Subgroups — #86652

Order 384.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	#5825	C₂	1	1	yes	maximal, characteristic, complemented
4	#5806	C₂	1	1	yes	maximal, characteristic, complemented
5	#5804	C₂	1	1	yes	maximal, characteristic, complemented
6	#5670	C₂	1	1	yes	maximal, characteristic, complemented
7	#5669	C₂	1	1	yes	maximal, characteristic, complemented
8	#5667	C₂	1	1	yes	maximal, characteristic, complemented
9	#5662	C₂	1	1	yes	maximal, characteristic, complemented
10	#5658	C₂	1	1	yes	maximal, characteristic, complemented
11	#5648	C₂	1	1	yes	maximal, characteristic, complemented
12	#5646	C₂	1	1	yes	maximal, characteristic, complemented
13	#5640	C₂	1	1	yes	maximal, characteristic, complemented
14	#5621	C₂	1	1	yes	maximal, characteristic, complemented
15	#5617	C₂	1	1	yes	maximal, characteristic, complemented
16	#5616	C₂	1	1	yes	maximal, characteristic, complemented
17	#5613	C₂	1	1	yes	maximal, characteristic, complemented
18	#5610	C₂	1	1	yes	maximal, characteristic, complemented
19	#5600	C₂	1	1	yes	maximal, characteristic, complemented
20	#5594	C₂	1	1	yes	maximal, characteristic, complemented
21	#5593	C₂	1	1	yes	maximal, characteristic, complemented
22	#5589	C₂	1	1	yes	maximal, characteristic, complemented
23	#5587	C₂	1	1	yes	maximal, characteristic, complemented
24	#5561	C₂	1	1	yes	maximal, characteristic, complemented
25	#5556	C₂	1	1	yes	maximal, characteristic, complemented
26	#5556	C₂	1	1	yes	maximal, characteristic, complemented
27	#5538	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	C₂×#885	C₂	1	1	yes	maximal, characteristic, complemented
32	#3545	—	3	1	no	maximal, Sylow
33	C₂×C₃×#41	C₂²	1	1	yes	characteristic
34	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#67	C₂²	1	1	yes	characteristic
36	C₂×#237	C₂²	1	1	yes	characteristic
37	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
39	C₃×#124	C₂²	1	1	yes	characteristic, complemented
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×#121	C₂²	1	1	yes	characteristic
44	C₃×#121	C₂²	1	1	yes	characteristic, complemented
45	C₃×#121	C₂²	1	1	yes	characteristic, complemented
46	C₃×#120	C₂²	1	1	yes	characteristic
47	C₃×#120	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	#953	C₂²	1	1	yes	characteristic
53	#953	C₂²	1	1	yes	characteristic
54	#953	C₂²	1	1	yes	characteristic, complemented
55	#953	C₂²	1	1	yes	characteristic, complemented
56	C₂×#217	C₂²	1	1	yes	characteristic, complemented
57	C₂×#217	C₂²	1	1	yes	characteristic, complemented
58	C₂×#217	C₂²	1	1	yes	characteristic, complemented
59	#947	C₂²	1	1	yes	characteristic, complemented
60	#946	C₂²	1	1	yes	characteristic, complemented
61	#944	C₂²	1	1	yes	characteristic, complemented
62	#944	C₂²	1	1	yes	characteristic, complemented
63	#939	C₂²	1	1	yes	characteristic
64	#939	C₂²	1	1	yes	characteristic
65	#939	C₂²	1	1	yes	characteristic
66	#939	C₂²	1	1	yes	characteristic, complemented
67	#939	C₂²	1	1	yes	characteristic, complemented
68	#939	C₂²	1	1	yes	characteristic, complemented
69	#939	C₂²	1	1	yes	characteristic, complemented
70	#939	C₂²	1	1	yes	characteristic, complemented
71	#938	C₂²	1	1	yes	characteristic
72	#938	C₂²	1	1	yes	characteristic, complemented
73	#938	C₂²	1	1	yes	characteristic, complemented
74	#937	C₂²	1	1	yes	characteristic
75	#937	C₂²	1	1	yes	characteristic
76	#937	C₂²	1	1	yes	characteristic
77	#937	C₂²	1	1	yes	characteristic, complemented
78	#937	C₂²	1	1	yes	characteristic, complemented
79	#937	C₂²	1	1	yes	characteristic, complemented
80	#936	C₂²	1	1	yes	characteristic, complemented
81	#936	C₂²	1	1	yes	characteristic, complemented
82	#936	C₂²	1	1	yes	characteristic, complemented
83	#936	C₂²	1	1	yes	characteristic, complemented
84	#936	C₂²	1	1	yes	characteristic, complemented
85	#935	C₂²	1	1	yes	characteristic, complemented
86	#935	C₂²	1	1	yes	characteristic, complemented
87	#935	C₂²	1	1	yes	characteristic, complemented
88	#935	C₂²	1	1	yes	characteristic, complemented
89	#935	C₂²	1	1	yes	characteristic, complemented
90	#935	C₂²	1	1	yes	characteristic, complemented
91	#935	C₂²	1	1	yes	characteristic, complemented
