Subgroups — C₂×C₃×#3327 #10679754

Order 768.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#548	C₂	1	1	yes	maximal, characteristic
3	C₃×#3327	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#3327	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₃×#552	—	2	4	no	—
26	C₃×#552	C₂²	1	8	yes	complemented
27	C₃×#548	—	2	4	no	—
28	C₃×#548	C₂²	1	8	yes	—
29	C₂×C₃×#126	—	2	1	no	—
30	C₂×C₃×#125	—	2	1	no	—
31	C₂×C₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₃×#124	—	2	1	no	—
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#123	—	2	1	no	—
35	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×#121	—	2	1	no	—
40	C₂×C₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×D₄	—	2	1	no	—
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×#117	—	2	1	no	—
46	C₂×C₃×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₃×#488	C₂²	1	8	yes	complemented
49	C₃×#484	C₂²	1	8	yes	complemented
50	C₃×#482	C₂²	1	8	yes	complemented
51	C₃×#479	C₂²	1	8	yes	complemented
52	C₃×#470	C₂²	1	8	yes	complemented
53	C₃×#468	C₂²	1	8	yes	complemented
54	C₃×#464	C₂²	1	8	yes	complemented
55	C₃×#452	C₂²	1	8	yes	complemented
56	C₃×#451	C₂²	1	8	yes	complemented
57	C₃×C₄×Q₁₆	C₂²	1	8	yes	complemented
58	C₃×#436	C₂²	1	8	yes	complemented
59	C₂×C₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₃×#106	C₂²	1	1	yes	characteristic
62	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₃×#419	C₂²	1	8	yes	complemented
64	C₃×#417	C₂²	1	8	yes	complemented
65	C₂×C₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₃×#102	C₂²	1	1	yes	characteristic
75	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
78	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×#548	C₂×C₃	1	1	yes	characteristic
80	#3327	C₂×C₃	1	16	yes	direct product factor
81	C₂×#488	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#484	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#482	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#479	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#470	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂×#468	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#464	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂×#452	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×#451	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#436	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×#417	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#419	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃×#41	—	2	2	no	—
95	C₂×C₃×#41	—	2	4	no	—
96	C₂×C₃×#41	—	4	2	no	—
97	C₂×C₃×#41	C₂³	1	4	yes	—
98	C₂²×C₃×Q₈	—	2	1	no	—
99	C₂²×C₃×Q₈	—	2	2	no	—
100	C₂²×C₃×Q₈	—	2	4	no	—
101	C₂²×C₃×Q₈	—	4	2	no	—
102	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Q₈	C₂³	1	4	yes	—
105	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×D₄	—	2	1	no	—
107	C₂²×C₃×D₄	—	2	1	no	—
108	C₂²×C₃×D₄	D₄	1	1	yes	characteristic
109	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
110	C₂³×C₃×C₄	—	2	1	no	—
111	C₂³×C₃×C₄	—	2	1	no	—
112	C₂³×C₃×C₄	—	2	1	no	—
113	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₂×C₃×Q₁₆	—	2	4	no	—
116	C₂×C₃×Q₁₆	—	4	2	no	—
117	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
