Subgroups — C₃×#85776 #11901973

Order 1152.

2533 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5804	C₂	1	2	yes	maximal, complemented
3	C₃×#5791	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄×#67	C₂	1	2	yes	maximal, complemented
5	C₃×#5564	C₂	1	4	yes	maximal, complemented
6	C₃×#5560	C₂	1	4	yes	maximal, complemented
7	C₃×#5547	C₂	1	4	yes	maximal, complemented
8	C₃×#5538	C₂	1	4	yes	maximal, complemented
9	C₃×#5515	C₂	1	2	yes	maximal, complemented
10	C₃×#5494	C₂	1	2	yes	maximal, complemented
11	C₃×#5493	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5483	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5479	C₂	1	2	yes	maximal, complemented
14	C₃×#3459	—	3	1	no	maximal
15	#85776	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×#67	C₂²	1	2	yes	—
20	C₂×C₃×#235	C₂²	1	2	yes	complemented
21	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
22	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
23	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
24	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
28	C₃×#953	C₂²	1	4	yes	complemented
29	C₂×C₃×#217	C₂²	1	2	yes	—
30	C₃×#939	C₂²	1	4	yes	—
31	C₃×#939	C₂²	1	4	yes	—
32	C₃×#937	C₂²	1	4	yes	complemented
33	C₃×#935	C₂²	1	4	yes	complemented
34	C₃×#930	C₂²	1	2	yes	—
35	C₃×#930	C₂²	1	2	yes	—
36	C₃×#930	C₂²	1	2	yes	complemented
37	C₃×#929	C₂²	1	4	yes	complemented
38	C₃×#929	C₂²	1	4	yes	complemented
39	C₃×C₄×#67	C₂²	1	4	yes	complemented
40	C₃×C₄×#67	C₂²	1	4	yes	complemented
41	C₃×C₄×#67	C₂²	1	4	yes	complemented
42	C₃×C₄×#67	C₂²	1	4	yes	complemented
43	C₃×C₄×#67	C₂²	1	4	yes	complemented
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
45	C₃×#926	C₂²	1	2	yes	complemented
46	C₃×#924	C₂²	1	2	yes	complemented
47	C₃×#924	C₂²	1	2	yes	complemented
48	C₃×#924	C₂²	1	2	yes	complemented
49	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
50	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
51	C₃×#898	C₂²	1	4	yes	complemented
52	C₃×#896	C₂²	1	4	yes	complemented
53	C₃×#894	C₂²	1	4	yes	complemented
54	C₃×#889	C₂²	1	4	yes	complemented
55	C₃×#886	C₂²	1	4	yes	complemented
56	C₃×#885	C₂²	1	4	yes	complemented
57	C₃×#884	C₂²	1	4	yes	complemented
58	C₃×#883	C₂²	1	4	yes	complemented
59	C₃×#882	C₂²	1	4	yes	complemented
60	C₃×#879	C₂²	1	4	yes	complemented
61	C₃×#878	C₂²	1	4	yes	complemented
62	C₃×#878	C₂²	1	4	yes	complemented
63	C₃×#876	C₂²	1	4	yes	complemented
64	C₃×#875	C₂²	1	2	yes	complemented
65	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
66	C₃×#872	C₂²	1	4	yes	complemented
67	C₃×#870	C₂²	1	2	yes	complemented
68	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
69	C₃×#543	—	3	1	no	—
70	C₃×#539	—	3	4	no	—
71	C₃×#539	—	3	2	no	—
72	C₃×#538	—	3	4	no	—
73	C₃×#538	—	3	2	no	—
74	C₃×#534	—	3	2	no	—
75	C₃×#534	—	3	1	no	—
76	C₃×#529	—	3	4	no	—
77	C₃×#529	—	3	2	no	—
78	C₃×#525	—	3	2	no	—
79	C₃×#525	—	3	4	no	—
80	C₂×C₃×C₄×D₄	—	2	1	no	—
81	C₂×C₃×C₄×D₄	—	3	2	no	—
82	C₂×C₃×C₄×D₄	D₃	1	1	yes	characteristic, complemented
83	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
84	#5804	C₂×C₃	1	2	yes	complemented
85	#5791	C₂×C₃	1	2	yes	complemented
86	C₂×C₄×#67	C₂×C₃	1	2	yes	complemented
87	#5564	C₂×C₃	1	4	yes	complemented
88	#5560	C₂×C₃	1	4	yes	complemented
89	#5547	C₂×C₃	1	4	yes	complemented
90	#5538	C₂×C₃	1	4	yes	complemented
91	#5515	C₂×C₃	1	2	yes	complemented
92	#5494	C₂×C₃	1	2	yes	complemented
93	#5493	C₂×C₃	1	1	yes	characteristic, complemented
94	#5483	C₂×C₃	1	1	yes	characteristic, complemented
95	#5479	C₂×C₃	1	2	yes	complemented
96	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
97	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
98	C₂³×C₃×D₃	C₂³	1	2	yes	—
99	C₂×C₃²×D₄	—	2	4	no	—
100	C₂×C₃²×D₄	C₂³	1	4	yes	—
101	C₂²×C₃²×C₄	—	4	2	no	—
102	C₂²×C₃²×C₄	—	4	2	no	—
103	C₂²×C₃²×C₄	C₂³	1	2	yes	—
104	C₂²×C₃²×C₄	C₂³	1	2	yes	—
105	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃²×C₄	C₂³	1	2	yes	—
108	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
110	C₂²×C₃²×C₄	C₂³	1	2	yes	—
111	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
