Subgroups — C₂×C₃×#65415 #14411628

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65415	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3952	C₂	1	4	yes	maximal, complemented
6	C₂×#65415	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁴×C₃×D₅	C₄	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×Dic₅	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₅	—	2	4	no	—
11	C₂²×C₃×C₄×D₅	—	2	4	no	—
12	C₂²×C₃×C₄×D₅	C₄	1	4	yes	—
13	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
16	C₂×C₃×C₅×M₁₆	—	2	4	no	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	complemented
18	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
19	C₂×C₃×#681	—	2	4	no	—
20	C₂×C₃×#681	C₂²	1	4	yes	complemented
21	C₂²×C₃×#168	C₂²	1	2	yes	complemented
22	C₃×#3952	C₂²	1	16	yes	complemented
23	C₂×C₃×#407	—	5	1	no	maximal, Hall
24	C₂³×C₄×D₅	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×#681	C₂×C₃	1	1	yes	characteristic, complemented
27	#65415	C₂×C₃	1	8	yes	direct product factor
28	C₂×#3952	C₂×C₃	1	4	yes	complemented
29	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₃×D₅	—	2	4	no	—
31	C₂³×C₃×D₅	—	2	8	no	—
32	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
33	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₅	—	2	4	no	—
41	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	—	2	16	no	—
44	C₂×C₃×C₄×D₅	—	2	8	no	—
45	C₂×C₃×C₄×D₅	—	2	4	no	—
46	C₂×C₃×C₄×D₅	—	2	8	no	—
47	C₂×C₃×C₄×D₅	—	2	4	no	—
48	C₂×C₃×C₄×D₅	—	2	8	no	—
49	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
50	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
51	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
52	C₃×C₅×M₁₆	—	2	8	no	—
53	C₂×C₃×C₅×C₈	—	2	4	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	4	yes	complemented
55	C₃×#681	—	2	8	no	—
56	C₂×C₃×#168	—	2	4	no	—
57	C₂×C₃×#168	C₂³	1	4	yes	complemented
58	C₂⁴×C₃×C₄	—	5	1	no	—
59	C₂²×C₃×M₁₆	—	5	1	no	—
60	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
61	C₃×#407	—	5	8	no	—
62	C₂×C₃×C₂²⋊C₈	—	5	4	no	—
63	C₂⁴×D₅	C₃×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂³×Dic₅	C₃×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₅	—	2	4	no	—
67	C₂²×C₄×D₅	—	2	4	no	—
68	C₂²×C₄×D₅	C₃×C₄	1	4	yes	—
69	C₂²×C₄×D₅	C₃×C₄	1	2	yes	—
70	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
71	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
72	C₂×C₅×M₁₆	—	2	4	no	—
73	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	complemented
74	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
75	C₂×#681	—	2	4	no	—
76	C₂×#681	C₂²×C₃	1	4	yes	complemented
77	C₂²×#168	C₂²×C₃	1	2	yes	complemented
78	#3952	C₂²×C₃	1	16	yes	complemented
79	C₂×#407	—	5	1	no	Sylow
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
82	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₃×D₅	—	2	32	no	—
85	C₂²×C₃×D₅	—	2	8	no	—
86	C₂²×C₃×D₅	—	2	4	no	—
87	C₂²×C₃×D₅	—	2	4	no	—
88	C₂²×C₃×D₅	—	2	16	no	—
89	C₂²×C₃×D₅	M₁₆	1	8	yes	complemented
90	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	8	yes	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×Dic₅	—	2	8	no	—
101	C₂×C₃×Dic₅	—	2	4	no	—
102	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
103	C₃×C₄×D₅	—	2	8	no	—
104	C₃×C₄×D₅	—	2	16	no	—
105	C₃×C₄×D₅	—	2	4	no	—
106	C₃×C₄×D₅	—	2	4	no	—
107	C₃×C₅×C₈	—	2	4	no	—
108	C₃×#168	—	2	4	no	—
109	C₂⁵×C₃	—	5	1	no	—
110	C₂³×C₃×C₄	—	5	1	no	—
111	C₂³×C₃×C₄	—	5	2	no	—
112	C₂³×C₃×C₄	—	5	4	no	—
113	C₂³×C₃×C₄	—	5	4	no	—
114	C₂³×C₃×C₄	—	5	2	no	—
115	C₂³×C₃×C₄	—	10	4	no	—
116	C₂³×C₃×C₄	—	10	4	no	—
117	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