118	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
119	C₂×C₃×SD₁₆	—	4	2	no	—
120	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₃×M₁₆	—	4	2	no	—
122	C₂×C₃×M₁₆	—	4	2	no	—
123	C₂×C₃×M₁₆	C₂³	1	4	yes	—
124	C₂×C₃×M₁₆	C₂³	1	4	yes	—
125	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
126	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
127	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
129	C₃×#126	—	2	8	no	—
130	C₃×#125	—	2	8	no	—
131	C₃×#125	—	2	2	no	—
132	C₃×#125	C₂³	1	4	yes	—
133	C₃×#124	—	2	8	no	—
134	C₃×#124	—	2	2	no	—
135	C₃×#124	C₂³	1	4	yes	—
136	C₃×#123	—	2	8	no	—
137	C₃×C₂²⋊Q₈	—	2	2	no	—
138	C₃×C₂²⋊Q₈	—	2	2	no	—
139	C₃×C₂²⋊Q₈	—	2	2	no	—
140	C₃×C₂²⋊Q₈	—	2	8	no	—
141	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
142	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₃×#121	—	2	8	no	—
145	C₃×#121	—	2	2	no	—
146	C₃×#121	C₂³	1	4	yes	—
147	C₃×C₄×Q₈	—	2	2	no	—
148	C₃×C₄×Q₈	—	2	2	no	—
149	C₃×C₄×Q₈	C₂³	1	4	yes	—
150	C₃×C₄×Q₈	C₂³	1	4	yes	—
151	C₃×C₄×D₄	—	2	8	no	—
152	C₃×C₄×D₄	D₄	1	4	yes	—
153	C₃×C₄×D₄	C₂³	1	4	yes	—
154	C₃×#117	—	2	2	no	—
155	C₃×#117	—	2	8	no	—
156	C₃×#117	C₂³	1	4	yes	—
157	C₂×C₃×C₄⋊C₄	—	2	1	no	—
158	C₂×C₃×C₄⋊C₄	—	2	2	no	—
159	C₂×C₃×C₄⋊C₄	—	2	1	no	—
160	C₂×C₃×C₄⋊C₄	—	2	1	no	—
161	C₂×C₃×C₄⋊C₄	—	2	1	no	—
162	C₂×C₃×C₄⋊C₄	—	2	1	no	—
163	C₂×C₃×C₄⋊C₄	—	2	1	no	—
164	C₂×C₃×C₄⋊C₄	—	2	1	no	—
165	C₂×C₃×C₄⋊C₄	—	2	1	no	—
166	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
173	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
174	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
175	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
180	C₂×C₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
181	C₂×C₃×C₄²	—	2	1	no	—
182	C₂×C₃×C₄²	—	2	1	no	—
183	C₂×C₃×C₄²	—	2	1	no	—
184	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
185	C₃×#107	C₂³	1	4	yes	—
186	C₃×#107	C₂³	1	4	yes	—
187	C₃×#106	C₂³	1	4	yes	—
188	C₃×C₄⋊C₈	C₂³	1	4	yes	—
189	C₃×#103	C₂³	1	4	yes	—
190	C₃×#103	C₂³	1	4	yes	—
191	C₃×#103	C₂³	1	4	yes	—
192	C₃×#103	C₂³	1	4	yes	—
193	C₃×#103	C₂³	1	4	yes	—
194	C₃×#103	C₂³	1	4	yes	—
195	C₃×#103	C₂³	1	4	yes	—
196	C₃×#102	C₂³	1	4	yes	—
197	C₃×#102	C₂³	1	4	yes	—
198	C₃×#102	C₂³	1	4	yes	—
199	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
201	C₃×C₄×C₈	C₂³	1	4	yes	—
202	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
203	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
209	#552	—	2	4	no	—
210	#552	C₂²×C₃	1	8	yes	complemented
211	#548	—	2	4	no	—
212	#548	C₂²×C₃	1	8	yes	—
213	C₂×#126	—	2	1	no	—
214	C₂×#125	—	2	1	no	—
215	C₂×#125	C₂²×C₃	1	1	yes	characteristic
216	C₂×#124	—	2	1	no	—
217	C₂×#124	C₂²×C₃	1	1	yes	characteristic
218	C₂×#123	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
223	C₂×#121	—	2	1	no	—
224	C₂×#121	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×#117	—	2	1	no	—
230	C₂×#117	C₂²×C₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
232	#488	C₂²×C₃	1	8	yes	complemented
233	#484	C₂²×C₃	1	8	yes	complemented
234	#482	C₂²×C₃	1	8	yes	complemented
235	#479	C₂²×C₃	1	8	yes	complemented
236	#470	C₂²×C₃	1	8	yes	complemented
237	#468	C₂²×C₃	1	8	yes	complemented
238	#464	C₂²×C₃	1	8	yes	complemented
239	#452	C₂²×C₃	1	8	yes	complemented