112	C₂×C₃×#67	—	2	8	no	—
113	C₂×C₃×#67	C₂³	1	4	yes	—
114	C₂×C₃×#67	C₂³	1	4	yes	—
115	C₂×C₃×#67	C₂³	1	4	yes	—
116	C₂×C₃×#67	C₂³	1	4	yes	—
117	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
118	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
119	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
120	C₃×#235	—	4	4	no	—
121	C₂×C₃×D₁₂	C₂³	1	2	yes	—
122	C₂×C₃×D₁₂	C₂³	1	2	yes	—
123	C₂×C₃×C₄×D₃	—	4	4	no	—
124	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
125	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
126	C₂×C₃×Dic₆	C₂³	1	2	yes	—
127	C₂×C₃×Dic₆	C₂³	1	2	yes	—
128	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₃²×C₄²	C₂³	1	2	yes	—
132	C₃²×C₄²	C₂³	1	2	yes	—
133	C₃×#217	C₂³	1	4	yes	—
134	C₃×#217	C₂³	1	4	yes	—
135	C₃×#217	C₂³	1	4	yes	—
136	C₃×#217	C₂³	1	4	yes	—
137	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
139	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
140	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
141	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
142	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
143	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
144	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
145	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
146	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
147	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
148	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
149	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
150	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
151	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
152	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
153	C₃×C₄×Dic₃	C₂³	1	4	yes	—
154	C₃×C₄×Dic₃	C₂³	1	4	yes	—
155	#3459	—	3	1	no	Sylow
156	C₂×C₃×#41	—	3	2	no	—
157	C₂²×C₃×D₄	—	2	1	no	—
158	C₂²×C₃×D₄	—	3	2	no	—
159	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₂³×C₃×C₄	—	2	1	no	—
162	C₂³×C₃×C₄	—	2	1	no	—
163	C₂³×C₃×C₄	—	3	2	no	—
164	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
166	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂²×#67	C₂²×C₃	1	2	yes	—
169	C₂×#235	C₂²×C₃	1	2	yes	complemented
170	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
171	C₃×#126	—	3	4	no	—
172	C₃×#126	—	3	4	no	—
173	C₃×#126	—	3	4	no	—
174	C₃×#125	—	3	4	no	—
175	C₃×#125	—	3	2	no	—
176	C₃×#124	—	3	4	no	—
177	C₃×#124	—	3	2	no	—
178	C₃×#123	—	3	4	no	—
179	C₃×#123	—	3	4	no	—
180	C₃×#123	—	3	4	no	—
181	C₃×#123	—	3	4	no	—
182	C₃×#123	—	3	4	no	—
183	C₃×#123	—	3	4	no	—
184	C₃×C₂²⋊Q₈	—	3	2	no	—
185	C₃×C₂²⋊Q₈	—	3	2	no	—
186	C₃×C₂²⋊Q₈	—	3	2	no	—
187	C₃×C₂²⋊Q₈	—	3	4	no	—
188	C₃×C₂²⋊Q₈	—	3	4	no	—
189	C₃×C₂²⋊Q₈	—	3	4	no	—
190	C₃×#121	—	3	4	no	—
191	C₃×#121	—	3	4	no	—
192	C₃×#121	—	3	2	no	—
193	C₃×#121	—	3	2	no	—
194	C₃×#121	—	3	2	no	—
195	C₃×#121	—	3	4	no	—
196	C₃×#120	—	3	4	no	—
197	C₃×#120	—	3	4	no	—
198	C₃×#120	—	3	4	no	—
199	C₃×C₄×Q₈	—	3	2	no	—
200	C₃×C₄×D₄	—	2	4	no	—
201	C₃×C₄×D₄	—	2	4	no	—
202	C₃×C₄×D₄	—	3	4	no	—
203	C₃×C₄×D₄	—	3	4	no	—
204	C₃×C₄×D₄	—	3	4	no	—
205	C₃×C₄×D₄	—	3	4	no	—
206	C₃×C₄×D₄	—	3	4	no	—
207	C₃×C₄×D₄	—	3	2	no	—
208	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
209	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
210	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
211	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
212	C₃×#117	—	3	2	no	—
213	C₃×#117	—	3	4	no	—
214	C₂×C₃×C₄⋊C₄	—	2	1	no	—
215	C₂×C₃×C₄⋊C₄	—	3	2	no	—
216	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
217	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
221	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
222	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
224	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
226	C₂×C₃×C₄²	—	2	1	no	—
227	C₂×C₃×C₄²	—	3	2	no	—
228	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
229	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
230	#953	C₂²×C₃	1	4	yes	complemented
231	C₂×#217	C₂²×C₃	1	2	yes	—
232	#939	C₂²×C₃	1	4	yes	—
233	#939	C₂²×C₃	1	4	yes	—
