Subgroups — #86813

Order 384.

958 conjugacy classes of subgroups.

The subgroup lattice has 954 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	#5712	C₂	1	1	yes	maximal, characteristic, complemented
3	#5710	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	#5678	C₂	1	1	yes	maximal, characteristic, complemented
7	#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	#5662	C₂	1	1	yes	maximal, characteristic, complemented
9	#5662	C₂	1	1	yes	maximal, characteristic, complemented
10	#5659	C₂	1	1	yes	maximal, characteristic, complemented
11	#5658	C₂	1	1	yes	maximal, characteristic, complemented
12	#5657	C₂	1	1	yes	maximal, characteristic, complemented
13	#5651	C₂	1	1	yes	maximal, characteristic, complemented
14	#5646	C₂	1	1	yes	maximal, characteristic, complemented
15	#5643	C₂	1	1	yes	maximal, characteristic, complemented
16	#5641	C₂	1	1	yes	maximal, characteristic, complemented
17	#5640	C₂	1	1	yes	maximal, characteristic, complemented
18	#5594	C₂	1	1	yes	maximal, characteristic, complemented
19	#5593	C₂	1	1	yes	maximal, characteristic, complemented
20	#5560	C₂	1	1	yes	maximal, characteristic, complemented
21	#5557	C₂	1	1	yes	maximal, characteristic, complemented
22	#5556	C₂	1	1	yes	maximal, characteristic, complemented
23	#5542	C₂	1	1	yes	maximal, characteristic, complemented
24	#5534	C₂	1	1	yes	maximal, characteristic, complemented
25	#5533	C₂	1	1	yes	maximal, characteristic, complemented
26	#5533	C₂	1	1	yes	maximal, characteristic, complemented
27	#5528	C₂	1	1	yes	maximal, characteristic, complemented
28	#5495	C₂	1	1	yes	maximal, characteristic, complemented
29	#5495	C₂	1	1	yes	maximal, characteristic, complemented
30	#5494	C₂	1	1	yes	maximal, characteristic, complemented
31	#5494	C₂	1	1	yes	maximal, characteristic, complemented
32	#3568	—	3	1	no	maximal, Sylow
33	C₃×#126	C₂²	1	1	yes	characteristic, complemented
34	C₃×#126	C₂²	1	1	yes	characteristic, complemented
35	C₃×#124	C₂²	1	1	yes	characteristic
36	C₃×#123	C₂²	1	1	yes	characteristic
37	C₃×#123	C₂²	1	1	yes	characteristic
38	C₃×#123	C₂²	1	1	yes	characteristic
39	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×#120	C₂²	1	1	yes	characteristic
42	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₃×#117	C₂²	1	1	yes	characteristic, complemented
45	C₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	#953	C₂²	1	1	yes	characteristic
49	#953	C₂²	1	1	yes	characteristic
50	#953	C₂²	1	1	yes	characteristic, complemented
51	C₂×#217	C₂²	1	1	yes	characteristic, complemented
52	#947	C₂²	1	1	yes	characteristic, complemented
53	#946	C₂²	1	1	yes	characteristic, complemented
54	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
55	#944	C₂²	1	1	yes	characteristic, complemented
56	#939	C₂²	1	1	yes	characteristic
57	#939	C₂²	1	1	yes	characteristic
58	#938	C₂²	1	1	yes	characteristic
59	#937	C₂²	1	1	yes	characteristic
60	#937	C₂²	1	1	yes	characteristic
61	#937	C₂²	1	1	yes	characteristic
62	#936	C₂²	1	1	yes	characteristic
63	#936	C₂²	1	1	yes	characteristic
64	#936	C₂²	1	1	yes	characteristic
65	#936	C₂²	1	1	yes	characteristic
66	#935	C₂²	1	1	yes	characteristic