240	#451	C₂²×C₃	1	8	yes	complemented
241	C₄×Q₁₆	C₂²×C₃	1	8	yes	complemented
242	#436	C₂²×C₃	1	8	yes	complemented
243	C₂×#107	C₂²×C₃	1	1	yes	characteristic
244	C₂×#107	C₂²×C₃	1	1	yes	characteristic
245	C₂×#106	C₂²×C₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
247	#419	C₂²×C₃	1	8	yes	complemented
248	#417	C₂²×C₃	1	8	yes	complemented
249	C₂×#103	C₂²×C₃	1	1	yes	characteristic
250	C₂×#103	C₂²×C₃	1	1	yes	characteristic
251	C₂×#103	C₂²×C₃	1	1	yes	characteristic
252	C₂×#103	C₂²×C₃	1	1	yes	characteristic
253	C₂×#103	C₂²×C₃	1	1	yes	characteristic
254	C₂×#103	C₂²×C₃	1	1	yes	characteristic
255	C₂×#103	C₂²×C₃	1	1	yes	characteristic
256	C₂×#102	C₂²×C₃	1	1	yes	characteristic
257	C₂×#102	C₂²×C₃	1	1	yes	characteristic
258	C₂×#102	C₂²×C₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
262	C₂⁴×C₃	—	2	1	no	—
263	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
264	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
265	C₃×#41	—	2	8	no	—
266	C₃×#41	—	4	4	no	—
267	C₃×#41	—	4	8	no	—
268	C₂×C₃×Q₈	—	2	1	no	—
269	C₂×C₃×Q₈	—	2	1	no	—
270	C₂×C₃×Q₈	—	2	4	no	—
271	C₂×C₃×Q₈	—	2	1	no	—
272	C₂×C₃×Q₈	—	2	2	no	—
273	C₂×C₃×Q₈	—	2	8	no	—
274	C₂×C₃×Q₈	—	2	2	no	—
275	C₂×C₃×Q₈	—	2	2	no	—
276	C₂×C₃×Q₈	—	2	2	no	—
277	C₂×C₃×Q₈	—	2	2	no	—
278	C₂×C₃×Q₈	—	4	4	no	—
279	C₂×C₃×Q₈	—	4	4	no	—
280	C₂×C₃×Q₈	—	4	8	no	—
281	C₂×C₃×Q₈	#41	1	4	yes	—
282	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
283	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
284	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
285	C₂×C₃×D₄	—	2	4	no	—
286	C₂×C₃×D₄	—	2	4	no	—
287	C₂×C₃×D₄	—	2	1	no	—
288	C₂×C₃×D₄	—	2	2	no	—
289	C₂×C₃×D₄	—	2	2	no	—
290	C₂×C₃×D₄	—	4	2	no	—
291	C₂×C₃×D₄	—	4	4	no	—
292	C₂×C₃×D₄	—	4	4	no	—
293	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
294	C₂×C₃×D₄	C₂⁴	1	2	yes	—
295	C₂²×C₃×C₄	—	2	1	no	—
296	C₂²×C₃×C₄	—	2	2	no	—
297	C₂²×C₃×C₄	—	2	2	no	—
298	C₂²×C₃×C₄	—	2	2	no	—
299	C₂²×C₃×C₄	—	2	2	no	—
300	C₂²×C₃×C₄	—	2	4	no	—
301	C₂²×C₃×C₄	—	2	4	no	—
302	C₂²×C₃×C₄	—	2	1	no	—
303	C₂²×C₃×C₄	—	2	1	no	—
304	C₂²×C₃×C₄	—	2	1	no	—
305	C₂²×C₃×C₄	—	2	1	no	—
306	C₂²×C₃×C₄	—	2	1	no	—
307	C₂²×C₃×C₄	—	2	1	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	4	4	no	—
310	C₂²×C₃×C₄	—	4	4	no	—
311	C₂²×C₃×C₄	—	4	4	no	—
312	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
313	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
314	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
321	C₃×Q₁₆	—	2	8	no	—
322	C₃×Q₁₆	—	4	4	no	—
323	C₃×SD₁₆	—	4	4	no	—
324	C₃×M₁₆	—	4	4	no	—
325	C₃×M₁₆	—	4	4	no	—
326	C₂×C₃×C₈	—	2	2	no	—
327	C₂×C₃×C₈	—	2	2	no	—
328	C₂×C₃×C₈	—	2	2	no	—
329	C₂×C₃×C₈	—	2	2	no	—
330	C₂×C₃×C₈	C₂⁴	1	2	yes	—
331	C₂×C₃×C₈	C₂⁴	1	2	yes	—
332	C₂×C₃×C₈	C₂⁴	1	2	yes	—
333	C₂×C₃×C₈	C₂⁴	1	2	yes	—
334	C₃×C₄⋊C₄	—	2	1	no	—
335	C₃×C₄⋊C₄	—	2	1	no	—
336	C₃×C₄⋊C₄	—	2	4	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	4	no	—
339	C₃×C₄⋊C₄	—	2	4	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	4	no	—
344	C₃×C₄⋊C₄	—	2	1	no	—
345	C₃×C₄⋊C₄	—	2	1	no	—
346	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
347	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	4	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
359	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
