Subgroups — C₃×#79480 #11859511

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#907	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5548	C₂	1	1	yes	maximal, characteristic
4	C₃²×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5127	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5111	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4837	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4836	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4730	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4728	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4727	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4727	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2932	—	3	1	no	maximal
17	#79480	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×#235	C₂²	1	1	yes	characteristic
19	C₂×C₃×#235	C₂²	1	1	yes	characteristic
20	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
22	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₃×#940	C₄	1	1	yes	characteristic
24	C₃×#938	C₄	1	1	yes	characteristic
25	C₃×C₄×#67	C₂²	1	1	yes	characteristic
26	C₃×C₄×#67	C₂²	1	1	yes	characteristic
27	C₂×C₃×#208	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×#907	—	2	4	no	—
30	C₃×#901	—	2	4	no	—
31	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
32	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
33	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
34	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
35	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
39	C₃×#895	C₄	1	1	yes	characteristic
40	C₃×#888	C₄	1	1	yes	characteristic
41	C₃×#885	C₄	1	1	yes	characteristic
42	C₃×#885	C₄	1	1	yes	characteristic
43	C₃×#884	C₄	1	1	yes	characteristic
44	C₃×#884	C₄	1	1	yes	characteristic
45	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
46	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
47	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₃²×#97	C₂²	1	1	yes	characteristic
51	C₃×#830	C₂²	1	1	yes	characteristic
52	C₃×#830	C₂²	1	1	yes	characteristic
53	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
54	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
55	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
56	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×#815	C₂²	1	1	yes	characteristic
58	C₃×#815	C₂²	1	1	yes	characteristic
59	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
61	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
62	C₃×#803	C₂²	1	1	yes	characteristic
63	C₂×C₃×#131	—	3	1	no	—
64	C₂×C₃×#131	—	3	1	no	—
65	C₃×#532	—	3	1	no	—
66	C₂×#907	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
68	#5548	C₂×C₃	1	1	yes	characteristic
69	C₃×#435	—	2	1	no	—
70	C₃×#435	—	3	1	no	—
71	C₃×#435	—	3	1	no	—
72	C₃×#435	—	3	1	no	—
73	C₃×#435	—	3	1	no	—
74	C₃×#435	—	3	1	no	—
75	C₃×#435	—	3	1	no	—
76	C₃×#435	—	3	1	no	—
77	C₃×#435	D₃	1	1	yes	characteristic, complemented
78	C₃×#435	C₂×C₃	1	1	yes	characteristic, complemented
79	C₃×#423	—	3	1	no	—
80	C₃×#408	—	3	1	no	—
81	C₃×#408	—	3	1	no	—
82	C₂×C₃×#97	—	3	1	no	—
83	#5127	C₂×C₃	1	1	yes	characteristic, complemented
84	#5111	C₂×C₃	1	1	yes	characteristic, complemented
85	#5011	C₂×C₃	1	1	yes	characteristic, complemented
86	#4837	C₂×C₃	1	1	yes	characteristic, complemented
87	#4836	C₂×C₃	1	1	yes	characteristic, complemented
88	#4730	C₂×C₃	1	1	yes	characteristic, complemented
89	#4728	C₂×C₃	1	1	yes	characteristic, complemented
90	#4727	C₂×C₃	1	1	yes	characteristic, complemented