67	D₄×Dic₃	C₂²	1	1	yes	characteristic
68	#930	C₂²	1	1	yes	characteristic
69	#930	C₂²	1	1	yes	characteristic
70	#929	C₂²	1	1	yes	characteristic
71	#929	C₂²	1	1	yes	characteristic
72	C₄×#67	C₂²	1	1	yes	characteristic
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, complemented
77	C₄×#67	C₂²	1	1	yes	characteristic, complemented
78	C₄×#67	C₂²	1	1	yes	characteristic, complemented
79	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	#926	C₂²	1	1	yes	characteristic, complemented
81	#926	C₂²	1	1	yes	characteristic, complemented
82	#926	C₂²	1	1	yes	characteristic, complemented
83	#924	C₂²	1	1	yes	characteristic, complemented
84	#924	C₂²	1	1	yes	characteristic, complemented
85	#924	C₂²	1	1	yes	characteristic, complemented
86	#924	C₂²	1	1	yes	characteristic, complemented
87	#924	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	#898	C₂²	1	1	yes	characteristic, complemented
93	#898	C₂²	1	1	yes	characteristic, complemented
94	#898	C₂²	1	1	yes	characteristic, complemented
95	#897	C₂²	1	1	yes	characteristic, complemented
96	#897	C₂²	1	1	yes	characteristic, complemented
97	#897	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	#894	C₂²	1	1	yes	characteristic, complemented
104	#894	C₂²	1	1	yes	characteristic, complemented
105	#893	C₂²	1	1	yes	characteristic, complemented
106	#892	C₂²	1	1	yes	characteristic, complemented
107	#892	C₂²	1	1	yes	characteristic, complemented
108	#892	C₂²	1	1	yes	characteristic, complemented
109	#890	C₂²	1	1	yes	characteristic, complemented
110	#889	C₂²	1	1	yes	characteristic, complemented
111	#889	C₂²	1	1	yes	characteristic, complemented
112	#888	C₂²	1	1	yes	characteristic, complemented
113	#888	C₂²	1	1	yes	characteristic, complemented
114	#888	C₂²	1	1	yes	characteristic, complemented
115	#888	C₂²	1	1	yes	characteristic, complemented
116	#887	C₂²	1	1	yes	characteristic, complemented
117	#887	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
122	#885	C₂²	1	1	yes	characteristic
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
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
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
140	#883	C₂²	1	1	yes	characteristic
141	#883	C₂²	1	1	yes	characteristic
142	#883	C₂²	1	1	yes	characteristic
143	#883	C₂²	1	1	yes	characteristic
144	#883	C₂²	1	1	yes	characteristic, complemented
145	#883	C₂²	1	1	yes	characteristic, complemented
146	#883	C₂²	1	1	yes	characteristic, complemented
147	#883	C₂²	1	1	yes	characteristic, complemented
148	#882	C₂²	1	1	yes	characteristic, complemented
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, complemented
153	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	#879	C₂²	1	1	yes	characteristic, complemented
155	#879	C₂²	1	1	yes	characteristic, complemented
156	#879	C₂²	1	1	yes	characteristic, complemented
157	#879	C₂²	1	1	yes	characteristic, complemented
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	#879	C₂²	1	1	yes	characteristic, complemented
164	#879	C₂²	1	1	yes	characteristic, complemented
165	#879	C₂²	1	1	yes	characteristic, complemented