360	C₃×C₄²	—	2	4	no	—
361	C₃×C₄²	—	2	4	no	—
362	C₃×C₄²	—	2	4	no	—
363	C₃×C₄²	C₂×D₄	1	2	yes	—
364	C₃×C₄²	C₂⁴	1	2	yes	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	4	no	—
367	C₂×#41	—	4	2	no	—
368	C₂×#41	C₂³×C₃	1	4	yes	—
369	C₂²×Q₈	—	2	1	no	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	—	2	4	no	—
372	C₂²×Q₈	—	4	2	no	—
373	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₃	1	4	yes	—
376	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	C₃×D₄	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂×Q₁₆	—	2	4	no	—
387	C₂×Q₁₆	—	4	2	no	—
388	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
389	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
390	C₂×SD₁₆	—	4	2	no	—
391	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
392	C₂×M₁₆	—	4	2	no	—
393	C₂×M₁₆	—	4	2	no	—
394	C₂×M₁₆	C₂³×C₃	1	4	yes	—
395	C₂×M₁₆	C₂³×C₃	1	4	yes	—
396	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
400	#126	—	2	8	no	—
401	#125	—	2	8	no	—
402	#125	—	2	2	no	—
403	#125	C₂³×C₃	1	4	yes	—
404	#124	—	2	8	no	—
405	#124	—	2	2	no	—
406	#124	C₂³×C₃	1	4	yes	—
407	#123	—	2	8	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	8	no	—
412	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
413	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
414	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
415	#121	—	2	8	no	—
416	#121	—	2	2	no	—
417	#121	C₂³×C₃	1	4	yes	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	C₂³×C₃	1	4	yes	—
421	C₄×Q₈	C₂³×C₃	1	4	yes	—
422	C₄×D₄	—	2	8	no	—
423	C₄×D₄	C₃×D₄	1	4	yes	—
424	C₄×D₄	C₂³×C₃	1	4	yes	—
425	#117	—	2	2	no	—
426	#117	—	2	8	no	—
427	#117	C₂³×C₃	1	4	yes	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
456	#107	C₂³×C₃	1	4	yes	—
457	#107	C₂³×C₃	1	4	yes	—
458	#106	C₂³×C₃	1	4	yes	—
459	C₄⋊C₈	C₂³×C₃	1	4	yes	—
460	#103	C₂³×C₃	1	4	yes	—
461	#103	C₂³×C₃	1	4	yes	—
462	#103	C₂³×C₃	1	4	yes	—
463	#103	C₂³×C₃	1	4	yes	—
464	#103	C₂³×C₃	1	4	yes	—
465	#103	C₂³×C₃	1	4	yes	—
466	#103	C₂³×C₃	1	4	yes	—
467	#102	C₂³×C₃	1	4	yes	—
468	#102	C₂³×C₃	1	4	yes	—
469	#102	C₂³×C₃	1	4	yes	—
470	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
471	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
472	C₄×C₈	C₂³×C₃	1	4	yes	—
473	C₂³×C₃	—	2	2	no	—
474	C₂³×C₃	—	2	2	no	—
475	C₂³×C₃	—	2	2	no	—
476	C₂³×C₃	—	2	2	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	2	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	4	2	no	—
481	C₂³×C₃	—	4	2	no	—
482	C₂³×C₃	—	4	2	no	—
483	C₂³×C₃	C₂²×D₄	1	2	yes	—
484	C₂³×C₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
486	C₃×Q₈	—	2	4	no	—
487	C₃×Q₈	—	2	2	no	—
488	C₃×Q₈	—	2	2	no	—
489	C₃×Q₈	—	2	2	no	—
490	C₃×Q₈	—	2	2	no	—
491	C₃×Q₈	—	2	2	no	—
492	C₃×Q₈	—	4	8	no	—
493	C₃×Q₈	—	4	2	no	—
494	C₃×Q₈	—	4	2	no	—
495	C₃×Q₈	C₂×#41	1	4	yes	—
496	C₃×D₄	—	2	2	no	—
497	C₃×D₄	—	2	2	no	—
498	C₃×D₄	—	4	4	no	—
499	C₃×D₄	—	4	8	no	—
500	C₃×D₄	—	4	8	no	—
501	C₃×D₄	—	4	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	4	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	4	no	—
509	C₂×C₃×C₄	—	2	4	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	4	8	no	—
521	C₂×C₃×C₄	—	4	8	no	—
522	C₂×C₃×C₄	—	4	8	no	—
523	C₂×C₃×C₄	—	4	2	no	—
524	C₂×C₃×C₄	—	4	2	no	—
