Subgroups — C₂×C₃×#65418 #14411687

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65418	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3952	C₂	1	4	yes	maximal, complemented
6	C₂×#65418	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₂²⋊D₅	C₄	1	2	yes	—
9	C₂×C₃×#709	—	2	4	no	—
10	C₂×C₃×#709	—	2	4	no	—
11	C₂×C₃×#709	C₄	1	4	yes	—
12	C₂×C₃×#709	C₂²	1	4	yes	—
13	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×Dic₁₀	C₄	1	1	yes	characteristic
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	—
19	C₂²×C₃×#168	—	2	4	no	—
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₂²×C₃×#168	C₂²	1	4	yes	complemented
22	C₃×#3952	C₂²	1	16	yes	complemented
23	C₂×C₃×#408	—	5	1	no	maximal, Hall
24	C₂²×#709	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂³×#168	C₂×C₃	1	1	yes	characteristic, complemented
27	#65418	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	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
38	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	8	yes	—
39	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
40	C₃×#709	—	2	16	no	—
41	C₃×#709	—	2	8	no	—
42	C₃×#709	—	2	8	no	—
43	C₂×C₃×D₂₀	—	2	4	no	—
44	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₄×D₅	—	2	4	no	—
46	C₂×C₃×C₄×D₅	—	2	4	no	—
47	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
49	C₂×C₃×Dic₁₀	—	2	4	no	—
50	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
51	C₃×C₅×M₁₆	—	2	8	no	—
52	C₂×C₃×C₅×C₈	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₂×C₃×#168	—	2	4	no	—
55	C₂×C₃×#168	—	2	8	no	—
56	C₂×C₃×#168	C₂³	1	4	yes	—
57	C₂²×C₃×#41	—	5	1	no	—
58	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
59	C₂³×C₃×C₈	—	5	1	no	—
60	C₃×#408	—	5	8	no	—
61	C₂×C₃×C₂²⋊C₈	—	5	4	no	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₂²⋊D₅	C₃×C₄	1	2	yes	—
64	C₂×#709	—	2	4	no	—
65	C₂×#709	—	2	4	no	—
66	C₂×#709	C₃×C₄	1	4	yes	—
67	C₂×#709	C₂²×C₃	1	4	yes	—
68	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
70	C₂²×Dic₁₀	C₃×C₄	1	1	yes	characteristic
71	C₂×C₅×M₁₆	—	2	4	no	—
72	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	complemented
73	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
74	C₂²×#168	—	2	4	no	—
75	C₂²×#168	C₂²×C₃	1	2	yes	—
76	C₂²×#168	C₂²×C₃	1	4	yes	complemented
77	#3952	C₂²×C₃	1	16	yes	complemented
78	C₂×#408	—	5	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
81	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₃×D₅	—	2	4	no	—
84	C₂²×C₃×D₅	—	2	8	no	—
85	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	8	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
95	C₃×C₂²⋊D₅	—	2	16	no	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
98	C₃×D₂₀	—	2	8	no	—
99	C₃×C₄×D₅	—	2	8	no	—
100	C₃×C₄×D₅	—	2	4	no	—
101	C₃×C₄×D₅	—	2	4	no	—
102	C₃×Dic₁₀	—	2	8	no	—
103	C₃×C₅×C₈	—	2	4	no	—
104	C₃×#168	—	2	4	no	—
105	C₂×C₃×#41	—	5	4	no	—
106	C₂×C₃×#41	—	5	4	no	—
107	C₂×C₃×#41	—	10	4	no	—
108	C₂×C₃×#41	—	10	4	no	—
109	C₂²×C₃×Q₈	—	5	1	no	—
110	C₂²×C₃×D₄	—	5	2	no	—
111	C₂²×C₃×D₄	—	5	1	no	—
112	C₂³×C₃×C₄	—	5	2	no	—
113	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
114	C₂×C₃×M₁₆	—	2	4	no	—
115	C₂×C₃×M₁₆	C₂×D₅	1	4	yes	complemented
116	C₂²×C₃×C₈	—	5	4	no	—
117	C₂²×C₃×C₈	—	5	2	no	—
118	C₂²×C₃×C₈	—	10	4	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
120	C₃×C₂²⋊C₈	—	5	16	no	—
121	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
125	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
126	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
129	C₂×C₂²⋊D₅	—	2	8	no	—
130	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	8	yes	—
131	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
132	#709	—	2	16	no	—
133	#709	—	2	8	no	—
134	#709	—	2	8	no	—
135	C₂×D₂₀	—	2	4	no	—
136	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
137	C₂×C₄×D₅	—	2	4	no	—
138	C₂×C₄×D₅	—	2	4	no	—
139	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
140	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
141	C₂×Dic₁₀	—	2	4	no	—
142	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
143	C₅×M₁₆	—	2	8	no	—
144	C₂×C₅×C₈	—	2	4	no	—
145	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
146	C₂×#168	—	2	4	no	—
147	C₂×#168	—	2	8	no	—
148	C₂×#168	C₂³×C₃	1	4	yes	—
149	C₂²×#41	—	5	1	no	—
150	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
