	1	yes	maximal, characteristic, complemented
7	#5696	C₂	1	1	yes	maximal, characteristic, complemented
8	#5693	C₂	1	1	yes	maximal, characteristic, complemented
9	#5693	C₂	1	1	yes	maximal, characteristic, complemented
10	#5690	C₂	1	1	yes	maximal, characteristic, complemented
11	#5688	C₂	1	1	yes	maximal, characteristic, complemented
12	#5658	C₂	1	1	yes	maximal, characteristic, complemented
13	#5656	C₂	1	1	yes	maximal, characteristic
14	#5650	C₂	1	1	yes	maximal, characteristic, complemented
15	#5648	C₂	1	1	yes	maximal, characteristic, complemented
16	#5640	C₂	1	1	yes	maximal, characteristic, complemented
17	#5637	C₂	1	1	yes	maximal, characteristic, complemented
18	#5636	C₂	1	1	yes	maximal, characteristic, complemented
19	#5623	C₂	1	1	yes	maximal, characteristic, complemented
20	#5578	C₂	1	1	yes	maximal, characteristic, complemented
21	#5568	C₂	1	1	yes	maximal, characteristic, complemented
22	#5556	C₂	1	1	yes	maximal, characteristic, complemented
23	#5546	C₂	1	1	yes	maximal, characteristic, complemented
24	#5531	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	#5527	C₂	1	1	yes	maximal, characteristic, complemented
28	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
29	#5516	C₂	1	1	yes	maximal, characteristic, complemented
30	#5513	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#896	C₂	1	1	yes	maximal, characteristic, complemented
32	#3495	—	3	1	no	maximal, Sylow
33	C₂×#237	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
35	C₂²×Dic₆	C₂²	1	1	yes	characteristic
36	C₃×#126	C₂²	1	1	yes	characteristic, complemented
37	C₃×#126	C₂²	1	1	yes	characteristic, complemented
38	C₃×#125	C₂²	1	1	yes	characteristic, complemented
39	C₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₃×#125	C₂²	1	1	yes	characteristic, complemented
41	C₃×#123	C₂²	1	1	yes	characteristic
42	C₃×#123	C₂²	1	1	yes	characteristic
43	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₃×#117	C₂²	1	1	yes	characteristic
48	C₃×#117	C₂²	1	1	yes	characteristic
49	C₃×#117	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	#947	C₂²	1	1	yes	characteristic
52	#946	C₂²	1	1	yes	characteristic
53	#944	C₂²	1	1	yes	characteristic, complemented
54	#944	C₂²	1	1	yes	characteristic, complemented
55	#937	C₂²	1	1	yes	characteristic
56	#935	C₂²	1	1	yes	characteristic
57	D₄×Dic₃	C₂²	1	1	yes	characteristic
58	#929	C₂²	1	1	yes	characteristic
59	#929	C₂²	1	1	yes	characteristic
60	#929	C₂²	1	1	yes	characteristic
61	C₄×#67	C₂²	1	1	yes	characteristic
62	C₄×#67	C₂²	1	1	yes	characteristic
63	C₄×#67	C₂²	1	1	yes	characteristic, complemented
64	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
65	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
66	#926	C₂²	1	1	yes	characteristic
67	#926	C₂²	1	1	yes	characteristic
68	#924	C₂²	1	1	yes	characteristic
69	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
70	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
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, complemented
79	#898	C₂²	1	1	yes	characteristic, complemented
80	#898	C₂²	1	1	yes	characteristic, complemented
81	#897	C₂²	1	1	yes	characteristic
82	#897	C₂²	1	1	yes	characteristic, complemented
83	#896	C₂²	1	1	yes	characteristic
84	#896	C₂²	1	1	yes	characteristic
