Subgroups — C₂×C₃×#64997 #14411304

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64997	C₂	1	8	yes	maximal, direct product factor
9	C₂×#64997	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×#685	C₄	1	2	yes	—
15	C₂×C₃×#683	C₄	1	2	yes	—
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
19	C₂×C₃×#676	C₄	1	8	yes	complemented
20	C₂×C₃×#676	C₂²	1	4	yes	—
21	C₂×C₃×C₈×D₅	C₄	1	8	yes	complemented
22	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
23	C₃×#4018	C₄	1	4	yes	—
24	C₃×#4018	C₂²	1	4	yes	—
25	C₃×C₅×#97	C₂²	1	4	yes	complemented
26	C₃×#3947	C₂²	1	4	yes	complemented
27	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
28	C₃×C₄×#168	C₂²	1	4	yes	complemented
29	C₂×C₃×#405	—	5	1	no	maximal, Hall
30	C₂²×#676	C₂×C₃	1	1	yes	characteristic
31	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
32	C₂×#4018	C₂×C₃	1	1	yes	characteristic
33	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
37	#64997	C₂×C₃	1	8	yes	direct product factor
38	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
46	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
52	C₃×C₄²×C₅	C₂³	1	2	yes	—
53	C₃×#685	C₂×C₄	1	8	yes	—
54	C₃×#683	C₂×C₄	1	8	yes	—
55	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₅	C₂³	1	2	yes	—
57	C₂×C₃×#168	C₂×C₄	1	4	yes	—
58	C₂×C₃×#168	C₂×C₄	1	4	yes	—
59	C₂×C₃×#168	C₂³	1	2	yes	—
60	C₂×C₃×#168	C₂³	1	2	yes	—
61	C₃×#676	C₂×C₄	1	16	yes	complemented
62	C₃×C₈×D₅	C₂×C₄	1	16	yes	complemented
63	C₂²×C₃×M₁₆	—	5	1	no	—
64	C₂³×C₃×C₈	—	5	1	no	—
65	C₂×C₃×#117	—	5	1	no	—
66	C₃×#405	—	5	8	no	—
67	C₂×C₃×#97	—	5	1	no	—
68	C₂×C₃×#97	D₅	1	1	yes	characteristic, complemented
69	C₂×C₃×C₄×C₈	—	5	1	no	—
70	C₂×C₃×C₄×C₈	—	5	1	no	—
71	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×#685	C₃×C₄	1	2	yes	—
76	C₂×#683	C₃×C₄	1	2	yes	—
77	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
78	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
79	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
80	C₂×#676	C₃×C₄	1	8	yes	complemented
81	C₂×#676	C₂²×C₃	1	4	yes	—
82	C₂×C₈×D₅	C₃×C₄	1	8	yes	complemented
83	C₂×C₈×D₅	C₂²×C₃	1	4	yes	—
84	#4018	C₃×C₄	1	4	yes	—
85	#4018	C₂²×C₃	1	4	yes	—
86	C₅×#97	C₂²×C₃	1	4	yes	complemented
87	#3947	C₂²×C₃	1	4	yes	complemented
88	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
89	C₄×#168	C₂²×C₃	1	4	yes	complemented
90	C₂×#405	—	5	1	no	Sylow
91	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₃×D₅	—	2	4	no	—
93	C₂²×C₃×D₅	C₄²	1	4	yes	—
94	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×Dic₅	—	2	4	no	—
102	C₂×C₃×Dic₅	C₄²	1	4	yes	—
103	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
104	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
105	C₃×C₄×D₅	C₄²	1	8	yes	—
106	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
107	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
108	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
109	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
110	C₃×#168	C₂²×C₄	1	4	yes	—
111	C₃×#168	C₂²×C₄	1	4	yes	—
112	C₂³×C₃×C₄	—	5	1	no	—
113	C₂×C₃×M₁₆	—	5	8	no	—
114	C₂×C₃×M₁₆	—	5	4	no	—
115	C₂²×C₃×C₈	—	5	1	no	—
