Subgroups — C₃×#10615830 #14412630

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₃×#66161	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	3	yes	maximal, complemented
5	C₃×#65521	C₂	1	3	yes	maximal, complemented
6	C₃×#65504	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#3964	C₂	1	3	yes	maximal, complemented
8	#10615830	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
10	C₃×C₅×H(5,𝔽₂)	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×#41	—	2	1	no	—
12	C₂×C₃×C₅×#41	C₂²	1	3	yes	—
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	—	2	3	no	—
15	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
16	C₃×#4094	—	2	4	no	—
17	C₃×Q₈×Dic₅	—	2	1	no	—
18	C₃×D₄×Dic₅	—	2	3	no	—
19	C₃×#4072	C₂²	1	3	yes	complemented
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	complemented
21	C₂×C₃×#681	C₂²	1	3	yes	complemented
22	C₂²×C₃×#168	C₂²	1	3	yes	complemented
23	C₃×#3967	C₂²	1	3	yes	complemented
24	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
25	C₃×#3964	C₂²	1	3	yes	complemented
26	C₃×#3964	C₂²	1	6	yes	complemented
27	C₃×#3964	C₂²	1	3	yes	complemented
28	C₃×#2897	—	5	1	no	maximal, Hall
29	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
30	#66161	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
32	#65522	C₂×C₃	1	3	yes	complemented
33	#65521	C₂×C₃	1	3	yes	complemented
34	#65504	C₂×C₃	1	3	yes	complemented
35	C₂×#3964	C₂×C₃	1	3	yes	complemented
36	C₂⁴×C₃×C₅	—	2	3	no	—
37	C₃×C₅×#41	—	2	8	no	—
38	C₃×C₅×#41	—	2	6	no	—
39	C₃×C₅×#41	C₂×C₄	1	4	yes	—
40	C₃×C₅×#41	C₂×C₄	1	12	yes	complemented
41	C₃×C₅×#41	D₄	1	4	yes	—
42	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×D₄	—	2	3	no	—
45	C₂×C₃×C₅×D₄	—	2	24	no	—
46	C₂×C₃×C₅×D₄	—	2	3	no	—
47	C₂×C₃×C₅×D₄	—	2	6	no	—
48	C₂×C₃×C₅×D₄	C₂×C₄	1	12	yes	complemented
49	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
50	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
51	C₂²×C₃×C₄×C₅	—	2	3	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
53	C₂²×C₃×Dic₅	—	2	3	no	—
54	C₃×C₂²⋊Dic₅	—	2	3	no	—
55	C₃×C₄⋊Dic₅	—	2	3	no	—
56	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
57	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
58	C₃×C₄×Dic₅	—	2	3	no	—
59	C₃×#681	—	2	6	no	—
60	C₂×C₃×#168	—	2	6	no	—
61	C₂×C₃×#168	C₂³	1	1	yes	characteristic
62	C₂×C₃×#168	C₂³	1	3	yes	—
63	C₂×C₃×H(5,𝔽₂)	D₅	1	1	yes	characteristic
64	C₂×C₃×#131	—	5	1	no	—
65	C₃×#520	—	5	1	no	—
66	C₃×#418	—	5	3	no	—
67	C₃×#417	—	5	3	no	—
68	C₃×#416	—	5	3	no	—
69	C₂×C₃×#102	—	5	3	no	—
70	C₅×H(5,𝔽₂)	—	2	4	no	—
71	C₅×H(5,𝔽₂)	C₃×C₄	1	8	yes	complemented
72	C₂×C₅×#41	—	2	1	no	—
73	C₂×C₅×#41	C₂²×C₃	1	3	yes	—
74	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×D₄	—	2	3	no	—
76	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
77	#4094	—	2	4	no	—
78	Q₈×Dic₅	—	2	1	no	—
79	D₄×Dic₅	—	2	3	no	—
