Subgroups — C₂×C₃×#3102 #10679136

Order 768.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3102	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#449	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#3102	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
23	C₃×#529	—	2	4	no	—
24	C₃×#529	C₂²	1	8	yes	complemented
25	C₂×C₃×#126	—	2	1	no	—
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃×#123	—	2	1	no	—
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₃×C₄×#41	—	2	4	no	—
32	C₃×C₄×#41	C₂²	1	8	yes	complemented
33	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	—	2	1	no	—
37	C₂×C₃×C₄×D₄	—	2	1	no	—
38	C₂×C₃×C₄×D₄	—	2	1	no	—
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	—	2	1	no	—
43	C₂×C₃×#117	—	2	1	no	—
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₃×C₄²	—	2	1	no	—
46	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
47	C₃×#485	C₂²	1	8	yes	complemented
48	C₃×#482	C₂²	1	8	yes	complemented
49	C₃×#479	C₂²	1	8	yes	complemented
50	C₃×#478	C₂²	1	8	yes	complemented
51	C₃×#464	C₂²	1	8	yes	complemented
52	C₃×#463	C₂²	1	8	yes	complemented
53	C₃×#452	C₂²	1	8	yes	complemented
54	C₃×#449	C₂²	1	8	yes	—
55	C₃×C₄×Q₁₆	C₂²	1	8	yes	complemented
56	C₃×C₄×SD₁₆	C₂²	1	8	yes	complemented
57	C₃×C₄×SD₁₆	C₂²	1	8	yes	complemented
58	C₃×C₄×D₈	C₂²	1	8	yes	complemented
59	C₃×#431	C₂²	1	8	yes	complemented
60	C₂×C₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₃×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
71	C₂×C₃×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
78	C₂×#529	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
80	#3102	C₂×C₃	1	16	yes	direct product factor
81	C₂×#485	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#482	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#479	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#478	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#464	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂×#463	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#452	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂×#449	C₂×C₃	1	1	yes	characteristic
89	C₂×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#431	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃×#41	—	2	4	no	—
95	C₂×C₃×#41	—	2	4	no	—
96	C₂×C₃×#41	—	2	2	no	—
97	C₂×C₃×#41	C₂³	1	4	yes	—
98	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
99	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
100	C₂²×C₃×D₄	—	2	1	no	—
101	C₂²×C₃×D₄	—	2	1	no	—
102	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
103	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
104	C₂³×C₃×C₄	—	2	1	no	—
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂³×C₃×C₄	—	2	1	no	—
107	C₂³×C₃×C₄	—	2	1	no	—
108	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
109	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