91	#4727	C₂×C₃	1	1	yes	characteristic, complemented
92	#4706	C₂×C₃	1	1	yes	characteristic, complemented
93	D₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
101	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
102	C₂×C₃×#67	C₂×C₄	1	1	yes	characteristic
103	C₃×#235	—	2	2	no	—
104	C₃×#235	—	2	2	no	—
105	C₃×#235	—	2	2	no	—
106	C₃×#235	—	2	2	no	—
107	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
108	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
109	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
115	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
116	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
117	C₃²×M₁₆	—	2	2	no	—
118	C₂×C₃²×C₈	—	2	2	no	—
119	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
120	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
121	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
122	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
123	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₃²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₃²×C₄²	C₂³	1	1	yes	characteristic
127	C₃×#217	C₂×C₄	1	1	yes	characteristic
128	C₃×#217	C₂×C₄	1	1	yes	characteristic
129	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
130	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
131	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
132	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
133	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
134	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
135	C₃×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
136	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
137	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
138	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
139	C₃×#208	—	2	2	no	—
140	C₂×C₃×C₃⋊C₈	—	2	2	no	—
141	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
145	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
146	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
147	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
148	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
149	C₃×D₃×C₈	—	2	2	no	—
150	C₃×D₃×C₈	—	2	2	no	—
151	C₃×D₃×C₈	—	2	2	no	—
152	C₃×D₃×C₈	D₄	1	4	yes	complemented
153	#2932	—	3	1	no	Sylow
154	C₂×C₃×#41	—	3	1	no	—
155	C₂×C₃×#41	—	3	1	no	—
156	C₂×#235	C₂²×C₃	1	1	yes	characteristic
157	C₂×#235	C₂²×C₃	1	1	yes	characteristic
158	C₃×#131	—	6	4	no	—
159	C₃×#131	—	6	4	no	—
160	C₂×C₃×M₁₆	—	2	1	no	—
161	C₂×C₃×M₁₆	—	3	1	no	—
162	C₂×C₃×M₁₆	—	3	1	no	—
163	C₂×C₃×M₁₆	—	3	1	no	—
164	C₂×C₃×M₁₆	—	3	1	no	—
165	C₂×C₃×M₁₆	—	3	1	no	—
166	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
167	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
168	C₂²×C₃×C₈	—	2	1	no	—
169	C₂²×C₃×C₈	—	3	1	no	—
170	C₂²×C₃×C₈	—	3	1	no	—
171	C₂²×C₃×C₈	—	3	1	no	—
172	C₂²×C₃×C₈	—	3	1	no	—
173	C₂²×C₃×C₈	—	3	1	no	—
174	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
176	C₃×C₄⋊Q₈	—	3	1	no	—
177	C₃×#127	—	3	1	no	—
178	C₃×#124	—	3	1	no	—
179	C₃×#124	—	3	1	no	—
180	C₃×#121	—	3	1	no	—
181	C₃×#121	—	3	1	no	—
182	C₃×#121	—	3	1	no	—
183	C₃×#121	—	3	1	no	—
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	—	3	1	no	—
186	C₃×C₄×D₄	—	3	1	no	—
187	C₃×C₄×D₄	—	3	1	no	—
188	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
189	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
190	C₂×C₃×C₄²	—	3	1	no	—
191	#940	C₃×C₄	1	1	yes	characteristic
192	#938	C₃×C₄	1	1	yes	characteristic
193	C₄×#67	C₂²×C₃	1	1	yes	characteristic
194	C₄×#67	C₂²×C₃	1	1	yes	characteristic