85	#896	C₂²	1	1	yes	characteristic
86	#896	C₂²	1	1	yes	characteristic
87	#896	C₂²	1	1	yes	characteristic
88	#896	C₂²	1	1	yes	characteristic
89	#896	C₂²	1	1	yes	characteristic
90	#896	C₂²	1	1	yes	characteristic
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, complemented
96	#896	C₂²	1	1	yes	characteristic, complemented
97	#896	C₂²	1	1	yes	characteristic, complemented
98	#894	C₂²	1	1	yes	characteristic
99	#894	C₂²	1	1	yes	characteristic
100	#894	C₂²	1	1	yes	characteristic
101	#894	C₂²	1	1	yes	characteristic
102	#893	C₂²	1	1	yes	characteristic
103	#893	C₂²	1	1	yes	characteristic
104	#893	C₂²	1	1	yes	characteristic
105	#892	C₂²	1	1	yes	characteristic
106	#892	C₂²	1	1	yes	characteristic
107	#892	C₂²	1	1	yes	characteristic
108	#892	C₂²	1	1	yes	characteristic
109	#892	C₂²	1	1	yes	characteristic, complemented
110	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	#890	C₂²	1	1	yes	characteristic, complemented
114	#890	C₂²	1	1	yes	characteristic, complemented
115	#889	C₂²	1	1	yes	characteristic, complemented
116	#889	C₂²	1	1	yes	characteristic, complemented
117	#889	C₂²	1	1	yes	characteristic, complemented
118	#889	C₂²	1	1	yes	characteristic, complemented
119	#889	C₂²	1	1	yes	characteristic, complemented
120	#889	C₂²	1	1	yes	characteristic, complemented
121	#889	C₂²	1	1	yes	characteristic, complemented
122	#889	C₂²	1	1	yes	characteristic, complemented
123	#889	C₂²	1	1	yes	characteristic, complemented
124	#889	C₂²	1	1	yes	characteristic, complemented
125	#888	C₂²	1	1	yes	characteristic, complemented
126	#888	C₂²	1	1	yes	characteristic, complemented
127	#888	C₂²	1	1	yes	characteristic, complemented
128	#888	C₂²	1	1	yes	characteristic, complemented
129	#887	C₂²	1	1	yes	characteristic, complemented
130	#887	C₂²	1	1	yes	characteristic, complemented
131	#887	C₂²	1	1	yes	characteristic, complemented
132	#887	C₂²	1	1	yes	characteristic, complemented
133	#887	C₂²	1	1	yes	characteristic, complemented
134	#887	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic
137	#886	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, complemented
141	#885	C₂²	1	1	yes	characteristic, complemented
142	#884	C₂²	1	1	yes	characteristic
143	#884	C₂²	1	1	yes	characteristic
144	#883	C₂²	1	1	yes	characteristic
145	#883	C₂²	1	1	yes	characteristic
146	#882	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
150	#67⋊C₄	C₂²	1	1	yes	characteristic
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	#879	C₂²	1	1	yes	characteristic, complemented
155	#879	C₂²	1	1	yes	characteristic, complemented
156	#878	C₂²	1	1	yes	characteristic
157	#878	C₂²	1	1	yes	characteristic
158	#878	C₂²	1	1	yes	characteristic, complemented
159	#878	C₂²	1	1	yes	characteristic, complemented
160	#878	C₂²	1	1	yes	characteristic, complemented
161	#877	C₂²	1	1	yes	characteristic
162	#877	C₂²	1	1	yes	characteristic
163	#877	C₂²	1	1	yes	characteristic
164	#877	C₂²	1	1	yes	characteristic
165	#877	C₂²	1	1	yes	characteristic
166	#877	C₂²	1	1	yes	characteristic, complemented
167	#877	C₂²	1	1	yes	characteristic, complemented
168	#876	C₂²	1	1	yes	characteristic
169	#876	C₂²	1	1	yes	characteristic
170	#876	C₂²	1	1	yes	characteristic, complemented
171	#875	C₂²	1	1	yes	characteristic
172	C₄×D₁₂	C₂²	1	1	yes	characteristic