234	#937	C₂²×C₃	1	4	yes	complemented
235	#935	C₂²×C₃	1	4	yes	complemented
236	#930	C₂²×C₃	1	2	yes	—
237	#930	C₂²×C₃	1	2	yes	—
238	#930	C₂²×C₃	1	2	yes	complemented
239	#929	C₂²×C₃	1	4	yes	complemented
240	#929	C₂²×C₃	1	4	yes	complemented
241	C₄×#67	C₂²×C₃	1	4	yes	complemented
242	C₄×#67	C₂²×C₃	1	4	yes	complemented
243	C₄×#67	C₂²×C₃	1	4	yes	complemented
244	C₄×#67	C₂²×C₃	1	4	yes	complemented
245	C₄×#67	C₂²×C₃	1	4	yes	complemented
246	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
247	#926	C₂²×C₃	1	2	yes	complemented
248	#924	C₂²×C₃	1	2	yes	complemented
249	#924	C₂²×C₃	1	2	yes	complemented
250	#924	C₂²×C₃	1	2	yes	complemented
251	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
252	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
253	#898	C₂²×C₃	1	4	yes	complemented
254	#896	C₂²×C₃	1	4	yes	complemented
255	#894	C₂²×C₃	1	4	yes	complemented
256	#889	C₂²×C₃	1	4	yes	complemented
257	#886	C₂²×C₃	1	4	yes	complemented
258	#885	C₂²×C₃	1	4	yes	complemented
259	#884	C₂²×C₃	1	4	yes	complemented
260	#883	C₂²×C₃	1	4	yes	complemented
261	#882	C₂²×C₃	1	4	yes	complemented
262	#879	C₂²×C₃	1	4	yes	complemented
263	#878	C₂²×C₃	1	4	yes	complemented
264	#878	C₂²×C₃	1	4	yes	complemented
265	#876	C₂²×C₃	1	4	yes	complemented
266	#875	C₂²×C₃	1	2	yes	complemented
267	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
268	#872	C₂²×C₃	1	4	yes	complemented
269	#870	C₂²×C₃	1	2	yes	complemented
270	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
271	C₂³×C₃²	—	2	2	no	—
272	C₂³×C₃²	—	4	1	no	—
273	C₂³×C₃²	—	4	1	no	—
274	C₂³×C₃²	—	4	1	no	—
275	C₂³×C₃²	—	4	1	no	—
276	C₂³×C₃²	#41	1	4	yes	complemented
277	C₂³×C₃²	C₂⁴	1	2	yes	—
278	C₂³×C₃²	C₂⁴	1	2	yes	—
279	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
280	C₂²×C₃×D₃	—	2	4	no	—
281	C₂²×C₃×D₃	—	4	2	no	—
282	C₂²×C₃×D₃	—	4	2	no	—
283	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
284	C₃²×D₄	—	2	8	no	—
285	C₂×C₃²×C₄	—	2	2	no	—
286	C₂×C₃²×C₄	—	2	2	no	—
287	C₂×C₃²×C₄	—	2	4	no	—
288	C₂×C₃²×C₄	—	2	4	no	—
289	C₂×C₃²×C₄	—	4	2	no	—
290	C₂×C₃²×C₄	—	4	2	no	—
291	C₂×C₃²×C₄	—	4	1	no	—
292	C₂×C₃²×C₄	—	4	1	no	—
293	C₂×C₃²×C₄	—	4	1	no	—
294	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
295	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
296	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
297	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
298	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
299	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
300	C₃×#67	—	2	8	no	—
301	C₃×#67	—	2	8	no	—
302	C₃×#67	—	4	4	no	—
303	C₃×#67	—	4	4	no	—
304	C₂×C₃×Dic₃	—	2	4	no	—
305	C₂×C₃×Dic₃	—	4	2	no	—
306	C₂×C₃×Dic₃	—	4	2	no	—
307	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
308	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
309	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
310	C₃×D₁₂	—	4	2	no	—
311	C₃×D₁₂	—	4	2	no	—
312	C₃×C₄×D₃	—	2	8	no	—
313	C₃×C₄×D₃	—	4	4	no	—
314	C₃×Dic₆	—	4	2	no	—
315	C₃×Dic₆	—	4	2	no	—
316	#543	—	3	1	no	—
317	#539	—	3	4	no	—
318	#539	—	3	2	no	—
319	#538	—	3	4	no	—
320	#538	—	3	2	no	—
321	#534	—	3	2	no	—
322	#534	—	3	1	no	—
323	#529	—	3	4	no	—
324	#529	—	3	2	no	—
325	#525	—	3	2	no	—
326	#525	—	3	4	no	—
327	C₂×C₄×D₄	—	3	2	no	—
328	C₂×C₄×D₄	C₃×D₃	1	1	yes	characteristic, complemented
329	C₂⁴×C₃	—	2	1	no	—
330	C₂⁴×C₃	—	2	1	no	—
331	C₂⁴×C₃	—	3	2	no	—
332	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
333	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
334	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
335	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
336	C₂³×D₃	C₂³×C₃	1	2	yes	—
337	C₃×#41	—	12	4	no	—
338	C₂×C₃×Q₈	—	3	2	no	—
339	C₂×C₃×Q₈	—	3	2	no	—
340	C₂×C₃×D₄	—	2	8	no	—
341	C₂×C₃×D₄	—	2	4	no	—
342	C₂×C₃×D₄	—	2	4	no	—
343	C₂×C₃×D₄	—	2	4	no	—
344	C₂×C₃×D₄	—	3	4	no	—
345	C₂×C₃×D₄	—	3	4	no	—
346	C₂×C₃×D₄	—	3	4	no	—
347	C₂×C₃×D₄	—	3	4	no	—
348	C₂×C₃×D₄	—	3	2	no	—
349	C₂×C₃×D₄	—	3	2	no	—
350	C₂×C₃×D₄	—	6	8	no	—
351	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
