Subgroups — C₃×C₅×D₄×D₈ #14276313

Order 1920.

1240 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₄²	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#459	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#447	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×D₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	—	2	2	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
12	C₂×C₃×C₅×D₈	—	2	8	no	—
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
18	C₃×C₅×#127	C₂²	1	2	yes	complemented
19	C₃×C₅×#121	—	2	2	no	—
20	C₃×C₅×#121	C₂²	1	4	yes	complemented
21	C₃×C₅×#120	—	2	4	no	—
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
24	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#102	C₂²	1	4	yes	complemented
27	C₃×C₅×#102	C₂²	1	2	yes	complemented
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×D₄×D₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂²×C₅×D₈	C₂×C₃	1	2	yes	complemented
32	C₅×D₄²	C₂×C₃	1	2	yes	complemented
33	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#466	C₂×C₃	1	2	yes	complemented
35	C₅×#459	C₂×C₃	1	2	yes	complemented
36	C₅×#447	C₂×C₃	1	4	yes	complemented
37	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	—	2	4	no	—
40	C₂×C₃×C₅×D₄	—	2	8	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	4	4	no	—
46	C₂×C₃×C₅×D₄	—	4	8	no	—
47	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₃×C₅×D₈	—	2	8	no	—
53	C₃×C₅×D₈	—	2	4	no	—
54	C₃×C₅×D₈	—	4	2	no	—
55	C₃×C₅×D₈	D₄	1	4	yes	direct product factor
56	C₂×C₃×C₅×C₈	—	2	4	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×D₈	C₂×C₅	1	2	yes	complemented
67	C₃×D₄²	C₂×C₅	1	2	yes	complemented
68	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#466	C₂×C₅	1	2	yes	complemented
70	C₃×#459	C₂×C₅	1	2	yes	complemented
71	C₃×#447	C₂×C₅	1	4	yes	complemented
72	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	—	2	2	no	—
75	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
76	C₂×C₅×D₈	—	2	8	no	—
77	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
79	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
80	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
81	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
82	C₅×#127	C₂²×C₃	1	2	yes	complemented
83	C₅×#121	—	2	2	no	—
84	C₅×#121	C₂²×C₃	1	4	yes	complemented
85	C₅×#120	—	2	4	no	—
86	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
88	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₅×#102	C₂²×C₃	1	2	yes	complemented
91	C₅×#102	C₂²×C₃	1	4	yes	complemented
92	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
93	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
94	D₄×D₈	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	4	8	no	—
98	C₂³×C₃×C₅	—	4	8	no	—
99	C₂³×C₃×C₅	—	8	4	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
101	C₃×C₅×D₄	—	2	4	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	—	2	4	no	—
104	C₃×C₅×D₄	—	4	8	no	—
105	C₃×C₅×D₄	—	4	8	no	—
106	C₃×C₅×D₄	—	4	4	no	—
107	C₃×C₅×D₄	—	8	2	no	—
108	C₃×C₅×D₄	D₈	1	4	yes	direct product factor
109	C₃×C₅×D₄	C₂×D₄	1	4	yes	complemented
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	4	4	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃×C₅×C₈	—	2	1	no	—
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
121	C₂²×C₃×D₄	—	2	2	no	—
122	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
123	C₂×C₃×D₈	—	2	8	no	—
124	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
126	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
127	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
128	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
129	C₃×#127	C₂²×C₅	1	2	yes	complemented
130	C₃×#121	—	2	2	no	—
131	C₃×#121	C₂²×C₅	1	4	yes	complemented
132	C₃×#120	—	2	4	no	—
133	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
134	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
135	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₃×#102	C₂²×C₅	1	2	yes	complemented