173	#872	C₂²	1	1	yes	characteristic
174	#872	C₂²	1	1	yes	characteristic
175	#872	C₂²	1	1	yes	characteristic
176	#872	C₂²	1	1	yes	characteristic
177	#872	C₂²	1	1	yes	characteristic, complemented
178	#872	C₂²	1	1	yes	characteristic, complemented
179	C₄²×D₃	C₂²	1	1	yes	characteristic
180	C₄²×D₃	C₂²	1	1	yes	characteristic
181	#870	C₂²	1	1	yes	characteristic, complemented
182	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₆	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	#554	—	3	1	no	—
192	#552	—	3	1	no	—
193	#552	—	3	1	no	—
194	#552	—	3	1	no	—
195	#552	—	3	1	no	—
196	#552	—	3	1	no	—
197	#552	—	3	1	no	—
198	#552	—	3	1	no	—
199	#552	D₃	1	1	yes	characteristic, complemented
200	#551	—	3	1	no	—
201	#551	—	3	1	no	—
202	#551	—	3	1	no	—
203	#551	—	3	1	no	—
204	#544	—	3	1	no	—
205	#542	—	3	1	no	—
206	#542	—	3	1	no	—
207	#541	—	3	1	no	—
208	#541	—	3	1	no	—
209	#536	—	3	1	no	—
210	#533	—	3	1	no	—
211	#533	—	3	1	no	—
212	#529	—	3	1	no	—
213	#529	—	3	1	no	—
214	#525	—	3	1	no	—
215	C₂×C₂²⋊Q₈	—	3	1	no	—
216	#520	—	3	1	no	—
217	#519	—	3	1	no	—
218	C₂×#117	—	3	1	no	—
219	C₂³×D₃	C₂³	1	1	yes	characteristic
220	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
226	C₂×#67	C₂³	1	1	yes	characteristic
227	C₂×#67	C₂³	1	1	yes	characteristic
228	C₂×#67	C₂³	1	1	yes	characteristic
229	C₂×#67	C₂³	1	1	yes	characteristic
230	C₂²×Dic₃	C₂³	1	1	yes	characteristic
231	C₂²×Dic₃	C₂³	1	1	yes	characteristic
232	C₂²×Dic₃	C₂³	1	1	yes	characteristic
233	C₂²×Dic₃	C₂³	1	1	yes	characteristic
234	C₂²×Dic₃	C₂³	1	1	yes	characteristic
235	#237	—	2	4	no	—
236	C₂×D₁₂	C₂³	1	1	yes	characteristic
237	C₂×D₁₂	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₃	—	2	4	no	—
239	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
250	C₂×Dic₆	—	2	4	no	—
251	C₂×Dic₆	C₂³	1	1	yes	characteristic
252	C₂×Dic₆	C₂³	1	1	yes	characteristic
253	C₂×Dic₆	C₂³	1	1	yes	characteristic
254	C₂×Dic₆	C₂³	1	1	yes	characteristic
255	C₂×Dic₆	C₂³	1	1	yes	characteristic
256	C₂×Dic₆	C₂³	1	1	yes	characteristic
257	C₂×Dic₆	C₂³	1	1	yes	characteristic
258	C₂×Dic₆	C₂³	1	1	yes	characteristic
259	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₃×C₄⋊C₄	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×C₄²	C₂³	1	1	yes	characteristic
284	C₃×C₄²	C₂³	1	1	yes	characteristic
285	C₃×C₄²	C₂³	1	1	yes	characteristic
286	C₃×C₄²	C₂³	1	1	yes	characteristic
287	C₃×C₄²	C₂³	1	1	yes	characteristic
288	#217	C₂³	1	1	yes	characteristic
289	#217	C₂³	1	1	yes	characteristic
290	#217	C₂³	1	1	yes	characteristic
291	#217	C₂³	1	1	yes	characteristic
292	#217	C₂³	1	1	yes	characteristic
293	#217	C₂³	1	1	yes	characteristic
294	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₃	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	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	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	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×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	C₂²×Q₈	—	3	1	no	—
379	C₂³×C₄	—	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	#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	C₂×D₃	1	1	yes	characteristic, complemented
401	#126	C₂×D₃	1	1	yes	characteristic, complemented
402	#125	—	3	1	no	—
403	#125	—	3	1	no	—