352	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
353	C₂²×C₃×C₄	—	2	1	no	—
354	C₂²×C₃×C₄	—	2	1	no	—
355	C₂²×C₃×C₄	—	2	1	no	—
356	C₂²×C₃×C₄	—	2	1	no	—
357	C₂²×C₃×C₄	—	2	1	no	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	—	2	2	no	—
360	C₂²×C₃×C₄	—	2	2	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	3	2	no	—
363	C₂²×C₃×C₄	—	3	2	no	—
364	C₂²×C₃×C₄	—	3	2	no	—
365	C₂²×C₃×C₄	—	3	4	no	—
366	C₂²×C₃×C₄	—	3	4	no	—
367	C₂²×C₃×C₄	—	4	2	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	—	4	2	no	—
370	C₂²×C₃×C₄	—	4	2	no	—
371	C₂²×C₃×C₄	—	4	4	no	—
372	C₂²×C₃×C₄	—	4	4	no	—
373	C₂²×C₃×C₄	—	12	4	no	—
374	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
376	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
378	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
380	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
383	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
384	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
385	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
388	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
391	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
392	C₂×#67	—	2	8	no	—
393	C₂×#67	C₂³×C₃	1	4	yes	—
394	C₂×#67	C₂³×C₃	1	4	yes	—
395	C₂×#67	C₂³×C₃	1	4	yes	—
396	C₂×#67	C₂³×C₃	1	4	yes	—
397	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
398	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
399	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
400	#235	—	4	4	no	—
401	C₂×D₁₂	C₂³×C₃	1	2	yes	—
402	C₂×D₁₂	C₂³×C₃	1	2	yes	—
403	C₂×C₄×D₃	—	4	4	no	—
404	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
405	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
406	C₂×Dic₆	C₂³×C₃	1	2	yes	—
407	C₂×Dic₆	C₂³×C₃	1	2	yes	—
408	C₃×C₄⋊C₄	—	2	4	no	—
409	C₃×C₄⋊C₄	—	3	4	no	—
410	C₃×C₄⋊C₄	—	3	4	no	—
411	C₃×C₄⋊C₄	—	3	4	no	—
412	C₃×C₄⋊C₄	—	3	4	no	—
413	C₃×C₄⋊C₄	—	3	4	no	—
414	C₃×C₄⋊C₄	—	3	4	no	—
415	C₃×C₄⋊C₄	—	3	2	no	—
416	C₃×C₄⋊C₄	—	3	2	no	—
417	C₃×C₄⋊C₄	—	3	2	no	—
418	C₃×C₄⋊C₄	—	3	2	no	—
419	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
420	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
421	C₃×C₂²⋊C₄	—	2	4	no	—
422	C₃×C₂²⋊C₄	—	2	4	no	—
423	C₃×C₂²⋊C₄	—	3	4	no	—
424	C₃×C₂²⋊C₄	—	3	4	no	—
425	C₃×C₂²⋊C₄	—	3	4	no	—
426	C₃×C₂²⋊C₄	—	3	4	no	—
427	C₃×C₂²⋊C₄	—	3	4	no	—
428	C₃×C₂²⋊C₄	—	3	4	no	—
429	C₃×C₂²⋊C₄	—	3	4	no	—
430	C₃×C₂²⋊C₄	—	3	4	no	—
431	C₃×C₂²⋊C₄	—	3	4	no	—
432	C₃×C₂²⋊C₄	—	3	4	no	—
433	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
434	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
435	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
436	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
437	C₃×C₄²	—	2	2	no	—
438	C₃×C₄²	—	2	2	no	—
439	C₃×C₄²	—	3	4	no	—
440	C₃×C₄²	—	3	4	no	—
441	C₃×C₄²	C₂²×D₃	1	2	yes	—
442	C₃×C₄²	C₂²×D₃	1	2	yes	—
443	C₃×C₄²	C₂³×C₃	1	2	yes	—
444	C₃×C₄²	C₂³×C₃	1	2	yes	—
445	#217	C₂³×C₃	1	4	yes	—
446	#217	C₂³×C₃	1	4	yes	—
447	#217	C₂³×C₃	1	4	yes	—
448	#217	C₂³×C₃	1	4	yes	—
449	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
450	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
451	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
452	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
453	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
454	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
455	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
456	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
457	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
458	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
459	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
460	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
461	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
462	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
463	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
464	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
465	C₄×Dic₃	C₂³×C₃	1	4	yes	—
466	C₄×Dic₃	C₂³×C₃	1	4	yes	—
467	C₂²×C₃²	—	2	1	no	—
468	C₂²×C₃²	—	2	1	no	—
469	C₂²×C₃²	—	2	2	no	—