110	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
111	C₂×C₃×Q₁₆	—	2	4	no	—
112	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₃×SD₁₆	—	2	4	no	—
114	C₂×C₃×SD₁₆	—	2	4	no	—
115	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₃×D₈	—	2	4	no	—
118	C₂×C₃×D₈	C₂³	1	4	yes	—
119	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
122	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
123	C₃×#126	—	2	8	no	—
124	C₃×#125	—	2	2	no	—
125	C₃×#125	C₂³	1	4	yes	—
126	C₃×#124	—	2	2	no	—
127	C₃×#124	C₂³	1	4	yes	—
128	C₃×#123	—	2	8	no	—
129	C₃×C₂²⋊Q₈	—	2	2	no	—
130	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₃×#121	—	2	2	no	—
132	C₃×#121	C₂³	1	4	yes	—
133	C₃×C₄×Q₈	—	2	2	no	—
134	C₃×C₄×Q₈	—	2	2	no	—
135	C₃×C₄×Q₈	—	2	2	no	—
136	C₃×C₄×Q₈	C₂³	1	4	yes	—
137	C₃×C₄×Q₈	C₂³	1	4	yes	—
138	C₃×C₄×Q₈	C₂³	1	4	yes	—
139	C₃×C₄×D₄	—	2	8	no	—
140	C₃×C₄×D₄	—	2	8	no	—
141	C₃×C₄×D₄	—	2	8	no	—
142	C₃×C₄×D₄	—	2	2	no	—
143	C₃×C₄×D₄	—	2	2	no	—
144	C₃×C₄×D₄	—	2	2	no	—
145	C₃×C₄×D₄	C₂³	1	4	yes	—
146	C₃×C₄×D₄	C₂³	1	4	yes	—
147	C₃×C₄×D₄	C₂³	1	4	yes	—
148	C₃×#117	—	2	2	no	—
149	C₃×#117	—	2	8	no	—
150	C₃×#117	—	2	8	no	—
151	C₃×#117	C₂³	1	4	yes	—
152	C₂×C₃×C₄⋊C₄	—	2	1	no	—
153	C₂×C₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₃×C₄⋊C₄	—	2	1	no	—
155	C₂×C₃×C₄⋊C₄	—	2	1	no	—
156	C₂×C₃×C₄⋊C₄	—	2	1	no	—
157	C₂×C₃×C₄⋊C₄	—	2	1	no	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
165	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
167	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
170	C₂×C₃×C₄²	—	2	1	no	—
171	C₂×C₃×C₄²	—	2	1	no	—
172	C₂×C₃×C₄²	—	2	1	no	—
173	C₂×C₃×C₄²	—	2	1	no	—
174	C₂×C₃×C₄²	—	2	8	no	—
175	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
176	C₂×C₃×C₄²	D₄	1	4	yes	—
177	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	4	yes	—
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₃×#107	C₂³	1	4	yes	—
182	C₃×#107	C₂³	1	4	yes	—
183	C₃×#106	C₂³	1	4	yes	—
184	C₃×#106	C₂³	1	4	yes	—
185	C₃×C₄⋊C₈	C₂³	1	4	yes	—
186	C₃×C₄⋊C₈	C₂³	1	4	yes	—
187	C₃×#103	C₂³	1	4	yes	—
188	C₃×#103	C₂³	1	4	yes	—
189	C₃×#103	C₂³	1	4	yes	—
190	C₃×#103	C₂³	1	4	yes	—
191	C₃×#102	C₂³	1	4	yes	—
192	C₃×#102	C₂³	1	4	yes	—
193	C₃×#102	C₂³	1	4	yes	—
194	C₃×#102	C₂³	1	4	yes	—
195	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₃×C₄×C₈	C₂³	1	4	yes	—
198	C₃×C₄×C₈	C₂³	1	4	yes	—
199	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
200	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
201	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
202	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
203	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
204	#529	—	2	4	no	—
205	#529	C₂²×C₃	1	8	yes	complemented
206	C₂×#126	—	2	1	no	—
207	C₂×#125	C₂²×C₃	1	1	yes	characteristic
208	C₂×#124	C₂²×C₃	1	1	yes	characteristic
209	C₂×#123	—	2	1	no	—
210	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