166	#879	C₂²	1	1	yes	characteristic, complemented
167	#879	C₂²	1	1	yes	characteristic, complemented
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	#878	C₂²	1	1	yes	characteristic, complemented
173	#877	C₂²	1	1	yes	characteristic, complemented
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	#876	C₂²	1	1	yes	characteristic, complemented
179	#875	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
181	#872	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
183	#869	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	#563	—	3	1	no	—
189	#563	—	3	1	no	—
190	#563	—	3	1	no	—
191	H(3,𝔽₄)	—	3	1	no	—
192	#556	—	3	1	no	—
193	#556	—	3	1	no	—
194	#556	—	3	1	no	—
195	#556	—	3	1	no	—
196	#556	—	3	1	no	—
197	#556	—	3	1	no	—
198	#551	—	3	1	no	—
199	#551	—	3	1	no	—
200	#551	—	3	1	no	—
201	#551	—	3	1	no	—
202	#551	—	3	1	no	—
203	#551	D₃	1	1	yes	characteristic, complemented
204	#542	—	3	1	no	—
205	#542	—	3	1	no	—
206	#542	—	3	1	no	—
207	#542	—	3	1	no	—
208	#542	—	3	1	no	—
209	#542	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#538	—	3	1	no	—
213	#538	—	3	1	no	—
214	#538	—	3	1	no	—
215	#538	—	3	1	no	—
216	#529	—	3	1	no	—
217	#529	—	3	1	no	—
218	#529	—	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	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	C₂×#67	C₂³	1	1	yes	characteristic
239	C₂×#67	C₂³	1	1	yes	characteristic
240	C₂²×Dic₃	C₂³	1	1	yes	characteristic
241	C₂²×Dic₃	C₂³	1	1	yes	characteristic
242	C₂²×Dic₃	C₂³	1	1	yes	characteristic
243	C₂×D₁₂	C₂³	1	1	yes	characteristic
244	C₂×D₁₂	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×C₄×D₃	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₃	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	C₂×Dic₆	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₃×C₂²⋊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×C₄²	C₂³	1	1	yes	characteristic
283	C₃×C₄²	C₂³	1	1	yes	characteristic
284	C₃×C₄²	C₂³	1	1	yes	characteristic
285	#217	C₂³	1	1	yes	characteristic
286	#217	C₂³	1	1	yes	characteristic
287	#217	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	#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	(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	(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	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	C₄⋊Dic₃	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	C₄×Dic₃	C₂³	1	1	yes	characteristic
360	C₄×Dic₃	C₂³	1	1	yes	characteristic
361	C₄×Dic₃	C₂³	1	1	yes	characteristic
362	C₄×Dic₃	C₂³	1	1	yes	characteristic
363	C₄×Dic₃	C₂³	1	1	yes	characteristic
364	C₄×Dic₃	C₂³	1	1	yes	characteristic
365	C₄×Dic₃	C₂³	1	1	yes	characteristic
366	C₄×Dic₃	C₂³	1	1	yes	characteristic
367	C₄×Dic₃	C₂³	1	1	yes	characteristic
368	C₄×Dic₃	C₂³	1	1	yes	characteristic
369	C₄×Dic₃	C₂³	1	1	yes	characteristic
370	C₄×Dic₃	C₂³	1	1	yes	characteristic
371	C₄×Dic₃	C₂³	1	1	yes	characteristic
372	C₄×Dic₃	C₂³	1	1	yes	characteristic
373	C₄×Dic₃	C₂³	1	1	yes	characteristic
374	C₄⋊Q₈	—	3	1	no	—
375	C₄⋊Q₈	—	3	1	no	—
376	C₄⋊Q₈	—	3	1	no	—
377	C₄⋊Q₈	—	3	1	no	—
378	C₄⋊Q₈	—	3	1	no	—
379	C₄⋊Q₈	—	3	1	no	—
380	#126	—	3	1	no	—