470	C₂²×C₃²	—	2	2	no	—
471	C₂²×C₃²	—	2	2	no	—
472	C₂²×C₃²	—	2	2	no	—
473	C₂²×C₃²	—	2	2	no	—
474	C₂²×C₃²	—	4	4	no	—
475	C₂²×C₃²	—	4	4	no	—
476	C₂²×C₃²	C₂×#41	1	4	yes	—
477	C₂²×C₃²	C₂×#41	1	2	yes	—
478	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
479	C₂×C₃×D₃	—	2	4	no	—
480	C₂×C₃×D₃	—	2	4	no	—
481	C₂×C₃×D₃	—	2	4	no	—
482	C₂×C₃×D₃	—	4	8	no	—
483	C₃²×C₄	—	2	2	no	—
484	C₃²×C₄	—	2	1	no	—
485	C₃²×C₄	—	2	2	no	—
486	C₃²×C₄	—	2	2	no	—
487	C₃²×C₄	—	2	2	no	—
488	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
489	C₃×Dic₃	—	2	4	no	—
490	C₃×Dic₃	—	2	4	no	—
491	C₃×Dic₃	—	2	4	no	—
492	C₂×#41	—	3	2	no	—
493	C₂²×D₄	—	3	2	no	—
494	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
495	C₂³×C₄	—	3	2	no	—
496	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
497	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
498	#126	—	3	4	no	—
499	#126	—	3	4	no	—
500	#126	—	3	4	no	—
501	#125	—	3	4	no	—
502	#125	—	3	2	no	—
503	#124	—	3	4	no	—
504	#124	—	3	2	no	—
505	#123	—	3	4	no	—
506	#123	—	3	4	no	—
507	#123	—	3	4	no	—
508	#123	—	3	4	no	—
509	#123	—	3	4	no	—
510	#123	—	3	4	no	—
511	C₂²⋊Q₈	—	3	2	no	—
512	C₂²⋊Q₈	—	3	2	no	—
513	C₂²⋊Q₈	—	3	2	no	—
514	C₂²⋊Q₈	—	3	4	no	—
515	C₂²⋊Q₈	—	3	4	no	—
516	C₂²⋊Q₈	—	3	4	no	—
517	#121	—	3	4	no	—
518	#121	—	3	4	no	—
519	#121	—	3	2	no	—
520	#121	—	3	2	no	—
521	#121	—	3	2	no	—
522	#121	—	3	4	no	—
523	#120	—	3	4	no	—
524	#120	—	3	4	no	—
525	#120	—	3	4	no	—
526	C₄×Q₈	—	3	2	no	—
527	C₄×D₄	—	3	4	no	—
528	C₄×D₄	—	3	4	no	—
529	C₄×D₄	—	3	4	no	—
530	C₄×D₄	—	3	4	no	—
531	C₄×D₄	—	3	4	no	—
532	C₄×D₄	—	3	2	no	—
533	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
534	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
535	#117	—	3	2	no	—
536	#117	—	3	4	no	—
537	C₂×C₄⋊C₄	—	3	2	no	—
538	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
539	C₂×C₂²⋊C₄	—	3	2	no	—
540	C₂×C₂²⋊C₄	—	3	2	no	—
541	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
543	C₂×C₄²	—	3	2	no	—
544	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
545	C₂³×C₃	—	2	4	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	2	2	no	—
548	C₂³×C₃	—	2	1	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	4	no	—
552	C₂³×C₃	—	3	4	no	—
553	C₂³×C₃	—	4	1	no	—
554	C₂³×C₃	—	4	1	no	—
555	C₂³×C₃	—	4	1	no	—
556	C₂³×C₃	—	4	1	no	—
557	C₂³×C₃	—	4	1	no	—
558	C₂³×C₃	—	4	1	no	—
559	C₂³×C₃	—	4	1	no	—
560	C₂³×C₃	—	4	1	no	—
561	C₂³×C₃	—	4	2	no	—
562	C₂³×C₃	—	4	2	no	—
563	C₂³×C₃	—	4	2	no	—
564	C₂³×C₃	—	4	2	no	—
565	C₂³×C₃	—	6	4	no	—
566	C₂³×C₃	—	12	2	no	—
567	C₂³×C₃	—	12	2	no	—
568	C₂³×C₃	#235	1	4	yes	complemented
569	C₂³×C₃	C₃×#41	1	4	yes	complemented
570	C₂³×C₃	C₂³×D₃	1	2	yes	—
571	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
572	C₂³×C₃	C₂³×D₃	1	2	yes	—
573	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
574	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
575	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
576	C₂²×D₃	—	2	4	no	—
577	C₂²×D₃	—	4	2	no	—
578	C₂²×D₃	—	4	2	no	—
579	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
580	C₃×Q₈	—	12	2	no	—
581	C₃×Q₈	—	12	2	no	—
582	C₃×D₄	—	2	16	no	—
583	C₃×D₄	—	2	8	no	—
584	C₃×D₄	—	2	8	no	—
585	C₃×D₄	—	6	8	no	—
586	C₃×D₄	—	6	8	no	—
587	C₃×D₄	—	12	2	no	—
588	C₃×D₄	—	12	2	no	—
589	C₃×D₄	—	12	4	no	—
590	C₃×D₄	—	12	4	no	—
591	C₂×C₃×C₄	—	2	4	no	—
592	C₂×C₃×C₄	—	2	4	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	4	no	—
597	C₂×C₃×C₄	—	2	4	no	—
598	C₂×C₃×C₄	—	2	4	no	—
599	C₂×C₃×C₄	—	2	4	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	3	4	no	—
608	C₂×C₃×C₄	—	3	4	no	—
609	C₂×C₃×C₄	—	3	4	no	—
610	C₂×C₃×C₄	—	4	4	no	—
611	C₂×C₃×C₄	—	4	4	no	—
612	C₂×C₃×C₄	—	4	2	no	—
613	C₂×C₃×C₄	—	4	2	no	—
614	C₂×C₃×C₄	—	4	1	no	—
615	C₂×C₃×C₄	—	4	1	no	—
616	C₂×C₃×C₄	—	4	1	no	—
617	C₂×C₃×C₄	—	4	2	no	—
618	C₂×C₃×C₄	—	4	1	no	—
619	C₂×C₃×C₄	—	4	2	no	—
620	C₂×C₃×C₄	—	4	1	no	—
621	C₂×C₃×C₄	—	4	1	no	—
622	C₂×C₃×C₄	—	4	4	no	—
623	C₂×C₃×C₄	—	4	4	no	—
624	C₂×C₃×C₄	—	4	2	no	—
625	C₂×C₃×C₄	—	4	2	no	—
626	C₂×C₃×C₄	—	4	2	no	—
627	C₂×C₃×C₄	—	6	4	no	—
628	C₂×C₃×C₄	—	6	8	no	—
629	C₂×C₃×C₄	—	12	4	no	—
