Subgroups — C₃×C₅×#2613 #14275647

Order 1920.

2268 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#120	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#392	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#379	C₂	1	2	yes	maximal, complemented
8	C₅×#2613	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	—	2	8	no	—
11	C₂²×C₃×C₅×D₄	—	2	4	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#123	—	2	4	no	—
17	C₃×C₅×#120	—	2	8	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
24	C₃×C₅×#95	C₂²	1	4	yes	complemented
25	C₃×#2613	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₅×#120	C₂×C₃	1	2	yes	complemented
29	C₅×#394	C₂×C₃	1	4	yes	complemented
30	C₅×#392	C₂×C₃	1	4	yes	complemented
31	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#379	C₂×C₃	1	2	yes	complemented
33	C₂⁴×C₃×C₅	—	2	4	no	—
34	C₂⁴×C₃×C₅	—	2	4	no	—
35	C₂⁴×C₃×C₅	—	4	8	no	—
36	C₂⁴×C₃×C₅	D₄	1	8	yes	complemented
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
39	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	—	2	32	no	—
41	C₂×C₃×C₅×D₄	—	2	16	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	8	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	8	no	—
46	C₂×C₃×C₅×D₄	—	4	8	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
59	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂×C₃×#120	C₂×C₅	1	2	yes	complemented
62	C₃×#394	C₂×C₅	1	4	yes	complemented
63	C₃×#392	C₂×C₅	1	4	yes	complemented
64	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×#379	C₂×C₅	1	2	yes	complemented
66	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
67	C₂²×C₅×D₄	—	2	8	no	—
68	C₂²×C₅×D₄	—	2	4	no	—
69	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
70	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×#123	—	2	4	no	—
74	C₅×#120	—	2	8	no	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
76	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
81	C₅×#95	C₂²×C₃	1	4	yes	complemented
82	#2613	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	2	16	no	—
85	C₂³×C₃×C₅	—	2	4	no	—
86	C₂³×C₃×C₅	—	2	4	no	—
87	C₂³×C₃×C₅	—	2	8	no	—
88	C₂³×C₃×C₅	—	2	8	no	—
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	4	no	—
92	C₂³×C₃×C₅	—	4	16	no	—
93	C₂³×C₃×C₅	—	4	16	no	—
94	C₂³×C₃×C₅	—	4	16	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
96	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
97	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
98	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
99	C₃×C₅×D₄	—	2	32	no	—
100	C₃×C₅×D₄	—	4	16	no	—
101	C₃×C₅×D₄	—	4	4	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	8	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
112	C₂²×C₃×D₄	—	2	8	no	—
113	C₂²×C₃×D₄	—	2	4	no	—
114	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
115	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
117	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
118	C₃×#123	—	2	4	no	—
119	C₃×#120	—	2	8	no	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
121	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
124	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
125	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
126	C₃×#95	C₂²×C₅	1	4	yes	complemented
127	C₂⁴×C₅	—	2	4	no	—
128	C₂⁴×C₅	—	2	4	no	—
129	C₂⁴×C₅	—	4	8	no	—
130	C₂⁴×C₅	C₃×D₄	1	8	yes	complemented
131	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
133	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂×C₅×D₄	—	2	32	no	—
135	C₂×C₅×D₄	—	2	16	no	—
136	C₂×C₅×D₄	—	2	4	no	—
137	C₂×C₅×D₄	—	2	8	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	—	2	8	no	—
140	C₂×C₅×D₄	—	4	8	no	—
141	C₂²×C₄×C₅	—	2	4	no	—
142	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
147	C₅×C₄⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	—	2	4	no	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	2	8	no	—
151	C₅×C₂²⋊C₄	—	2	4	no	—
152	C₅×C₂²⋊C₄	—	4	8	no	—
153	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
154	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	C₂×#120	C₂×C₃×C₅	1	2	yes	complemented
156	#394	C₂×C₃×C₅	1	4	yes	complemented
157	#392	C₂×C₃×C₅	1	4	yes	complemented
158	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	#379	C₂×C₃×C₅	1	2	yes	complemented
160	C₂²×C₃×C₅	—	2	8	no	—
161	C₂²×C₃×C₅	—	2	4	no	—
162	C₂²×C₃×C₅	—	2	8	no	—
163	C₂²×C₃×C₅	—	2	8	no	—
164	C₂²×C₃×C₅	—	2	8	no	—
165	C₂²×C₃×C₅	—	4	32	no	—
166	C₂²×C₃×C₅	—	4	8	no	—
167	C₂²×C₃×C₅	—	4	8	no	—
168	C₂²×C₃×C₅	—	4	1	no	—