211	C₂×#121	C₂²×C₃	1	1	yes	characteristic
212	C₄×#41	—	2	4	no	—
213	C₄×#41	C₂²×C₃	1	8	yes	complemented
214	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
216	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
223	C₂×#117	—	2	1	no	—
224	C₂×#117	—	2	1	no	—
225	C₂×#117	C₂²×C₃	1	1	yes	characteristic
226	C₂²×C₄²	—	2	1	no	—
227	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
228	#485	C₂²×C₃	1	8	yes	complemented
229	#482	C₂²×C₃	1	8	yes	complemented
230	#479	C₂²×C₃	1	8	yes	complemented
231	#478	C₂²×C₃	1	8	yes	complemented
232	#464	C₂²×C₃	1	8	yes	complemented
233	#463	C₂²×C₃	1	8	yes	complemented
234	#452	C₂²×C₃	1	8	yes	complemented
235	#449	C₂²×C₃	1	8	yes	—
236	C₄×Q₁₆	C₂²×C₃	1	8	yes	complemented
237	C₄×SD₁₆	C₂²×C₃	1	8	yes	complemented
238	C₄×SD₁₆	C₂²×C₃	1	8	yes	complemented
239	C₄×D₈	C₂²×C₃	1	8	yes	complemented
240	#431	C₂²×C₃	1	8	yes	complemented
241	C₂×#107	C₂²×C₃	1	1	yes	characteristic
242	C₂×#107	C₂²×C₃	1	1	yes	characteristic
243	C₂×#106	C₂²×C₃	1	1	yes	characteristic
244	C₂×#106	C₂²×C₃	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
247	C₂×#103	C₂²×C₃	1	1	yes	characteristic
248	C₂×#103	C₂²×C₃	1	1	yes	characteristic
249	C₂×#103	C₂²×C₃	1	1	yes	characteristic
250	C₂×#103	C₂²×C₃	1	1	yes	characteristic
251	C₂×#102	C₂²×C₃	1	1	yes	characteristic
252	C₂×#102	C₂²×C₃	1	1	yes	characteristic
253	C₂×#102	C₂²×C₃	1	1	yes	characteristic
254	C₂×#102	C₂²×C₃	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
259	C₂⁴×C₃	—	2	1	no	—
260	C₂⁴×C₃	—	2	1	no	—
261	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
262	C₃×#41	—	2	16	no	—
263	C₃×#41	—	2	8	no	—
264	C₃×#41	—	2	8	no	—
265	C₂×C₃×Q₈	—	2	1	no	—
266	C₂×C₃×Q₈	—	2	1	no	—
267	C₂×C₃×Q₈	—	2	2	no	—
268	C₂×C₃×Q₈	—	2	2	no	—
269	C₂×C₃×Q₈	—	2	2	no	—
270	C₂×C₃×Q₈	#41	1	4	yes	—
271	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
272	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
273	C₂×C₃×D₄	—	2	8	no	—
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	1	no	—
277	C₂×C₃×D₄	—	2	1	no	—
278	C₂×C₃×D₄	—	2	2	no	—
279	C₂×C₃×D₄	—	2	2	no	—
280	C₂×C₃×D₄	—	2	2	no	—
281	C₂×C₃×D₄	—	4	4	no	—
282	C₂×C₃×D₄	#41	1	4	yes	—
283	C₂×C₃×D₄	C₂⁴	1	2	yes	—
284	C₂×C₃×D₄	C₂⁴	1	2	yes	—
285	C₂²×C₃×C₄	—	2	8	no	—
286	C₂²×C₃×C₄	—	2	1	no	—
287	C₂²×C₃×C₄	—	2	4	no	—
288	C₂²×C₃×C₄	—	2	4	no	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	2	no	—
291	C₂²×C₃×C₄	—	2	1	no	—
292	C₂²×C₃×C₄	—	2	1	no	—
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	2	1	no	—
295	C₂²×C₃×C₄	—	2	1	no	—
296	C₂²×C₃×C₄	—	2	4	no	—
297	C₂²×C₃×C₄	—	2	4	no	—
298	C₂²×C₃×C₄	—	2	4	no	—
299	C₂²×C₃×C₄	—	4	2	no	—
300	C₂²×C₃×C₄	—	4	4	no	—
301	C₂²×C₃×C₄	—	4	4	no	—
302	C₂²×C₃×C₄	—	4	4	no	—
303	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
306	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
309	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