630	C₂×C₃×C₄	—	12	2	no	—
631	C₂×C₃×C₄	—	12	2	no	—
632	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
633	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
634	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
635	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
636	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
637	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
638	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
640	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
643	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
644	#67	—	2	8	no	—
645	#67	—	2	8	no	—
646	#67	—	4	4	no	—
647	#67	—	4	4	no	—
648	C₂×Dic₃	—	2	4	no	—
649	C₂×Dic₃	—	4	2	no	—
650	C₂×Dic₃	—	4	2	no	—
651	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
652	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
653	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
654	D₁₂	—	4	2	no	—
655	D₁₂	—	4	2	no	—
656	C₄×D₃	—	2	8	no	—
657	C₄×D₃	—	4	4	no	—
658	Dic₆	—	4	2	no	—
659	Dic₆	—	4	2	no	—
660	C₂×C₃²	—	2	2	no	—
661	C₂×C₃²	—	2	4	no	—
662	C₂×C₃²	—	4	2	no	—
663	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
664	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂×C₃²	#585	1	1	yes	characteristic
666	C₃×D₃	—	4	4	no	—
667	C₂⁴	—	3	2	no	—
668	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
669	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
670	#41	—	12	4	no	—
671	C₂×Q₈	—	3	2	no	—
672	C₂×Q₈	—	3	2	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	3	4	no	—
675	C₂×D₄	—	3	4	no	—
676	C₂×D₄	—	3	4	no	—
677	C₂×D₄	—	3	4	no	—
678	C₂×D₄	—	3	2	no	—
679	C₂×D₄	—	3	2	no	—
680	C₂×D₄	—	6	8	no	—
681	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
682	C₂²×C₄	—	3	2	no	—
683	C₂²×C₄	—	3	2	no	—
684	C₂²×C₄	—	3	2	no	—
685	C₂²×C₄	—	3	4	no	—
686	C₂²×C₄	—	3	4	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	12	4	no	—
690	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
691	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
692	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
693	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
694	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
695	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
696	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
697	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
698	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
699	C₄⋊C₄	—	3	4	no	—
700	C₄⋊C₄	—	3	4	no	—
701	C₄⋊C₄	—	3	4	no	—
702	C₄⋊C₄	—	3	2	no	—
703	C₄⋊C₄	—	3	4	no	—
704	C₄⋊C₄	—	3	2	no	—
705	C₄⋊C₄	—	3	4	no	—
706	C₄⋊C₄	—	3	2	no	—
707	C₄⋊C₄	—	3	4	no	—
708	C₄⋊C₄	—	3	2	no	—
709	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
710	C₂²⋊C₄	—	3	4	no	—
711	C₂²⋊C₄	—	3	4	no	—
712	C₂²⋊C₄	—	3	4	no	—
713	C₂²⋊C₄	—	3	4	no	—
714	C₂²⋊C₄	—	3	4	no	—
715	C₂²⋊C₄	—	3	4	no	—
716	C₂²⋊C₄	—	3	4	no	—
717	C₂²⋊C₄	—	3	4	no	—
718	C₂²⋊C₄	—	3	4	no	—
719	C₂²⋊C₄	—	3	4	no	—
720	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
721	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
722	C₄²	—	3	4	no	—
723	C₄²	—	3	4	no	—
724	C₄²	C₂²×C₃×D₃	1	2	yes	—
725	C₄²	C₂²×C₃×D₃	1	2	yes	—
726	C₂²×C₃	—	2	2	no	—
727	C₂²×C₃	—	2	2	no	—
728	C₂²×C₃	—	2	1	no	—
729	C₂²×C₃	—	2	2	no	—
730	C₂²×C₃	—	2	1	no	—
731	C₂²×C₃	—	2	2	no	—
732	C₂²×C₃	—	2	2	no	—
733	C₂²×C₃	—	2	1	no	—
734	C₂²×C₃	—	2	2	no	—
735	C₂²×C₃	—	2	1	no	—
736	C₂²×C₃	—	2	4	no	—
737	C₂²×C₃	—	2	2	no	—
738	C₂²×C₃	—	2	2	no	—
739	C₂²×C₃	—	2	2	no	—
740	C₂²×C₃	—	2	2	no	—
741	C₂²×C₃	—	2	2	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	2	2	no	—
744	C₂²×C₃	—	2	4	no	—
745	C₂²×C₃	—	2	1	no	—
746	C₂²×C₃	—	4	2	no	—
747	C₂²×C₃	—	4	2	no	—
748	C₂²×C₃	—	4	2	no	—
749	C₂²×C₃	—	4	2	no	—
750	C₂²×C₃	—	4	4	no	—
751	C₂²×C₃	—	4	4	no	—
752	C₂²×C₃	—	4	8	no	—
753	C₂²×C₃	—	4	8	no	—
754	C₂²×C₃	—	4	4	no	—
755	C₂²×C₃	—	4	4	no	—
756	C₂²×C₃	—	6	4	no	—
757	C₂²×C₃	—	6	4	no	—
758	C₂²×C₃	—	6	4	no	—
759	C₂²×C₃	—	12	8	no	—
760	C₂²×C₃	C₂×#235	1	2	yes	—
761	C₂²×C₃	C₂×#235	1	4	yes	—
762	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