381	#126	—	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	—	3	1	no	—
403	#126	—	3	1	no	—
404	#126	C₂×D₃	1	1	yes	characteristic, complemented
405	#126	C₂×D₃	1	1	yes	characteristic, complemented
406	#125	—	3	1	no	—
407	#125	—	3	1	no	—
408	#125	—	3	1	no	—
409	#124	—	3	1	no	—
410	#124	—	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	—	3	1	no	—
428	#124	—	3	1	no	—
429	#124	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
446	#123	C₂×D₃	1	1	yes	characteristic
447	#123	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic, complemented
468	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
469	#121	—	3	1	no	—
470	#121	—	3	1	no	—
471	#121	—	3	1	no	—
472	#121	—	3	1	no	—
473	#121	—	3	1	no	—
474	#121	—	3	1	no	—
475	#121	—	3	1	no	—
476	#121	—	3	1	no	—
477	#121	—	3	1	no	—
478	#120	—	3	1	no	—
479	#120	—	3	1	no	—
480	#120	—	3	1	no	—
481	#120	—	3	1	no	—
482	#120	—	3	1	no	—
483	#120	—	3	1	no	—
484	#120	—	3	1	no	—
485	#120	C₂×D₃	1	1	yes	characteristic
486	C₄×Q₈	—	3	1	no	—
487	C₄×Q₈	—	3	1	no	—
488	C₄×Q₈	—	3	1	no	—
489	C₄×Q₈	—	3	1	no	—
490	C₄×Q₈	—	3	1	no	—
491	C₄×Q₈	—	3	1	no	—
492	C₄×Q₈	—	3	1	no	—
493	C₄×Q₈	—	3	1	no	—
494	C₄×Q₈	—	3	1	no	—
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	3	1	no	—
501	C₄×D₄	—	3	1	no	—
502	C₄×D₄	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	—	3	1	no	—
505	C₄×D₄	—	3	1	no	—
506	C₄×D₄	—	3	1	no	—
507	C₄×D₄	—	3	1	no	—
508	C₄×D₄	C₂×D₃	1	1	yes	characteristic
509	C₄×D₄	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
517	#117	—	3	1	no	—
518	#117	—	3	1	no	—
519	#117	—	3	1	no	—
520	#117	C₂×D₃	1	1	yes	characteristic, complemented
521	#117	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
527	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
528	C₂×C₄²	—	3	1	no	—
529	C₂³×C₃	—	4	1	no	—
530	C₂³×C₃	—	4	1	no	—
531	C₂³×C₃	—	4	1	no	—
532	C₂³×C₃	C₂⁴	1	1	yes	characteristic
533	C₂³×C₃	C₂⁴	1	1	yes	characteristic
534	C₂³×C₃	C₂⁴	1	1	yes	characteristic
535	C₂³×C₃	C₂⁴	1	1	yes	characteristic
536	C₂²×D₃	—	4	1	no	—
537	C₂²×D₃	—	4	1	no	—
538	C₂²×D₃	—	4	1	no	—
539	C₂²×D₃	C₂⁴	1	1	yes	characteristic
540	C₂²×D₃	C₂⁴	1	1	yes	characteristic
541	C₂²×D₃	C₂⁴	1	1	yes	characteristic
542	C₃×Q₈	—	4	1	no	—
543	C₃×D₄	—	4	1	no	—
544	C₃×D₄	—	4	1	no	—
545	C₃×D₄	—	4	1	no	—
546	C₂×C₃×C₄	—	4	1	no	—
547	C₂×C₃×C₄	—	4	1	no	—
548	C₂×C₃×C₄	—	4	1	no	—
549	C₂×C₃×C₄	—	4	1	no	—
550	C₂×C₃×C₄	—	4	1	no	—
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	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	#67	—	4	1	no	—
563	#67	—	4	1	no	—
564	#67	—	4	1	no	—
565	#67	—	4	1	no	—
566	#67	—	4	1	no	—
567	#67	—	4	1	no	—
568	#67	—	4	1	no	—
569	#67	—	4	1	no	—
570	#67	—	4	1	no	—
571	#67	—	4	1	no	—
572	C₂×Dic₃	—	4	1	no	—
573	C₂×Dic₃	—	4	1	no	—
574	C₂×Dic₃	—	4	1	no	—
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	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	D₁₂	—	4	1	no	—
589	D₁₂	—	4	1	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	C₄×D₃	—	4	1	no	—
595	C₄×D₃	—	4	1	no	—
596	C₄×D₃	—	4	1	no	—
597	Dic₆	—	4	1	no	—
598	Dic₆	—	4	1	no	—
599	Dic₆	—	4	1	no	—
600	Dic₆	—	4	1	no	—
601	Dic₆	—	4	1	no	—