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	#125	—	3	1	no	—
414	#125	—	3	1	no	—
415	#125	C₂×D₃	1	1	yes	characteristic, complemented
416	#125	C₂×D₃	1	1	yes	characteristic, complemented
417	#125	C₂×D₃	1	1	yes	characteristic, complemented
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	#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	—	3	1	no	—
436	#123	C₂×D₃	1	1	yes	characteristic
437	#123	C₂×D₃	1	1	yes	characteristic
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	—	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	C₂×D₃	1	1	yes	characteristic
463	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
464	#121	—	3	1	no	—
465	#121	—	3	1	no	—
466	#120	—	3	1	no	—
467	#120	—	3	1	no	—
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×Q₈	—	3	1	no	—
476	C₄×Q₈	—	3	1	no	—
477	C₄×Q₈	—	3	1	no	—
478	C₄×Q₈	—	3	1	no	—
479	C₄×Q₈	—	3	1	no	—
480	C₄×Q₈	—	3	1	no	—
481	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic
496	#117	—	3	1	no	—
497	#117	—	3	1	no	—
498	#117	—	3	1	no	—
499	#117	—	3	1	no	—
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	—	3	1	no	—
513	#117	—	3	1	no	—
514	#117	—	3	1	no	—
515	#117	—	3	1	no	—
516	#117	C₂×D₃	1	1	yes	characteristic
517	#117	C₂×D₃	1	1	yes	characteristic
518	#117	C₂×D₃	1	1	yes	characteristic, complemented
519	C₂×C₄⋊C₄	—	3	1	no	—
520	C₂×C₄⋊C₄	—	3	1	no	—
521	C₂×C₄⋊C₄	—	3	1	no	—
522	C₂×C₄⋊C₄	—	3	1	no	—
523	C₂×C₄⋊C₄	—	3	1	no	—
524	C₂×C₄⋊C₄	—	3	1	no	—
525	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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×C₄²	—	3	1	no	—
531	C₂×C₄²	—	3	1	no	—
532	C₂³×C₃	C₂⁴	1	1	yes	characteristic
533	C₂³×C₃	C₂⁴	1	1	yes	characteristic
534	C₂²×D₃	—	2	2	no	—
535	C₂²×D₃	—	2	2	no	—
536	C₂²×D₃	—	4	1	no	—
537	C₂²×D₃	C₂⁴	1	1	yes	characteristic
538	C₂²×D₃	C₂⁴	1	1	yes	characteristic
539	C₂²×D₃	C₂⁴	1	1	yes	characteristic
540	C₃×Q₈	—	4	1	no	—
541	C₃×D₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	4	1	no	—
545	C₂×C₃×C₄	—	4	1	no	—
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	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	2	no	—
560	#67	—	2	2	no	—
561	#67	—	2	2	no	—
562	#67	—	4	1	no	—
563	C₂×Dic₃	—	2	2	no	—
564	C₂×Dic₃	—	2	2	no	—
565	C₂×Dic₃	—	4	1	no	—
566	C₂×Dic₃	—	4	1	no	—
567	C₂×Dic₃	#41	1	4	yes	—
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	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
573	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
574	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
575	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
576	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
577	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
578	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
579	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
580	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
581	D₁₂	—	2	2	no	—
582	D₁₂	—	4	1	no	—
583	C₄×D₃	—	2	2	no	—
584	C₄×D₃	—	2	2	no	—
585	C₄×D₃	—	2	2	no	—
586	C₄×D₃	—	2	2	no	—
587	C₄×D₃	—	2	2	no	—
588	C₄×D₃	—	2	2	no	—
589	C₄×D₃	—	2	2	no	—
590	C₄×D₃	—	4	1	no	—
591	C₄×D₃	—	4	1	no	—
592	C₄×D₃	—	4	1	no	—
593	C₄×D₃	—	4	1	no	—
594	Dic₆	—	2	2	no	—
595	Dic₆	—	2	2	no	—
596	Dic₆	—	2	2	no	—
597	Dic₆	—	2	2	no	—
598	Dic₆	—	2	2	no	—
599	Dic₆	—	4	1	no	—
600	Dic₆	—	4	1	no	—
