Subgroups — C₃×C₅×#2435 #14275469

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 432 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
2	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#379	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2435	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃×C₅×D₄	—	2	8	no	—
12	C₂²×C₃×C₅×D₄	—	2	4	no	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#124	—	2	8	no	—
17	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
25	C₃×C₅×#95	C₂²	1	2	yes	complemented
26	C₃×#2435	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
28	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#394	C₂×C₃	1	4	yes	complemented
31	C₅×#390	C₂×C₃	1	2	yes	complemented
32	C₅×#379	C₂×C₃	1	4	yes	complemented
33	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃×C₅	—	2	8	no	—
35	C₂⁴×C₃×C₅	—	2	4	no	—
36	C₂⁴×C₃×C₅	—	2	8	no	—
37	C₂⁴×C₃×C₅	—	4	4	no	—
38	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
39	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	32	no	—
43	C₂×C₃×C₅×D₄	—	2	8	no	—
44	C₂×C₃×C₅×D₄	—	2	4	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	D₄	1	8	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic
63	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
64	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×#394	C₂×C₅	1	4	yes	complemented
66	C₃×#390	C₂×C₅	1	2	yes	complemented
67	C₃×#379	C₂×C₅	1	4	yes	complemented
68	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
70	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
71	C₂²×C₅×D₄	—	2	8	no	—
72	C₂²×C₅×D₄	—	2	4	no	—
73	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
74	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₅×#124	—	2	8	no	—
77	C₅×C₂²⋊Q₈	—	2	4	no	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
84	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
85	C₅×#95	C₂²×C₃	1	2	yes	complemented
86	#2435	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	16	no	—
90	C₂³×C₃×C₅	—	2	4	no	—
91	C₂³×C₃×C₅	—	2	4	no	—
92	C₂³×C₃×C₅	—	2	8	no	—
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	4	32	no	—
95	C₂³×C₃×C₅	—	4	8	no	—
96	C₂³×C₃×C₅	—	4	8	no	—
97	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
98	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
99	C₂³×C₃×C₅	#41	1	4	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	4	4	no	—
102	C₃×C₅×D₄	—	2	16	no	—
103	C₃×C₅×D₄	—	2	16	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	8	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
117	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
118	C₂²×C₃×D₄	—	2	8	no	—
119	C₂²×C₃×D₄	—	2	4	no	—
120	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
121	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
122	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
123	C₃×#124	—	2	8	no	—
124	C₃×C₂²⋊Q₈	—	2	4	no	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
127	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
130	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
131	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
132	C₃×#95	C₂²×C₅	1	2	yes	complemented
133	C₂⁴×C₅	—	2	8	no	—
134	C₂⁴×C₅	—	2	4	no	—
135	C₂⁴×C₅	—	2	8	no	—
136	C₂⁴×C₅	—	4	4	no	—
137	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
138	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂×C₅×Q₈	—	2	2	no	—
140	C₂×C₅×Q₈	—	2	4	no	—
141	C₂×C₅×D₄	—	2	32	no	—
142	C₂×C₅×D₄	—	2	8	no	—
143	C₂×C₅×D₄	—	2	4	no	—
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	2	4	no	—
146	C₂×C₅×D₄	C₃×D₄	1	8	yes	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	2	16	no	—
158	C₅×C₂²⋊C₄	—	2	4	no	—
159	C₅×C₂²⋊C₄	—	4	8	no	—
160	C₄²×C₅	—	2	4	no	—
161	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic
162	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
163	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
164	#394	C₂×C₃×C₅	1	4	yes	complemented
165	#390	C₂×C₃×C₅	1	2	yes	complemented
166	#379	C₂×C₃×C₅	1	4	yes	complemented
167	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	8	no	—
171	C₂²×C₃×C₅	—	2	8	no	—
172	C₂²×C₃×C₅	—	2	16	no	—
173	C₂²×C₃×C₅	—	4	32	no	—
174	C₂²×C₃×C₅	—	4	4	no	—
175	C₂²×C₃×C₅	—	4	4	no	—
176	C₂²×C₃×C₅	—	4	8	no	—
177	C₂²×C₃×C₅	#124	1	4	yes	complemented
178	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
180	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
181	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
182	C₃×C₄×C₅	—	2	2	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	—	4	4	no	—