525	C₂×C₃×C₄	—	4	2	no	—
526	C₂×C₃×C₄	—	4	2	no	—
527	C₂×C₃×C₄	—	4	2	no	—
528	C₂×C₃×C₄	—	4	2	no	—
529	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
530	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
531	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
532	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
533	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂×#41	1	2	yes	—
535	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
537	C₃×C₈	—	2	2	no	—
538	C₃×C₈	—	2	2	no	—
539	C₃×C₈	—	2	2	no	—
540	C₃×C₈	—	2	2	no	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
543	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
544	#41	—	2	8	no	—
545	#41	—	4	4	no	—
546	#41	—	4	8	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	4	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	8	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	4	no	—
558	C₂×Q₈	—	4	4	no	—
559	C₂×Q₈	—	4	8	no	—
560	C₂×Q₈	C₃×#41	1	4	yes	—
561	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
562	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
563	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
573	C₂×D₄	C₂⁴×C₃	1	2	yes	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
593	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
594	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
596	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
600	Q₁₆	—	2	8	no	—
601	Q₁₆	—	4	4	no	—
602	SD₁₆	—	4	4	no	—
603	M₁₆	—	4	4	no	—
604	M₁₆	—	4	4	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	C₂⁴×C₃	1	2	yes	—
610	C₂×C₈	C₂⁴×C₃	1	2	yes	—
611	C₂×C₈	C₂⁴×C₃	1	2	yes	—
612	C₂×C₈	C₂⁴×C₃	1	2	yes	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
626	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
638	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	C₂×C₃×D₄	1	2	yes	—
643	C₄²	C₂⁴×C₃	1	2	yes	—
644	C₂²×C₃	—	2	2	no	—
645	C₂²×C₃	—	2	2	no	—
646	C₂²×C₃	—	2	2	no	—
647	C₂²×C₃	—	2	2	no	—
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	4	4	no	—
651	C₂²×C₃	—	4	4	no	—
652	C₂²×C₃	—	4	2	no	—
653	C₂²×C₃	—	4	2	no	—
654	C₂²×C₃	—	4	2	no	—
655	C₂²×C₃	—	8	4	no	—
656	C₂²×C₃	#546	1	2	yes	—
657	C₂²×C₃	#575	1	2	yes	—
658	C₂²×C₃	#578	1	2	yes	—
659	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
660	C₃×C₄	—	2	2	no	—
661	C₃×C₄	—	2	2	no	—
662	C₃×C₄	—	2	4	no	—
663	C₃×C₄	—	2	2	no	—
664	C₃×C₄	—	2	2	no	—
665	C₃×C₄	—	4	2	no	—
666	C₃×C₄	—	4	2	no	—
667	C₃×C₄	—	4	2	no	—
668	C₃×C₄	—	4	2	no	—
669	C₃×C₄	—	4	2	no	—
670	C₃×C₄	—	4	2	no	—
671	C₃×C₄	#546	1	2	yes	—
672	C₃×C₄	C₂²×#41	1	1	yes	characteristic
673	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	C₂²×C₃×D₄	1	2	yes	—
685	C₂³	C₂²×C₃×D₄	1	2	yes	—
686	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
687	Q₈	—	2	2	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	4	8	no	—
694	Q₈	—	4	2	no	—
695	Q₈	—	4	2	no	—
696	Q₈	C₂×C₃×#41	1	4	yes	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	8	no	—
701	D₄	—	4	8	no	—
702	D₄	—	4	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
731	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
732	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
733	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