92	#935	C₂²	1	1	yes	characteristic, complemented
93	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
94	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
97	#930	C₂²	1	1	yes	characteristic, complemented
98	#929	C₂²	1	1	yes	characteristic
99	#929	C₂²	1	1	yes	characteristic, complemented
100	#929	C₂²	1	1	yes	characteristic, complemented
101	#929	C₂²	1	1	yes	characteristic, complemented
102	#929	C₂²	1	1	yes	characteristic, complemented
103	C₄×#67	C₂²	1	1	yes	characteristic, complemented
104	C₄×#67	C₂²	1	1	yes	characteristic, complemented
105	C₄×#67	C₂²	1	1	yes	characteristic, complemented
106	C₄×#67	C₂²	1	1	yes	characteristic, complemented
107	C₄×#67	C₂²	1	1	yes	characteristic, complemented
108	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	#926	C₂²	1	1	yes	characteristic, complemented
112	#926	C₂²	1	1	yes	characteristic, complemented
113	#924	C₂²	1	1	yes	characteristic, complemented
114	#924	C₂²	1	1	yes	characteristic, complemented
115	#924	C₂²	1	1	yes	characteristic, complemented
116	#924	C₂²	1	1	yes	characteristic, complemented
117	#924	C₂²	1	1	yes	characteristic, complemented
118	#924	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
120	#898	C₂²	1	1	yes	characteristic, complemented
121	#898	C₂²	1	1	yes	characteristic, complemented
122	#898	C₂²	1	1	yes	characteristic, complemented
123	#898	C₂²	1	1	yes	characteristic, complemented
124	#897	C₂²	1	1	yes	characteristic, complemented
125	#896	C₂²	1	1	yes	characteristic, complemented
126	#896	C₂²	1	1	yes	characteristic, complemented
127	#896	C₂²	1	1	yes	characteristic, complemented
128	#896	C₂²	1	1	yes	characteristic, complemented
129	#894	C₂²	1	1	yes	characteristic, complemented
130	#892	C₂²	1	1	yes	characteristic, complemented
131	#890	C₂²	1	1	yes	characteristic, complemented
132	#889	C₂²	1	1	yes	characteristic, complemented
133	#888	C₂²	1	1	yes	characteristic, complemented
134	#888	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic, complemented
137	#886	C₂²	1	1	yes	characteristic, complemented
138	#886	C₂²	1	1	yes	characteristic, complemented
139	#885	C₂²	1	1	yes	characteristic
140	#885	C₂²	1	1	yes	characteristic
141	#885	C₂²	1	1	yes	characteristic, complemented
142	#885	C₂²	1	1	yes	characteristic, complemented
143	#885	C₂²	1	1	yes	characteristic, complemented
144	#885	C₂²	1	1	yes	characteristic, complemented
145	#885	C₂²	1	1	yes	characteristic, complemented
146	#885	C₂²	1	1	yes	characteristic, complemented
147	#885	C₂²	1	1	yes	characteristic, complemented
148	#885	C₂²	1	1	yes	characteristic, complemented
149	#885	C₂²	1	1	yes	characteristic, complemented
150	#885	C₂²	1	1	yes	characteristic, complemented
151	#885	C₂²	1	1	yes	characteristic, complemented
152	#885	C₂²	1	1	yes	characteristic, complemented
153	#885	C₂²	1	1	yes	characteristic, complemented
154	#884	C₂²	1	1	yes	characteristic
155	#884	C₂²	1	1	yes	characteristic, complemented
156	#884	C₂²	1	1	yes	characteristic, complemented
157	#883	C₂²	1	1	yes	characteristic
158	#883	C₂²	1	1	yes	characteristic, complemented
159	#883	C₂²	1	1	yes	characteristic, complemented
160	#883	C₂²	1	1	yes	characteristic, complemented
161	#883	C₂²	1	1	yes	characteristic, complemented
162	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	#879	C₂²	1	1	yes	characteristic, complemented
168	#879	C₂²	1	1	yes	characteristic, complemented
169	#879	C₂²	1	1	yes	characteristic, complemented
170	#879	C₂²	1	1	yes	characteristic, complemented
171	#879	C₂²	1	1	yes	characteristic, complemented
172	#879	C₂²	1	1	yes	characteristic, complemented
173	#879	C₂²	1	1	yes	characteristic, complemented
174	#878	C₂²	1	1	yes	characteristic, complemented
175	#878	C₂²	1	1	yes	characteristic, complemented
176	#878	C₂²	1	1	yes	characteristic, complemented
177	#878	C₂²	1	1	yes	characteristic, complemented
178	#878	C₂²	1	1	yes	characteristic, complemented
179	#877	C₂²	1	1	yes	characteristic, complemented
180	#877	C₂²	1	1	yes	characteristic, complemented
181	#877	C₂²	1	1	yes	characteristic, complemented
182	#877	C₂²	1	1	yes	characteristic, complemented
183	#877	C₂²	1	1	yes	characteristic, complemented