169	C₂²×C₃×C₅	—	4	4	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	#120	1	4	yes	—
172	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
173	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
175	C₃×C₄×C₅	—	2	4	no	—
176	C₃×C₄×C₅	—	4	1	no	—
177	C₃×C₄×C₅	—	4	4	no	—
178	C₃×C₄×C₅	—	4	2	no	—
179	C₂⁴×C₃	—	2	4	no	—
180	C₂⁴×C₃	—	2	4	no	—
181	C₂⁴×C₃	—	4	8	no	—
182	C₂⁴×C₃	C₅×D₄	1	8	yes	complemented
183	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
184	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
185	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
186	C₂×C₃×D₄	—	2	32	no	—
187	C₂×C₃×D₄	—	2	16	no	—
188	C₂×C₃×D₄	—	2	4	no	—
189	C₂×C₃×D₄	—	2	8	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	8	no	—
192	C₂×C₃×D₄	—	4	8	no	—
193	C₂²×C₃×C₄	—	2	4	no	—
194	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
195	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
199	C₃×C₄⋊C₄	—	2	4	no	—
200	C₃×C₂²⋊C₄	—	2	4	no	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	2	8	no	—
203	C₃×C₂²⋊C₄	—	2	4	no	—
204	C₃×C₂²⋊C₄	—	4	8	no	—
205	C₂³×C₅	—	2	4	no	—
206	C₂³×C₅	—	2	16	no	—
207	C₂³×C₅	—	2	4	no	—
208	C₂³×C₅	—	2	4	no	—
209	C₂³×C₅	—	2	8	no	—
210	C₂³×C₅	—	2	8	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	—	2	2	no	—
213	C₂³×C₅	—	2	4	no	—
214	C₂³×C₅	—	4	16	no	—
215	C₂³×C₅	—	4	16	no	—
216	C₂³×C₅	—	4	16	no	—
217	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
218	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
219	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
220	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
221	C₅×D₄	—	2	32	no	—
222	C₅×D₄	—	4	16	no	—
223	C₅×D₄	—	4	4	no	—
224	C₂×C₄×C₅	—	2	8	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	4	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	8	no	—
232	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
233	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
238	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
239	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
240	#123	—	2	4	no	—
241	#120	—	2	8	no	—
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
243	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
246	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
247	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
248	#95	C₂²×C₃×C₅	1	4	yes	complemented
249	C₂×C₃×C₅	—	2	4	no	—
250	C₂×C₃×C₅	—	4	8	no	—
251	C₂×C₃×C₅	—	8	1	no	—
252	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
253	C₂×C₃×C₅	#534	1	4	yes	—
254	C₂×C₃×C₅	#535	1	2	yes	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	16	no	—
257	C₂³×C₃	—	2	4	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	—	2	8	no	—
260	C₂³×C₃	—	2	8	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	4	no	—
264	C₂³×C₃	—	4	16	no	—
265	C₂³×C₃	—	4	16	no	—
266	C₂³×C₃	—	4	16	no	—
267	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
268	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
269	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
270	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
271	C₃×D₄	—	2	32	no	—
272	C₃×D₄	—	4	16	no	—
273	C₃×D₄	—	4	4	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	8	no	—
282	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
283	C₂²×C₅	—	2	8	no	—
284	C₂²×C₅	—	2	4	no	—
285	C₂²×C₅	—	2	8	no	—
286	C₂²×C₅	—	2	8	no	—
287	C₂²×C₅	—	2	8	no	—
288	C₂²×C₅	—	4	32	no	—
289	C₂²×C₅	—	4	8	no	—
290	C₂²×C₅	—	4	8	no	—
291	C₂²×C₅	—	4	1	no	—
292	C₂²×C₅	—	4	4	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	C₃×#120	1	4	yes	—
295	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
296	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
298	C₄×C₅	—	2	4	no	—
299	C₄×C₅	—	4	1	no	—
300	C₄×C₅	—	4	4	no	—
301	C₄×C₅	—	4	2	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	4	8	no	—
305	C₂⁴	C₃×C₅×D₄	1	8	yes	complemented
306	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
307	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
308	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
309	C₂×D₄	—	2	32	no	—
310	C₂×D₄	—	2	16	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	4	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
318	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
319	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
320	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	8	no	—
328	C₃×C₅	#2613	1	1	yes	characteristic, direct product factor, Hall
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	8	no	—
