Subgroups — C₃×C₅×#2434 #14275468

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#395	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	4	yes	maximal
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₅×#2434	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	8	no	—
10	C₂²×C₃×C₅×Q₈	—	2	4	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	—	2	8	no	—
17	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	8	yes	—
26	C₃×#2434	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
28	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
30	C₅×#395	C₂×C₃	1	4	yes	complemented
31	C₅×#391	C₂×C₃	1	2	yes	complemented
32	C₅×#385	C₂×C₃	1	4	yes	—
33	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₅×Q₈	—	2	32	no	—
36	C₂×C₃×C₅×Q₈	—	2	8	no	—
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	4	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	D₄	1	8	yes	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	2	8	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	16	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	Q₈	1	8	yes	complemented
58	C₃×C₄²×C₅	—	2	4	no	—
59	C₂³×C₃×Q₈	C₂×C₅	1	1	yes	characteristic
60	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
61	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
62	C₃×#395	C₂×C₅	1	4	yes	complemented
63	C₃×#391	C₂×C₅	1	2	yes	complemented
64	C₃×#385	C₂×C₅	1	4	yes	—
65	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
66	C₂²×C₅×Q₈	—	2	8	no	—
67	C₂²×C₅×Q₈	—	2	4	no	—
68	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
69	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
71	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×C₄⋊Q₈	—	2	8	no	—
74	C₅×C₂²⋊Q₈	—	2	4	no	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
81	C₅×#95	C₂²×C₃	1	2	yes	—
82	C₅×#95	C₂²×C₃	1	8	yes	—
83	#2434	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂³×C₃×C₅	—	2	2	no	—
86	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
87	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₃×C₅×Q₈	—	2	16	no	—
90	C₃×C₅×Q₈	—	2	16	no	—
91	C₃×C₅×Q₈	—	4	4	no	—
92	C₂×C₃×C₄×C₅	—	2	16	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	8	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×Q₈	1	8	yes	complemented
108	C₂²×C₃×Q₈	—	2	8	no	—
109	C₂²×C₃×Q₈	—	2	4	no	—
110	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
111	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
112	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
113	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
114	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
115	C₃×C₄⋊Q₈	—	2	8	no	—
116	C₃×C₂²⋊Q₈	—	2	4	no	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
123	C₃×#95	C₂²×C₅	1	2	yes	—
124	C₃×#95	C₂²×C₅	1	8	yes	—
125	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₅×Q₈	—	2	32	no	—
127	C₂×C₅×Q₈	—	2	8	no	—
128	C₂×C₅×Q₈	—	2	4	no	—
129	C₂×C₅×Q₈	—	2	4	no	—
130	C₂×C₅×Q₈	—	2	4	no	—
131	C₂×C₅×Q₈	—	2	2	no	—
132	C₂×C₅×Q₈	—	2	4	no	—
133	C₂×C₅×Q₈	C₃×D₄	1	8	yes	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	—	2	8	no	—
136	C₂²×C₄×C₅	—	2	4	no	—
137	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	4	no	—
146	C₅×C₄⋊C₄	—	2	16	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	C₃×Q₈	1	8	yes	complemented
149	C₄²×C₅	—	2	4	no	—
150	C₂³×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
151	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
152	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
153	#395	C₂×C₃×C₅	1	4	yes	complemented
154	#391	C₂×C₃×C₅	1	2	yes	complemented
155	#385	C₂×C₃×C₅	1	4	yes	—
156	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
157	C₂²×C₃×C₅	—	2	2	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	2	8	no	—
160	C₂²×C₃×C₅	C₄⋊Q₈	1	4	yes	complemented
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
163	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
164	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
165	C₃×C₄×C₅	—	2	8	no	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	2	8	no	—
168	C₃×C₄×C₅	—	4	2	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	#120	1	4	yes	—
171	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
172	C₂×C₃×Q₈	—	2	32	no	—
173	C₂×C₃×Q₈	—	2	8	no	—
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	—	2	4	no	—
176	C₂×C₃×Q₈	—	2	4	no	—
177	C₂×C₃×Q₈	—	2	2	no	—
178	C₂×C₃×Q₈	—	2	4	no	—
179	C₂×C₃×Q₈	C₅×D₄	1	8	yes	—
180	C₂²×C₃×C₄	—	2	4	no	—
181	C₂²×C₃×C₄	—	2	8	no	—
182	C₂²×C₃×C₄	—	2	4	no	—
183	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
189	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	4	no	—
192	C₃×C₄⋊C₄	—	2	16	no	—
193	C₃×C₂²⋊C₄	—	2	4	no	—
194	C₃×C₂²⋊C₄	C₅×Q₈	1	8	yes	complemented
195	C₃×C₄²	—	2	4	no	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	—
200	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
201	C₅×Q₈	—	2	16	no	—
202	C₅×Q₈	—	2	16	no	—
203	C₅×Q₈	—	4	4	no	—
204	C₂×C₄×C₅	—	2	16	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	8	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×Q₈	1	8	yes	complemented
220	C₂²×Q₈	—	2	8	no	—
221	C₂²×Q₈	—	2	4	no	—
222	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
224	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
225	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₄⋊Q₈	—	2	8	no	—