195	C₂×#208	C₂²×C₃	1	1	yes	characteristic
196	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
197	#907	—	2	4	no	—
198	#901	—	2	4	no	—
199	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
200	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
201	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
202	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
203	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
204	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
205	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
206	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
207	#895	C₃×C₄	1	1	yes	characteristic
208	#888	C₃×C₄	1	1	yes	characteristic
209	#885	C₃×C₄	1	1	yes	characteristic
210	#885	C₃×C₄	1	1	yes	characteristic
211	#884	C₃×C₄	1	1	yes	characteristic
212	#884	C₃×C₄	1	1	yes	characteristic
213	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
214	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
215	C₃×C₄⋊C₈	—	2	1	no	—
216	C₃×C₄⋊C₈	—	3	1	no	—
217	C₃×C₄⋊C₈	—	3	1	no	—
218	C₃×C₄⋊C₈	—	3	1	no	—
219	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
220	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
221	C₃×C₂²⋊C₈	—	2	1	no	—
222	C₃×C₂²⋊C₈	—	2	1	no	—
223	C₃×C₂²⋊C₈	—	3	1	no	—
224	C₃×C₂²⋊C₈	—	3	1	no	—
225	C₃×C₂²⋊C₈	—	3	1	no	—
226	C₃×C₂²⋊C₈	—	3	1	no	—
227	C₃×C₂²⋊C₈	—	3	1	no	—
228	C₃×C₂²⋊C₈	—	3	1	no	—
229	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
230	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
231	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
232	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
233	C₃×#97	—	2	1	no	—
234	C₃×#97	—	3	1	no	—
235	C₃×#97	—	3	1	no	—
236	C₃×#97	—	3	1	no	—
237	C₃×#97	C₂×D₃	1	1	yes	characteristic
238	C₃×#97	C₂²×C₃	1	1	yes	characteristic
239	#830	C₂²×C₃	1	1	yes	characteristic
240	#830	C₂²×C₃	1	1	yes	characteristic
241	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
242	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
243	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
244	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
245	#815	C₂²×C₃	1	1	yes	characteristic
246	#815	C₂²×C₃	1	1	yes	characteristic
247	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
248	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
249	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
250	#803	C₂²×C₃	1	1	yes	characteristic
251	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
252	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
255	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
256	C₃²×D₄	—	4	1	no	—
257	C₂×C₃²×C₄	—	2	1	no	—
258	C₂×C₃²×C₄	—	2	1	no	—
259	C₂×C₃²×C₄	—	2	1	no	—
260	C₂×C₃²×C₄	—	2	1	no	—
261	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
262	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
266	C₃×#67	—	2	2	no	—
267	C₃×#67	—	2	2	no	—
268	C₃×#67	—	2	2	no	—
269	C₃×#67	—	2	2	no	—
270	C₃×#67	—	4	1	no	—
271	C₃×#67	—	4	1	no	—
272	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
273	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
274	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
275	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
276	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
277	C₃×D₁₂	—	2	2	no	—
278	C₃×D₁₂	—	2	2	no	—
279	C₃×D₁₂	—	4	1	no	—
280	C₃×C₄×D₃	—	2	1	no	—
281	C₃×C₄×D₃	—	2	1	no	—
282	C₃×C₄×D₃	—	2	1	no	—
283	C₃×C₄×D₃	—	2	1	no	—
284	C₃×C₄×D₃	—	4	1	no	—
285	C₃×C₄×D₃	—	4	1	no	—