138	C₃×#102	C₂²×C₅	1	4	yes	complemented
139	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
140	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₂⁴×C₅	—	2	4	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	2	no	—
146	C₂×C₅×D₄	—	2	2	no	—
147	C₂×C₅×D₄	—	4	4	no	—
148	C₂×C₅×D₄	—	4	8	no	—
149	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
150	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
151	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	—	2	2	no	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₅×D₈	—	2	8	no	—
155	C₅×D₈	—	2	4	no	—
156	C₅×D₈	—	4	2	no	—
157	C₅×D₈	C₃×D₄	1	4	yes	direct product factor
158	C₂×C₅×C₈	—	2	4	no	—
159	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
160	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
162	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
164	C₅×C₂²⋊C₄	—	2	2	no	—
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
167	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×D₈	C₂×C₃×C₅	1	2	yes	complemented
169	D₄²	C₂×C₃×C₅	1	2	yes	complemented
170	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
171	#466	C₂×C₃×C₅	1	2	yes	complemented
172	#459	C₂×C₃×C₅	1	2	yes	complemented
173	#447	C₂×C₃×C₅	1	4	yes	complemented
174	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
175	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	2	4	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	4	4	no	—
182	C₂²×C₃×C₅	—	4	4	no	—
183	C₂²×C₃×C₅	—	4	4	no	—
184	C₂²×C₃×C₅	—	8	16	no	—
185	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
186	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	2	1	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂×D₈	1	2	yes	complemented
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂⁴×C₃	—	2	4	no	—
194	C₂×C₃×D₄	—	2	8	no	—
195	C₂×C₃×D₄	—	2	4	no	—
196	C₂×C₃×D₄	—	2	4	no	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂×C₃×D₄	—	4	4	no	—
200	C₂×C₃×D₄	—	4	8	no	—
201	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
202	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
203	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	—	2	2	no	—
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₃×D₈	—	2	8	no	—
207	C₃×D₈	—	2	4	no	—
208	C₃×D₈	—	4	2	no	—
209	C₃×D₈	C₅×D₄	1	4	yes	direct product factor
210	C₂×C₃×C₈	—	2	4	no	—
211	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
213	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
214	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
215	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
216	C₃×C₂²⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	2	4	no	—
218	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
219	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	4	no	—
222	C₂³×C₅	—	4	8	no	—
223	C₂³×C₅	—	4	8	no	—
224	C₂³×C₅	—	8	4	no	—
225	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
226	C₅×D₄	—	2	4	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	2	4	no	—
229	C₅×D₄	—	4	8	no	—
230	C₅×D₄	—	4	8	no	—
231	C₅×D₄	—	4	4	no	—
232	C₅×D₄	—	8	2	no	—
233	C₅×D₄	C₃×D₈	1	4	yes	direct product factor
234	C₅×D₄	C₂×C₃×D₄	1	4	yes	complemented
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	4	4	no	—
239	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	2	1	no	—
245	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
248	C₂×D₈	—	2	8	no	—
249	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
251	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
252	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
253	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
254	#127	C₂²×C₃×C₅	1	2	yes	complemented
255	#121	—	2	2	no	—
256	#121	C₂²×C₃×C₅	1	4	yes	complemented
257	#120	—	2	4	no	—
258	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
259	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
260	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
261	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
262	#102	C₂²×C₃×C₅	1	2	yes	complemented