80	#4072	C₂²×C₃	1	3	yes	complemented
81	C₂×C₄⋊Dic₅	C₂²×C₃	1	3	yes	complemented
82	C₂×#681	C₂²×C₃	1	3	yes	complemented
83	C₂²×#168	C₂²×C₃	1	3	yes	complemented
84	#3967	C₂²×C₃	1	3	yes	complemented
85	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
86	#3964	C₂²×C₃	1	3	yes	complemented
87	#3964	C₂²×C₃	1	6	yes	complemented
88	#3964	C₂²×C₃	1	3	yes	complemented
89	#2897	—	5	1	no	Sylow
90	C₂³×C₃×C₅	—	2	3	no	—
91	C₂³×C₃×C₅	—	2	12	no	—
92	C₂³×C₃×C₅	—	8	3	no	—
93	C₂³×C₃×C₅	—	8	3	no	—
94	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
97	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
98	C₃×C₅×D₄	—	2	12	no	—
99	C₃×C₅×D₄	—	2	12	no	—
100	C₃×C₅×D₄	—	2	3	no	—
101	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
102	C₃×C₅×D₄	C₂²×C₄	1	6	yes	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	12	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×Dic₅	—	2	1	no	—
110	C₂×C₃×Dic₅	—	2	3	no	—
111	C₂×C₃×Dic₅	—	8	3	no	—
112	C₃×#168	—	2	1	no	—
113	C₃×#168	—	2	3	no	—
114	C₃×H(5,𝔽₂)	—	2	4	no	—
115	C₃×H(5,𝔽₂)	Dic₅	1	8	yes	complemented
116	C₂×C₃×#41	—	2	1	no	—
117	C₂×C₃×#41	C₂×D₅	1	3	yes	—
118	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
119	C₂²×C₃×D₄	—	2	3	no	—
120	C₂²×C₃×D₄	C₂×D₅	1	3	yes	—
121	C₃×#131	—	10	4	no	—
122	C₂×C₃×M₁₆	—	5	3	no	—
123	C₂²×C₃×C₈	—	5	3	no	—
124	C₃×C₄×Q₈	—	10	1	no	—
125	C₃×C₄×D₄	—	10	3	no	—
126	C₃×#117	—	5	3	no	—
127	C₂×C₃×C₄⋊C₄	—	5	3	no	—
128	C₃×#103	—	5	1	no	—
129	C₃×#103	—	5	3	no	—
130	C₃×#102	—	5	3	no	—
131	C₃×#102	—	5	6	no	—
132	C₃×#102	—	5	3	no	—
133	C₂⁴×C₅	—	2	3	no	—
134	C₅×#41	—	2	8	no	—
135	C₅×#41	—	2	6	no	—
136	C₅×#41	C₂×C₃×C₄	1	4	yes	—
137	C₅×#41	C₂×C₃×C₄	1	12	yes	complemented
138	C₅×#41	C₃×D₄	1	4	yes	—
139	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
140	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
141	C₂×C₅×D₄	—	2	3	no	—
142	C₂×C₅×D₄	—	2	24	no	—
143	C₂×C₅×D₄	—	2	3	no	—
144	C₂×C₅×D₄	—	2	6	no	—
145	C₂×C₅×D₄	C₂×C₃×C₄	1	12	yes	complemented
146	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
147	C₂×C₅×D₄	C₂³×C₃	1	3	yes	—
148	C₂²×C₄×C₅	—	2	3	no	—
149	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
150	C₂²×Dic₅	—	2	3	no	—
151	C₂²⋊Dic₅	—	2	3	no	—
152	C₄⋊Dic₅	—	2	3	no	—
153	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
154	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
155	C₄×Dic₅	—	2	3	no	—
156	#681	—	2	6	no	—
157	C₂×#168	—	2	6	no	—
158	C₂×#168	C₂³×C₃	1	1	yes	characteristic
159	C₂×#168	C₂³×C₃	1	3	yes	—
160	C₂×H(5,𝔽₂)	C₃×D₅	1	1	yes	characteristic
161	C₂×#131	—	5	1	no	—
162	#520	—	5	1	no	—
163	#418	—	5	3	no	—
164	#417	—	5	3	no	—
165	#416	—	5	3	no	—
166	C₂×#102	—	5	3	no	—
167	C₂²×C₃×C₅	—	2	3	no	—
168	C₂²×C₃×C₅	—	2	3	no	—
169	C₂²×C₃×C₅	—	2	6	no	—
170	C₂²×C₃×C₅	—	4	3	no	—
171	C₂²×C₃×C₅	—	4	3	no	—
172	C₂²×C₃×C₅	—	8	12	no	—
173	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