286	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
287	C₃×C₄×D₃	#41	1	2	yes	—
288	C₃×Dic₆	—	2	2	no	—
289	C₃×Dic₆	—	2	2	no	—
290	C₃²×C₈	—	2	1	no	—
291	C₃²×C₈	—	2	1	no	—
292	C₃²×C₈	—	2	1	no	—
293	C₃²×C₈	C₂×D₄	1	2	yes	—
294	C₃×C₃⋊C₈	—	2	1	no	—
295	C₃×C₃⋊C₈	—	2	1	no	—
296	C₃×C₃⋊C₈	—	2	1	no	—
297	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
298	C₂×#131	—	3	1	no	—
299	C₂×#131	—	3	1	no	—
300	#532	—	3	1	no	—
301	#435	—	3	1	no	—
302	#435	—	3	1	no	—
303	#435	—	3	1	no	—
304	#435	—	3	1	no	—
305	#435	—	3	1	no	—
306	#435	—	3	1	no	—
307	#435	—	3	1	no	—
308	#435	C₃×D₃	1	1	yes	characteristic, complemented
309	#423	—	3	1	no	—
310	#408	—	3	1	no	—
311	#408	—	3	1	no	—
312	C₂×#97	—	3	1	no	—
313	C₃×#41	—	6	2	no	—
314	C₃×#41	—	6	2	no	—
315	C₃×#41	—	6	2	no	—
316	C₃×#41	—	6	2	no	—
317	C₂×C₃×Q₈	—	3	1	no	—
318	C₂×C₃×Q₈	—	3	1	no	—
319	C₂×C₃×D₄	—	2	1	no	—
320	C₂×C₃×D₄	—	3	1	no	—
321	C₂×C₃×D₄	—	3	1	no	—
322	C₂×C₃×D₄	—	3	1	no	—
323	C₂×C₃×D₄	—	3	1	no	—
324	C₂×C₃×D₄	—	3	1	no	—
325	C₂×C₃×D₄	—	3	1	no	—
326	C₂×C₃×D₄	—	3	1	no	—
327	C₂×C₃×D₄	—	3	1	no	—
328	C₂×C₃×D₄	—	3	1	no	—
329	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
330	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
331	C₂²×C₃×C₄	—	2	1	no	—
332	C₂²×C₃×C₄	—	2	1	no	—
333	C₂²×C₃×C₄	—	3	1	no	—
334	C₂²×C₃×C₄	—	3	1	no	—
335	C₂²×C₃×C₄	—	3	1	no	—
336	C₂²×C₃×C₄	—	3	1	no	—
337	C₂²×C₃×C₄	—	3	1	no	—
338	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
342	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
343	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
344	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
345	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
346	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
347	C₂×#67	C₂×C₃×C₄	1	1	yes	characteristic
348	#235	—	2	2	no	—
349	#235	—	2	2	no	—
350	#235	—	2	2	no	—
351	#235	—	2	2	no	—
352	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
353	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
354	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
355	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
356	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
357	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
359	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
360	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
361	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
362	C₃×M₁₆	—	2	2	no	—
363	C₃×M₁₆	—	2	2	no	—
364	C₃×M₁₆	—	4	2	no	—
365	C₃×M₁₆	—	6	2	no	—
366	C₃×M₁₆	—	6	2	no	—
367	C₃×M₁₆	—	6	2	no	—
368	C₃×M₁₆	—	6	2	no	—
369	C₃×M₁₆	—	6	2	no	—
370	C₂×C₃×C₈	—	2	2	no	—
371	C₂×C₃×C₈	—	2	2	no	—
372	C₂×C₃×C₈	—	2	1	no	—
373	C₂×C₃×C₈	—	2	1	no	—
374	C₂×C₃×C₈	—	2	1	no	—
375	C₂×C₃×C₈	—	2	1	no	—
376	C₂×C₃×C₈	—	3	1	no	—
377	C₂×C₃×C₈	—	3	4	no	—
378	C₂×C₃×C₈	—	3	1	no	—
379	C₂×C₃×C₈	—	3	1	no	—
380	C₂×C₃×C₈	—	3	1	no	—
381	C₂×C₃×C₈	—	4	2	no	—
382	C₂×C₃×C₈	—	6	2	no	—
383	C₂×C₃×C₈	—	6	2	no	—
384	C₂×C₃×C₈	—	6	2	no	—
385	C₂×C₃×C₈	—	6	2	no	—
386	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
387	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
388	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
389	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
390	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
391	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
392	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
393	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
394	C₃×C₄⋊C₄	—	2	1	no	—
395	C₃×C₄⋊C₄	—	3	1	no	—
396	C₃×C₄⋊C₄	—	3	1	no	—