118	C₂×C₃×M₁₆	—	2	4	no	—
119	C₂×C₃×M₁₆	—	5	4	no	—
120	C₂×C₃×M₁₆	—	10	4	no	—
121	C₂×C₃×M₁₆	C₂×D₅	1	4	yes	complemented
122	C₂²×C₃×C₈	—	5	2	no	—
123	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
124	C₃×C₂²⋊C₈	—	5	16	no	—
125	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂³×D₅	—	2	4	no	—
127	C₂³×D₅	—	2	8	no	—
128	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
129	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
131	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
133	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₂²×Dic₅	—	2	4	no	—
137	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
138	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
139	C₂×C₄×D₅	—	2	16	no	—
140	C₂×C₄×D₅	—	2	8	no	—
141	C₂×C₄×D₅	—	2	4	no	—
142	C₂×C₄×D₅	—	2	8	no	—
143	C₂×C₄×D₅	—	2	4	no	—
144	C₂×C₄×D₅	—	2	8	no	—
145	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
146	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
147	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
148	C₅×M₁₆	—	2	8	no	—
149	C₂×C₅×C₈	—	2	4	no	—
150	C₂×C₅×C₈	C₂³×C₃	1	4	yes	complemented
151	#681	—	2	8	no	—
152	C₂×#168	—	2	4	no	—
153	C₂×#168	C₂³×C₃	1	4	yes	complemented
154	C₂⁴×C₄	—	5	1	no	—
155	C₂²×M₁₆	—	5	1	no	—
156	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
157	#407	—	5	8	no	—
158	C₂×C₂²⋊C₈	—	5	4	no	—
159	C₂²×C₃×C₅	—	2	4	no	—
160	C₂²×C₃×C₅	—	2	8	no	—
161	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
164	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₃×D₅	—	2	32	no	—
166	C₂×C₃×D₅	—	2	4	no	—
167	C₂×C₃×D₅	—	2	4	no	—
168	C₂×C₃×D₅	—	2	16	no	—
169	C₂×C₃×D₅	C₂×M₁₆	1	8	yes	complemented
170	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
171	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
172	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₃×Dic₅	—	2	4	no	—
175	C₂⁴×C₃	—	5	2	no	—
176	C₂⁴×C₃	—	5	4	no	—
177	C₂⁴×C₃	—	10	8	no	—
178	C₂⁴×C₃	—	10	4	no	—
179	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
180	C₂²×C₃×C₄	—	5	4	no	—
181	C₂²×C₃×C₄	—	5	2	no	—
182	C₂²×C₃×C₄	—	5	8	no	—
183	C₂²×C₃×C₄	—	5	4	no	—
184	C₂²×C₃×C₄	—	5	4	no	—
185	C₂²×C₃×C₄	—	10	4	no	—
186	C₂²×C₃×C₄	—	10	16	no	—
187	C₂²×C₃×C₄	—	10	8	no	—
188	C₂²×C₃×C₄	—	10	4	no	—
189	C₂²×C₃×C₄	—	10	8	no	—
190	C₂²×C₃×C₄	—	10	4	no	—
191	C₂²×C₃×C₄	—	10	8	no	—
192	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
194	C₂²×C₃×C₄	D₂₀	1	4	yes	—
195	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
196	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
197	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
198	C₃×M₁₆	—	2	8	no	—
199	C₃×M₁₆	—	10	8	no	—
200	C₂×C₃×C₈	—	2	4	no	—
201	C₂×C₃×C₈	—	5	4	no	—
202	C₂×C₃×C₈	—	10	4	no	—
203	C₂×C₃×C₈	C₂²×D₅	1	4	yes	complemented
204	C₂³×C₅	—	2	4	no	—
205	C₂³×C₅	C₃×C₂²⋊C₄	1	4	yes	—
206	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
207	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₂²×D₅	—	2	32	no	—
209	C₂²×D₅	—	2	8	no	—
210	C₂²×D₅	—	2	4	no	—
211	C₂²×D₅	—	2	4	no	—
212	C₂²×D₅	—	2	16	no	—
213	C₂²×D₅	C₃×M₁₆	1	8	yes	complemented
214	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
215	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	8	yes	—
216	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
222	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
223	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
224	C₂×Dic₅	—	2	8	no	—
225	C₂×Dic₅	—	2	4	no	—
226	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
227	C₄×D₅	—	2	8	no	—
228	C₄×D₅	—	2	16	no	—
229	C₄×D₅	—	2	4	no	—
230	C₄×D₅	—	2	4	no	—
231	C₅×C₈	—	2	4	no	—