151	C₂³×C₈	—	5	1	no	—
152	#408	—	5	8	no	—
153	C₂×C₂²⋊C₈	—	5	4	no	—
154	C₂²×C₃×C₅	—	2	4	no	—
155	C₂²×C₃×C₅	—	2	8	no	—
156	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂²×C₃×C₅	#131	1	4	yes	—
159	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₃×D₅	—	2	4	no	—
161	C₂×C₃×D₅	—	2	8	no	—
162	C₂×C₃×D₅	—	4	8	no	—
163	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
164	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
165	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₃×Dic₅	—	2	4	no	—
168	C₂⁴×C₃	—	5	2	no	—
169	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
170	C₃×#41	—	10	16	no	—
171	C₃×#41	—	10	8	no	—
172	C₃×#41	—	10	8	no	—
173	C₂×C₃×Q₈	—	5	4	no	—
174	C₂×C₃×Q₈	—	10	4	no	—
175	C₂×C₃×D₄	—	5	8	no	—
176	C₂×C₃×D₄	—	5	4	no	—
177	C₂×C₃×D₄	—	10	8	no	—
178	C₂×C₃×D₄	—	10	4	no	—
179	C₂²×C₃×C₄	—	5	2	no	—
180	C₂²×C₃×C₄	—	5	4	no	—
181	C₂²×C₃×C₄	—	5	4	no	—
182	C₂²×C₃×C₄	—	10	4	no	—
183	C₂²×C₃×C₄	—	10	4	no	—
184	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
186	C₂²×C₃×C₄	D₂₀	1	4	yes	—
187	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
188	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₃×M₁₆	—	2	8	no	—
191	C₂×C₃×C₈	—	2	4	no	—
192	C₂×C₃×C₈	—	5	4	no	—
193	C₂×C₃×C₈	—	10	4	no	—
194	C₂×C₃×C₈	—	10	8	no	—
195	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	C₃×C₂²⋊C₄	1	4	yes	—
198	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
199	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
200	C₂²×D₅	—	2	4	no	—
201	C₂²×D₅	—	2	8	no	—
202	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
203	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
204	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	8	yes	—
205	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
211	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
212	C₂²⋊D₅	—	2	16	no	—
213	C₂×Dic₅	—	2	4	no	—
214	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
215	D₂₀	—	2	8	no	—
216	C₄×D₅	—	2	8	no	—
217	C₄×D₅	—	2	4	no	—
218	C₄×D₅	—	2	4	no	—
219	Dic₁₀	—	2	8	no	—
220	C₅×C₈	—	2	4	no	—
221	#168	—	2	4	no	—
222	C₂×#41	—	5	4	no	—
223	C₂×#41	—	5	4	no	—
224	C₂×#41	—	10	4	no	—
225	C₂×#41	—	10	4	no	—
226	C₂²×Q₈	—	5	1	no	—
227	C₂²×D₄	—	5	2	no	—
228	C₂²×D₄	—	5	1	no	—
229	C₂³×C₄	—	5	2	no	—
230	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
231	C₂×M₁₆	—	2	4	no	—
232	C₂×M₁₆	C₂×C₃×D₅	1	4	yes	complemented
233	C₂²×C₈	—	5	2	no	—
234	C₂²×C₈	—	5	4	no	—
235	C₂²×C₈	—	10	4	no	—
236	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
237	C₂²⋊C₈	—	5	16	no	—
238	C₂×C₃×C₅	—	2	4	no	—
239	C₂×C₃×C₅	#408	1	4	yes	complemented
240	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#131	1	2	yes	—
242	C₃×D₅	—	4	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	5	4	no	—
245	C₂³×C₃	—	10	8	no	—
246	C₂³×C₃	—	10	4	no	—
247	C₂³×C₃	#685	1	4	yes	—
248	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
249	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
250	C₃×Q₈	—	10	8	no	—
251	C₃×D₄	—	10	16	no	—
252	C₃×D₄	—	10	8	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	—	10	4	no	—
255	C₂×C₃×C₄	—	10	4	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	10	8	no	—
258	C₂×C₃×C₄	#685	1	4	yes	—
259	C₂×C₃×C₄	#685	1	8	yes	—
260	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
262	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
263	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
264	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
266	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
267	C₃×C₈	—	2	4	no	—
268	C₃×C₈	—	10	4	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	8	no	—
271	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
272	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
273	C₂²×C₅	C₃×#131	1	4	yes	—
274	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
275	C₂×D₅	—	2	8	no	—
276	C₂×D₅	—	2	4	no	—
277	C₂×D₅	—	4	8	no	—
278	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
279	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
280	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
282	Dic₅	—	2	4	no	—
283	C₂⁴	—	5	2	no	—
284	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
285	#41	—	10	16	no	—
286	#41	—	10	8	no	—
287	#41	—	10	8	no	—
288	C₂×Q₈	—	5	4	no	—
289	C₂×Q₈	—	10	4	no	—
290	C₂×D₄	—	5	8	no	—