228	C₂²⋊Q₈	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
234	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
235	#95	C₂²×C₃×C₅	1	2	yes	—
236	#95	C₂²×C₃×C₅	1	8	yes	—
237	C₂×C₃×C₅	—	2	4	no	—
238	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
239	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
240	C₂×C₃×C₅	#536	1	1	yes	characteristic
241	C₂×C₃×C₅	D₄×Q₈	1	4	yes	—
242	C₂³×C₃	—	2	2	no	—
243	C₂³×C₃	—	2	2	no	—
244	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
245	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
246	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
247	C₃×Q₈	—	2	16	no	—
248	C₃×Q₈	—	2	16	no	—
249	C₃×Q₈	—	4	4	no	—
250	C₂×C₃×C₄	—	2	16	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₅×Q₈	1	8	yes	complemented
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	2	8	no	—
269	C₂²×C₅	C₃×C₄⋊Q₈	1	4	yes	complemented
270	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
271	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
272	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
273	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
274	C₄×C₅	—	2	8	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	8	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	C₃×#120	1	4	yes	—
280	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
281	C₂×Q₈	—	2	32	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₃×C₅×D₄	1	8	yes	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
293	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
295	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
298	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	C₃×C₅×Q₈	1	8	yes	complemented
304	C₄²	—	2	4	no	—
305	C₃×C₅	#2434	1	1	yes	characteristic, direct product factor, Hall
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	8	no	—
309	C₂²×C₃	C₅×C₄⋊Q₈	1	4	yes	complemented
310	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
312	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
313	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
314	C₃×C₄	—	2	8	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	8	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	2	no	—
319	C₃×C₄	C₅×#120	1	4	yes	—
320	C₂×C₅	—	2	4	no	—
321	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
322	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
323	C₂×C₅	C₃×#536	1	1	yes	characteristic
324	C₂×C₅	C₃×D₄×Q₈	1	4	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
328	C₂³	C₂×C₃×C₅×Q₈	1	4	yes	—
329	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
330	Q₈	—	2	16	no	—
331	Q₈	—	2	16	no	—
332	Q₈	—	4	4	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	—
345	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
346	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
347	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
348	C₂×C₄	C₂×C₃×C₅×Q₈	1	8	yes	complemented
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
351	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
352	C₂×C₃	C₅×#536	1	1	yes	characteristic
353	C₂×C₃	C₅×D₄×Q₈	1	4	yes	—
354	C₅	C₃×#2434	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	8	no	—
358	C₂²	C₃×C₅×C₄⋊Q₈	1	4	yes	complemented
359	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
360	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
361	C₂²	C₂²×C₃×C₅×Q₈	1	2	yes	—
362	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
363	C₄	—	2	8	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	8	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₃×C₅×#120	1	4	yes	—
369	C₃	C₅×#2434	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	4	no	—
371	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
372	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
373	C₂	C₃×C₅×#536	1	1	yes	characteristic
374	C₂	C₃×C₅×D₄×Q₈	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#395	C₂	semidirect
5. C₃×C₅×#391	C₂	semidirect
8. C₅×#2434	C₃	direct (N × H)
26. C₃×#2434	C₅	direct (N × H)
28. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
30. C₅×#395	C₂×C₃	semidirect
31. C₅×#391	C₂×C₃	semidirect
57. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
60. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
62. C₃×#395	C₂×C₅	semidirect
63. C₃×#391	C₂×C₅	semidirect
83. #2434	C₃×C₅	direct (N × H)
107. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
148. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
151. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
153. #395	C₂×C₃×C₅	semidirect
154. #391	C₂×C₃×C₅	semidirect
160. C₂²×C₃×C₅	C₄⋊Q₈	semidirect
194. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
219. C₂×C₄×C₅	C₂×C₃×Q₈	semidirect
265. C₂×C₃×C₄	C₂×C₅×Q₈	semidirect
269. C₂²×C₅	C₃×C₄⋊Q₈	semidirect
303. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
305. C₃×C₅	#2434	direct (N × H)
309. C₂²×C₃	C₅×C₄⋊Q₈	semidirect
348. C₂×C₄	C₂×C₃×C₅×Q₈	semidirect
354. C₅	C₃×#2434	direct (N × H)
358. C₂²	C₃×C₅×C₄⋊Q₈	semidirect
369. C₃	C₅×#2434	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×Q₈	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#395	2
C₃×C₅×#391	2
C₃×C₅×#385	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2434	3
C₃×#2434	5

Subgroups — C3×C5×#2434 #14275468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2434 #14275468