397	C₃×C₄⋊C₄	—	3	1	no	—
398	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
399	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
400	C₃×C₂²⋊C₄	—	2	1	no	—
401	C₃×C₂²⋊C₄	—	2	1	no	—
402	C₃×C₂²⋊C₄	—	3	1	no	—
403	C₃×C₂²⋊C₄	—	3	1	no	—
404	C₃×C₂²⋊C₄	—	3	1	no	—
405	C₃×C₂²⋊C₄	—	3	1	no	—
406	C₃×C₂²⋊C₄	—	3	1	no	—
407	C₃×C₂²⋊C₄	—	3	1	no	—
408	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
409	C₃×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
410	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
411	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
412	C₃×C₄²	—	2	1	no	—
413	C₃×C₄²	—	3	1	no	—
414	C₃×C₄²	—	3	1	no	—
415	C₃×C₄²	—	3	1	no	—
416	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
417	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
418	#217	C₂×C₃×C₄	1	1	yes	characteristic
419	#217	C₂×C₃×C₄	1	1	yes	characteristic
420	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
421	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
422	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
423	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
424	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
425	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
426	Dic₃⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
427	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
428	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
429	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
430	#208	—	2	2	no	—
431	C₂×C₃⋊C₈	—	2	2	no	—
432	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
434	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
436	ΓL(1,𝔽₂₅)	—	2	2	no	—
437	ΓL(1,𝔽₂₅)	—	2	2	no	—
438	ΓL(1,𝔽₂₅)	—	2	2	no	—
439	ΓL(1,𝔽₂₅)	—	2	2	no	—
440	D₃×C₈	—	2	2	no	—
441	D₃×C₈	—	2	2	no	—
442	D₃×C₈	—	2	2	no	—
443	D₃×C₈	C₃×D₄	1	4	yes	complemented
444	C₂²×C₃²	—	2	1	no	—
445	C₂²×C₃²	—	2	1	no	—
446	C₂²×C₃²	—	2	1	no	—
447	C₂²×C₃²	—	2	1	no	—
448	C₂²×C₃²	—	2	1	no	—
449	C₂²×C₃²	—	2	1	no	—
450	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
451	C₂×C₃×D₃	—	2	1	no	—
452	C₂×C₃×D₃	—	2	1	no	—
453	C₂×C₃×D₃	—	2	1	no	—
454	C₂×C₃×D₃	—	2	1	no	—
455	C₂×C₃×D₃	—	2	1	no	—
456	C₂×C₃×D₃	—	2	1	no	—
457	C₂×C₃×D₃	—	2	1	no	—
458	C₂×C₃×D₃	—	2	1	no	—
459	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
460	C₃²×C₄	—	2	1	no	—
461	C₃²×C₄	—	2	1	no	—
462	C₃²×C₄	—	2	1	no	—
463	C₃²×C₄	—	2	1	no	—
464	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
465	C₃²×C₄	C₂×#41	1	1	yes	characteristic
466	C₃×Dic₃	—	2	1	no	—
467	C₃×Dic₃	—	2	1	no	—
468	C₃×Dic₃	—	2	1	no	—
469	C₃×Dic₃	—	2	1	no	—
470	C₃×Dic₃	C₄×D₄	1	2	yes	—
471	C₂×#41	—	3	1	no	—
472	C₂×#41	—	3	1	no	—
473	#131	—	6	4	no	—
474	#131	—	6	4	no	—
475	C₂×M₁₆	—	3	1	no	—
476	C₂×M₁₆	—	3	1	no	—
477	C₂×M₁₆	—	3	1	no	—
478	C₂×M₁₆	—	3	1	no	—
479	C₂×M₁₆	—	3	1	no	—
480	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
481	C₂²×C₈	—	3	1	no	—
482	C₂²×C₈	—	3	1	no	—
483	C₂²×C₈	—	3	1	no	—
484	C₂²×C₈	—	3	1	no	—
485	C₂²×C₈	—	3	1	no	—
486	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
487	C₄⋊Q₈	—	3	1	no	—
488	#127	—	3	1	no	—
489	#124	—	3	1	no	—
490	#124	—	3	1	no	—
491	#121	—	3	1	no	—
492	#121	—	3	1	no	—
493	#121	—	3	1	no	—
494	#121	—	3	1	no	—
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
499	C₂×C₄²	—	3	1	no	—
500	C₄⋊C₈	—	3	1	no	—
501	C₄⋊C₈	—	3	1	no	—
502	C₄⋊C₈	—	3	1	no	—
503	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
504	C₂²⋊C₈	—	3	1	no	—
505	C₂²⋊C₈	—	3	1	no	—
506	C₂²⋊C₈	—	3	1	no	—
507	C₂²⋊C₈	—	3	1	no	—
508	C₂²⋊C₈	—	3	1	no	—