263	#102	C₂²×C₃×C₅	1	4	yes	complemented
264	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
265	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
266	C₂×C₃×C₅	—	2	4	no	—
267	C₂×C₃×C₅	—	4	4	no	—
268	C₂×C₃×C₅	—	8	4	no	—
269	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
271	C₂×C₃×C₅	#576	1	1	yes	characteristic
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	2	4	no	—
274	C₂³×C₃	—	4	8	no	—
275	C₂³×C₃	—	4	8	no	—
276	C₂³×C₃	—	8	4	no	—
277	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
278	C₃×D₄	—	2	4	no	—
279	C₃×D₄	—	2	2	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	4	8	no	—
282	C₃×D₄	—	4	8	no	—
283	C₃×D₄	—	4	4	no	—
284	C₃×D₄	—	8	2	no	—
285	C₃×D₄	C₅×D₈	1	4	yes	direct product factor
286	C₃×D₄	C₂×C₅×D₄	1	4	yes	complemented
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	4	4	no	—
291	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
298	C₂²×C₅	—	2	2	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	4	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	4	no	—
304	C₂²×C₅	—	4	4	no	—
305	C₂²×C₅	—	4	4	no	—
306	C₂²×C₅	—	8	16	no	—
307	C₂²×C₅	C₂×C₃×D₈	1	4	yes	complemented
308	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	C₂×C₃×D₈	1	2	yes	complemented
313	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂⁴	—	2	4	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	8	no	—
323	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
324	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
325	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
328	D₈	—	2	8	no	—
329	D₈	—	2	4	no	—
330	D₈	—	4	2	no	—
331	D₈	C₃×C₅×D₄	1	4	yes	direct product factor
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
334	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
335	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
336	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
337	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
341	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
342	C₃×C₅	D₄×D₈	1	1	yes	characteristic, direct product factor, Hall
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	4	no	—
346	C₂²×C₃	—	4	2	no	—
347	C₂²×C₃	—	4	2	no	—
348	C₂²×C₃	—	4	4	no	—
349	C₂²×C₃	—	4	4	no	—
350	C₂²×C₃	—	4	4	no	—
351	C₂²×C₃	—	8	16	no	—
352	C₂²×C₃	C₂×C₅×D₈	1	4	yes	complemented
353	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	C₂×C₅×D₈	1	2	yes	complemented
358	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₅	—	2	4	no	—
361	C₂×C₅	—	4	4	no	—
362	C₂×C₅	—	8	4	no	—
363	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
364	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
365	C₂×C₅	C₃×#576	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	8	4	no	—
371	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
372	D₄	—	2	4	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	8	no	—
376	D₄	—	4	8	no	—
377	D₄	—	4	4	no	—
378	D₄	—	8	2	no	—
379	D₄	C₃×C₅×D₈	1	4	yes	direct product factor
380	D₄	C₂×C₃×C₅×D₄	1	4	yes	complemented
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
387	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	1	no	—
391	C₈	C₂×C₃×C₅×D₄	1	2	yes	complemented
392	C₂×C₃	—	2	4	no	—
393	C₂×C₃	—	4	4	no	—
394	C₂×C₃	—	8	4	no	—
395	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
396	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
397	C₂×C₃	C₅×#576	1	1	yes	characteristic
398	C₅	C₃×D₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	16	no	—
408	C₂²	C₂×C₃×C₅×D₈	1	4	yes	complemented
409	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	C₂×C₃×C₅×D₈	1	2	yes	complemented
414	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
415	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
416	C₃	C₅×D₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
417	C₂	—	2	4	no	—
418	C₂	—	4	4	no	—
419	C₂	—	8	4	no	—
420	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
421	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