184	#876	C₂²	1	1	yes	characteristic, complemented
185	#872	C₂²	1	1	yes	characteristic, complemented
186	#872	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#563	—	3	1	no	—
189	#562	—	3	1	no	—
190	#562	—	3	1	no	—
191	H(3,𝔽₄)	—	3	1	no	—
192	#555	—	3	1	no	—
193	#555	—	3	1	no	—
194	#551	—	3	1	no	—
195	#551	—	3	1	no	—
196	#551	—	3	1	no	—
197	#551	—	3	1	no	—
198	#551	—	3	1	no	—
199	#551	—	3	1	no	—
200	#546	—	3	1	no	—
201	#546	—	3	1	no	—
202	#546	—	3	1	no	—
203	#546	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	#538	—	3	1	no	—
209	#538	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#536	—	3	1	no	—
213	#536	—	3	1	no	—
214	#534	—	3	1	no	—
215	#534	—	3	1	no	—
216	#529	—	3	1	no	—
217	#529	—	3	1	no	—
218	C₂×#124	—	3	1	no	—
219	C₂⁴×C₃	C₂³	1	1	yes	characteristic
220	C₂⁴×C₃	C₂³	1	1	yes	characteristic
221	C₂³×D₃	C₂³	1	1	yes	characteristic
222	C₂³×D₃	C₂³	1	1	yes	characteristic
223	C₃×#41	—	4	2	no	—
224	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₃×D₄	—	4	2	no	—
226	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
241	C₂×#67	—	4	2	no	—
242	C₂×#67	C₂³	1	1	yes	characteristic
243	C₂×#67	C₂³	1	1	yes	characteristic
244	C₂×#67	C₂³	1	1	yes	characteristic
245	C₂×#67	C₂³	1	1	yes	characteristic
246	C₂×#67	C₂³	1	1	yes	characteristic
247	C₂×#67	C₂³	1	1	yes	characteristic
248	C₂×#67	C₂³	1	1	yes	characteristic
249	C₂×#67	C₂³	1	1	yes	characteristic
250	C₂×#67	C₂³	1	1	yes	characteristic
251	C₂×#67	C₂³	1	1	yes	characteristic
252	C₂×#67	C₂³	1	1	yes	characteristic
253	C₂×#67	C₂³	1	1	yes	characteristic
254	C₂×#67	C₂³	1	1	yes	characteristic
255	C₂×#67	C₂³	1	1	yes	characteristic
256	C₂²×Dic₃	C₂³	1	1	yes	characteristic
257	C₂²×Dic₃	C₂³	1	1	yes	characteristic
258	C₂²×Dic₃	C₂³	1	1	yes	characteristic
259	C₂²×Dic₃	C₂³	1	1	yes	characteristic
260	C₂²×Dic₃	C₂³	1	1	yes	characteristic
261	C₂²×Dic₃	C₂³	1	1	yes	characteristic
262	C₂²×Dic₃	C₂³	1	1	yes	characteristic
263	C₂²×Dic₃	C₂³	1	1	yes	characteristic
264	#237	—	4	2	no	—
265	D₃×D₄	—	4	2	no	—
266	C₂×D₁₂	C₂³	1	1	yes	characteristic
267	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
268	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
269	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
272	C₂×Dic₆	—	4	2	no	—
273	C₂×Dic₆	C₂³	1	1	yes	characteristic
274	C₂×Dic₆	C₂³	1	1	yes	characteristic
275	C₂×Dic₆	C₂³	1	1	yes	characteristic
276	C₂×Dic₆	C₂³	1	1	yes	characteristic
277	C₂×Dic₆	C₂³	1	1	yes	characteristic
278	C₂×Dic₆	C₂³	1	1	yes	characteristic
279	C₂×Dic₆	C₂³	1	1	yes	characteristic
280	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₃×C₄²	C₂³	1	1	yes	characteristic
297	#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	#217	C₂³	1	1	yes	characteristic
307	#217	C₂³	1	1	yes	characteristic
308	#217	C₂³	1	1	yes	characteristic
309	#217	C₂³	1	1	yes	characteristic
310	#217	C₂³	1	1	yes	characteristic
311	#217	C₂³	1	1	yes	characteristic
312	#217	C₂³	1	1	yes	characteristic
313	#217	C₂³	1	1	yes	characteristic
314	#217	C₂³	1	1	yes	characteristic
315	#217	C₂³	1	1	yes	characteristic
316	#217	C₂³	1	1	yes	characteristic
317	#217	C₂³	1	1	yes	characteristic
318	#217	C₂³	1	1	yes	characteristic
319	#217	C₂³	1	1	yes	characteristic
320	#217	C₂³	1	1	yes	characteristic
321	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
322	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
323	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
324	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
325	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
326	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
327	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
328	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
329	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
330	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
331	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
332	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
333	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
334	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
335	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