601	Dic₆	—	4	1	no	—
602	C₂⁴	—	3	1	no	—
603	#41	—	6	4	no	—
604	C₂×Q₈	—	3	1	no	—
605	C₂×Q₈	—	3	1	no	—
606	C₂×Q₈	—	3	1	no	—
607	C₂×Q₈	—	3	1	no	—
608	C₂×Q₈	—	3	1	no	—
609	C₂×Q₈	—	3	1	no	—
610	C₂×Q₈	—	3	1	no	—
611	C₂×Q₈	—	3	1	no	—
612	C₂×Q₈	—	6	4	no	—
613	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
614	C₂×D₄	—	3	1	no	—
615	C₂×D₄	—	3	1	no	—
616	C₂×D₄	—	3	1	no	—
617	C₂×D₄	—	3	1	no	—
618	C₂×D₄	—	3	1	no	—
619	C₂×D₄	—	3	1	no	—
620	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
621	C₂²×C₄	—	3	1	no	—
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	1	no	—
626	C₂²×C₄	—	3	1	no	—
627	C₂²×C₄	—	3	1	no	—
628	C₂²×C₄	—	3	1	no	—
629	C₂²×C₄	—	3	1	no	—
630	C₂²×C₄	—	3	1	no	—
631	C₂²×C₄	—	3	1	no	—
632	C₂²×C₄	—	3	1	no	—
633	C₂²×C₄	—	3	1	no	—
634	C₂²×C₄	—	3	1	no	—
635	C₂²×C₄	—	3	1	no	—
636	C₂²×C₄	—	3	1	no	—
637	C₂²×C₄	—	6	4	no	—
638	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
639	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
640	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
641	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
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	—	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	C₂²×D₃	1	1	yes	characteristic
685	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
686	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
687	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
688	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
689	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
690	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
691	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
692	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
694	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
695	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
696	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
699	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
705	C₂²⋊C₄	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
731	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
732	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
733	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
734	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
735	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
736	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
737	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
738	C₄²	—	3	1	no	—
739	C₄²	—	3	1	no	—
740	C₄²	—	3	1	no	—
741	C₄²	—	3	1	no	—
742	C₄²	—	3	1	no	—
743	C₄²	—	3	1	no	—
744	C₄²	—	3	1	no	—
745	C₄²	—	3	1	no	—
746	C₄²	—	3	1	no	—
747	C₄²	—	3	1	no	—
748	C₄²	—	3	1	no	—
749	C₄²	—	3	1	no	—
750	C₄²	—	3	1	no	—
751	C₄²	—	3	1	no	—
752	C₄²	—	3	1	no	—
753	C₄²	—	3	1	no	—
754	C₄²	—	3	1	no	—
755	C₄²	C₂²×D₃	1	1	yes	characteristic
756	C₄²	C₂²×D₃	1	1	yes	characteristic
757	C₄²	C₂²×D₃	1	1	yes	characteristic
758	C₄²	C₂²×D₃	1	1	yes	characteristic
759	C₄²	C₂²×D₃	1	1	yes	characteristic
760	C₂²×C₃	—	2	1	no	—
761	C₂²×C₃	—	2	1	no	—
762	C₂²×C₃	—	2	1	no	—
763	C₂²×C₃	—	2	1	no	—
764	C₂²×C₃	—	2	1	no	—
765	C₂²×C₃	C₂×#41	1	2	yes	—
766	C₂²×C₃	C₂⁵	1	1	yes	characteristic
767	C₂×D₃	—	2	1	no	—
768	C₂×D₃	—	2	1	no	—
769	C₂×D₃	—	2	1	no	—
770	C₂×D₃	—	2	1	no	—
771	C₂×D₃	—	2	1	no	—
772	C₂×D₃	—	2	1	no	—