422	C₂	C₃×C₅×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₃×C₅×D₄²	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₃×C₅×#459	C₂	semidirect
6. C₃×C₅×#447	C₂	semidirect
7. C₃×C₄×C₅×D₈	C₂	semidirect
8. C₃×C₅×C₈×D₄	C₂	semidirect
9. C₅×D₄×D₈	C₃	direct (N × H)
11. C₂²×C₃×C₅×D₄	C₂²	semidirect
14. C₂×C₃×C₅×D₈	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₅×#121	C₂²	semidirect
23. C₃×C₄×C₅×D₄	C₂²	semidirect
24. C₃×C₅×#107	C₂²	semidirect
25. C₃×C₅×C₄⋊C₈	C₂²	semidirect
26. C₃×C₅×#102	C₂²	semidirect
27. C₃×C₅×#102	C₂²	semidirect
28. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
30. C₃×D₄×D₈	C₅	direct (N × H)
31. C₂²×C₅×D₈	C₂×C₃	semidirect
32. C₅×D₄²	C₂×C₃	semidirect
33. C₅×#493	C₂×C₃	semidirect
34. C₅×#466	C₂×C₃	semidirect
35. C₅×#459	C₂×C₃	semidirect
36. C₅×#447	C₂×C₃	semidirect
37. C₄×C₅×D₈	C₂×C₃	semidirect
38. C₅×C₈×D₄	C₂×C₃	semidirect
55. C₃×C₅×D₈	D₄	direct (N × H)
66. C₂²×C₃×D₈	C₂×C₅	semidirect
67. C₃×D₄²	C₂×C₅	semidirect
68. C₃×#493	C₂×C₅	semidirect
69. C₃×#466	C₂×C₅	semidirect
70. C₃×#459	C₂×C₅	semidirect
71. C₃×#447	C₂×C₅	semidirect
72. C₃×C₄×D₈	C₂×C₅	semidirect
73. C₃×C₈×D₄	C₂×C₅	semidirect
75. C₂²×C₅×D₄	C₂²×C₃	semidirect
78. C₂×C₅×D₈	C₂²×C₃	semidirect
79. C₂×C₅×D₈	C₂²×C₃	semidirect
80. C₂×C₅×D₈	C₂²×C₃	semidirect
81. C₂²×C₅×C₈	C₂²×C₃	semidirect
82. C₅×#127	C₂²×C₃	semidirect
84. C₅×#121	C₂²×C₃	semidirect
87. C₄×C₅×D₄	C₂²×C₃	semidirect
88. C₅×#107	C₂²×C₃	semidirect
89. C₅×C₄⋊C₈	C₂²×C₃	semidirect
90. C₅×#102	C₂²×C₃	semidirect
91. C₅×#102	C₂²×C₃	semidirect
92. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
93. C₄×C₅×C₈	C₂²×C₃	semidirect
94. D₄×D₈	C₃×C₅	direct (N × H)
108. C₃×C₅×D₄	D₈	direct (N × H)
109. C₃×C₅×D₄	C₂×D₄	semidirect
120. C₃×C₅×C₈	C₂×D₄	semidirect
122. C₂²×C₃×D₄	C₂²×C₅	semidirect
125. C₂×C₃×D₈	C₂²×C₅	semidirect
126. C₂×C₃×D₈	C₂²×C₅	semidirect
127. C₂×C₃×D₈	C₂²×C₅	semidirect
128. C₂²×C₃×C₈	C₂²×C₅	semidirect
129. C₃×#127	C₂²×C₅	semidirect
131. C₃×#121	C₂²×C₅	semidirect
134. C₃×C₄×D₄	C₂²×C₅	semidirect
135. C₃×#107	C₂²×C₅	semidirect
136. C₃×C₄⋊C₈	C₂²×C₅	semidirect
137. C₃×#102	C₂²×C₅	semidirect
138. C₃×#102	C₂²×C₅	semidirect
139. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
140. C₃×C₄×C₈	C₂²×C₅	semidirect
157. C₅×D₈	C₃×D₄	direct (N × H)
168. C₂²×D₈	C₂×C₃×C₅	semidirect
169. D₄²	C₂×C₃×C₅	semidirect
170. #493	C₂×C₃×C₅	semidirect
171. #466	C₂×C₃×C₅	semidirect
172. #459	C₂×C₃×C₅	semidirect
173. #447	C₂×C₃×C₅	semidirect
174. C₄×D₈	C₂×C₃×C₅	semidirect
175. C₈×D₄	C₂×C₃×C₅	semidirect
185. C₂²×C₃×C₅	C₂×D₈	semidirect
190. C₃×C₄×C₅	C₂×D₈	semidirect
209. C₃×D₈	C₅×D₄	direct (N × H)
233. C₅×D₄	C₃×D₈	direct (N × H)
234. C₅×D₄	C₂×C₃×D₄	semidirect
245. C₅×C₈	C₂×C₃×D₄	semidirect
247. C₂²×D₄	C₂²×C₃×C₅	semidirect
250. C₂×D₈	C₂²×C₃×C₅	semidirect
251. C₂×D₈	C₂²×C₃×C₅	semidirect
252. C₂×D₈	C₂²×C₃×C₅	semidirect
253. C₂²×C₈	C₂²×C₃×C₅	semidirect
254. #127	C₂²×C₃×C₅	semidirect
256. #121	C₂²×C₃×C₅	semidirect
259. C₄×D₄	C₂²×C₃×C₅	semidirect
260. #107	C₂²×C₃×C₅	semidirect
261. C₄⋊C₈	C₂²×C₃×C₅	semidirect
262. #102	C₂²×C₃×C₅	semidirect
263. #102	C₂²×C₃×C₅	semidirect
264. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
265. C₄×C₈	C₂²×C₃×C₅	semidirect
285. C₃×D₄	C₅×D₈	direct (N × H)
286. C₃×D₄	C₂×C₅×D₄	semidirect
297. C₃×C₈	C₂×C₅×D₄	semidirect
307. C₂²×C₅	C₂×C₃×D₈	semidirect
312. C₄×C₅	C₂×C₃×D₈	semidirect
331. D₈	C₃×C₅×D₄	direct (N × H)
342. C₃×C₅	D₄×D₈	direct (N × H)
352. C₂²×C₃	C₂×C₅×D₈	semidirect
357. C₃×C₄	C₂×C₅×D₈	semidirect
379. D₄	C₃×C₅×D₈	direct (N × H)
380. D₄	C₂×C₃×C₅×D₄	semidirect
391. C₈	C₂×C₃×C₅×D₄	semidirect
398. C₅	C₃×D₄×D₈	direct (N × H)
408. C₂²	C₂×C₃×C₅×D₈	semidirect
413. C₄	C₂×C₃×C₅×D₈	semidirect
416. C₃	C₅×D₄×D₈	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×D₈	2
C₃×C₅×D₄²	2
C₃×C₅×#493	2
C₃×C₅×#466	2
C₃×C₅×#459	2
C₃×C₅×#447	2
C₃×C₄×C₅×D₈	2
C₃×C₅×C₈×D₄	2
C₅×D₄×D₈	3
C₃×D₄×D₈	5

Subgroups — C3×C5×D4×D8 #14276313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₄×D₈ #14276313