186	C₃×C₄×C₅	#120	1	4	yes	—
187	C₂⁴×C₃	—	2	8	no	—
188	C₂⁴×C₃	—	2	4	no	—
189	C₂⁴×C₃	—	2	8	no	—
190	C₂⁴×C₃	—	4	4	no	—
191	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
192	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	—	2	4	no	—
195	C₂×C₃×D₄	—	2	32	no	—
196	C₂×C₃×D₄	—	2	8	no	—
197	C₂×C₃×D₄	—	2	4	no	—
198	C₂×C₃×D₄	—	2	4	no	—
199	C₂×C₃×D₄	—	2	4	no	—
200	C₂×C₃×D₄	C₅×D₄	1	8	yes	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	2	4	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	2	16	no	—
212	C₃×C₂²⋊C₄	—	2	4	no	—
213	C₃×C₂²⋊C₄	—	4	8	no	—
214	C₃×C₄²	—	2	4	no	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	16	no	—
218	C₂³×C₅	—	2	4	no	—
219	C₂³×C₅	—	2	4	no	—
220	C₂³×C₅	—	2	8	no	—
221	C₂³×C₅	—	2	8	no	—
222	C₂³×C₅	—	4	32	no	—
223	C₂³×C₅	—	4	8	no	—
224	C₂³×C₅	—	4	8	no	—
225	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
226	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
227	C₂³×C₅	C₃×#41	1	4	yes	—
228	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
229	C₅×Q₈	—	4	4	no	—
230	C₅×D₄	—	2	16	no	—
231	C₅×D₄	—	2	16	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	8	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
243	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
244	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
245	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
246	C₂²×D₄	—	2	8	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
249	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
250	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
251	#124	—	2	8	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
254	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
255	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
258	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
259	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
260	#95	C₂²×C₃×C₅	1	2	yes	complemented
261	C₂×C₃×C₅	—	2	4	no	—
262	C₂×C₃×C₅	—	4	8	no	—
263	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
265	C₂×C₃×C₅	#535	1	1	yes	characteristic
266	C₂×C₃×C₅	#546	1	4	yes	—
267	C₂³×C₃	—	2	2	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	2	16	no	—
270	C₂³×C₃	—	2	4	no	—
271	C₂³×C₃	—	2	4	no	—
272	C₂³×C₃	—	2	8	no	—
273	C₂³×C₃	—	2	8	no	—
274	C₂³×C₃	—	4	32	no	—
275	C₂³×C₃	—	4	8	no	—
276	C₂³×C₃	—	4	8	no	—
277	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
278	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
279	C₂³×C₃	C₅×#41	1	4	yes	—
280	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
281	C₃×Q₈	—	4	4	no	—
282	C₃×D₄	—	2	16	no	—
283	C₃×D₄	—	2	16	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	8	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂²×C₅	—	2	2	no	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	2	8	no	—
299	C₂²×C₅	—	2	8	no	—
300	C₂²×C₅	—	2	16	no	—
301	C₂²×C₅	—	4	32	no	—
302	C₂²×C₅	—	4	4	no	—
303	C₂²×C₅	—	4	4	no	—
304	C₂²×C₅	—	4	8	no	—
305	C₂²×C₅	C₃×#124	1	4	yes	complemented
306	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
307	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
308	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
309	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	4	4	no	—
314	C₄×C₅	C₃×#120	1	4	yes	—
315	C₂⁴	—	2	8	no	—
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	8	no	—
318	C₂⁴	—	4	4	no	—
319	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
320	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×D₄	—	2	32	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	C₃×C₅×D₄	1	8	yes	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
331	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
332	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
333	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
335	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	16	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	4	8	no	—
342	C₄²	—	2	4	no	—
343	C₃×C₅	#2435	1	1	yes	characteristic, direct product factor, Hall
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	8	no	—
347	C₂²×C₃	—	2	8	no	—
348	C₂²×C₃	—	2	16	no	—
349	C₂²×C₃	—	4	32	no	—
350	C₂²×C₃	—	4	4	no	—
351	C₂²×C₃	—	4	4	no	—
352	C₂²×C₃	—	4	8	no	—
353	C₂²×C₃	C₅×#124	1	4	yes	complemented
354	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
356	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
357	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	—	4	4	no	—
362	C₃×C₄	C₅×#120	1	4	yes	—
363	C₂×C₅	—	2	4	no	—
364	C₂×C₅	—	4	8	no	—