174	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
177	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₃×Dic₅	—	4	3	no	—
180	C₃×Dic₅	—	4	1	no	—
181	C₂⁴×C₃	—	2	3	no	—
182	C₃×#41	—	2	8	no	—
183	C₃×#41	—	2	6	no	—
184	C₃×#41	C₂×Dic₅	1	4	yes	—
185	C₃×#41	C₂×Dic₅	1	12	yes	complemented
186	C₃×#41	C₂²⋊D₅	1	4	yes	—
187	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
188	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
189	C₂×C₃×D₄	—	2	3	no	—
190	C₂×C₃×D₄	—	2	24	no	—
191	C₂×C₃×D₄	—	2	3	no	—
192	C₂×C₃×D₄	—	2	6	no	—
193	C₂×C₃×D₄	C₂×Dic₅	1	12	yes	complemented
194	C₂×C₃×D₄	C₂²⋊D₅	1	3	yes	—
195	C₂×C₃×D₄	C₂²×D₅	1	3	yes	—
196	C₂²×C₃×C₄	—	2	3	no	—
197	C₂²×C₃×C₄	—	10	3	no	—
198	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
199	C₃×M₁₆	—	10	6	no	—
200	C₂×C₃×C₈	—	5	1	no	—
201	C₂×C₃×C₈	—	5	3	no	—
202	C₂×C₃×C₈	—	10	6	no	—
203	C₃×C₄⋊C₄	—	5	3	no	—
204	C₃×C₄⋊C₄	—	5	1	no	—
205	C₃×C₄⋊C₄	—	10	3	no	—
206	C₃×C₂²⋊C₄	—	10	3	no	—
207	C₃×C₄²	—	10	3	no	—
208	C₂³×C₅	—	2	3	no	—
209	C₂³×C₅	—	2	12	no	—
210	C₂³×C₅	—	8	3	no	—
211	C₂³×C₅	—	8	3	no	—
212	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
213	C₅×Q₈	—	2	1	no	—
214	C₅×Q₈	C₃×C₂²⋊C₄	1	4	yes	—
215	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
216	C₅×D₄	—	2	12	no	—
217	C₅×D₄	—	2	12	no	—
218	C₅×D₄	—	2	3	no	—
219	C₅×D₄	C₃×C₂²⋊C₄	1	12	yes	—
220	C₅×D₄	C₂²×C₃×C₄	1	6	yes	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	12	no	—
223	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	—
224	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
225	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
226	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₂×Dic₅	—	2	1	no	—
228	C₂×Dic₅	—	2	3	no	—
229	C₂×Dic₅	—	8	3	no	—
230	#168	—	2	1	no	—
231	#168	—	2	3	no	—
232	H(5,𝔽₂)	—	2	4	no	—
233	H(5,𝔽₂)	C₃×Dic₅	1	8	yes	complemented
234	C₂×#41	—	2	1	no	—
235	C₂×#41	C₂×C₃×D₅	1	3	yes	—
236	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
237	C₂²×D₄	—	2	3	no	—
238	C₂²×D₄	C₂×C₃×D₅	1	3	yes	—
239	#131	—	10	4	no	—
240	C₂×M₁₆	—	5	3	no	—
241	C₂²×C₈	—	5	3	no	—
242	C₄×Q₈	—	10	1	no	—
243	C₄×D₄	—	10	3	no	—
244	#117	—	5	3	no	—
245	C₂×C₄⋊C₄	—	5	3	no	—
246	#103	—	5	1	no	—
247	#103	—	5	3	no	—
248	#102	—	5	3	no	—
249	#102	—	5	6	no	—
250	#102	—	5	3	no	—
251	C₂×C₃×C₅	—	2	6	no	—
252	C₂×C₃×C₅	—	4	6	no	—
253	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₅	#576	1	1	yes	characteristic
255	C₂×C₃×C₅	#577	1	1	yes	characteristic
256	C₂³×C₃	—	2	3	no	—
257	C₂³×C₃	—	2	12	no	—
258	C₂³×C₃	—	8	3	no	—
259	C₂³×C₃	—	8	3	no	—
260	C₂³×C₃	C₂×C₂²⋊D₅	1	3	yes	—
261	C₃×Q₈	—	2	1	no	—
262	C₃×Q₈	C₂²⋊Dic₅	1	4	yes	—
263	C₃×Q₈	C₂²×Dic₅	1	2	yes	—
264	C₃×D₄	—	2	12	no	—
265	C₃×D₄	—	2	12	no	—
266	C₃×D₄	—	2	3	no	—
267	C₃×D₄	C₂²⋊Dic₅	1	12	yes	—
268	C₃×D₄	C₂²×Dic₅	1	6	yes	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	12	no	—