291	C₂×D₄	—	5	4	no	—
292	C₂×D₄	—	10	8	no	—
293	C₂×D₄	—	10	4	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	5	4	no	—
296	C₂²×C₄	—	5	4	no	—
297	C₂²×C₄	—	10	4	no	—
298	C₂²×C₄	—	10	4	no	—
299	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
300	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
301	C₂²×C₄	C₃×D₂₀	1	4	yes	—
302	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
303	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
305	M₁₆	—	2	8	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	5	4	no	—
308	C₂×C₈	—	10	4	no	—
309	C₂×C₈	—	10	8	no	—
310	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
311	C₃×C₅	C₂×#408	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	8	no	—
314	C₂²×C₃	—	10	8	no	—
315	C₂²×C₃	—	10	4	no	—
316	C₂²×C₃	—	20	8	no	—
317	C₂²×C₃	#4053	1	4	yes	—
318	C₂²×C₃	C₂×#685	1	4	yes	—
319	C₂²×C₃	C₂×#685	1	2	yes	—
320	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
321	C₃×C₄	—	10	4	no	—
322	C₃×C₄	C₂×#685	1	2	yes	—
323	C₃×C₄	C₂×#685	1	4	yes	—
324	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
325	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
326	C₂×C₅	—	2	4	no	—
327	C₂×C₅	C₃×#408	1	4	yes	complemented
328	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₅	C₂×C₃×#131	1	2	yes	—
330	D₅	—	4	4	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	5	4	no	—
333	C₂³	—	10	8	no	—
334	C₂³	—	10	4	no	—
335	C₂³	C₃×#685	1	4	yes	—
336	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
337	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
338	Q₈	—	10	8	no	—
339	D₄	—	10	16	no	—
340	D₄	—	10	8	no	—
341	C₂×C₄	—	5	4	no	—
342	C₂×C₄	—	10	4	no	—
343	C₂×C₄	—	10	4	no	—
344	C₂×C₄	—	10	4	no	—
345	C₂×C₄	—	10	8	no	—
346	C₂×C₄	C₃×#685	1	4	yes	—
347	C₂×C₄	C₃×#685	1	8	yes	—
348	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
349	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
350	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
351	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
352	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
353	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
354	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
355	C₈	—	2	4	no	—
356	C₈	—	10	4	no	—
357	C₂×C₃	—	2	4	no	—
358	C₂×C₃	—	20	4	no	—
359	C₂×C₃	#65418	1	4	yes	direct product factor
360	C₂×C₃	C₂×#4053	1	2	yes	—
361	C₂×C₃	C₂²×#685	1	1	yes	characteristic
362	C₅	C₂×C₃×#408	1	1	yes	characteristic, complemented, Sylow
363	C₂²	—	2	8	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	10	4	no	—
366	C₂²	—	10	8	no	—
367	C₂²	—	20	8	no	—
368	C₂²	C₃×#4053	1	4	yes	—
369	C₂²	C₂×C₃×#685	1	4	yes	—
370	C₂²	C₂×C₃×#685	1	2	yes	—
371	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
372	C₄	—	10	4	no	—
373	C₄	C₂×C₃×#685	1	2	yes	—
374	C₄	C₂×C₃×#685	1	4	yes	—
375	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
376	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
377	C₃	C₂×#65418	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	4	no	—
379	C₂	—	20	4	no	—
380	C₂	C₃×#65418	1	4	yes	direct product factor
381	C₂	C₂×C₃×#4053	1	2	yes	—
382	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	C₂²×C₃×#709	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₂×C₃×#408
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. C₂³×C₃×#168	C₂	semidirect
4. C₃×#65418	C₂	direct (N × H)
5. C₂×C₃×#3952	C₂	semidirect
6. C₂×#65418	C₃	direct (N × H)
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
21. C₂²×C₃×#168	C₂²	semidirect
22. C₃×#3952	C₂²	semidirect
25. C₂²×C₅×M₁₆	C₂×C₃	semidirect
26. C₂³×#168	C₂×C₃	semidirect
27. #65418	C₂×C₃	direct (N × H)
28. C₂×#3952	C₂×C₃	semidirect
58. C₂²×C₃×M₁₆	D₅	semidirect
72. C₂×C₅×M₁₆	C₂²×C₃	semidirect
76. C₂²×#168	C₂²×C₃	semidirect
77. #3952	C₂²×C₃	semidirect
115. C₂×C₃×M₁₆	C₂×D₅	semidirect
150. C₂²×M₁₆	C₃×D₅	semidirect
232. C₂×M₁₆	C₂×C₃×D₅	semidirect
239. C₂×C₃×C₅	#408	semidirect
311. C₃×C₅	C₂×#408	semidirect
327. C₂×C₅	C₃×#408	semidirect
359. C₂×C₃	#65418	direct (N × H)
362. C₅	C₂×C₃×#408	semidirect
377. C₃	C₂×#65418	direct (N × H)
380. C₂	C₃×#65418	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#709	2
C₂²×C₃×C₅×M₁₆	2
C₂³×C₃×#168	2
C₃×#65418	2
C₂×C₃×#3952	2
C₂×#65418	3
C₂×C₃×#408	5

Subgroups — C2×C3×#65418 #14411687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65418 #14411687