332	C₂²×C₃	—	2	8	no	—
333	C₂²×C₃	—	2	8	no	—
334	C₂²×C₃	—	4	32	no	—
335	C₂²×C₃	—	4	8	no	—
336	C₂²×C₃	—	4	8	no	—
337	C₂²×C₃	—	4	1	no	—
338	C₂²×C₃	—	4	4	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	C₅×#120	1	4	yes	—
341	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
342	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
343	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	4	1	no	—
346	C₃×C₄	—	4	4	no	—
347	C₃×C₄	—	4	2	no	—
348	C₂×C₅	—	2	4	no	—
349	C₂×C₅	—	4	8	no	—
350	C₂×C₅	—	8	1	no	—
351	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
352	C₂×C₅	C₃×#534	1	4	yes	—
353	C₂×C₅	C₃×#535	1	2	yes	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	16	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	4	16	no	—
364	C₂³	—	4	16	no	—
365	C₂³	—	4	16	no	—
366	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
367	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
368	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
369	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
370	D₄	—	2	32	no	—
371	D₄	—	4	16	no	—
372	D₄	—	4	4	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
382	C₂×C₃	—	2	4	no	—
383	C₂×C₃	—	4	8	no	—
384	C₂×C₃	—	8	1	no	—
385	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
386	C₂×C₃	C₅×#534	1	4	yes	—
387	C₂×C₃	C₅×#535	1	2	yes	—
388	C₅	C₃×#2613	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	8	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	2	8	no	—
394	C₂²	—	4	32	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	4	8	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	C₃×C₅×#120	1	4	yes	—
401	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
402	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
403	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₃	C₅×#2613	1	1	yes	characteristic, direct product factor, Sylow
409	C₂	—	2	4	no	—
410	C₂	—	4	8	no	—
411	C₂	—	8	1	no	—
412	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
413	C₂	C₃×C₅×#534	1	4	yes	—
414	C₂	C₃×C₅×#535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#381	C₂	semidirect
7. C₃×C₅×#379	C₂	semidirect
8. C₅×#2613	C₃	direct (N × H)
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
24. C₃×C₅×#95	C₂²	semidirect
25. C₃×#2613	C₅	direct (N × H)
26. C₂³×C₅×D₄	C₂×C₃	semidirect
27. C₂×C₅×#123	C₂×C₃	semidirect
28. C₂×C₅×#120	C₂×C₃	semidirect
29. C₅×#394	C₂×C₃	semidirect
30. C₅×#392	C₂×C₃	semidirect
31. C₅×#381	C₂×C₃	semidirect
32. C₅×#379	C₂×C₃	semidirect
36. C₂⁴×C₃×C₅	D₄	semidirect
48. C₂²×C₃×C₄×C₅	D₄	semidirect
59. C₂³×C₃×D₄	C₂×C₅	semidirect
60. C₂×C₃×#123	C₂×C₅	semidirect
61. C₂×C₃×#120	C₂×C₅	semidirect
62. C₃×#394	C₂×C₅	semidirect
63. C₃×#392	C₂×C₅	semidirect
64. C₃×#381	C₂×C₅	semidirect
65. C₃×#379	C₂×C₅	semidirect
71. C₂²×C₅×D₄	C₂²×C₃	semidirect
75. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
78. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
79. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
80. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
81. C₅×#95	C₂²×C₃	semidirect
82. #2613	C₃×C₅	direct (N × H)
116. C₂²×C₃×D₄	C₂²×C₅	semidirect
120. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
123. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
124. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
125. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
126. C₃×#95	C₂²×C₅	semidirect
130. C₂⁴×C₅	C₃×D₄	semidirect
142. C₂²×C₄×C₅	C₃×D₄	semidirect
153. C₂³×D₄	C₂×C₃×C₅	semidirect
154. C₂×#123	C₂×C₃×C₅	semidirect
155. C₂×#120	C₂×C₃×C₅	semidirect
156. #394	C₂×C₃×C₅	semidirect
157. #392	C₂×C₃×C₅	semidirect
158. #381	C₂×C₃×C₅	semidirect
159. #379	C₂×C₃×C₅	semidirect
182. C₂⁴×C₃	C₅×D₄	semidirect
194. C₂²×C₃×C₄	C₅×D₄	semidirect
238. C₂²×D₄	C₂²×C₃×C₅	semidirect
242. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
245. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
246. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
247. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
248. #95	C₂²×C₃×C₅	semidirect
305. C₂⁴	C₃×C₅×D₄	semidirect
317. C₂²×C₄	C₃×C₅×D₄	semidirect
328. C₃×C₅	#2613	direct (N × H)
388. C₅	C₃×#2613	direct (N × H)
408. C₃	C₅×#2613	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×C₅×D₄	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×#120	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#381	2
C₃×C₅×#379	2
C₅×#2613	3
C₃×#2613	5

Subgroups — C3×C5×#2613 #14275647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2613 #14275647