271	C₂×C₃×C₄	—	10	1	no	—
272	C₂×C₃×C₄	—	10	3	no	—
273	C₂×C₃×C₄	—	40	3	no	—
274	C₂×C₃×C₄	C₂²×Dic₅	1	6	yes	—
275	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
276	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	6	yes	—
277	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
278	C₃×C₈	—	10	1	no	—
279	C₃×C₈	—	10	3	no	—
280	C₂²×C₅	—	2	3	no	—
281	C₂²×C₅	—	2	3	no	—
282	C₂²×C₅	—	2	6	no	—
283	C₂²×C₅	—	4	3	no	—
284	C₂²×C₅	—	4	3	no	—
285	C₂²×C₅	—	8	12	no	—
286	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
287	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
290	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
291	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
292	Dic₅	—	4	3	no	—
293	Dic₅	—	4	1	no	—
294	C₂⁴	—	2	3	no	—
295	#41	—	2	8	no	—
296	#41	—	2	6	no	—
297	#41	C₂×C₃×Dic₅	1	4	yes	—
298	#41	C₂×C₃×Dic₅	1	12	yes	complemented
299	#41	C₃×C₂²⋊D₅	1	4	yes	—
300	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
301	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
302	C₂×D₄	—	2	3	no	—
303	C₂×D₄	—	2	24	no	—
304	C₂×D₄	—	2	3	no	—
305	C₂×D₄	—	2	6	no	—
306	C₂×D₄	C₂×C₃×Dic₅	1	12	yes	complemented
307	C₂×D₄	C₃×C₂²⋊D₅	1	3	yes	—
308	C₂×D₄	C₂²×C₃×D₅	1	3	yes	—
309	C₂²×C₄	—	2	3	no	—
310	C₂²×C₄	—	10	3	no	—
311	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
312	M₁₆	—	10	6	no	—
313	C₂×C₈	—	5	1	no	—
314	C₂×C₈	—	5	3	no	—
315	C₂×C₈	—	10	6	no	—
316	C₄⋊C₄	—	5	3	no	—
317	C₄⋊C₄	—	5	1	no	—
318	C₄⋊C₄	—	10	3	no	—
319	C₂²⋊C₄	—	10	3	no	—
320	C₄²	—	10	3	no	—
321	C₃×C₅	#2897	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	—	2	3	no	—
323	C₂²×C₃	—	2	3	no	—
324	C₂²×C₃	—	2	6	no	—
325	C₂²×C₃	—	4	3	no	—
326	C₂²×C₃	—	4	3	no	—
327	C₂²×C₃	—	8	12	no	—
328	C₂²×C₃	C₂×C₂²⋊Dic₅	1	6	yes	—
329	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	20	3	no	—
332	C₃×C₄	—	20	1	no	—
333	C₃×C₄	C₂×C₂²⋊Dic₅	1	6	yes	—
334	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
335	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
336	C₂×C₅	—	2	6	no	—
337	C₂×C₅	—	4	6	no	—
338	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×C₅	C₃×#576	1	1	yes	characteristic
340	C₂×C₅	C₃×#577	1	1	yes	characteristic
341	C₂³	—	2	3	no	—
342	C₂³	—	2	12	no	—
343	C₂³	—	8	3	no	—
344	C₂³	—	8	3	no	—
345	C₂³	C₂×C₃×C₂²⋊D₅	1	3	yes	—
346	Q₈	—	2	1	no	—
347	Q₈	C₃×C₂²⋊Dic₅	1	4	yes	—
348	Q₈	C₂²×C₃×Dic₅	1	2	yes	—
349	D₄	—	2	12	no	—
350	D₄	—	2	12	no	—
351	D₄	—	2	3	no	—
352	D₄	C₃×C₂²⋊Dic₅	1	12	yes	—
353	D₄	C₂²×C₃×Dic₅	1	6	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	12	no	—
356	C₂×C₄	—	10	1	no	—
357	C₂×C₄	—	10	3	no	—
358	C₂×C₄	—	40	3	no	—
359	C₂×C₄	C₂²×C₃×Dic₅	1	6	yes	—
360	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
361	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	6	yes	—
362	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