310	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
313	C₃×Q₁₆	—	2	8	no	—
314	C₃×SD₁₆	—	2	8	no	—
315	C₃×SD₁₆	—	2	8	no	—
316	C₃×D₈	—	2	8	no	—
317	C₂×C₃×C₈	—	2	2	no	—
318	C₂×C₃×C₈	—	2	2	no	—
319	C₂×C₃×C₈	—	2	2	no	—
320	C₂×C₃×C₈	—	2	2	no	—
321	C₂×C₃×C₈	C₂⁴	1	2	yes	—
322	C₂×C₃×C₈	C₂⁴	1	2	yes	—
323	C₂×C₃×C₈	C₂⁴	1	2	yes	—
324	C₂×C₃×C₈	C₂⁴	1	2	yes	—
325	C₃×C₄⋊C₄	—	2	4	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	—	2	4	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	4	no	—
331	C₃×C₄⋊C₄	—	2	1	no	—
332	C₃×C₄⋊C₄	—	2	1	no	—
333	C₃×C₄⋊C₄	—	2	1	no	—
334	C₃×C₄⋊C₄	—	2	1	no	—
335	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
336	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
338	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₃×C₂²⋊C₄	—	2	4	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	4	no	—
342	C₃×C₂²⋊C₄	—	2	4	no	—
343	C₃×C₂²⋊C₄	—	2	4	no	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	2	4	no	—
346	C₃×C₂²⋊C₄	—	2	4	no	—
347	C₃×C₄²	—	2	4	no	—
348	C₃×C₄²	—	2	4	no	—
349	C₃×C₄²	—	2	4	no	—
350	C₃×C₄²	—	2	4	no	—
351	C₃×C₄²	C₂×D₄	1	4	yes	—
352	C₃×C₄²	C₂×D₄	1	4	yes	—
353	C₃×C₄²	C₂×D₄	1	2	yes	—
354	C₃×C₄²	C₂×D₄	1	2	yes	—
355	C₃×C₄²	C₂⁴	1	2	yes	—
356	C₃×C₄²	C₂⁴	1	2	yes	—
357	C₂×#41	—	2	4	no	—
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	C₂³×C₃	1	4	yes	—
361	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
372	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
374	C₂×Q₁₆	—	2	4	no	—
375	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	—	2	4	no	—
378	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
379	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
380	C₂×D₈	—	2	4	no	—
381	C₂×D₈	C₂³×C₃	1	4	yes	—
382	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
386	#126	—	2	8	no	—
387	#125	—	2	2	no	—
388	#125	C₂³×C₃	1	4	yes	—
389	#124	—	2	2	no	—
390	#124	C₂³×C₃	1	4	yes	—
391	#123	—	2	8	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
394	#121	—	2	2	no	—
395	#121	C₂³×C₃	1	4	yes	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	C₂³×C₃	1	4	yes	—
400	C₄×Q₈	C₂³×C₃	1	4	yes	—
401	C₄×Q₈	C₂³×C₃	1	4	yes	—
402	C₄×D₄	—	2	8	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	—	2	8	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	C₂³×C₃	1	4	yes	—
409	C₄×D₄	C₂³×C₃	1	4	yes	—
410	C₄×D₄	C₂³×C₃	1	4	yes	—
411	#117	—	2	2	no	—
412	#117	—	2	8	no	—
413	#117	—	2	8	no	—
414	#117	C₂³×C₃	1	4	yes	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	8	no	—
438	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
439	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
440	C₂×C₄²	C₃×D₄	1	4	yes	—
441	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₃	1	4	yes	—
444	#107	C₂³×C₃	1	4	yes	—
445	#107	C₂³×C₃	1	4	yes	—
446	#106	C₂³×C₃	1	4	yes	—
447	#106	C₂³×C₃	1	4	yes	—
448	C₄⋊C₈	C₂³×C₃	1	4	yes	—
449	C₄⋊C₈	C₂³×C₃	1	4	yes	—
450	#103	C₂³×C₃	1	4	yes	—