773	C₂×D₃	—	2	1	no	—
774	C₂×D₃	—	2	1	no	—
775	C₂×D₃	—	4	4	no	—
776	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
777	C₃×C₄	—	2	1	no	—
778	C₃×C₄	—	2	1	no	—
779	C₃×C₄	—	2	1	no	—
780	C₃×C₄	—	2	1	no	—
781	C₃×C₄	—	2	1	no	—
782	C₃×C₄	—	2	1	no	—
783	C₃×C₄	—	2	1	no	—
784	C₃×C₄	—	2	1	no	—
785	C₃×C₄	—	2	1	no	—
786	C₃×C₄	—	2	1	no	—
787	C₃×C₄	—	2	1	no	—
788	C₃×C₄	—	2	1	no	—
789	C₃×C₄	—	2	1	no	—
790	Dic₃	—	2	1	no	—
791	Dic₃	—	2	1	no	—
792	Dic₃	—	2	1	no	—
793	Dic₃	—	2	1	no	—
794	Dic₃	—	2	1	no	—
795	Dic₃	—	2	1	no	—
796	Dic₃	—	2	1	no	—
797	Dic₃	—	2	1	no	—
798	Dic₃	—	2	1	no	—
799	Dic₃	—	2	1	no	—
800	Dic₃	—	2	1	no	—
801	Dic₃	C₂×#41	1	2	yes	—
802	Dic₃	C₂×#41	1	2	yes	—
803	C₂³	—	3	1	no	—
804	C₂³	—	3	1	no	—
805	C₂³	—	3	1	no	—
806	C₂³	—	6	2	no	—
807	C₂³	—	6	2	no	—
808	C₂³	—	12	1	no	—
809	C₂³	C₂³×D₃	1	1	yes	characteristic
810	C₂³	C₂³×D₃	1	1	yes	characteristic
811	Q₈	—	4	1	no	—
812	Q₈	—	6	2	no	—
813	Q₈	—	6	2	no	—
814	Q₈	—	6	2	no	—
815	Q₈	—	6	2	no	—
816	Q₈	—	6	2	no	—
817	Q₈	—	12	1	no	—
818	Q₈	—	12	1	no	—
819	Q₈	—	12	1	no	—
820	D₄	—	2	2	no	—
821	D₄	—	6	2	no	—
822	D₄	—	6	2	no	—
823	D₄	—	6	2	no	—
824	D₄	—	6	2	no	—
825	D₄	—	12	1	no	—
826	D₄	—	12	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	3	4	no	—
830	C₂×C₄	—	3	1	no	—
831	C₂×C₄	—	3	1	no	—
832	C₂×C₄	—	3	1	no	—
833	C₂×C₄	—	3	1	no	—
834	C₂×C₄	—	3	1	no	—
835	C₂×C₄	—	3	1	no	—
836	C₂×C₄	—	3	1	no	—
837	C₂×C₄	—	3	1	no	—
838	C₂×C₄	—	3	1	no	—
839	C₂×C₄	—	3	1	no	—
840	C₂×C₄	—	3	1	no	—
841	C₂×C₄	—	3	1	no	—
842	C₂×C₄	—	3	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	6	2	no	—
846	C₂×C₄	—	6	2	no	—
847	C₂×C₄	—	6	2	no	—
848	C₂×C₄	—	6	2	no	—
849	C₂×C₄	—	6	2	no	—
850	C₂×C₄	—	6	2	no	—
851	C₂×C₄	—	6	2	no	—
852	C₂×C₄	—	6	2	no	—
853	C₂×C₄	—	6	2	no	—
854	C₂×C₄	—	12	1	no	—
855	C₂×C₄	—	12	1	no	—
856	C₂×C₄	—	12	1	no	—
857	C₂×C₄	—	12	1	no	—
858	C₂×C₄	—	12	1	no	—
859	C₂×C₄	—	12	1	no	—
860	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
867	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
868	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
869	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
870	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
871	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
872	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
873	C₂×C₃	—	2	2	no	—
874	C₂×C₃	—	4	1	no	—
875	C₂×C₃	C₂²×#41	1	1	yes	characteristic
876	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂×C₃	#585	1	1	yes	characteristic
878	D₃	—	2	2	no	—
879	D₃	—	4	1	no	—
880	D₃	—	4	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	3	2	no	—
887	C₂²	—	6	1	no	—
888	C₂²	—	6	1	no	—
889	C₂²	—	6	1	no	—
890	C₂²	—	6	1	no	—
891	C₂²	—	6	1	no	—
892	C₂²	—	6	1	no	—
893	C₂²	—	6	1	no	—
894	C₂²	—	6	1	no	—
895	C₂²	—	12	4	no	—
896	C₂²	D₃×#41	1	2	yes	—
897	C₂²	C₂⁴×D₃	1	1	yes	characteristic
898	C₄	—	2	1	no	—
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	1	no	—
911	C₄	—	3	2	no	—
912	C₄	—	3	2	no	—
913	C₄	—	6	1	no	—
914	C₄	—	6	1	no	—
915	C₄	—	6	1	no	—
916	C₄	—	6	1	no	—
917	C₄	—	6	1	no	—
918	C₄	—	6	1	no	—
919	C₄	—	6	1	no	—
920	C₄	—	6	1	no	—
921	C₄	—	6	1	no	—
922	C₄	—	6	1	no	—
923	C₄	—	6	1	no	—
924	C₃	#3495	1	1	yes	characteristic, complemented, Sylow
925	C₂	—	2	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	6	2	no	—