363	C₈	—	10	1	no	—
364	C₈	—	10	3	no	—
365	C₂×C₃	—	2	6	no	—
366	C₂×C₃	—	4	6	no	—
367	C₂×C₃	#66169	1	1	yes	characteristic
368	C₂×C₃	#66170	1	1	yes	characteristic
369	C₂×C₃	C₂²×C₂²⋊Dic₅	1	1	yes	characteristic
370	C₅	C₃×#2897	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	3	no	—
372	C₂²	—	2	3	no	—
373	C₂²	—	2	6	no	—
374	C₂²	—	4	3	no	—
375	C₂²	—	4	3	no	—
376	C₂²	—	8	12	no	—
377	C₂²	C₂×C₃×C₂²⋊Dic₅	1	6	yes	—
378	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	20	3	no	—
381	C₄	—	20	1	no	—
382	C₄	C₂×C₃×C₂²⋊Dic₅	1	6	yes	—
383	C₄	C₂³×C₃×Dic₅	1	1	yes	characteristic
384	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
385	C₃	#10615830	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	2	6	no	—
387	C₂	—	4	6	no	—
388	C₂	C₃×#66169	1	1	yes	characteristic
389	C₂	C₃×#66170	1	1	yes	characteristic
390	C₂	C₂²×C₃×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×H(5,𝔽₂)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×H(5,𝔽₂)	D₅
hypocenter	C₅	C₃×#2897
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
2. C₃×#66161	C₂	semidirect
3. C₂×C₃×#4094	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×#65521	C₂	semidirect
6. C₃×#65504	C₂	semidirect
7. C₂×C₃×#3964	C₂	semidirect
8. #10615830	C₃	direct (N × H)
10. C₃×C₅×H(5,𝔽₂)	C₄	semidirect
19. C₃×#4072	C₂²	semidirect
20. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
21. C₂×C₃×#681	C₂²	semidirect
22. C₂²×C₃×#168	C₂²	semidirect
23. C₃×#3967	C₂²	semidirect
24. C₃×#3967	C₂²	semidirect
25. C₃×#3964	C₂²	semidirect
26. C₃×#3964	C₂²	semidirect
27. C₃×#3964	C₂²	semidirect
30. #66161	C₂×C₃	semidirect
31. C₂×#4094	C₂×C₃	semidirect
32. #65522	C₂×C₃	semidirect
33. #65521	C₂×C₃	semidirect
34. #65504	C₂×C₃	semidirect
35. C₂×#3964	C₂×C₃	semidirect
40. C₃×C₅×#41	C₂×C₄	semidirect
48. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
71. C₅×H(5,𝔽₂)	C₃×C₄	semidirect
80. #4072	C₂²×C₃	semidirect
81. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
82. C₂×#681	C₂²×C₃	semidirect
83. C₂²×#168	C₂²×C₃	semidirect
84. #3967	C₂²×C₃	semidirect
85. #3967	C₂²×C₃	semidirect
86. #3964	C₂²×C₃	semidirect
87. #3964	C₂²×C₃	semidirect
88. #3964	C₂²×C₃	semidirect
115. C₃×H(5,𝔽₂)	Dic₅	semidirect
137. C₅×#41	C₂×C₃×C₄	semidirect
145. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
185. C₃×#41	C₂×Dic₅	semidirect
193. C₂×C₃×D₄	C₂×Dic₅	semidirect
233. H(5,𝔽₂)	C₃×Dic₅	semidirect
298. #41	C₂×C₃×Dic₅	semidirect
306. C₂×D₄	C₂×C₃×Dic₅	semidirect
321. C₃×C₅	#2897	semidirect
370. C₅	C₃×#2897	semidirect
385. C₃	#10615830	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×C₅×H(5,𝔽₂)	2
C₃×#66161	2
C₂×C₃×#4094	2
C₃×#65522	2
C₃×#65521	2
C₃×#65504	2
C₂×C₃×#3964	2
#10615830	3
C₃×#2897	5

Subgroups — C3×#10615830 #14412630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615830 #14412630