763	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
764	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
765	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
766	C₂×D₃	—	2	4	no	—
767	C₂×D₃	—	2	4	no	—
768	C₂×D₃	—	2	4	no	—
769	C₂×D₃	—	4	8	no	—
770	C₃×C₄	—	2	2	no	—
771	C₃×C₄	—	2	4	no	—
772	C₃×C₄	—	2	2	no	—
773	C₃×C₄	—	2	1	no	—
774	C₃×C₄	—	2	2	no	—
775	C₃×C₄	—	2	2	no	—
776	C₃×C₄	—	2	2	no	—
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	2	no	—
779	C₃×C₄	—	2	2	no	—
780	C₃×C₄	—	2	1	no	—
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	—	4	2	no	—
784	C₃×C₄	—	4	2	no	—
785	C₃×C₄	—	4	2	no	—
786	C₃×C₄	—	6	4	no	—
787	C₃×C₄	—	6	4	no	—
788	C₃×C₄	—	6	4	no	—
789	C₃×C₄	#1004	1	2	yes	—
790	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
791	Dic₃	—	2	4	no	—
792	Dic₃	—	2	4	no	—
793	Dic₃	—	2	4	no	—
794	C₃²	#3459	1	1	yes	characteristic, complemented, Sylow
795	C₂³	—	2	2	no	—
796	C₂³	—	3	4	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	1	no	—
799	C₂³	—	4	1	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	6	4	no	—
802	C₂³	—	12	2	no	—
803	C₂³	—	12	2	no	—
804	C₂³	C₃×#235	1	4	yes	complemented
805	C₂³	C₂³×C₃×D₃	1	2	yes	—
806	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
807	C₂³	C₂³×C₃×D₃	1	2	yes	—
808	Q₈	—	12	2	no	—
809	Q₈	—	12	2	no	—
810	D₄	—	2	8	no	—
811	D₄	—	6	8	no	—
812	D₄	—	6	8	no	—
813	D₄	—	12	2	no	—
814	D₄	—	12	2	no	—
815	D₄	—	12	4	no	—
816	D₄	—	12	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	3	4	no	—
822	C₂×C₄	—	3	4	no	—
823	C₂×C₄	—	3	4	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	6	4	no	—
830	C₂×C₄	—	6	8	no	—
831	C₂×C₄	—	12	4	no	—
832	C₂×C₄	—	12	2	no	—
833	C₂×C₄	—	12	2	no	—
834	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
835	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
836	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
837	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
838	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
839	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
840	C₂×C₃	—	2	4	no	—
841	C₂×C₃	—	2	2	no	—
842	C₂×C₃	—	2	4	no	—
843	C₂×C₃	—	2	4	no	—
844	C₂×C₃	—	2	2	no	—
845	C₂×C₃	—	2	1	no	—
846	C₂×C₃	—	2	1	no	—
847	C₂×C₃	—	2	1	no	—
848	C₂×C₃	—	4	4	no	—
849	C₂×C₃	—	4	4	no	—
850	C₂×C₃	—	4	2	no	—
851	C₂×C₃	—	4	2	no	—
852	C₂×C₃	—	12	4	no	—
853	C₂×C₃	C₂²×#235	1	1	yes	characteristic
854	C₂×C₃	C₂×#1004	1	1	yes	characteristic
855	C₂×C₃	#5964	1	1	yes	characteristic
856	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
857	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂×C₃	C₃×#585	1	1	yes	characteristic
859	D₃	—	4	4	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	4	4	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	6	4	no	—
870	C₂²	—	6	4	no	—
871	C₂²	—	6	4	no	—
872	C₂²	—	12	8	no	—
873	C₂²	C₂×C₃×#235	1	2	yes	—
874	C₂²	C₂×C₃×#235	1	4	yes	—
875	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
876	C₄	—	2	2	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	6	4	no	—
882	C₄	—	6	4	no	—
883	C₄	—	6	4	no	—
884	C₄	C₃×#1004	1	2	yes	—
885	C₃	—	2	1	no	—
886	C₃	#85776	1	1	yes	characteristic, direct product factor
887	C₃	C₃×#3459	1	1	yes	characteristic, complemented
888	C₂	—	2	2	no	—
889	C₂	—	2	4	no	—
890	C₂	—	4	2	no	—
891	C₂	—	12	4	no	—
892	C₂	C₂²×C₃×#235	1	1	yes	characteristic
893	C₂	C₂×C₃×#1004	1	1	yes	characteristic
894	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×C₄×D₄	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×C₄×D₄	D₃
hypocenter	C₃	C₃×#3459
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄×D₄	C₂	semidirect
2. C₃×#5804	C₂	semidirect
3. C₃×#5791	C₂	semidirect
4. C₂×C₃×C₄×#67	C₂	semidirect
5. C₃×#5564	C₂	semidirect
6. C₃×#5560	C₂	semidirect
7. C₃×#5547	C₂	semidirect
8. C₃×#5538	C₂	semidirect
9. C₃×#5515	C₂	semidirect
10. C₃×#5494	C₂	semidirect
11. C₃×#5493	C₂	semidirect
12. C₃×#5483	C₂	semidirect
13. C₃×#5479	C₂	semidirect
15. #85776	C₃	direct (N × H)
18. C₂³×C₃²×C₄	C₂²	semidirect
20. C₂×C₃×#235	C₂²	semidirect
21. C₂²×C₃×C₄×D₃	C₂²	semidirect
22. C₃²×C₄×D₄	C₂²	semidirect
