Subgroups — C₃×#10614000 #14322429

Order 1920.

2208 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65277	C₂	1	4	yes	maximal, complemented
5	C₃×#65244	C₂	1	4	yes	maximal, complemented
6	C₃×#65228	C₂	1	4	yes	maximal, complemented
7	#10614000	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₂₀	—	2	4	no	—
11	C₂²×C₃×D₂₀	—	2	4	no	—
12	C₂²×C₃×D₂₀	C₄	1	8	yes	complemented
13	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
15	C₃×C₅×#117	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
19	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
20	C₂×C₃×#685	C₂²	1	16	yes	complemented
21	C₃×#4072	—	2	4	no	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
24	C₃×#2309	—	5	1	no	maximal, Hall
25	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic
26	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
28	#65277	C₂×C₃	1	4	yes	complemented
29	#65244	C₂×C₃	1	4	yes	complemented
30	#65228	C₂×C₃	1	4	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂³×C₃×D₅	—	2	4	no	—
33	C₂³×C₃×D₅	—	2	4	no	—
34	C₂³×C₃×D₅	—	4	8	no	—
35	C₂³×C₃×D₅	C₂×C₄	1	8	yes	—
36	C₂³×C₃×D₅	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
44	C₂×C₃×D₂₀	—	2	32	no	—
45	C₂×C₃×D₂₀	—	2	4	no	—
46	C₂×C₃×D₂₀	—	2	4	no	—
47	C₂×C₃×D₂₀	—	2	4	no	—
48	C₂×C₃×D₂₀	—	2	4	no	—
49	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	—
50	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₃×C₂²⋊Dic₅	—	2	4	no	—
55	C₃×#685	—	4	16	no	—
56	C₃×C₄⋊Dic₅	—	2	4	no	—
57	C₃×C₄×Dic₅	—	2	4	no	—
58	C₂³×C₃×D₄	—	5	1	no	—
59	C₂×C₃×#117	—	5	1	no	—
60	C₂×C₃×#117	D₅	1	1	yes	characteristic, complemented
61	C₃×#390	—	5	4	no	—
62	C₃×#390	—	5	4	no	—
63	C₃×#379	—	5	4	no	—
64	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
65	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
66	C₂²×D₂₀	—	2	4	no	—
67	C₂²×D₂₀	—	2	4	no	—
68	C₂²×D₂₀	C₃×C₄	1	8	yes	complemented
69	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
70	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
71	C₅×#117	—	2	4	no	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
73	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
75	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
76	C₂×#685	C₂²×C₃	1	16	yes	complemented
77	#4072	—	2	4	no	—
78	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
79	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
80	#2309	—	5	1	no	Sylow
81	C₂³×C₃×C₅	—	2	4	no	—
82	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₂²×C₃×D₅	—	2	16	no	—
87	C₂²×C₃×D₅	—	2	4	no	—
88	C₂²×C₃×D₅	—	2	4	no	—
89	C₂²×C₃×D₅	—	2	16	no	—
90	C₂²×C₃×D₅	—	4	16	no	—
91	C₂²×C₃×D₅	—	4	16	no	—
92	C₂²×C₃×D₅	—	4	16	no	—
93	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×Dic₅	—	2	4	no	—
104	C₂×C₃×Dic₅	—	2	8	no	—
105	C₃×D₂₀	—	2	16	no	—
106	C₃×D₂₀	—	2	16	no	—
107	C₂⁵×C₃	—	5	2	no	—
108	C₂²×C₃×D₄	—	5	8	no	—
109	C₂²×C₃×D₄	—	5	2	no	—
110	C₂²×C₃×D₄	—	5	2	no	—
111	C₂²×C₃×D₄	—	10	4	no	—
112	C₂²×C₃×D₄	—	10	4	no	—
113	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
114	C₃×#117	—	2	4	no	—
115	C₃×#117	—	10	4	no	—
116	C₂×C₃×C₄⋊C₄	—	5	2	no	—
117	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
118	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
119	C₂×C₃×C₂²⋊C₄	—	5	16	no	—
120	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
121	C₂×C₃×C₄²	—	5	2	no	—