339	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
340	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
341	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
342	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
343	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
344	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
345	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
346	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
347	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
348	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
349	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
350	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
351	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
352	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
353	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
354	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
355	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
356	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
369	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	C₄×Dic₃	C₂³	1	1	yes	characteristic
378	C₄×Dic₃	C₂³	1	1	yes	characteristic
379	C₄×Dic₃	C₂³	1	1	yes	characteristic
380	C₂×#41	—	3	1	no	—
381	C₂×#41	C₂×D₃	1	1	yes	characteristic
382	C₂²×Q₈	—	3	1	no	—
383	C₂²×D₄	—	3	1	no	—
384	C₂²×D₄	—	3	1	no	—
385	C₂²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
386	C₄⋊Q₈	—	3	1	no	—
387	C₄⋊Q₈	—	3	1	no	—
388	C₄⋊Q₈	—	3	1	no	—
389	C₄⋊Q₈	—	3	1	no	—
390	#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	#125	—	3	1	no	—
403	#125	—	3	1	no	—
404	#124	—	3	1	no	—
405	#124	—	3	1	no	—
406	#124	—	3	1	no	—
407	#124	—	3	1	no	—
408	#124	—	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	C₂×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
437	#123	—	3	1	no	—
438	#123	—	3	1	no	—
439	#123	—	3	1	no	—
440	#123	—	3	1	no	—
441	#123	—	3	1	no	—
442	#123	—	3	1	no	—
443	#123	—	3	1	no	—
444	#123	—	3	1	no	—
445	#123	—	3	1	no	—
446	#123	—	3	1	no	—
447	#123	—	3	1	no	—
448	#123	C₂×D₃	1	1	yes	characteristic, complemented
449	#123	C₂×D₃	1	1	yes	characteristic, complemented
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	#121	—	3	1	no	—
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	#121	—	3	1	no	—
479	#121	—	3	1	no	—
480	#121	—	3	1	no	—
481	#121	—	3	1	no	—
482	#121	—	3	1	no	—
483	#121	C₂×D₃	1	1	yes	characteristic
484	#121	C₂×D₃	1	1	yes	characteristic, complemented
485	#121	C₂×D₃	1	1	yes	characteristic, complemented
486	#120	—	3	1	no	—
487	#120	—	3	1	no	—
488	#120	—	3	1	no	—
489	#120	—	3	1	no	—
490	#120	—	3	1	no	—
491	#120	—	3	1	no	—
492	#120	—	3	1	no	—
493	#120	—	3	1	no	—
494	#120	—	3	1	no	—
495	#120	—	3	1	no	—
496	#120	C₂×D₃	1	1	yes	characteristic
497	#120	C₂×D₃	1	1	yes	characteristic, complemented
498	C₄×Q₈	—	3	1	no	—
499	C₄×Q₈	—	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	—	3	1	no	—
509	C₄×D₄	—	3	1	no	—
510	C₄×D₄	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
513	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
514	#117	—	3	1	no	—
515	#117	—	3	1	no	—
516	#117	—	3	1	no	—
517	#117	—	3	1	no	—
518	#117	—	3	1	no	—
519	#117	—	3	1	no	—
520	#117	—	3	1	no	—
521	#117	—	3	1	no	—
522	#117	—	3	1	no	—
523	#117	—	3	1	no	—
524	C₂×C₂²⋊C₄	—	3	1	no	—
525	C₂×C₂²⋊C₄	—	3	1	no	—
526	C₂×C₂²⋊C₄	—	3	1	no	—
527	C₂×C₂²⋊C₄	—	3	1	no	—
528	C₂×C₂²⋊C₄	—	3	1	no	—
529	C₂×C₂²⋊C₄	—	3	1	no	—
530	C₂×C₂²⋊C₄	—	3	1	no	—
531	C₂×C₂²⋊C₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
533	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
534	C₂×C₄²	—	3	1	no	—
535	C₂³×C₃	—	2	2	no	—
536	C₂³×C₃	—	4	1	no	—
537	C₂³×C₃	—	4	1	no	—
538	C₂³×C₃	—	4	1	no	—
539	C₂³×C₃	—	4	1	no	—
540	C₂³×C₃	—	4	1	no	—
541	C₂³×C₃	C₂⁴	1	1	yes	characteristic
542	C₂³×C₃	C₂⁴	1	1	yes	characteristic
543	C₂³×C₃	C₂⁴	1	1	yes	characteristic
544	C₂³×C₃	C₂⁴	1	1	yes	characteristic
545	C₂³×C₃	C₂⁴	1	1	yes	characteristic
546	C₂³×C₃	C₂⁴	1	1	yes	characteristic
547	C₂²×D₃	—	2	2	no	—
548	C₂²×D₃	—	4	1	no	—
549	C₂²×D₃	—	4	1	no	—
550	C₂²×D₃	—	4	1	no	—
551	C₂²×D₃	—	4	1	no	—
552	C₂²×D₃	—	4	1	no	—