116	C₂²×C₃×C₈	—	5	1	no	—
117	C₂²×C₃×C₈	—	5	8	no	—
118	C₂²×C₃×C₈	—	5	4	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
121	C₃×#117	—	5	4	no	—
122	C₃×#117	—	5	4	no	—
123	C₂×C₃×C₄⋊C₄	—	5	2	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	C₃×#97	—	5	4	no	—
128	C₃×#97	C₂×D₅	1	4	yes	complemented
129	C₃×C₄×C₈	—	5	4	no	—
130	C₃×C₄×C₈	—	5	4	no	—
131	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
135	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
138	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
139	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
140	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
141	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
142	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
143	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
144	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
145	C₄²×C₅	C₂³×C₃	1	2	yes	—
146	#685	C₂×C₃×C₄	1	8	yes	—
147	#683	C₂×C₃×C₄	1	8	yes	—
148	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
149	C₄×Dic₅	C₂³×C₃	1	2	yes	—
150	C₂×#168	C₂×C₃×C₄	1	4	yes	—
151	C₂×#168	C₂×C₃×C₄	1	4	yes	—
152	C₂×#168	C₂³×C₃	1	2	yes	—
153	C₂×#168	C₂³×C₃	1	2	yes	—
154	#676	C₂×C₃×C₄	1	16	yes	complemented
155	C₈×D₅	C₂×C₃×C₄	1	16	yes	complemented
156	C₂²×M₁₆	—	5	1	no	—
157	C₂³×C₈	—	5	1	no	—
158	C₂×#117	—	5	1	no	—
159	#405	—	5	8	no	—
160	C₂×#97	—	5	1	no	—
161	C₂×#97	C₃×D₅	1	1	yes	characteristic, complemented
162	C₂×C₄×C₈	—	5	1	no	—
163	C₂×C₄×C₈	—	5	1	no	—
164	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
165	C₂²×C₃×C₅	#131	1	4	yes	—
166	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₃×D₅	—	2	4	no	—
168	C₂×C₃×D₅	—	2	8	no	—
169	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
170	C₃×C₄×C₅	—	2	4	no	—
171	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
172	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₃×Dic₅	—	2	4	no	—
175	C₃×Dic₅	C₂×C₄²	1	4	yes	—
176	C₂⁴×C₃	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	2	no	—
179	C₂²×C₃×C₄	—	5	4	no	—
180	C₂²×C₃×C₄	—	5	4	no	—
181	C₂²×C₃×C₄	—	5	2	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
185	C₃×M₁₆	—	5	16	no	—
186	C₂×C₃×C₈	—	5	4	no	—
187	C₂×C₃×C₈	—	5	4	no	—
188	C₂×C₃×C₈	—	5	2	no	—
189	C₂×C₃×C₈	—	5	2	no	—
190	C₂×C₃×C₈	—	5	16	no	—
191	C₂×C₃×C₈	C₄×D₅	1	4	yes	—
192	C₂×C₃×C₈	C₄×D₅	1	4	yes	—
193	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
194	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
195	C₃×C₄⋊C₄	—	5	8	no	—
196	C₃×C₂²⋊C₄	—	5	8	no	—
197	C₃×C₄²	—	5	2	no	—
198	C₃×C₄²	—	5	2	no	—
199	C₃×C₄²	C₄×D₅	1	2	yes	—
200	C₃×C₄²	C₂²×D₅	1	2	yes	—
201	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂²×D₅	—	2	4	no	—
203	C₂²×D₅	C₃×C₄²	1	4	yes	—
204	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
210	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
211	C₂×Dic₅	—	2	4	no	—
212	C₂×Dic₅	C₃×C₄²	1	4	yes	—
213	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
214	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
215	C₄×D₅	C₃×C₄²	1	8	yes	—
216	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