451	#103	C₂³×C₃	1	4	yes	—
452	#103	C₂³×C₃	1	4	yes	—
453	#103	C₂³×C₃	1	4	yes	—
454	#102	C₂³×C₃	1	4	yes	—
455	#102	C₂³×C₃	1	4	yes	—
456	#102	C₂³×C₃	1	4	yes	—
457	#102	C₂³×C₃	1	4	yes	—
458	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
459	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
460	C₄×C₈	C₂³×C₃	1	4	yes	—
461	C₄×C₈	C₂³×C₃	1	4	yes	—
462	C₂³×C₃	—	2	2	no	—
463	C₂³×C₃	—	2	4	no	—
464	C₂³×C₃	—	2	2	no	—
465	C₂³×C₃	—	2	2	no	—
466	C₂³×C₃	—	2	2	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	4	2	no	—
469	C₂³×C₃	—	4	2	no	—
470	C₂³×C₃	—	4	2	no	—
471	C₂³×C₃	—	4	2	no	—
472	C₂³×C₃	—	4	2	no	—
473	C₂³×C₃	C₂²×D₄	1	2	yes	—
474	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
475	C₃×Q₈	—	2	4	no	—
476	C₃×Q₈	—	2	2	no	—
477	C₃×Q₈	—	2	2	no	—
478	C₃×Q₈	—	2	2	no	—
479	C₃×Q₈	—	4	2	no	—
480	C₃×Q₈	C₂×#41	1	4	yes	—
481	C₃×D₄	—	2	16	no	—
482	C₃×D₄	—	2	4	no	—
483	C₃×D₄	—	2	2	no	—
484	C₃×D₄	—	2	2	no	—
485	C₃×D₄	—	2	2	no	—
486	C₃×D₄	—	4	8	no	—
487	C₃×D₄	—	4	2	no	—
488	C₃×D₄	C₂×#41	1	4	yes	—
489	C₂×C₃×C₄	—	2	16	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	4	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	2	8	no	—
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	4	4	no	—
506	C₂×C₃×C₄	—	4	8	no	—
507	C₂×C₃×C₄	—	4	2	no	—
508	C₂×C₃×C₄	—	4	2	no	—
509	C₂×C₃×C₄	—	4	2	no	—
510	C₂×C₃×C₄	—	4	2	no	—
511	C₂×C₃×C₄	—	4	2	no	—
512	C₂×C₃×C₄	—	4	8	no	—
513	C₂×C₃×C₄	—	4	8	no	—
514	C₂×C₃×C₄	#135	1	4	yes	—
515	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
516	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
517	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
518	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
519	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
521	C₂×C₃×C₄	C₂×#41	1	2	yes	—
522	C₂×C₃×C₄	C₂×#41	1	2	yes	—
523	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
524	C₃×C₈	—	2	2	no	—
525	C₃×C₈	—	2	2	no	—
526	C₃×C₈	—	2	2	no	—
527	C₃×C₈	—	2	2	no	—
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
531	#41	—	2	16	no	—
532	#41	—	2	8	no	—
533	#41	—	2	8	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	C₃×#41	1	4	yes	—
540	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
541	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	C₃×#41	1	4	yes	—
552	C₂×D₄	C₂⁴×C₃	1	2	yes	—
553	C₂×D₄	C₂⁴×C₃	1	2	yes	—
554	C₂²×C₄	—	2	8	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
573	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
574	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
575	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
576	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
577	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
578	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
579	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
582	Q₁₆	—	2	8	no	—
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	2	8	no	—