928	C₂	—	12	1	no	—
929	C₂	—	12	1	no	—
930	C₂	C₂×D₃×#41	1	1	yes	characteristic
931	C₂	#5964	1	1	yes	characteristic
932	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×#552	C₂
prime radical	#5656	C₂
hypercenter	#552	D₃
hypocenter	C₃	#3495
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₃×#552	C₂	semidirect
2. #5710	C₂	semidirect
3. #5708	C₂	semidirect
4. #5706	C₂	semidirect
5. #5702	C₂	semidirect
6. #5696	C₂	semidirect
7. #5696	C₂	semidirect
8. #5693	C₂	semidirect
9. #5693	C₂	semidirect
10. #5690	C₂	semidirect
11. #5688	C₂	semidirect
12. #5658	C₂	semidirect
14. #5650	C₂	semidirect
15. #5648	C₂	semidirect
16. #5640	C₂	semidirect
17. #5637	C₂	semidirect
18. #5636	C₂	semidirect
19. #5623	C₂	semidirect
20. #5578	C₂	semidirect
21. #5568	C₂	semidirect
22. #5556	C₂	semidirect
23. #5546	C₂	semidirect
24. #5531	C₂	semidirect
25. #5531	C₂	semidirect
26. #5528	C₂	semidirect
27. #5527	C₂	semidirect
28. D₃×#117	C₂	semidirect
29. #5516	C₂	semidirect
30. #5513	C₂	semidirect
31. C₂×#896	C₂	semidirect
36. C₃×#126	C₂²	semidirect
37. C₃×#126	C₂²	semidirect
38. C₃×#125	C₂²	semidirect
39. C₃×#125	C₂²	semidirect
40. C₃×#125	C₂²	semidirect
44. C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₄×Q₈	C₂²	semidirect
49. C₃×#117	C₂²	semidirect
53. #944	C₂²	semidirect
54. #944	C₂²	semidirect
63. C₄×#67	C₂²	semidirect
71. C₂×Dic₃⋊C₄	C₂²	semidirect
78. #898	C₂²	semidirect
79. #898	C₂²	semidirect
80. #898	C₂²	semidirect
82. #897	C₂²	semidirect
95. #896	C₂²	semidirect
96. #896	C₂²	semidirect
97. #896	C₂²	semidirect
109. #892	C₂²	semidirect
112. D₃×C₄⋊C₄	C₂²	semidirect
113. #890	C₂²	semidirect
114. #890	C₂²	semidirect
115. #889	C₂²	semidirect
116. #889	C₂²	semidirect
117. #889	C₂²	semidirect
118. #889	C₂²	semidirect
119. #889	C₂²	semidirect
120. #889	C₂²	semidirect
121. #889	C₂²	semidirect
122. #889	C₂²	semidirect
123. #889	C₂²	semidirect
124. #889	C₂²	semidirect
125. #888	C₂²	semidirect
126. #888	C₂²	semidirect
127. #888	C₂²	semidirect
128. #888	C₂²	semidirect
129. #887	C₂²	semidirect
130. #887	C₂²	semidirect
131. #887	C₂²	semidirect
132. #887	C₂²	semidirect
133. #887	C₂²	semidirect
134. #887	C₂²	semidirect
135. #887	C₂²	semidirect
140. #885	C₂²	semidirect
141. #885	C₂²	semidirect
151. #67⋊C₄	C₂²	semidirect
154. #879	C₂²	semidirect
155. #879	C₂²	semidirect
158. #878	C₂²	semidirect
159. #878	C₂²	semidirect
160. #878	C₂²	semidirect
166. #877	C₂²	semidirect
167. #877	C₂²	semidirect
170. #876	C₂²	semidirect
177. #872	C₂²	semidirect
178. #872	C₂²	semidirect
181. #870	C₂²	semidirect
182. C₄×Dic₆	C₂²	semidirect
183. C₄×Dic₆	C₂²	semidirect
184. C₄×Dic₆	C₂²	semidirect
185. C₄×Dic₆	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
199. #552	D₃	semidirect
400. #126	C₂×D₃	semidirect
401. #126	C₂×D₃	semidirect
415. #125	C₂×D₃	semidirect
416. #125	C₂×D₃	semidirect
417. #125	C₂×D₃	semidirect
463. C₂²⋊Q₈	C₂×D₃	semidirect
481. C₄×Q₈	C₂×D₃	semidirect
518. #117	C₂×D₃	semidirect
924. C₃	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₃×#552	2
#5710	2
#5708	2
#5706	2
#5702	2
#5696	2
#5693	2
#5690	2
#5688	2
#5658	2
#5656	2
#5650	2
#5648	2
#5640	2
#5637	2
#5636	2
#5623	2
#5578	2
#5568	2
#5556	2
#5546	2
#5531	2
#5528	2
#5527	2
D₃×#117	2
#5516	2
#5513	2
C₂×#896	2
#3495	3