553	C₂²×D₃	C₂⁴	1	1	yes	characteristic
554	C₂²×D₃	C₂⁴	1	1	yes	characteristic
555	C₂²×D₃	C₂⁴	1	1	yes	characteristic
556	C₃×Q₈	—	4	1	no	—
557	C₃×D₄	—	2	2	no	—
558	C₃×D₄	—	2	2	no	—
559	C₃×D₄	—	2	2	no	—
560	C₃×D₄	—	4	1	no	—
561	C₃×D₄	—	4	1	no	—
562	C₃×D₄	—	4	1	no	—
563	C₃×D₄	—	4	1	no	—
564	C₃×D₄	—	4	1	no	—
565	C₃×D₄	—	4	1	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	4	1	no	—
568	C₂×C₃×C₄	—	4	1	no	—
569	C₂×C₃×C₄	—	4	1	no	—
570	C₂×C₃×C₄	—	4	1	no	—
571	C₂×C₃×C₄	—	4	1	no	—
572	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
581	#67	—	2	2	no	—
582	#67	—	4	1	no	—
583	#67	—	4	1	no	—
584	#67	—	4	1	no	—
585	#67	—	4	1	no	—
586	#67	—	4	1	no	—
587	#67	—	4	1	no	—
588	#67	—	4	1	no	—
589	#67	—	4	1	no	—
590	#67	—	4	1	no	—
591	#67	—	4	1	no	—
592	#67	—	4	1	no	—
593	#67	—	4	1	no	—
594	#67	—	4	1	no	—
595	C₂×Dic₃	—	2	2	no	—
596	C₂×Dic₃	—	2	2	no	—
597	C₂×Dic₃	—	4	1	no	—
598	C₂×Dic₃	—	4	1	no	—
599	C₂×Dic₃	—	4	1	no	—
600	C₂×Dic₃	—	4	1	no	—
601	C₂×Dic₃	—	4	1	no	—
602	C₂×Dic₃	—	4	1	no	—
603	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
604	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
605	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
606	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
607	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
608	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
609	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
610	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
611	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
612	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
613	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
614	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
615	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
616	D₁₂	—	4	1	no	—
617	C₄×D₃	—	4	1	no	—
618	C₄×D₃	—	4	1	no	—
619	C₄×D₃	—	4	1	no	—
620	C₄×D₃	—	4	1	no	—
621	C₄×D₃	—	4	1	no	—
622	Dic₆	—	4	1	no	—
623	Dic₆	—	4	1	no	—
624	Dic₆	—	4	1	no	—
625	Dic₆	—	4	1	no	—
626	Dic₆	—	4	1	no	—
627	Dic₆	—	4	1	no	—
628	Dic₆	—	4	1	no	—
629	C₂⁴	—	3	1	no	—
630	C₂⁴	—	3	1	no	—
631	C₂⁴	C₂²×D₃	1	1	yes	characteristic
632	C₂⁴	C₂²×D₃	1	1	yes	characteristic
633	#41	—	4	2	no	—
634	#41	—	12	2	no	—
635	C₂×Q₈	—	3	1	no	—
636	C₂×Q₈	—	3	1	no	—
637	C₂×Q₈	—	3	1	no	—
638	C₂×Q₈	—	3	1	no	—
639	C₂×Q₈	—	3	1	no	—
640	C₂×Q₈	—	3	1	no	—
641	C₂×Q₈	—	3	1	no	—
642	C₂×Q₈	—	12	2	no	—
643	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
644	C₂×D₄	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	3	1	no	—
649	C₂×D₄	—	3	1	no	—
650	C₂×D₄	—	3	1	no	—
651	C₂×D₄	—	3	1	no	—
652	C₂×D₄	—	3	1	no	—
653	C₂×D₄	—	3	1	no	—
654	C₂×D₄	—	3	1	no	—
655	C₂×D₄	—	3	1	no	—
656	C₂×D₄	—	3	1	no	—
657	C₂×D₄	—	3	1	no	—
658	C₂×D₄	—	3	1	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	12	2	no	—
661	C₂×D₄	—	12	2	no	—
662	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
663	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
664	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
665	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
666	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
667	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
668	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
669	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
670	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
671	C₂²×C₄	—	3	1	no	—
672	C₂²×C₄	—	3	1	no	—
673	C₂²×C₄	—	3	1	no	—
674	C₂²×C₄	—	3	1	no	—
675	C₂²×C₄	—	3	1	no	—
676	C₂²×C₄	—	3	1	no	—
677	C₂²×C₄	—	3	1	no	—
678	C₂²×C₄	—	3	1	no	—
679	C₂²×C₄	—	3	1	no	—
680	C₂²×C₄	—	3	1	no	—
681	C₂²×C₄	—	3	1	no	—
682	C₂²×C₄	—	3	1	no	—
683	C₂²×C₄	—	3	1	no	—
684	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
685	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
686	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
687	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
688	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
689	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
690	C₄⋊C₄	—	3	1	no	—
691	C₄⋊C₄	—	3	1	no	—
692	C₄⋊C₄	—	3	1	no	—
693	C₄⋊C₄	—	3	1	no	—
694	C₄⋊C₄	—	3	1	no	—
695	C₄⋊C₄	—	3	1	no	—