602	Dic₆	—	4	1	no	—
603	Dic₆	—	4	1	no	—
604	Dic₆	—	4	1	no	—
605	C₂⁴	—	3	1	no	—
606	C₂⁴	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
613	C₂×Q₈	—	3	1	no	—
614	C₂×Q₈	—	3	1	no	—
615	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
629	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
630	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
638	C₂²×C₄	—	3	1	no	—
639	C₂²×C₄	—	3	1	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
642	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
643	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
644	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
645	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
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	C₂²×D₃	1	1	yes	characteristic
681	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
684	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	C₂²⋊C₄	—	3	1	no	—
689	C₂²⋊C₄	—	3	1	no	—
690	C₂²⋊C₄	—	3	1	no	—
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	3	1	no	—
694	C₂²⋊C₄	—	3	1	no	—
695	C₂²⋊C₄	—	3	1	no	—
696	C₂²⋊C₄	—	3	1	no	—
697	C₂²⋊C₄	—	3	1	no	—
698	C₂²⋊C₄	—	3	1	no	—
699	C₂²⋊C₄	—	3	1	no	—
700	C₂²⋊C₄	—	3	1	no	—
701	C₂²⋊C₄	—	3	1	no	—
702	C₂²⋊C₄	—	3	1	no	—
703	C₂²⋊C₄	—	3	1	no	—
704	C₂²⋊C₄	—	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	C₂²×D₃	1	1	yes	characteristic
729	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	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	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	—	3	1	no	—
756	C₄²	—	3	1	no	—
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	—	2	1	no	—
766	C₂²×C₃	—	2	1	no	—
767	C₂²×C₃	—	2	1	no	—
768	C₂²×C₃	—	2	1	no	—
769	C₂²×C₃	—	2	1	no	—
770	C₂²×C₃	—	2	1	no	—
771	C₂²×C₃	—	2	1	no	—
772	C₂²×C₃	—	8	2	no	—
773	C₂²×C₃	C₂⁵	1	1	yes	characteristic
774	C₂×D₃	—	2	1	no	—
775	C₂×D₃	—	2	1	no	—
776	C₂×D₃	—	2	1	no	—
777	C₂×D₃	—	2	1	no	—
778	C₂×D₃	—	2	1	no	—
779	C₂×D₃	—	2	1	no	—
780	C₂×D₃	—	2	1	no	—
781	C₂×D₃	—	2	1	no	—
782	C₂×D₃	—	2	1	no	—
783	C₂×D₃	—	8	2	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	C₃×C₄	—	2	1	no	—
791	C₃×C₄	—	2	1	no	—
792	C₃×C₄	—	2	1	no	—
793	C₃×C₄	—	2	1	no	—
794	C₃×C₄	—	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	—	2	1	no	—
802	Dic₃	—	2	1	no	—
803	Dic₃	—	2	1	no	—
804	Dic₃	—	2	1	no	—
805	Dic₃	—	2	1	no	—
806	Dic₃	—	2	1	no	—
807	Dic₃	—	2	1	no	—
808	C₂³	—	3	1	no	—
809	C₂³	—	3	1	no	—
810	C₂³	—	3	1	no	—
811	C₂³	—	4	1	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	12	1	no	—
815	C₂³	—	12	1	no	—
816	C₂³	—	12	1	no	—
817	C₂³	C₂³×D₃	1	1	yes	characteristic
818	C₂³	C₂³×D₃	1	1	yes	characteristic
819	C₂³	C₂³×D₃	1	1	yes	characteristic
820	C₂³	C₂³×D₃	1	1	yes	characteristic
821	Q₈	—	4	1	no	—
822	Q₈	—	12	1	no	—
823	Q₈	—	12	1	no	—
824	Q₈	—	12	1	no	—
825	Q₈	—	12	1	no	—
826	Q₈	—	12	1	no	—
827	Q₈	—	12	1	no	—
828	Q₈	—	12	1	no	—
829	Q₈	—	12	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	1	no	—
833	D₄	—	12	1	no	—
834	D₄	—	12	1	no	—
835	D₄	—	12	1	no	—
836	D₄	—	12	1	no	—
837	D₄	—	12	1	no	—
838	D₄	—	12	1	no	—
839	D₄	—	12	1	no	—
840	D₄	—	12	1	no	—
841	D₄	—	12	1	no	—
842	D₄	—	12	1	no	—