365	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
366	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
367	C₂×C₅	C₃×#535	1	1	yes	characteristic
368	C₂×C₅	C₃×#546	1	4	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	16	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	8	no	—
376	C₂³	—	4	32	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	4	8	no	—
379	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
380	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
381	C₂³	C₃×C₅×#41	1	4	yes	—
382	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
383	Q₈	—	4	4	no	—
384	D₄	—	2	16	no	—
385	D₄	—	2	16	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
396	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
397	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
398	C₂×C₃	—	2	4	no	—
399	C₂×C₃	—	4	8	no	—
400	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
401	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
402	C₂×C₃	C₅×#535	1	1	yes	characteristic
403	C₂×C₃	C₅×#546	1	4	yes	—
404	C₅	C₃×#2435	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	16	no	—
410	C₂²	—	4	32	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	8	no	—
414	C₂²	C₃×C₅×#124	1	4	yes	complemented
415	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
416	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
417	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
418	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
419	C₄	—	2	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	4	no	—
423	C₄	C₃×C₅×#120	1	4	yes	—
424	C₃	C₅×#2435	1	1	yes	characteristic, direct product factor, Sylow
425	C₂	—	2	4	no	—
426	C₂	—	4	8	no	—
427	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
428	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
429	C₂	C₃×C₅×#535	1	1	yes	characteristic
430	C₂	C₃×C₅×#546	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅×D₄	C₂
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
2. C₂×C₃×C₅×#124	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₃×C₅×#379	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₅×#2435	C₃	direct (N × H)
10. C₂²×C₃×C₅×Q₈	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
24. C₂×C₃×C₄²×C₅	C₂²	semidirect
25. C₃×C₅×#95	C₂²	semidirect
26. C₃×#2435	C₅	direct (N × H)
28. C₂×C₅×#124	C₂×C₃	semidirect
29. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
30. C₅×#394	C₂×C₃	semidirect
31. C₅×#390	C₂×C₃	semidirect
32. C₅×#379	C₂×C₃	semidirect
33. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
63. C₂×C₃×#124	C₂×C₅	semidirect
64. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
65. C₃×#394	C₂×C₅	semidirect
66. C₃×#390	C₂×C₅	semidirect
67. C₃×#379	C₂×C₅	semidirect
68. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
70. C₂²×C₅×Q₈	C₂²×C₃	semidirect
78. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
79. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
82. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
83. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
84. C₂×C₄²×C₅	C₂²×C₃	semidirect
85. C₅×#95	C₂²×C₃	semidirect
86. #2435	C₃×C₅	direct (N × H)
117. C₂²×C₃×Q₈	C₂²×C₅	semidirect
125. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
126. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
129. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
130. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
131. C₂×C₃×C₄²	C₂²×C₅	semidirect
132. C₃×#95	C₂²×C₅	semidirect
162. C₂×#124	C₂×C₃×C₅	semidirect
163. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
164. #394	C₂×C₃×C₅	semidirect
165. #390	C₂×C₃×C₅	semidirect
166. #379	C₂×C₃×C₅	semidirect
167. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
177. C₂²×C₃×C₅	#124	semidirect
245. C₂²×Q₈	C₂²×C₃×C₅	semidirect
253. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
254. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
257. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
258. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
259. C₂×C₄²	C₂²×C₃×C₅	semidirect
260. #95	C₂²×C₃×C₅	semidirect
305. C₂²×C₅	C₃×#124	semidirect
343. C₃×C₅	#2435	direct (N × H)
353. C₂²×C₃	C₅×#124	semidirect
404. C₅	C₃×#2435	direct (N × H)
414. C₂²	C₃×C₅×#124	semidirect
424. C₃	C₅×#2435	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×#124	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2435	3
C₃×#2435	5

Subgroups — C3×C5×#2435 #14275469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2435 #14275469