232	#168	—	2	4	no	—
233	C₂⁵	—	5	1	no	—
234	C₂³×C₄	—	5	1	no	—
235	C₂³×C₄	—	5	2	no	—
236	C₂³×C₄	—	5	4	no	—
237	C₂³×C₄	—	5	2	no	—
238	C₂³×C₄	—	5	4	no	—
239	C₂³×C₄	—	10	4	no	—
240	C₂³×C₄	—	10	4	no	—
241	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	5	4	no	—
244	C₂×M₁₆	—	10	4	no	—
245	C₂×M₁₆	C₂×C₃×D₅	1	4	yes	complemented
246	C₂²×C₈	—	5	2	no	—
247	C₂²×C₈	C₂×C₃×D₅	1	2	yes	complemented
248	C₂²⋊C₈	—	5	16	no	—
249	C₂×C₃×C₅	—	2	4	no	—
250	C₂×C₃×C₅	#407	1	4	yes	complemented
251	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
253	C₃×D₅	—	2	8	no	—
254	C₂³×C₃	—	2	4	no	—
255	C₂³×C₃	—	5	4	no	—
256	C₂³×C₃	—	5	8	no	—
257	C₂³×C₃	—	10	16	no	—
258	C₂³×C₃	—	10	32	no	—
259	C₂³×C₃	—	10	4	no	—
260	C₂³×C₃	—	10	8	no	—
261	C₂³×C₃	—	10	4	no	—
262	C₂³×C₃	#685	1	4	yes	—
263	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
264	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
265	C₂×C₃×C₄	—	5	4	no	—
266	C₂×C₃×C₄	—	10	8	no	—
267	C₂×C₃×C₄	—	10	4	no	—
268	C₂×C₃×C₄	—	10	4	no	—
269	C₂×C₃×C₄	—	10	4	no	—
270	C₂×C₃×C₄	—	10	16	no	—
271	C₂×C₃×C₄	—	10	8	no	—
272	C₂×C₃×C₄	#685	1	8	yes	—
273	C₂×C₃×C₄	#685	1	4	yes	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
277	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
278	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
279	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
280	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
281	C₃×C₈	—	2	4	no	—
282	C₃×C₈	—	10	4	no	—
283	C₂²×C₅	—	2	4	no	—
284	C₂²×C₅	—	2	8	no	—
285	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
286	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
287	C₂²×C₅	C₂×C₃×M₁₆	1	4	yes	—
288	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
289	C₂×D₅	—	2	32	no	—
290	C₂×D₅	—	2	4	no	—
291	C₂×D₅	—	2	16	no	—
292	C₂×D₅	—	2	4	no	—
293	C₂×D₅	C₂×C₃×M₁₆	1	8	yes	complemented
294	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
295	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
296	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
298	Dic₅	—	2	4	no	—
299	C₂⁴	—	5	2	no	—
300	C₂⁴	—	5	4	no	—
301	C₂⁴	—	10	8	no	—
302	C₂⁴	—	10	4	no	—
303	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
304	C₂²×C₄	—	5	4	no	—
305	C₂²×C₄	—	5	2	no	—
306	C₂²×C₄	—	5	4	no	—
307	C₂²×C₄	—	5	8	no	—
308	C₂²×C₄	—	5	4	no	—
309	C₂²×C₄	—	10	4	no	—
310	C₂²×C₄	—	10	16	no	—
311	C₂²×C₄	—	10	8	no	—
312	C₂²×C₄	—	10	4	no	—
313	C₂²×C₄	—	10	8	no	—
314	C₂²×C₄	—	10	4	no	—
315	C₂²×C₄	—	10	8	no	—
316	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
317	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
318	C₂²×C₄	C₃×D₂₀	1	4	yes	—
319	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
320	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
322	M₁₆	—	2	8	no	—
323	M₁₆	—	10	8	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	5	4	no	—
326	C₂×C₈	—	10	4	no	—
327	C₂×C₈	C₂²×C₃×D₅	1	4	yes	complemented
328	C₃×C₅	C₂×#407	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	4	no	—
330	C₂²×C₃	—	2	8	no	—
331	C₂²×C₃	—	5	8	no	—
332	C₂²×C₃	—	10	32	no	—
333	C₂²×C₃	—	10	4	no	—
334	C₂²×C₃	—	10	4	no	—
335	C₂²×C₃	—	10	16	no	—
336	C₂²×C₃	D₅×M₁₆	1	4	yes	—
337	C₂²×C₃	C₂×#685	1	4	yes	—
338	C₂²×C₃	C₂×#685	1	2	yes	—
339	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
340	C₃×C₄	—	10	4	no	—
341	C₃×C₄	C₂×#685	1	4	yes	—
342	C₃×C₄	C₂×#685	1	2	yes	—
343	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
344	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
345	C₂×C₅	—	2	4	no	—
346	C₂×C₅	C₃×#407	1	4	yes	complemented
347	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₅	C₂²×C₃×M₁₆	1	2	yes	—