696	C₄⋊C₄	—	3	1	no	—
697	C₄⋊C₄	—	3	1	no	—
698	C₄⋊C₄	—	3	1	no	—
699	C₄⋊C₄	—	3	1	no	—
700	C₄⋊C₄	—	3	1	no	—
701	C₄⋊C₄	—	3	1	no	—
702	C₄⋊C₄	—	3	1	no	—
703	C₄⋊C₄	—	3	1	no	—
704	C₄⋊C₄	—	3	1	no	—
705	C₄⋊C₄	—	3	1	no	—
706	C₄⋊C₄	—	3	1	no	—
707	C₄⋊C₄	—	3	1	no	—
708	C₄⋊C₄	—	3	1	no	—
709	C₄⋊C₄	—	3	1	no	—
710	C₄⋊C₄	—	3	1	no	—
711	C₄⋊C₄	—	3	1	no	—
712	C₄⋊C₄	—	3	1	no	—
713	C₄⋊C₄	—	3	1	no	—
714	C₄⋊C₄	—	3	1	no	—
715	C₄⋊C₄	—	3	1	no	—
716	C₄⋊C₄	—	3	1	no	—
717	C₄⋊C₄	—	3	1	no	—
718	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
722	C₂²⋊C₄	—	3	1	no	—
723	C₂²⋊C₄	—	3	1	no	—
724	C₂²⋊C₄	—	3	1	no	—
725	C₂²⋊C₄	—	3	1	no	—
726	C₂²⋊C₄	—	3	1	no	—
727	C₂²⋊C₄	—	3	1	no	—
728	C₂²⋊C₄	—	3	1	no	—
729	C₂²⋊C₄	—	3	1	no	—
730	C₂²⋊C₄	—	3	1	no	—
731	C₂²⋊C₄	—	3	1	no	—
732	C₂²⋊C₄	—	3	1	no	—
733	C₂²⋊C₄	—	3	1	no	—
734	C₂²⋊C₄	—	3	1	no	—
735	C₂²⋊C₄	—	3	1	no	—
736	C₂²⋊C₄	—	3	1	no	—
737	C₂²⋊C₄	—	3	1	no	—
738	C₂²⋊C₄	—	3	1	no	—
739	C₂²⋊C₄	—	3	1	no	—
740	C₂²⋊C₄	—	3	1	no	—
741	C₂²⋊C₄	—	3	1	no	—
742	C₂²⋊C₄	—	3	1	no	—
743	C₂²⋊C₄	—	3	1	no	—
744	C₂²⋊C₄	—	3	1	no	—
745	C₂²⋊C₄	—	3	1	no	—
746	C₂²⋊C₄	—	3	1	no	—
747	C₂²⋊C₄	—	3	1	no	—
748	C₂²⋊C₄	—	3	1	no	—
749	C₂²⋊C₄	—	3	1	no	—
750	C₂²⋊C₄	—	3	1	no	—
751	C₂²⋊C₄	—	3	1	no	—
752	C₂²⋊C₄	—	3	1	no	—
753	C₂²⋊C₄	—	3	1	no	—
754	C₂²⋊C₄	—	3	1	no	—
755	C₂²⋊C₄	—	3	1	no	—
756	C₂²⋊C₄	—	3	1	no	—
757	C₂²⋊C₄	—	3	1	no	—
758	C₂²⋊C₄	—	3	1	no	—
759	C₂²⋊C₄	—	3	1	no	—
760	C₂²⋊C₄	—	3	1	no	—
761	C₂²⋊C₄	—	3	1	no	—
762	C₂²⋊C₄	—	3	1	no	—
763	C₂²⋊C₄	—	3	1	no	—
764	C₂²⋊C₄	—	3	1	no	—
765	C₂²⋊C₄	—	3	1	no	—
766	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
767	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
768	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
769	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
770	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
771	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
772	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
773	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
774	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
775	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
776	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
777	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
778	C₄²	—	3	1	no	—
779	C₄²	—	3	1	no	—
780	C₄²	—	3	1	no	—
781	C₄²	—	3	1	no	—
782	C₄²	—	3	1	no	—
783	C₄²	—	3	1	no	—
784	C₄²	—	3	1	no	—
785	C₄²	—	3	1	no	—
786	C₄²	—	3	1	no	—
787	C₄²	—	3	1	no	—
788	C₄²	—	3	1	no	—
789	C₄²	C₂²×D₃	1	1	yes	characteristic
790	C₂²×C₃	—	2	1	no	—
791	C₂²×C₃	—	2	1	no	—
792	C₂²×C₃	—	2	1	no	—
793	C₂²×C₃	—	2	1	no	—
794	C₂²×C₃	—	2	1	no	—
795	C₂²×C₃	—	2	1	no	—
796	C₂²×C₃	—	2	1	no	—
797	C₂²×C₃	—	2	1	no	—
798	C₂²×C₃	—	2	1	no	—
799	C₂²×C₃	—	2	1	no	—
800	C₂²×C₃	—	2	1	no	—
801	C₂²×C₃	—	2	1	no	—
802	C₂²×C₃	—	2	1	no	—
803	C₂²×C₃	—	2	1	no	—
804	C₂²×C₃	—	2	1	no	—
805	C₂²×C₃	—	2	1	no	—
806	C₂²×C₃	—	2	1	no	—
807	C₂²×C₃	—	8	2	no	—
808	C₂²×C₃	—	8	2	no	—
809	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
810	C₂²×C₃	C₂⁵	1	1	yes	characteristic
811	C₂×D₃	—	2	1	no	—
812	C₂×D₃	—	2	1	no	—
813	C₂×D₃	—	2	1	no	—
814	C₂×D₃	—	2	1	no	—
815	C₂×D₃	—	2	1	no	—
816	C₂×D₃	—	2	1	no	—
817	C₂×D₃	—	2	1	no	—
818	C₂×D₃	—	2	1	no	—
819	C₂×D₃	—	2	1	no	—
820	C₂×D₃	—	8	2	no	—
821	C₂×D₃	—	8	2	no	—
822	C₃×C₄	—	2	1	no	—
823	C₃×C₄	—	2	1	no	—
824	C₃×C₄	—	2	1	no	—
825	C₃×C₄	—	2	1	no	—
826	C₃×C₄	—	2	1	no	—
827	C₃×C₄	—	2	1	no	—
828	C₃×C₄	—	2	1	no	—
829	C₃×C₄	—	2	1	no	—
830	C₃×C₄	—	2	1	no	—
831	Dic₃	—	2	1	no	—
832	Dic₃	—	2	1	no	—
833	Dic₃	—	2	1	no	—
834	Dic₃	—	2	1	no	—
835	Dic₃	—	2	1	no	—
836	Dic₃	—	2	1	no	—
837	Dic₃	—	2	1	no	—
838	Dic₃	—	2	1	no	—
839	Dic₃	—	2	1	no	—
840	Dic₃	—	2	1	no	—
841	Dic₃	—	2	1	no	—
842	Dic₃	—	2	1	no	—
843	Dic₃	—	2	1	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	3	1	no	—
846	C₂³	—	3	1	no	—
847	C₂³	—	3	1	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	4	1	no	—
850	C₂³	—	4	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	1	no	—
853	C₂³	—	6	2	no	—
854	C₂³	—	12	1	no	—
855	C₂³	—	12	1	no	—
856	C₂³	—	12	1	no	—
857	C₂³	—	12	1	no	—
858	C₂³	—	12	1	no	—
859	C₂³	C₂³×D₃	1	1	yes	characteristic
860	C₂³	C₂³×D₃	1	1	yes	characteristic