122	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
123	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂³×D₅	—	2	4	no	—
125	C₂³×D₅	—	2	4	no	—
126	C₂³×D₅	—	4	8	no	—
127	C₂³×D₅	C₂×C₃×C₄	1	8	yes	—
128	C₂³×D₅	C₂³×C₃	1	4	yes	—
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
130	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
131	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
136	C₂×D₂₀	—	2	32	no	—
137	C₂×D₂₀	—	2	4	no	—
138	C₂×D₂₀	—	2	4	no	—
139	C₂×D₂₀	—	2	4	no	—
140	C₂×D₂₀	—	2	4	no	—
141	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	—
142	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	—
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₂²⋊C₄	—	2	4	no	—
145	C₄²×C₅	—	2	4	no	—
146	C₂²⋊Dic₅	—	2	4	no	—
147	#685	—	4	16	no	—
148	C₄⋊Dic₅	—	2	4	no	—
149	C₄×Dic₅	—	2	4	no	—
150	C₂³×D₄	—	5	1	no	—
151	C₂×#117	—	5	1	no	—
152	C₂×#117	C₃×D₅	1	1	yes	characteristic, complemented
153	#390	—	5	4	no	—
154	#390	—	5	4	no	—
155	#379	—	5	4	no	—
156	C₂²×C₃×C₅	—	2	4	no	—
157	C₂²×C₃×C₅	—	2	4	no	—
158	C₂²×C₃×C₅	—	2	4	no	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
164	C₂×C₃×D₅	—	2	8	no	—
165	C₂×C₃×D₅	—	2	16	no	—
166	C₂×C₃×D₅	—	4	32	no	—
167	C₂×C₃×D₅	—	4	8	no	—
168	C₂×C₃×D₅	—	4	8	no	—
169	C₃×C₄×C₅	—	4	4	no	—
170	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
171	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
172	C₃×Dic₅	—	4	4	no	—
173	C₂⁴×C₃	—	5	4	no	—
174	C₂⁴×C₃	—	5	8	no	—
175	C₂⁴×C₃	—	10	4	no	—
176	C₂⁴×C₃	—	10	4	no	—
177	C₂⁴×C₃	—	20	8	no	—
178	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
179	C₂×C₃×D₄	—	5	8	no	—
180	C₂×C₃×D₄	—	5	8	no	—
181	C₂×C₃×D₄	—	10	32	no	—
182	C₂×C₃×D₄	—	10	4	no	—
183	C₂×C₃×D₄	—	10	4	no	—
184	C₂×C₃×D₄	—	10	4	no	—
185	C₂×C₃×D₄	—	10	4	no	—
186	C₂²×C₃×C₄	—	5	4	no	—
187	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
188	C₂²×C₃×C₄	D₂₀	1	4	yes	—
189	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
190	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
193	C₃×C₄⋊C₄	—	2	4	no	—
194	C₃×C₄⋊C₄	—	10	4	no	—
195	C₃×C₂²⋊C₄	—	2	4	no	—
196	C₃×C₂²⋊C₄	—	10	4	no	—
197	C₃×C₂²⋊C₄	—	20	16	no	—
198	C₃×C₄²	—	2	4	no	—
199	C₃×C₄²	—	10	4	no	—
200	C₂³×C₅	—	2	4	no	—
201	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
202	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
203	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
204	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
205	C₂²×D₅	—	2	16	no	—
206	C₂²×D₅	—	2	4	no	—
207	C₂²×D₅	—	2	4	no	—
208	C₂²×D₅	—	2	16	no	—
209	C₂²×D₅	—	4	16	no	—
210	C₂²×D₅	—	4	16	no	—
211	C₂²×D₅	—	4	16	no	—
212	C₂²×D₅	C₂²×C₃×C₄	1	8	yes	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	8	no	—
215	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	16	yes	complemented
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
222	C₂×Dic₅	—	2	4	no	—
223	C₂×Dic₅	—	2	8	no	—
224	D₂₀	—	2	16	no	—
225	D₂₀	—	2	16	no	—
226	C₂⁵	—	5	2	no	—
227	C₂²×D₄	—	5	8	no	—
228	C₂²×D₄	—	5	2	no	—
229	C₂²×D₄	—	5	2	no	—
230	C₂²×D₄	—	10	4	no	—
231	C₂²×D₄	—	10	4	no	—
232	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
233	#117	—	2	4	no	—
234	#117	—	10	4	no	—
235	C₂×C₄⋊C₄	—	5	2	no	—
236	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
237	C₂×C₂²⋊C₄	—	5	2	no	—
238	C₂×C₂²⋊C₄	—	5	16	no	—
239	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