349	D₅	—	2	8	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	5	4	no	—
352	C₂³	—	5	8	no	—
353	C₂³	—	10	16	no	—
354	C₂³	—	10	32	no	—
355	C₂³	—	10	4	no	—
356	C₂³	—	10	8	no	—
357	C₂³	—	10	4	no	—
358	C₂³	C₃×#685	1	4	yes	—
359	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
360	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
361	C₂×C₄	—	5	4	no	—
362	C₂×C₄	—	10	8	no	—
363	C₂×C₄	—	10	4	no	—
364	C₂×C₄	—	10	4	no	—
365	C₂×C₄	—	10	4	no	—
366	C₂×C₄	—	10	8	no	—
367	C₂×C₄	—	10	16	no	—
368	C₂×C₄	C₃×#685	1	8	yes	—
369	C₂×C₄	C₃×#685	1	4	yes	—
370	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
372	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
373	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
374	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
375	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
376	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	10	4	no	—
379	C₂×C₃	—	2	4	no	—
380	C₂×C₃	—	10	8	no	—
381	C₂×C₃	#65415	1	4	yes	direct product factor
382	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
383	C₂×C₃	C₂²×#685	1	1	yes	characteristic
384	C₅	C₂×C₃×#407	1	1	yes	characteristic, complemented, Sylow
385	C₂²	—	2	8	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	5	8	no	—
388	C₂²	—	10	32	no	—
389	C₂²	—	10	4	no	—
390	C₂²	—	10	16	no	—
391	C₂²	—	10	4	no	—
392	C₂²	C₃×D₅×M₁₆	1	4	yes	—
393	C₂²	C₂×C₃×#685	1	4	yes	—
394	C₂²	C₂×C₃×#685	1	2	yes	—
395	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
396	C₄	—	10	4	no	—
397	C₄	C₂×C₃×#685	1	2	yes	—
398	C₄	C₂×C₃×#685	1	4	yes	—
399	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
400	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
401	C₃	C₂×#65415	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	4	no	—
403	C₂	—	10	8	no	—
404	C₂	C₃×#65415	1	4	yes	direct product factor
405	C₂	C₂×C₃×D₅×M₁₆	1	2	yes	—
406	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×D₅	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₂×C₃×#407
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₃×#681	C₂	semidirect
4. C₃×#65415	C₂	direct (N × H)
5. C₂×C₃×#3952	C₂	semidirect
6. C₂×#65415	C₃	direct (N × H)
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₂²×C₃×C₅×C₈	C₂²	semidirect
20. C₂×C₃×#681	C₂²	semidirect
21. C₂²×C₃×#168	C₂²	semidirect
22. C₃×#3952	C₂²	semidirect
25. C₂²×C₅×M₁₆	C₂×C₃	semidirect
26. C₂²×#681	C₂×C₃	semidirect
27. #65415	C₂×C₃	direct (N × H)
28. C₂×#3952	C₂×C₃	semidirect
54. C₂×C₃×C₅×C₈	C₂³	semidirect
57. C₂×C₃×#168	C₂³	semidirect
60. C₂²×C₃×M₁₆	D₅	semidirect
73. C₂×C₅×M₁₆	C₂²×C₃	semidirect
74. C₂²×C₅×C₈	C₂²×C₃	semidirect
76. C₂×#681	C₂²×C₃	semidirect
77. C₂²×#168	C₂²×C₃	semidirect
78. #3952	C₂²×C₃	semidirect
89. C₂²×C₃×D₅	M₁₆	semidirect
121. C₂×C₃×M₁₆	C₂×D₅	semidirect
123. C₂²×C₃×C₈	C₂×D₅	semidirect
150. C₂×C₅×C₈	C₂³×C₃	semidirect
153. C₂×#168	C₂³×C₃	semidirect
156. C₂²×M₁₆	C₃×D₅	semidirect
169. C₂×C₃×D₅	C₂×M₁₆	semidirect
203. C₂×C₃×C₈	C₂²×D₅	semidirect
213. C₂²×D₅	C₃×M₁₆	semidirect
245. C₂×M₁₆	C₂×C₃×D₅	semidirect
247. C₂²×C₈	C₂×C₃×D₅	semidirect
250. C₂×C₃×C₅	#407	semidirect
293. C₂×D₅	C₂×C₃×M₁₆	semidirect
327. C₂×C₈	C₂²×C₃×D₅	semidirect
328. C₃×C₅	C₂×#407	semidirect
346. C₂×C₅	C₃×#407	semidirect
381. C₂×C₃	#65415	direct (N × H)
384. C₅	C₂×C₃×#407	semidirect
401. C₃	C₂×#65415	direct (N × H)
404. C₂	C₃×#65415	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×D₅	2
C₂²×C₃×C₅×M₁₆	2
C₂²×C₃×#681	2
C₃×#65415	2
C₂×C₃×#3952	2
C₂×#65415	3
C₂×C₃×#407	5

Subgroups — C2×C3×#65415 #14411628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65415 #14411628