509	C₂²⋊C₈	—	3	1	no	—
510	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
511	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
512	#97	—	3	1	no	—
513	#97	—	3	1	no	—
514	#97	—	3	1	no	—
515	#97	C₂×C₃×D₃	1	1	yes	characteristic
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	3	1	no	—
519	C₂³×C₃	—	3	1	no	—
520	C₂³×C₃	—	3	1	no	—
521	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
522	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
523	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
524	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
525	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
526	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
527	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
528	C₃×Q₈	—	6	2	no	—
529	C₃×Q₈	—	6	2	no	—
530	C₃×D₄	—	4	1	no	—
531	C₃×D₄	—	4	1	no	—
532	C₃×D₄	—	4	2	no	—
533	C₃×D₄	—	6	2	no	—
534	C₃×D₄	—	6	2	no	—
535	C₃×D₄	—	6	2	no	—
536	C₃×D₄	—	6	2	no	—
537	C₃×D₄	—	6	2	no	—
538	C₃×D₄	—	6	2	no	—
539	C₃×D₄	—	12	1	no	—
540	C₃×D₄	—	12	1	no	—
541	C₃×D₄	—	12	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	3	1	no	—
556	C₂×C₃×C₄	—	3	2	no	—
557	C₂×C₃×C₄	—	3	2	no	—
558	C₂×C₃×C₄	—	3	1	no	—
559	C₂×C₃×C₄	—	3	1	no	—
560	C₂×C₃×C₄	—	3	1	no	—
561	C₂×C₃×C₄	—	3	1	no	—
562	C₂×C₃×C₄	—	4	1	no	—
563	C₂×C₃×C₄	—	4	1	no	—
564	C₂×C₃×C₄	—	4	1	no	—
565	C₂×C₃×C₄	—	4	1	no	—
566	C₂×C₃×C₄	—	6	1	no	—
567	C₂×C₃×C₄	—	6	1	no	—
568	C₂×C₃×C₄	—	6	1	no	—
569	C₂×C₃×C₄	—	6	1	no	—
570	C₂×C₃×C₄	—	12	1	no	—
571	C₂×C₃×C₄	—	12	1	no	—
572	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
582	#67	—	2	2	no	—
583	#67	—	2	2	no	—
584	#67	—	2	2	no	—
585	#67	—	2	2	no	—
586	#67	—	4	1	no	—
587	#67	—	4	1	no	—
588	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
589	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
590	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
591	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
592	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
593	D₁₂	—	2	2	no	—
594	D₁₂	—	2	2	no	—
595	D₁₂	—	4	1	no	—
596	C₄×D₃	—	2	1	no	—
597	C₄×D₃	—	2	1	no	—
598	C₄×D₃	—	2	1	no	—
599	C₄×D₃	—	2	1	no	—
600	C₄×D₃	—	4	1	no	—
601	C₄×D₃	—	4	1	no	—
602	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
603	C₄×D₃	C₃×#41	1	2	yes	—
604	Dic₆	—	2	2	no	—
605	Dic₆	—	2	2	no	—
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	2	1	no	—
608	C₃×C₈	—	2	1	no	—
609	C₃×C₈	—	2	1	no	—
610	C₃×C₈	—	2	1	no	—
611	C₃×C₈	—	2	1	no	—
612	C₃×C₈	—	2	2	no	—
613	C₃×C₈	—	3	2	no	—
614	C₃×C₈	—	4	1	no	—
615	C₃×C₈	—	4	1	no	—
616	C₃×C₈	—	4	1	no	—
617	C₃×C₈	—	6	1	no	—
618	C₃×C₈	—	6	1	no	—
619	C₃×C₈	—	6	1	no	—
620	C₃×C₈	D₃×D₄	1	2	yes	—
621	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
622	C₃⋊C₈	—	2	1	no	—
623	C₃⋊C₈	—	2	1	no	—
624	C₃⋊C₈	—	2	1	no	—
625	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
626	C₂×C₃²	—	4	1	no	—
627	C₂×C₃²	—	4	1	no	—
628	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
629	C₂×C₃²	#568	1	1	yes	characteristic
630	C₂×C₃²	#568	1	1	yes	characteristic
631	C₃×D₃	—	2	2	no	—
632	C₃×D₃	—	4	1	no	—
633	C₃×D₃	—	4	1	no	—
634	#41	—	6	2	no	—
635	#41	—	6	2	no	—
636	#41	—	6	2	no	—
637	#41	—	6	2	no	—
638	C₂×Q₈	—	3	1	no	—
639	C₂×Q₈	—	3	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	3	1	no	—
642	C₂×D₄	—	3	1	no	—
643	C₂×D₄	—	3	1	no	—
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	C₃×C₄×D₃	1	1	yes	characteristic
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
656	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