217	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
218	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
219	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
220	#168	C₂²×C₃×C₄	1	4	yes	—
221	#168	C₂²×C₃×C₄	1	4	yes	—
222	C₂³×C₄	—	5	1	no	—
223	C₂×M₁₆	—	5	8	no	—
224	C₂×M₁₆	—	5	4	no	—
225	C₂²×C₈	—	5	1	no	—
226	C₂²×C₈	—	5	1	no	—
227	C₂²×C₈	—	5	8	no	—
228	C₂²×C₈	—	5	4	no	—
229	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
230	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
231	#117	—	5	4	no	—
232	#117	—	5	4	no	—
233	C₂×C₄⋊C₄	—	5	2	no	—
234	C₂×C₂²⋊C₄	—	5	2	no	—
235	C₂×C₄²	—	5	1	no	—
236	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
237	#97	—	5	4	no	—
238	#97	C₂×C₃×D₅	1	4	yes	complemented
239	C₄×C₈	—	5	4	no	—
240	C₄×C₈	—	5	4	no	—
241	C₂×C₃×C₅	#405	1	4	yes	complemented
242	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#131	1	2	yes	—
244	C₃×D₅	—	2	4	no	—
245	C₂³×C₃	—	5	2	no	—
246	C₂³×C₃	—	5	4	no	—
247	C₂³×C₃	—	10	4	no	—
248	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	5	2	no	—
251	C₂×C₃×C₄	—	5	4	no	—
252	C₂×C₃×C₄	—	5	4	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	—	5	8	no	—
255	C₂×C₃×C₄	—	5	4	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
258	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₃×C₈	—	5	4	no	—
263	C₃×C₈	—	5	4	no	—
264	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
265	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
266	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
267	C₂²×C₅	C₃×#131	1	4	yes	—
268	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
269	C₂×D₅	—	2	4	no	—
270	C₂×D₅	—	2	8	no	—
271	C₂×D₅	C₂×C₃×C₄²	1	4	yes	—
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
274	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
275	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
276	Dic₅	—	2	4	no	—
277	Dic₅	C₂×C₃×C₄²	1	4	yes	—
278	C₂⁴	—	5	1	no	—
279	C₂²×C₄	—	5	1	no	—
280	C₂²×C₄	—	5	2	no	—
281	C₂²×C₄	—	5	4	no	—
282	C₂²×C₄	—	5	4	no	—
283	C₂²×C₄	—	5	2	no	—
284	C₂²×C₄	—	5	2	no	—
285	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
286	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
287	M₁₆	—	5	16	no	—
288	C₂×C₈	—	5	4	no	—
289	C₂×C₈	—	5	4	no	—
290	C₂×C₈	—	5	2	no	—
291	C₂×C₈	—	5	2	no	—
292	C₂×C₈	—	5	16	no	—
293	C₂×C₈	C₃×C₄×D₅	1	4	yes	—
294	C₂×C₈	C₃×C₄×D₅	1	4	yes	—
295	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
296	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
297	C₄⋊C₄	—	5	8	no	—
298	C₂²⋊C₄	—	5	8	no	—
299	C₄²	—	5	2	no	—
300	C₄²	—	5	2	no	—
301	C₄²	C₃×C₄×D₅	1	2	yes	—
302	C₄²	C₂²×C₃×D₅	1	2	yes	—
303	C₃×C₅	C₂×#405	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	5	4	no	—
305	C₂²×C₃	—	10	4	no	—
306	C₂²×C₃	—	10	8	no	—
307	C₂²×C₃	C₄²×D₅	1	2	yes	—
308	C₂²×C₃	#4053	1	4	yes	—
309	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	5	4	no	—
312	C₃×C₄	—	10	4	no	—
313	C₃×C₄	C₄²×D₅	1	2	yes	—
314	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
315	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
316	C₂×C₅	C₃×#405	1	4	yes	complemented