240	C₂×C₄²	—	5	2	no	—
241	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
242	C₂×C₃×C₅	—	2	4	no	—
243	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₅	#518	1	2	yes	—
245	C₂×C₃×C₅	#535	1	2	yes	—
246	C₂×C₃×C₅	#535	1	2	yes	—
247	C₃×D₅	—	4	8	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	5	8	no	—
250	C₂³×C₃	—	10	4	no	—
251	C₂³×C₃	—	10	16	no	—
252	C₂³×C₃	—	10	4	no	—
253	C₂³×C₃	—	10	16	no	—
254	C₂³×C₃	—	20	16	no	—
255	C₂³×C₃	—	20	16	no	—
256	C₂³×C₃	—	20	16	no	—
257	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
258	C₂³×C₃	C₂×D₂₀	1	2	yes	—
259	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
260	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
261	C₃×D₄	—	10	16	no	—
262	C₃×D₄	—	10	16	no	—
263	C₂×C₃×C₄	—	2	8	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	10	4	no	—
266	C₂×C₃×C₄	—	10	8	no	—
267	C₂×C₃×C₄	#685	1	16	yes	complemented
268	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
270	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
271	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
273	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
274	C₂²×C₅	—	2	4	no	—
275	C₂²×C₅	—	2	4	no	—
276	C₂²×C₅	—	2	4	no	—
277	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
278	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
279	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
280	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
282	C₂×D₅	—	2	8	no	—
283	C₂×D₅	—	2	16	no	—
284	C₂×D₅	—	4	32	no	—
285	C₂×D₅	—	4	8	no	—
286	C₂×D₅	—	4	8	no	—
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
289	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
290	Dic₅	—	4	4	no	—
291	C₂⁴	—	5	4	no	—
292	C₂⁴	—	5	8	no	—
293	C₂⁴	—	10	4	no	—
294	C₂⁴	—	10	4	no	—
295	C₂⁴	—	20	8	no	—
296	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
297	C₂×D₄	—	5	8	no	—
298	C₂×D₄	—	5	8	no	—
299	C₂×D₄	—	10	32	no	—
300	C₂×D₄	—	10	4	no	—
301	C₂×D₄	—	10	4	no	—
302	C₂×D₄	—	10	4	no	—
303	C₂×D₄	—	10	4	no	—
304	C₂²×C₄	—	5	4	no	—
305	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
306	C₂²×C₄	C₃×D₂₀	1	4	yes	—
307	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
308	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
309	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	10	4	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	10	4	no	—
315	C₂²⋊C₄	—	20	16	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	10	4	no	—
318	C₃×C₅	#2309	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	—	10	16	no	—
323	C₂²×C₃	—	10	8	no	—
324	C₂²×C₃	—	20	32	no	—
325	C₂²×C₃	—	20	8	no	—
326	C₂²×C₃	—	20	8	no	—
327	C₂²×C₃	C₂×#685	1	4	yes	—
328	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
329	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
330	C₂²×C₃	#4149	1	4	yes	—
331	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
332	C₃×C₄	—	4	4	no	—
333	C₃×C₄	—	20	4	no	—
334	C₃×C₄	C₂×#685	1	4	yes	—
335	C₃×C₄	C₂×#685	1	4	yes	—
336	C₂×C₅	—	2	4	no	—
337	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₅	C₃×#518	1	2	yes	—
339	C₂×C₅	C₃×#535	1	2	yes	—
340	C₂×C₅	C₃×#535	1	2	yes	—
341	D₅	—	4	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	5	8	no	—
344	C₂³	—	10	4	no	—
345	C₂³	—	10	16	no	—
346	C₂³	—	10	4	no	—
347	C₂³	—	10	16	no	—
348	C₂³	—	20	16	no	—
349	C₂³	—	20	16	no	—
350	C₂³	—	20	16	no	—