657	M₁₆	—	2	2	no	—
658	M₁₆	—	6	2	no	—
659	M₁₆	—	6	2	no	—
660	M₁₆	—	6	2	no	—
661	M₁₆	—	6	2	no	—
662	M₁₆	—	6	2	no	—
663	C₂×C₈	—	2	2	no	—
664	C₂×C₈	—	3	1	no	—
665	C₂×C₈	—	3	4	no	—
666	C₂×C₈	—	3	1	no	—
667	C₂×C₈	—	3	1	no	—
668	C₂×C₈	—	3	1	no	—
669	C₂×C₈	—	6	2	no	—
670	C₂×C₈	—	6	2	no	—
671	C₂×C₈	—	6	2	no	—
672	C₂×C₈	—	6	2	no	—
673	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
674	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
675	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
676	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
677	C₄⋊C₄	—	3	1	no	—
678	C₄⋊C₄	—	3	1	no	—
679	C₄⋊C₄	—	3	1	no	—
680	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
681	C₂²⋊C₄	—	3	1	no	—
682	C₂²⋊C₄	—	3	1	no	—
683	C₂²⋊C₄	—	3	1	no	—
684	C₂²⋊C₄	—	3	1	no	—
685	C₂²⋊C₄	—	3	1	no	—
686	C₂²⋊C₄	—	3	1	no	—
687	C₂²⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
688	C₂²⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
689	C₄²	—	3	1	no	—
690	C₄²	—	3	1	no	—
691	C₄²	—	3	1	no	—
692	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
693	C₂²×C₃	—	2	2	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	2	1	no	—
696	C₂²×C₃	—	2	1	no	—
697	C₂²×C₃	—	2	1	no	—
698	C₂²×C₃	—	2	1	no	—
699	C₂²×C₃	—	2	1	no	—
700	C₂²×C₃	—	2	1	no	—
701	C₂²×C₃	—	2	1	no	—
702	C₂²×C₃	—	2	1	no	—
703	C₂²×C₃	—	2	1	no	—
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	3	2	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	1	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	—	6	1	no	—
714	C₂²×C₃	—	6	1	no	—
715	C₂²×C₃	—	6	1	no	—
716	C₂²×C₃	—	6	1	no	—
717	C₂²×C₃	—	6	1	no	—
718	C₂²×C₃	—	6	1	no	—
719	C₂²×C₃	—	6	1	no	—
720	C₂²×C₃	—	6	1	no	—
721	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
722	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
723	C₂×D₃	—	2	1	no	—
724	C₂×D₃	—	2	1	no	—
725	C₂×D₃	—	2	1	no	—
726	C₂×D₃	—	2	1	no	—
727	C₂×D₃	—	2	1	no	—
728	C₂×D₃	—	2	1	no	—
729	C₂×D₃	—	2	1	no	—
730	C₂×D₃	—	2	1	no	—
731	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
732	C₃×C₄	—	2	1	no	—
733	C₃×C₄	—	2	1	no	—
734	C₃×C₄	—	2	1	no	—
735	C₃×C₄	—	2	1	no	—
736	C₃×C₄	—	2	1	no	—
737	C₃×C₄	—	2	1	no	—
738	C₃×C₄	—	2	1	no	—
739	C₃×C₄	—	2	1	no	—
740	C₃×C₄	—	2	1	no	—
741	C₃×C₄	—	2	1	no	—
742	C₃×C₄	—	3	2	no	—
743	C₃×C₄	—	4	1	no	—
744	C₃×C₄	—	4	1	no	—
745	C₃×C₄	—	4	1	no	—
746	C₃×C₄	—	4	1	no	—
747	C₃×C₄	—	6	1	no	—
748	C₃×C₄	—	6	1	no	—
749	C₃×C₄	—	6	1	no	—
750	C₃×C₄	—	6	1	no	—
751	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
752	C₃×C₄	D₃×#41	1	1	yes	characteristic
753	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
754	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
755	Dic₃	—	2	1	no	—
756	Dic₃	—	2	1	no	—
757	Dic₃	—	2	1	no	—
758	Dic₃	—	2	1	no	—
759	Dic₃	C₃×C₄×D₄	1	2	yes	—
760	C₃²	#2932	1	1	yes	characteristic, complemented, Sylow
761	C₂³	—	3	1	no	—
762	C₂³	—	3	1	no	—
763	C₂³	—	3	1	no	—
764	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
765	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
766	Q₈	—	6	2	no	—
767	Q₈	—	6	2	no	—
768	D₄	—	4	1	no	—
769	D₄	—	6	2	no	—
770	D₄	—	6	2	no	—
771	D₄	—	6	2	no	—
772	D₄	—	6	2	no	—
773	D₄	—	6	2	no	—
774	D₄	—	6	2	no	—
775	D₄	—	12	1	no	—
776	D₄	—	12	1	no	—
777	D₄	—	12	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	3	1	no	—
783	C₂×C₄	—	3	2	no	—
784	C₂×C₄	—	3	2	no	—
785	C₂×C₄	—	3	1	no	—
786	C₂×C₄	—	3	1	no	—
787	C₂×C₄	—	3	1	no	—
788	C₂×C₄	—	3	1	no	—
789	C₂×C₄	—	6	1	no	—
790	C₂×C₄	—	6	1	no	—
791	C₂×C₄	—	6	1	no	—
792	C₂×C₄	—	6	1	no	—
793	C₂×C₄	—	12	1	no	—