843	D₄	—	12	1	no	—
844	D₄	—	12	1	no	—
845	C₂×C₄	—	3	1	no	—
846	C₂×C₄	—	3	1	no	—
847	C₂×C₄	—	3	1	no	—
848	C₂×C₄	—	3	1	no	—
849	C₂×C₄	—	3	1	no	—
850	C₂×C₄	—	3	1	no	—
851	C₂×C₄	—	3	1	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	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	12	1	no	—
864	C₂×C₄	—	12	1	no	—
865	C₂×C₄	—	12	1	no	—
866	C₂×C₄	—	12	1	no	—
867	C₂×C₄	—	12	1	no	—
868	C₂×C₄	—	12	1	no	—
869	C₂×C₄	—	12	1	no	—
870	C₂×C₄	—	12	1	no	—
871	C₂×C₄	—	12	1	no	—
872	C₂×C₄	—	12	1	no	—
873	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
874	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
875	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
876	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
877	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
878	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
879	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
880	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
881	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
882	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
883	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
884	C₂×C₃	—	4	1	no	—
885	C₂×C₃	—	4	1	no	—
886	C₂×C₃	—	4	1	no	—
887	C₂×C₃	—	4	1	no	—
888	C₂×C₃	#585	1	1	yes	characteristic
889	C₂×C₃	#585	1	1	yes	characteristic
890	C₂×C₃	#585	1	1	yes	characteristic
891	D₃	—	4	1	no	—
892	D₃	—	4	1	no	—
893	D₃	—	4	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	6	1	no	—
907	C₂²	—	6	1	no	—
908	C₂²	—	6	1	no	—
909	C₂²	—	6	1	no	—
910	C₂²	—	6	1	no	—
911	C₂²	—	6	1	no	—
912	C₂²	—	6	1	no	—
913	C₂²	—	6	1	no	—
914	C₂²	—	6	1	no	—
915	C₂²	—	8	2	no	—
916	C₂²	—	24	2	no	—
917	C₂²	C₂⁴×D₃	1	1	yes	characteristic
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	6	1	no	—
930	C₄	—	6	1	no	—
931	C₄	—	6	1	no	—
932	C₄	—	6	1	no	—
933	C₄	—	6	1	no	—
934	C₄	—	6	1	no	—
935	C₄	—	6	1	no	—
936	C₄	—	6	1	no	—
937	C₄	—	6	1	no	—
938	C₄	—	6	1	no	—
939	C₄	—	6	1	no	—
940	C₄	—	6	1	no	—
941	C₄	—	6	1	no	—
942	C₃	#3568	1	1	yes	characteristic, complemented, Sylow
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	12	1	no	—
948	C₂	—	12	1	no	—
949	C₂	—	12	1	no	—
950	C₂	#5964	1	1	yes	characteristic
951	C₂	#5964	1	1	yes	characteristic
952	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	#3568
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. #5712	C₂	semidirect
3. #5710	C₂	semidirect
4. #5706	C₂	semidirect
5. #5702	C₂	semidirect
6. #5678	C₂	semidirect
7. #5671	C₂	semidirect
8. #5662	C₂	semidirect
9. #5662	C₂	semidirect
10. #5659	C₂	semidirect
11. #5658	C₂	semidirect
12. #5657	C₂	semidirect
13. #5651	C₂	semidirect
14. #5646	C₂	semidirect
15. #5643	C₂	semidirect
16. #5641	C₂	semidirect
17. #5640	C₂	semidirect
18. #5594	C₂	semidirect
19. #5593	C₂	semidirect
20. #5560	C₂	semidirect
21. #5557	C₂	semidirect
22. #5556	C₂	semidirect
23. #5542	C₂	semidirect
24. #5534	C₂	semidirect
25. #5533	C₂	semidirect
26. #5533	C₂	semidirect
27. #5528	C₂	semidirect
28. #5495	C₂	semidirect
29. #5495	C₂	semidirect
30. #5494	C₂	semidirect
31. #5494	C₂	semidirect
33. C₃×#126	C₂²	semidirect
34. C₃×#126	C₂²	semidirect