23. C₃²×C₄×D₄	C₂²	semidirect
24. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
27. C₂×C₃²×C₄²	C₂²	semidirect
28. C₃×#953	C₂²	semidirect
32. C₃×#937	C₂²	semidirect
33. C₃×#935	C₂²	semidirect
36. C₃×#930	C₂²	semidirect
37. C₃×#929	C₂²	semidirect
38. C₃×#929	C₂²	semidirect
39. C₃×C₄×#67	C₂²	semidirect
40. C₃×C₄×#67	C₂²	semidirect
41. C₃×C₄×#67	C₂²	semidirect
42. C₃×C₄×#67	C₂²	semidirect
43. C₃×C₄×#67	C₂²	semidirect
44. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₃×#926	C₂²	semidirect
46. C₃×#924	C₂²	semidirect
47. C₃×#924	C₂²	semidirect
48. C₃×#924	C₂²	semidirect
49. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
50. C₂×C₃×C₄×Dic₃	C₂²	semidirect
51. C₃×#898	C₂²	semidirect
52. C₃×#896	C₂²	semidirect
53. C₃×#894	C₂²	semidirect
54. C₃×#889	C₂²	semidirect
55. C₃×#886	C₂²	semidirect
56. C₃×#885	C₂²	semidirect
57. C₃×#884	C₂²	semidirect
58. C₃×#883	C₂²	semidirect
59. C₃×#882	C₂²	semidirect
60. C₃×#879	C₂²	semidirect
61. C₃×#878	C₂²	semidirect
62. C₃×#878	C₂²	semidirect
63. C₃×#876	C₂²	semidirect
64. C₃×#875	C₂²	semidirect
65. C₃×C₄×D₁₂	C₂²	semidirect
66. C₃×#872	C₂²	semidirect
67. C₃×#870	C₂²	semidirect
68. C₃×C₄×Dic₆	C₂²	semidirect
82. C₂×C₃×C₄×D₄	D₃	semidirect
83. C₂×C₃×C₄×D₄	C₂×C₃	semidirect
84. #5804	C₂×C₃	semidirect
85. #5791	C₂×C₃	semidirect
86. C₂×C₄×#67	C₂×C₃	semidirect
87. #5564	C₂×C₃	semidirect
88. #5560	C₂×C₃	semidirect
89. #5547	C₂×C₃	semidirect
90. #5538	C₂×C₃	semidirect
91. #5515	C₂×C₃	semidirect
92. #5494	C₂×C₃	semidirect
93. #5493	C₂×C₃	semidirect
94. #5483	C₂×C₃	semidirect
95. #5479	C₂×C₃	semidirect
165. C₂³×C₃×C₄	C₂×D₃	semidirect
167. C₂³×C₃×C₄	C₂²×C₃	semidirect
169. C₂×#235	C₂²×C₃	semidirect
170. C₂²×C₄×D₃	C₂²×C₃	semidirect
208. C₃×C₄×D₄	C₂×D₃	semidirect
209. C₃×C₄×D₄	C₂×D₃	semidirect
210. C₃×C₄×D₄	C₂²×C₃	semidirect
211. C₃×C₄×D₄	C₂²×C₃	semidirect
216. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
217. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
223. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
225. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
228. C₂×C₃×C₄²	C₂×D₃	semidirect
229. C₂×C₃×C₄²	C₂²×C₃	semidirect
230. #953	C₂²×C₃	semidirect
234. #937	C₂²×C₃	semidirect
235. #935	C₂²×C₃	semidirect
238. #930	C₂²×C₃	semidirect
239. #929	C₂²×C₃	semidirect
240. #929	C₂²×C₃	semidirect
241. C₄×#67	C₂²×C₃	semidirect
242. C₄×#67	C₂²×C₃	semidirect
243. C₄×#67	C₂²×C₃	semidirect
244. C₄×#67	C₂²×C₃	semidirect
245. C₄×#67	C₂²×C₃	semidirect
246. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
247. #926	C₂²×C₃	semidirect
248. #924	C₂²×C₃	semidirect
249. #924	C₂²×C₃	semidirect
250. #924	C₂²×C₃	semidirect
251. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
252. C₂×C₄×Dic₃	C₂²×C₃	semidirect
253. #898	C₂²×C₃	semidirect
254. #896	C₂²×C₃	semidirect
255. #894	C₂²×C₃	semidirect
256. #889	C₂²×C₃	semidirect
257. #886	C₂²×C₃	semidirect
258. #885	C₂²×C₃	semidirect
259. #884	C₂²×C₃	semidirect
260. #883	C₂²×C₃	semidirect
261. #882	C₂²×C₃	semidirect
262. #879	C₂²×C₃	semidirect
263. #878	C₂²×C₃	semidirect
264. #878	C₂²×C₃	semidirect
265. #876	C₂²×C₃	semidirect
266. #875	C₂²×C₃	semidirect
267. C₄×D₁₂	C₂²×C₃	semidirect
268. #872	C₂²×C₃	semidirect
269. #870	C₂²×C₃	semidirect
270. C₄×Dic₆	C₂²×C₃	semidirect
276. C₂³×C₃²	#41	semidirect
328. C₂×C₄×D₄	C₃×D₃	semidirect
497. C₂³×C₄	C₂×C₃×D₃	semidirect
533. C₄×D₄	C₂×C₃×D₃	semidirect
534. C₄×D₄	C₂×C₃×D₃	semidirect
538. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
542. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
544. C₂×C₄²	C₂×C₃×D₃	semidirect
568. C₂³×C₃	#235	semidirect
569. C₂³×C₃	C₃×#41	semidirect
794. C₃²	#3459	semidirect
804. C₂³	C₃×#235	semidirect
886. C₃	#85776	direct (N × H)
887. C₃	C₃×#3459	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄×D₄	2
C₃×#5804	2
C₃×#5791	2
C₂×C₃×C₄×#67	2
C₃×#5564	2
C₃×#5560	2
C₃×#5547	2
C₃×#5538	2
C₃×#5515	2
C₃×#5494	2
C₃×#5493	2
C₃×#5483	2
C₃×#5479	2
C₃×#3459	3
#85776	3

Subgroups — C3×#85776 #11901973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85776 #11901973