585	D₈	—	2	8	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	—	2	2	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	C₂⁴×C₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₃	1	2	yes	—
592	C₂×C₈	C₂⁴×C₃	1	2	yes	—
593	C₂×C₈	C₂⁴×C₃	1	2	yes	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
605	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
606	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
607	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	4	no	—
619	C₄²	—	2	4	no	—
620	C₄²	C₂×C₃×D₄	1	4	yes	—
621	C₄²	C₂×C₃×D₄	1	4	yes	—
622	C₄²	C₂×C₃×D₄	1	2	yes	—
623	C₄²	C₂×C₃×D₄	1	2	yes	—
624	C₄²	C₂⁴×C₃	1	2	yes	—
625	C₄²	C₂⁴×C₃	1	2	yes	—
626	C₂²×C₃	—	2	2	no	—
627	C₂²×C₃	—	2	4	no	—
628	C₂²×C₃	—	2	2	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	4	4	no	—
631	C₂²×C₃	—	4	8	no	—
632	C₂²×C₃	—	4	2	no	—
633	C₂²×C₃	—	4	2	no	—
634	C₂²×C₃	—	4	2	no	—
635	C₂²×C₃	—	4	2	no	—
636	C₂²×C₃	—	4	2	no	—
637	C₂²×C₃	—	8	4	no	—
638	C₂²×C₃	#525	1	2	yes	—
639	C₂²×C₃	C₂×#135	1	2	yes	—
640	C₂²×C₃	#575	1	2	yes	—
641	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
642	C₃×C₄	—	2	2	no	—
643	C₃×C₄	—	2	4	no	—
644	C₃×C₄	—	2	2	no	—
645	C₃×C₄	—	2	2	no	—
646	C₃×C₄	—	2	2	no	—
647	C₃×C₄	—	4	2	no	—
648	C₃×C₄	—	4	2	no	—
649	C₃×C₄	—	4	2	no	—
650	C₃×C₄	—	4	2	no	—
651	C₃×C₄	—	4	2	no	—
652	C₃×C₄	#525	1	2	yes	—
653	C₃×C₄	C₂×#135	1	4	yes	—
654	C₃×C₄	C₂²×#41	1	1	yes	characteristic
655	C₃×C₄	C₂²×#41	1	1	yes	characteristic
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	C₂²×C₃×D₄	1	2	yes	—
668	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	2	4	no	—
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	C₂×C₃×#41	1	4	yes	—
675	D₄	—	2	16	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	4	no	—
680	D₄	—	4	8	no	—
681	D₄	—	4	2	no	—
682	D₄	C₂×C₃×#41	1	4	yes	—
683	C₂×C₄	—	2	16	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	8	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	8	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	C₃×#135	1	4	yes	—
709	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
710	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
711	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
712	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
713	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
714	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
715	C₂×C₄	C₂×C₃×#41	1	2	yes	—
716	C₂×C₄	C₂×C₃×#41	1	2	yes	—
717	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	2	no	—
720	C₈	—	2	2	no	—
721	C₈	—	2	2	no	—
722	C₂×C₃	—	4	2	no	—
723	C₂×C₃	—	4	4	no	—
724	C₂×C₃	—	8	2	no	—
725	C₂×C₃	#3102	1	4	yes	direct product factor
726	C₂×C₃	C₂×#525	1	1	yes	characteristic
727	C₂×C₃	C₂²×#135	1	1	yes	characteristic
728	C₂×C₃	C₂×#575	1	1	yes	characteristic
729	C₂²	—	2	2	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	8	4	no	—