39. C₃×C₂²⋊Q₈	C₂²	semidirect
40. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×#117	C₂²	semidirect
45. C₃×#117	C₂²	semidirect
46. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
50. #953	C₂²	semidirect
51. C₂×#217	C₂²	semidirect
52. #947	C₂²	semidirect
53. #946	C₂²	semidirect
54. Q₈×Dic₃	C₂²	semidirect
55. #944	C₂²	semidirect
76. C₄×#67	C₂²	semidirect
77. C₄×#67	C₂²	semidirect
78. C₄×#67	C₂²	semidirect
79. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
80. #926	C₂²	semidirect
81. #926	C₂²	semidirect
82. #926	C₂²	semidirect
83. #924	C₂²	semidirect
84. #924	C₂²	semidirect
85. #924	C₂²	semidirect
86. #924	C₂²	semidirect
87. #924	C₂²	semidirect
88. #898	C₂²	semidirect
89. #898	C₂²	semidirect
90. #898	C₂²	semidirect
91. #898	C₂²	semidirect
92. #898	C₂²	semidirect
93. #898	C₂²	semidirect
94. #898	C₂²	semidirect
95. #897	C₂²	semidirect
96. #897	C₂²	semidirect
97. #897	C₂²	semidirect
98. #896	C₂²	semidirect
99. #896	C₂²	semidirect
100. #896	C₂²	semidirect
101. #896	C₂²	semidirect
102. #896	C₂²	semidirect
103. #894	C₂²	semidirect
104. #894	C₂²	semidirect
105. #893	C₂²	semidirect
106. #892	C₂²	semidirect
107. #892	C₂²	semidirect
108. #892	C₂²	semidirect
109. #890	C₂²	semidirect
110. #889	C₂²	semidirect
111. #889	C₂²	semidirect
112. #888	C₂²	semidirect
113. #888	C₂²	semidirect
114. #888	C₂²	semidirect
115. #888	C₂²	semidirect
116. #887	C₂²	semidirect
117. #887	C₂²	semidirect
118. #887	C₂²	semidirect
119. #887	C₂²	semidirect
132. #885	C₂²	semidirect
133. #885	C₂²	semidirect
134. #885	C₂²	semidirect
135. #885	C₂²	semidirect
144. #883	C₂²	semidirect
145. #883	C₂²	semidirect
146. #883	C₂²	semidirect
147. #883	C₂²	semidirect
148. #882	C₂²	semidirect
151. #67⋊C₄	C₂²	semidirect
152. D₃×C₂²⋊C₄	C₂²	semidirect
153. D₃×C₂²⋊C₄	C₂²	semidirect
154. #879	C₂²	semidirect
155. #879	C₂²	semidirect
156. #879	C₂²	semidirect
157. #879	C₂²	semidirect
158. #879	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
166. #879	C₂²	semidirect
167. #879	C₂²	semidirect
168. #878	C₂²	semidirect
169. #878	C₂²	semidirect
170. #878	C₂²	semidirect
171. #878	C₂²	semidirect
172. #878	C₂²	semidirect
173. #877	C₂²	semidirect
174. #877	C₂²	semidirect
175. #877	C₂²	semidirect
176. #876	C₂²	semidirect
177. #876	C₂²	semidirect
178. #876	C₂²	semidirect
179. #875	C₂²	semidirect
180. C₄×D₁₂	C₂²	semidirect
181. #872	C₂²	semidirect
182. C₄²×D₃	C₂²	semidirect
183. #869	C₂²	semidirect
184. C₄×Dic₆	C₂²	semidirect
185. C₄×Dic₆	C₂²	semidirect
186. C₄×Dic₆	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
203. #551	D₃	semidirect
404. #126	C₂×D₃	semidirect
405. #126	C₂×D₃	semidirect
467. C₂²⋊Q₈	C₂×D₃	semidirect
468. C₂²⋊Q₈	C₂×D₃	semidirect
520. #117	C₂×D₃	semidirect
521. #117	C₂×D₃	semidirect
526. C₂×C₂²⋊C₄	C₂×D₃	semidirect
527. C₂×C₂²⋊C₄	C₂×D₃	semidirect
942. C₃	#3568	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
#5712	2
#5710	2
#5706	2
#5702	2
#5678	2
#5671	2
#5662	2
#5659	2
#5658	2
#5657	2
#5651	2
#5646	2
#5643	2
#5641	2
#5640	2
#5594	2
#5593	2
#5560	2
#5557	2
#5556	2
#5542	2
#5534	2
#5533	2
#5528	2
#5495	2
#5494	2
#3568	3