861	C₂³	C₂³×D₃	1	1	yes	characteristic
862	C₂³	C₂³×D₃	1	1	yes	characteristic
863	C₂³	C₂³×D₃	1	1	yes	characteristic
864	C₂³	C₂³×D₃	1	1	yes	characteristic
865	Q₈	—	4	1	no	—
866	Q₈	—	12	1	no	—
867	Q₈	—	12	1	no	—
868	Q₈	—	12	1	no	—
869	Q₈	—	12	1	no	—
870	Q₈	—	12	1	no	—
871	Q₈	—	12	1	no	—
872	Q₈	—	12	1	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	4	1	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	1	no	—
882	D₄	—	6	2	no	—
883	D₄	—	12	1	no	—
884	D₄	—	12	1	no	—
885	D₄	—	12	1	no	—
886	D₄	—	12	1	no	—
887	D₄	—	12	1	no	—
888	D₄	—	12	1	no	—
889	D₄	—	12	1	no	—
890	D₄	—	12	1	no	—
891	D₄	—	12	1	no	—
892	D₄	—	12	1	no	—
893	D₄	—	12	1	no	—
894	D₄	—	12	1	no	—
895	D₄	—	12	1	no	—
896	D₄	—	12	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	3	1	no	—
899	C₂×C₄	—	3	1	no	—
900	C₂×C₄	—	3	1	no	—
901	C₂×C₄	—	3	1	no	—
902	C₂×C₄	—	3	1	no	—
903	C₂×C₄	—	3	1	no	—
904	C₂×C₄	—	3	1	no	—
905	C₂×C₄	—	3	1	no	—
906	C₂×C₄	—	3	1	no	—
907	C₂×C₄	—	3	1	no	—
908	C₂×C₄	—	3	1	no	—
909	C₂×C₄	—	3	1	no	—
910	C₂×C₄	—	3	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	6	2	no	—
917	C₂×C₄	—	6	2	no	—
918	C₂×C₄	—	12	1	no	—
919	C₂×C₄	—	12	1	no	—
920	C₂×C₄	—	12	1	no	—
921	C₂×C₄	—	12	1	no	—
922	C₂×C₄	—	12	1	no	—
923	C₂×C₄	—	12	1	no	—
924	C₂×C₄	—	12	1	no	—
925	C₂×C₄	—	12	1	no	—
926	C₂×C₄	—	12	1	no	—
927	C₂×C₄	—	12	1	no	—
928	C₂×C₄	—	12	1	no	—
929	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
935	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
936	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
937	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
938	C₂×C₃	—	2	2	no	—
939	C₂×C₃	—	4	1	no	—
940	C₂×C₃	—	4	1	no	—
941	C₂×C₃	—	4	1	no	—
942	C₂×C₃	—	4	1	no	—
943	C₂×C₃	—	4	1	no	—
944	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂×C₃	#585	1	1	yes	characteristic
946	C₂×C₃	#585	1	1	yes	characteristic
947	D₃	—	4	1	no	—
948	D₃	—	4	1	no	—
949	D₃	—	4	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	6	1	no	—
968	C₂²	—	6	1	no	—
969	C₂²	—	6	1	no	—
970	C₂²	—	6	1	no	—
971	C₂²	—	6	1	no	—
972	C₂²	—	6	1	no	—
973	C₂²	—	6	1	no	—
974	C₂²	—	6	1	no	—
975	C₂²	—	6	1	no	—
976	C₂²	—	8	2	no	—
977	C₂²	—	8	2	no	—
978	C₂²	—	24	2	no	—
979	C₂²	—	24	2	no	—
980	C₂²	#1004	1	2	yes	—
981	C₂²	C₂⁴×D₃	1	1	yes	characteristic
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	6	1	no	—
992	C₄	—	6	1	no	—
993	C₄	—	6	1	no	—
994	C₄	—	6	1	no	—
995	C₄	—	6	1	no	—
996	C₄	—	6	1	no	—
997	C₄	—	6	1	no	—
998	C₄	—	6	1	no	—
999	C₄	—	6	1	no	—
1000	C₄	—	6	1	no	—
1001	C₄	—	6	1	no	—
1002	C₄	—	6	1	no	—
1003	C₄	—	6	1	no	—
1004	C₃	#3545	1	1	yes	characteristic, complemented, Sylow
1005	C₂	—	2	2	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	4	1	no	—
1009	C₂	—	4	1	no	—
1010	C₂	—	4	1	no	—
1011	C₂	—	12	1	no	—
1012	C₂	—	12	1	no	—
1013	C₂	—	12	1	no	—
1014	C₂	C₂×#1004	1	1	yes	characteristic
1015	C₂	#5964	1	1	yes	characteristic
1016	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#546	C₂
hypercenter	#546	D₃
hypocenter	C₃	#3545
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₃×#546	C₂	semidirect
2. #5829	C₂	semidirect
3. #5825	C₂	semidirect
4. #5806	C₂	semidirect
5. #5804	C₂	semidirect
6. #5670	C₂	semidirect
7. #5669	C₂	semidirect
8. #5667	C₂	semidirect
9. #5662	C₂	semidirect
10. #5658	C₂	semidirect
11. #5648	C₂	semidirect
12. #5646	C₂	semidirect
13. #5640	C₂	semidirect
14. #5621	C₂	semidirect
15. #5617	C₂	semidirect
16. #5616	C₂	semidirect
17. #5613	C₂	semidirect
18. #5610	C₂	semidirect
19. #5600	C₂	semidirect
20. #5594	C₂	semidirect
21. #5593	C₂	semidirect
22. #5589	C₂	semidirect
23. #5587	C₂	semidirect
24. #5561	C₂	semidirect
25. #5556	C₂	semidirect
26. #5556	C₂	semidirect
27. #5538	C₂	semidirect
28. #5495	C₂	semidirect
29. #5495	C₂	semidirect
30. #5494	C₂	semidirect
31. C₂×#885	C₂	semidirect
34. C₂²×C₃×D₄	C₂²	semidirect
37. C₂×D₃×D₄	C₂²	semidirect
38. C₂²×Dic₆	C₂²	semidirect
39. C₃×#124	C₂²	semidirect
40. C₃×#123	C₂²	semidirect
41. C₃×#123	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×#121	C₂²	semidirect
45. C₃×#121	C₂²	semidirect
47. C₃×#120	C₂²	semidirect
48. C₃×C₄×D₄	C₂²	semidirect