741	C₂²	C₃×#525	1	2	yes	—
742	C₂²	C₂×C₃×#135	1	2	yes	—
743	C₂²	C₃×#575	1	2	yes	—
744	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	C₃×#525	1	2	yes	—
756	C₄	C₂×C₃×#135	1	4	yes	—
757	C₄	C₂²×C₃×#41	1	1	yes	characteristic
758	C₄	C₂²×C₃×#41	1	1	yes	characteristic
759	C₃	C₂×#3102	1	1	yes	characteristic, direct product factor, Sylow
760	C₂	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₃×#3102	1	4	yes	direct product factor
764	C₂	C₂×C₃×#525	1	1	yes	characteristic
765	C₂	C₂²×C₃×#135	1	1	yes	characteristic
766	C₂	C₂×C₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂³×C₃	C₂²×D₄
prime radical	C₂×C₃×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#529	C₂	semidirect
2. C₂×C₃×C₄×#41	C₂	semidirect
3. C₃×#3102	C₂	direct (N × H)
4. C₂×C₃×#485	C₂	semidirect
5. C₂×C₃×#482	C₂	semidirect
6. C₂×C₃×#479	C₂	semidirect
7. C₂×C₃×#478	C₂	semidirect
8. C₂×C₃×#464	C₂	semidirect
9. C₂×C₃×#463	C₂	semidirect
10. C₂×C₃×#452	C₂	semidirect
12. C₂×C₃×C₄×Q₁₆	C₂	semidirect
13. C₂×C₃×C₄×SD₁₆	C₂	semidirect
14. C₂×C₃×C₄×SD₁₆	C₂	semidirect
15. C₂×C₃×C₄×D₈	C₂	semidirect
16. C₂×C₃×#431	C₂	semidirect
17. C₂×#3102	C₃	direct (N × H)
24. C₃×#529	C₂²	semidirect
32. C₃×C₄×#41	C₂²	semidirect
47. C₃×#485	C₂²	semidirect
48. C₃×#482	C₂²	semidirect
49. C₃×#479	C₂²	semidirect
50. C₃×#478	C₂²	semidirect
51. C₃×#464	C₂²	semidirect
52. C₃×#463	C₂²	semidirect
53. C₃×#452	C₂²	semidirect
55. C₃×C₄×Q₁₆	C₂²	semidirect
56. C₃×C₄×SD₁₆	C₂²	semidirect
57. C₃×C₄×SD₁₆	C₂²	semidirect
58. C₃×C₄×D₈	C₂²	semidirect
59. C₃×#431	C₂²	semidirect
78. C₂×#529	C₂×C₃	semidirect
79. C₂×C₄×#41	C₂×C₃	semidirect
80. #3102	C₂×C₃	direct (N × H)
81. C₂×#485	C₂×C₃	semidirect
82. C₂×#482	C₂×C₃	semidirect
83. C₂×#479	C₂×C₃	semidirect
84. C₂×#478	C₂×C₃	semidirect
85. C₂×#464	C₂×C₃	semidirect
86. C₂×#463	C₂×C₃	semidirect
87. C₂×#452	C₂×C₃	semidirect
89. C₂×C₄×Q₁₆	C₂×C₃	semidirect
90. C₂×C₄×SD₁₆	C₂×C₃	semidirect
91. C₂×C₄×SD₁₆	C₂×C₃	semidirect
92. C₂×C₄×D₈	C₂×C₃	semidirect
93. C₂×#431	C₂×C₃	semidirect
205. #529	C₂²×C₃	semidirect
213. C₄×#41	C₂²×C₃	semidirect
228. #485	C₂²×C₃	semidirect
229. #482	C₂²×C₃	semidirect
230. #479	C₂²×C₃	semidirect
231. #478	C₂²×C₃	semidirect
232. #464	C₂²×C₃	semidirect
233. #463	C₂²×C₃	semidirect
234. #452	C₂²×C₃	semidirect
236. C₄×Q₁₆	C₂²×C₃	semidirect
237. C₄×SD₁₆	C₂²×C₃	semidirect
238. C₄×SD₁₆	C₂²×C₃	semidirect
239. C₄×D₈	C₂²×C₃	semidirect
240. #431	C₂²×C₃	semidirect
725. C₂×C₃	#3102	direct (N × H)
759. C₃	C₂×#3102	direct (N × H)
763. C₂	C₃×#3102	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×#529	2
C₂×C₃×C₄×#41	2
C₃×#3102	2
C₂×C₃×#485	2
C₂×C₃×#482	2
C₂×C₃×#479	2
C₂×C₃×#478	2
C₂×C₃×#464	2
C₂×C₃×#463	2
C₂×C₃×#452	2
C₂×C₃×#449	2
C₂×C₃×C₄×Q₁₆	2
C₂×C₃×C₄×SD₁₆	2
C₂×C₃×C₄×D₈	2
C₂×C₃×#431	2
C₂×#3102	3

Subgroups — C2×C3×#3102 #10679136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3102 #10679136