734	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
735	C₂×C₄	C₂×C₃×#41	1	2	yes	—
736	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
737	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	2	no	—
742	C₂×C₃	—	4	2	no	—
743	C₂×C₃	—	4	2	no	—
744	C₂×C₃	—	8	2	no	—
745	C₂×C₃	#3327	1	4	yes	direct product factor
746	C₂×C₃	C₂×#546	1	1	yes	characteristic
747	C₂×C₃	C₂×#575	1	1	yes	characteristic
748	C₂×C₃	C₂×#578	1	1	yes	characteristic
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	8	4	no	—
761	C₂²	C₃×#546	1	2	yes	—
762	C₂²	C₃×#575	1	2	yes	—
763	C₂²	C₃×#578	1	2	yes	—
764	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	C₃×#546	1	2	yes	—
777	C₄	C₂²×C₃×#41	1	1	yes	characteristic
778	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
779	C₃	C₂×#3327	1	1	yes	characteristic, direct product factor, Sylow
780	C₂	—	4	2	no	—
781	C₂	—	4	2	no	—
782	C₂	—	8	2	no	—
783	C₂	C₃×#3327	1	4	yes	direct product factor
784	C₂	C₂×C₃×#546	1	1	yes	characteristic
785	C₂	C₂×C₃×#575	1	1	yes	characteristic
786	C₂	C₂×C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#552	C₂	semidirect
3. C₃×#3327	C₂	direct (N × H)
4. C₂×C₃×#488	C₂	semidirect
5. C₂×C₃×#484	C₂	semidirect
6. C₂×C₃×#482	C₂	semidirect
7. C₂×C₃×#479	C₂	semidirect
8. C₂×C₃×#470	C₂	semidirect
9. C₂×C₃×#468	C₂	semidirect
10. C₂×C₃×#464	C₂	semidirect
11. C₂×C₃×#452	C₂	semidirect
12. C₂×C₃×#451	C₂	semidirect
13. C₂×C₃×C₄×Q₁₆	C₂	semidirect
14. C₂×C₃×#436	C₂	semidirect
15. C₂×C₃×#417	C₂	semidirect
16. C₂×C₃×#419	C₂	semidirect
17. C₂×#3327	C₃	direct (N × H)
26. C₃×#552	C₂²	semidirect
48. C₃×#488	C₂²	semidirect
49. C₃×#484	C₂²	semidirect
50. C₃×#482	C₂²	semidirect
51. C₃×#479	C₂²	semidirect
52. C₃×#470	C₂²	semidirect
53. C₃×#468	C₂²	semidirect
54. C₃×#464	C₂²	semidirect
55. C₃×#452	C₂²	semidirect
56. C₃×#451	C₂²	semidirect
57. C₃×C₄×Q₁₆	C₂²	semidirect
58. C₃×#436	C₂²	semidirect
63. C₃×#419	C₂²	semidirect
64. C₃×#417	C₂²	semidirect
78. C₂×#552	C₂×C₃	semidirect
80. #3327	C₂×C₃	direct (N × H)
81. C₂×#488	C₂×C₃	semidirect
82. C₂×#484	C₂×C₃	semidirect
83. C₂×#482	C₂×C₃	semidirect
84. C₂×#479	C₂×C₃	semidirect
85. C₂×#470	C₂×C₃	semidirect
86. C₂×#468	C₂×C₃	semidirect
87. C₂×#464	C₂×C₃	semidirect
88. C₂×#452	C₂×C₃	semidirect
89. C₂×#451	C₂×C₃	semidirect
90. C₂×C₄×Q₁₆	C₂×C₃	semidirect
91. C₂×#436	C₂×C₃	semidirect
92. C₂×#417	C₂×C₃	semidirect
93. C₂×#419	C₂×C₃	semidirect
210. #552	C₂²×C₃	semidirect
232. #488	C₂²×C₃	semidirect
233. #484	C₂²×C₃	semidirect
234. #482	C₂²×C₃	semidirect
235. #479	C₂²×C₃	semidirect
236. #470	C₂²×C₃	semidirect
237. #468	C₂²×C₃	semidirect
238. #464	C₂²×C₃	semidirect
239. #452	C₂²×C₃	semidirect
240. #451	C₂²×C₃	semidirect
241. C₄×Q₁₆	C₂²×C₃	semidirect
242. #436	C₂²×C₃	semidirect
247. #419	C₂²×C₃	semidirect
248. #417	C₂²×C₃	semidirect
745. C₂×C₃	#3327	direct (N × H)
779. C₃	C₂×#3327	direct (N × H)
783. C₂	C₃×#3327	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#552	2
C₂×C₃×#548	2
C₃×#3327	2
C₂×C₃×#488	2
C₂×C₃×#484	2
C₂×C₃×#482	2
C₂×C₃×#479	2
C₂×C₃×#470	2
C₂×C₃×#468	2
C₂×C₃×#464	2
C₂×C₃×#452	2
C₂×C₃×#451	2
C₂×C₃×C₄×Q₁₆	2
C₂×C₃×#436	2
C₂×C₃×#417	2
C₂×C₃×#419	2
C₂×#3327	3

Subgroups — C2×C3×#3327 #10679754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3327 #10679754