49. C₃×C₄×D₄	C₂²	semidirect
50. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
51. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
54. #953	C₂²	semidirect
55. #953	C₂²	semidirect
56. C₂×#217	C₂²	semidirect
57. C₂×#217	C₂²	semidirect
58. C₂×#217	C₂²	semidirect
59. #947	C₂²	semidirect
60. #946	C₂²	semidirect
61. #944	C₂²	semidirect
62. #944	C₂²	semidirect
66. #939	C₂²	semidirect
67. #939	C₂²	semidirect
68. #939	C₂²	semidirect
69. #939	C₂²	semidirect
70. #939	C₂²	semidirect
72. #938	C₂²	semidirect
73. #938	C₂²	semidirect
77. #937	C₂²	semidirect
78. #937	C₂²	semidirect
79. #937	C₂²	semidirect
80. #936	C₂²	semidirect
81. #936	C₂²	semidirect
82. #936	C₂²	semidirect
83. #936	C₂²	semidirect
84. #936	C₂²	semidirect
85. #935	C₂²	semidirect
86. #935	C₂²	semidirect
87. #935	C₂²	semidirect
88. #935	C₂²	semidirect
89. #935	C₂²	semidirect
90. #935	C₂²	semidirect
91. #935	C₂²	semidirect
92. #935	C₂²	semidirect
93. D₄×Dic₃	C₂²	semidirect
94. D₄×Dic₃	C₂²	semidirect
95. D₄×Dic₃	C₂²	semidirect
96. D₄×Dic₃	C₂²	semidirect
97. #930	C₂²	semidirect
99. #929	C₂²	semidirect
100. #929	C₂²	semidirect
101. #929	C₂²	semidirect
102. #929	C₂²	semidirect
103. C₄×#67	C₂²	semidirect
104. C₄×#67	C₂²	semidirect
105. C₄×#67	C₂²	semidirect
106. C₄×#67	C₂²	semidirect
107. C₄×#67	C₂²	semidirect
108. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
109. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
110. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
111. #926	C₂²	semidirect
112. #926	C₂²	semidirect
113. #924	C₂²	semidirect
114. #924	C₂²	semidirect
115. #924	C₂²	semidirect
116. #924	C₂²	semidirect
117. #924	C₂²	semidirect
118. #924	C₂²	semidirect
119. C₂×C₄×Dic₃	C₂²	semidirect
120. #898	C₂²	semidirect
121. #898	C₂²	semidirect
122. #898	C₂²	semidirect
123. #898	C₂²	semidirect
124. #897	C₂²	semidirect
125. #896	C₂²	semidirect
126. #896	C₂²	semidirect
127. #896	C₂²	semidirect
128. #896	C₂²	semidirect
129. #894	C₂²	semidirect
130. #892	C₂²	semidirect
131. #890	C₂²	semidirect
132. #889	C₂²	semidirect
133. #888	C₂²	semidirect
134. #888	C₂²	semidirect
135. #887	C₂²	semidirect
136. #886	C₂²	semidirect
137. #886	C₂²	semidirect
138. #886	C₂²	semidirect
141. #885	C₂²	semidirect
142. #885	C₂²	semidirect
143. #885	C₂²	semidirect
144. #885	C₂²	semidirect
145. #885	C₂²	semidirect
146. #885	C₂²	semidirect
147. #885	C₂²	semidirect
148. #885	C₂²	semidirect
149. #885	C₂²	semidirect
150. #885	C₂²	semidirect
151. #885	C₂²	semidirect
152. #885	C₂²	semidirect
153. #885	C₂²	semidirect
155. #884	C₂²	semidirect
156. #884	C₂²	semidirect
158. #883	C₂²	semidirect
159. #883	C₂²	semidirect
160. #883	C₂²	semidirect
161. #883	C₂²	semidirect
162. #67⋊C₄	C₂²	semidirect
163. #67⋊C₄	C₂²	semidirect
164. #67⋊C₄	C₂²	semidirect
165. D₃×C₂²⋊C₄	C₂²	semidirect
166. D₃×C₂²⋊C₄	C₂²	semidirect
167. #879	C₂²	semidirect
168. #879	C₂²	semidirect
169. #879	C₂²	semidirect
170. #879	C₂²	semidirect
171. #879	C₂²	semidirect
172. #879	C₂²	semidirect
173. #879	C₂²	semidirect
174. #878	C₂²	semidirect
175. #878	C₂²	semidirect
176. #878	C₂²	semidirect
177. #878	C₂²	semidirect
178. #878	C₂²	semidirect
179. #877	C₂²	semidirect
180. #877	C₂²	semidirect
181. #877	C₂²	semidirect
182. #877	C₂²	semidirect
183. #877	C₂²	semidirect
184. #876	C₂²	semidirect
185. #872	C₂²	semidirect
186. #872	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
203. #546	D₃	semidirect
385. C₂²×D₄	C₂×D₃	semidirect
425. #124	C₂×D₃	semidirect
448. #123	C₂×D₃	semidirect
449. #123	C₂×D₃	semidirect
467. C₂²⋊Q₈	C₂×D₃	semidirect
484. #121	C₂×D₃	semidirect
485. #121	C₂×D₃	semidirect
497. #120	C₂×D₃	semidirect
512. C₄×D₄	C₂×D₃	semidirect
513. C₄×D₄	C₂×D₃	semidirect
532. C₂×C₂²⋊C₄	C₂×D₃	semidirect
533. C₂×C₂²⋊C₄	C₂×D₃	semidirect
1004. C₃	#3545	semidirect

Maximal subgroups

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

subgroup	index
C₃×#546	2
#5829	2
#5825	2
#5806	2
#5804	2
#5670	2
#5669	2
#5667	2
#5662	2
#5658	2
#5648	2
#5646	2
#5640	2
#5621	2
#5617	2
#5616	2
#5613	2
#5610	2
#5600	2
#5594	2
#5593	2
#5589	2
#5587	2
#5561	2
#5556	2
#5538	2
#5495	2
#5494	2
C₂×#885	2
#3545	3