794	C₂×C₄	—	12	1	no	—
795	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
797	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
798	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
799	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
800	C₈	—	2	1	no	—
801	C₈	—	2	1	no	—
802	C₈	—	2	1	no	—
803	C₈	—	3	2	no	—
804	C₈	—	6	1	no	—
805	C₈	—	6	1	no	—
806	C₈	—	6	1	no	—
807	C₈	C₃×D₃×D₄	1	2	yes	—
808	C₂×C₃	—	2	1	no	—
809	C₂×C₃	—	2	1	no	—
810	C₂×C₃	—	2	1	no	—
811	C₂×C₃	—	4	2	no	—
812	C₂×C₃	—	4	1	no	—
813	C₂×C₃	—	4	1	no	—
814	C₂×C₃	—	4	1	no	—
815	C₂×C₃	—	4	1	no	—
816	C₂×C₃	—	6	2	no	—
817	C₂×C₃	—	8	1	no	—
818	C₂×C₃	—	12	1	no	—
819	C₂×C₃	—	12	1	no	—
820	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
821	C₂×C₃	#5745	1	1	yes	characteristic
822	C₂×C₃	#5750	1	1	yes	characteristic
823	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
824	C₂×C₃	C₃×#568	1	1	yes	characteristic
825	C₂×C₃	C₃×#568	1	1	yes	characteristic
826	D₃	—	2	2	no	—
827	D₃	—	4	1	no	—
828	D₃	—	4	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	3	2	no	—
836	C₂²	—	6	1	no	—
837	C₂²	—	6	1	no	—
838	C₂²	—	6	1	no	—
839	C₂²	—	6	1	no	—
840	C₂²	—	6	1	no	—
841	C₂²	—	6	1	no	—
842	C₂²	—	6	1	no	—
843	C₂²	—	6	1	no	—
844	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
845	C₄	—	2	1	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	3	2	no	—
850	C₄	—	6	1	no	—
851	C₄	—	6	1	no	—
852	C₄	—	6	1	no	—
853	C₄	—	6	1	no	—
854	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
855	C₄	C₃×D₃×#41	1	1	yes	characteristic
856	C₃	—	2	1	no	—
857	C₃	#79480	1	1	yes	characteristic, direct product factor
858	C₃	C₃×#2932	1	1	yes	characteristic, complemented
859	C₂	—	4	1	no	—
860	C₂	—	4	1	no	—
861	C₂	—	6	2	no	—
862	C₂	—	12	1	no	—
863	C₂	—	12	1	no	—
864	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
865	C₂	C₃×#5745	1	1	yes	characteristic
866	C₂	C₃×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#435	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5548	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#435	D₃
hypocenter	C₃	C₃×#2932
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#435

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#907	C₂	semidirect
2. C₂×C₃×#901	C₂	semidirect
4. C₃²×#435	C₂	semidirect
5. C₃×#5127	C₂	semidirect
6. C₃×#5111	C₂	semidirect
7. C₃×#5011	C₂	semidirect
8. C₃×#4837	C₂	semidirect
9. C₃×#4836	C₂	semidirect
10. C₃×#4730	C₂	semidirect
11. C₃×#4728	C₂	semidirect
12. C₃×#4727	C₂	semidirect
13. C₃×#4727	C₂	semidirect
14. C₃×#4706	C₂	semidirect
15. C₃×D₃×#97	C₂	semidirect
17. #79480	C₃	direct (N × H)
66. C₂×#907	C₂×C₃	semidirect
67. C₂×#901	C₂×C₃	semidirect
77. C₃×#435	D₃	semidirect
78. C₃×#435	C₂×C₃	semidirect
83. #5127	C₂×C₃	semidirect
84. #5111	C₂×C₃	semidirect
85. #5011	C₂×C₃	semidirect
86. #4837	C₂×C₃	semidirect
87. #4836	C₂×C₃	semidirect
88. #4730	C₂×C₃	semidirect
89. #4728	C₂×C₃	semidirect
90. #4727	C₂×C₃	semidirect
91. #4727	C₂×C₃	semidirect
92. #4706	C₂×C₃	semidirect
93. D₃×#97	C₂×C₃	semidirect
152. C₃×D₃×C₈	D₄	semidirect
308. #435	C₃×D₃	semidirect
443. D₃×C₈	C₃×D₄	semidirect
760. C₃²	#2932	semidirect
857. C₃	#79480	direct (N × H)
858. C₃	C₃×#2932	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#907	2
C₂×C₃×#901	2
C₃×#5548	2
C₃²×#435	2
C₃×#5127	2
C₃×#5111	2
C₃×#5011	2
C₃×#4837	2
C₃×#4836	2
C₃×#4730	2
C₃×#4728	2
C₃×#4727	2
C₃×#4706	2
C₃×D₃×#97	2
C₃×#2932	3
#79480	3

Subgroups — C3×#79480 #11859511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79480 #11859511