317	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
318	C₂×C₅	C₂×C₃×#131	1	2	yes	—
319	D₅	—	2	4	no	—
320	C₂³	—	5	2	no	—
321	C₂³	—	5	4	no	—
322	C₂³	—	10	4	no	—
323	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	5	2	no	—
326	C₂×C₄	—	5	4	no	—
327	C₂×C₄	—	5	4	no	—
328	C₂×C₄	—	5	4	no	—
329	C₂×C₄	—	5	8	no	—
330	C₂×C₄	—	5	4	no	—
331	C₂×C₄	—	10	4	no	—
332	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
333	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
335	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
336	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
337	C₈	—	5	4	no	—
338	C₈	—	5	4	no	—
339	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
340	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
341	C₂×C₃	—	10	4	no	—
342	C₂×C₃	#64997	1	4	yes	direct product factor
343	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
344	C₂×C₃	C₂×#4053	1	2	yes	—
345	C₅	C₂×C₃×#405	1	1	yes	characteristic, complemented, Sylow
346	C₂²	—	5	4	no	—
347	C₂²	—	10	8	no	—
348	C₂²	—	10	4	no	—
349	C₂²	C₃×C₄²×D₅	1	2	yes	—
350	C₂²	C₃×#4053	1	4	yes	—
351	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	5	4	no	—
354	C₄	—	10	4	no	—
355	C₄	C₃×C₄²×D₅	1	2	yes	—
356	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
357	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
358	C₃	C₂×#64997	1	1	yes	characteristic, direct product factor, Sylow
359	C₂	—	10	4	no	—
360	C₂	C₃×#64997	1	4	yes	direct product factor
361	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
362	C₂	C₂×C₃×#4053	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₂×C₃×#405
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×C₅×#97	C₂	semidirect
5. C₂×C₃×#3947	C₂	semidirect
6. C₂×C₃×C₈×Dic₅	C₂	semidirect
7. C₂×C₃×C₄×#168	C₂	semidirect
8. C₃×#64997	C₂	direct (N × H)
9. C₂×#64997	C₃	direct (N × H)
19. C₂×C₃×#676	C₄	semidirect
21. C₂×C₃×C₈×D₅	C₄	semidirect
25. C₃×C₅×#97	C₂²	semidirect
26. C₃×#3947	C₂²	semidirect
27. C₃×C₈×Dic₅	C₂²	semidirect
28. C₃×C₄×#168	C₂²	semidirect
33. C₂×C₅×#97	C₂×C₃	semidirect
34. C₂×#3947	C₂×C₃	semidirect
35. C₂×C₈×Dic₅	C₂×C₃	semidirect
36. C₂×C₄×#168	C₂×C₃	semidirect
37. #64997	C₂×C₃	direct (N × H)
61. C₃×#676	C₂×C₄	semidirect
62. C₃×C₈×D₅	C₂×C₄	semidirect
68. C₂×C₃×#97	D₅	semidirect
80. C₂×#676	C₃×C₄	semidirect
82. C₂×C₈×D₅	C₃×C₄	semidirect
86. C₅×#97	C₂²×C₃	semidirect
87. #3947	C₂²×C₃	semidirect
88. C₈×Dic₅	C₂²×C₃	semidirect
89. C₄×#168	C₂²×C₃	semidirect
128. C₃×#97	C₂×D₅	semidirect
154. #676	C₂×C₃×C₄	semidirect
155. C₈×D₅	C₂×C₃×C₄	semidirect
161. C₂×#97	C₃×D₅	semidirect
238. #97	C₂×C₃×D₅	semidirect
241. C₂×C₃×C₅	#405	semidirect
303. C₃×C₅	C₂×#405	semidirect
316. C₂×C₅	C₃×#405	semidirect
342. C₂×C₃	#64997	direct (N × H)
345. C₅	C₂×C₃×#405	semidirect
358. C₃	C₂×#64997	direct (N × H)
360. C₂	C₃×#64997	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×#676	2
C₂²×C₃×C₈×D₅	2
C₂×C₃×#4018	2
C₂×C₃×C₅×#97	2
C₂×C₃×#3947	2
C₂×C₃×C₈×Dic₅	2
C₂×C₃×C₄×#168	2
C₃×#64997	2
C₂×#64997	3
C₂×C₃×#405	5

Subgroups — C2×C3×#64997 #14411304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64997 #14411304