351	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
352	C₂³	C₂×C₃×D₂₀	1	2	yes	—
353	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
354	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
355	D₄	—	10	16	no	—
356	D₄	—	10	16	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	10	4	no	—
360	C₂×C₄	—	10	8	no	—
361	C₂×C₄	C₃×#685	1	16	yes	complemented
362	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
363	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
364	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
365	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
366	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
367	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
368	C₂×C₃	—	2	4	no	—
369	C₂×C₃	—	20	8	no	—
370	C₂×C₃	#65855	1	2	yes	—
371	C₂×C₃	#65859	1	2	yes	—
372	C₂×C₃	C₂²×#685	1	1	yes	characteristic
373	C₂×C₃	#66164	1	2	yes	—
374	C₅	C₃×#2309	1	1	yes	characteristic, complemented, Sylow
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	10	16	no	—
379	C₂²	—	10	8	no	—
380	C₂²	—	20	32	no	—
381	C₂²	—	20	8	no	—
382	C₂²	—	20	8	no	—
383	C₂²	C₂×C₃×#685	1	4	yes	—
384	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
385	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
386	C₂²	C₃×#4149	1	4	yes	—
387	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
388	C₄	—	4	4	no	—
389	C₄	—	20	4	no	—
390	C₄	C₂×C₃×#685	1	4	yes	—
391	C₄	C₂×C₃×#685	1	4	yes	—
392	C₃	#10614000	1	1	yes	characteristic, direct product factor, Sylow
393	C₂	—	2	4	no	—
394	C₂	—	20	8	no	—
395	C₂	C₃×#65855	1	2	yes	—
396	C₂	C₃×#65859	1	2	yes	—
397	C₂	C₂²×C₃×#685	1	1	yes	characteristic
398	C₂	C₃×#66164	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₂₀	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#2309
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂×C₃×#4072	C₂	semidirect
4. C₃×#65277	C₂	semidirect
5. C₃×#65244	C₂	semidirect
6. C₃×#65228	C₂	semidirect
7. #10614000	C₃	direct (N × H)
12. C₂²×C₃×D₂₀	C₄	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₂×C₃×C₄²×C₅	C₂²	semidirect
20. C₂×C₃×#685	C₂²	semidirect
22. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
23. C₂×C₃×C₄×Dic₅	C₂²	semidirect
26. C₂×C₅×#117	C₂×C₃	semidirect
27. C₂×#4072	C₂×C₃	semidirect
28. #65277	C₂×C₃	semidirect
29. #65244	C₂×C₃	semidirect
30. #65228	C₂×C₃	semidirect
60. C₂×C₃×#117	D₅	semidirect
68. C₂²×D₂₀	C₃×C₄	semidirect
72. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
74. C₂×C₄²×C₅	C₂²×C₃	semidirect
76. C₂×#685	C₂²×C₃	semidirect
78. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
79. C₂×C₄×Dic₅	C₂²×C₃	semidirect
96. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
117. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
122. C₂×C₃×C₄²	C₂×D₅	semidirect
152. C₂×#117	C₃×D₅	semidirect
215. C₂×C₄×C₅	C₃×C₂²⋊C₄	semidirect
236. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
241. C₂×C₄²	C₂×C₃×D₅	semidirect
267. C₂×C₃×C₄	#685	semidirect
318. C₃×C₅	#2309	semidirect
361. C₂×C₄	C₃×#685	semidirect
374. C₅	C₃×#2309	semidirect
392. C₃	#10614000	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×D₂₀	2
C₂×C₃×C₅×#117	2
C₂×C₃×#4072	2
C₃×#65277	2
C₃×#65244	2
C₃×#65228	2
#10614000	3
C₃×#2309	5

Subgroups — C3×#10614000 #14322429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614000 #14322429