Subgroups — C₃×D₄×Q₈×D₅ #14482897

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×D₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₈×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66061	C₂	1	3	yes	maximal, complemented
5	C₃×D₅×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
6	C₃×#65966	C₂	1	6	yes	maximal, complemented
7	C₃×D₅×C₂²⋊Q₈	C₂	1	6	yes	maximal, complemented
8	C₃×Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×D₄×D₅	C₂	1	3	yes	maximal
11	C₃×D₄×Dic₁₀	C₂	1	3	yes	maximal, complemented
12	D₄×Q₈×D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
14	C₂×C₃×Q₈×D₅	—	2	16	no	—
15	C₂×C₃×Q₈×D₅	C₂²	1	6	yes	—
16	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	complemented
18	C₂×C₃×Q₈×D₅	C₂²	1	6	yes	complemented
19	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₅	C₂²	1	6	yes	—
21	C₂²×C₃×Dic₁₀	C₂²	1	6	yes	complemented
22	C₃×C₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	6	yes	complemented
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₄	C₂²	1	3	yes	—
26	C₃×#4092	C₂²	1	6	yes	complemented
27	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4090	C₂²	1	6	yes	complemented
29	C₃×D₄×Dic₅	C₂²	1	3	yes	—
30	C₃×C₄×C₂²⋊D₅	C₂²	1	6	yes	—
31	C₃×#4070	C₂²	1	6	yes	complemented
32	C₃×#4043	C₂²	1	6	yes	complemented
33	C₃×#4042	C₂²	1	12	yes	complemented
34	C₃×#4039	C₂²	1	3	yes	—
35	C₃×D₅×C₄⋊C₄	C₂²	1	3	yes	—
36	C₃×D₅×C₄⋊C₄	C₂²	1	3	yes	—
37	C₃×D₅×C₄⋊C₄	C₂²	1	6	yes	—
38	C₃×#4034	C₂²	1	6	yes	complemented
39	C₃×#4034	C₂²	1	6	yes	complemented
40	C₃×#4033	C₂²	1	3	yes	complemented
41	C₃×#4027	C₂²	1	6	yes	—
42	C₃×D₅×C₂²⋊C₄	C₂²	1	6	yes	—
43	C₃×#4024	C₂²	1	12	yes	complemented
44	C₃×C₄×D₂₀	C₂²	1	3	yes	—
45	C₃×C₄²×D₅	C₂²	1	3	yes	—
46	C₃×#4015	C₂²	1	3	yes	complemented
47	C₃×C₄×Dic₁₀	C₂²	1	3	yes	complemented
48	C₂×C₃×D₄×Q₈	—	5	1	no	maximal, Hall
49	C₂²×Q₈×D₅	C₂×C₃	1	2	yes	complemented
50	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
51	Q₈×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
52	#66061	C₂×C₃	1	3	yes	complemented
53	D₅×C₄⋊Q₈	C₂×C₃	1	3	yes	complemented
54	#65966	C₂×C₃	1	6	yes	complemented
55	D₅×C₂²⋊Q₈	C₂×C₃	1	6	yes	complemented
56	Q₈×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×D₄×D₅	C₂×C₃	1	3	yes	—
59	D₄×Dic₁₀	C₂×C₃	1	3	yes	complemented
60	C₂³×C₃×D₅	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	—	2	8	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	—
63	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
66	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
67	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
68	C₃×Q₈×D₅	—	2	8	no	—
69	C₃×Q₈×D₅	—	2	24	no	—
70	C₃×Q₈×D₅	—	2	24	no	—
71	C₃×Q₈×D₅	D₄	1	8	yes	direct product factor
72	C₃×D₄×D₅	Q₈	1	8	yes	direct product factor
73	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	—	2	24	no	—
75	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
76	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
77	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
78	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
79	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
80	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×Dic₁₀	—	2	24	no	—
82	C₂×C₃×Dic₁₀	C₂³	1	6	yes	—
83	C₂×C₃×Dic₁₀	C₂³	1	12	yes	—
84	C₂×C₃×Dic₁₀	C₂³	1	3	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
89	C₃×C₄²×C₅	C₂³	1	3	yes	—
90	C₃×C₂²⋊Dic₅	C₂³	1	6	yes	—
91	C₃×#685	C₂³	1	6	yes	—
92	C₃×#685	C₂³	1	6	yes	—
93	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
94	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
95	C₃×C₄⋊Dic₅	C₂³	1	6	yes	—
96	C₃×#683	C₂³	1	6	yes	—
97	C₃×#683	C₂³	1	12	yes	—
98	C₃×#683	C₂³	1	6	yes	—
99	C₃×C₄×Dic₅	C₂³	1	3	yes	—
100	C₃×C₄×Dic₅	C₂³	1	3	yes	—
101	C₃×C₄×Dic₅	C₂³	1	3	yes	—
102	C₂³×C₃×Q₈	—	5	2	no	—
103	C₃×D₄×Q₈	—	5	2	no	—
104	C₃×D₄×Q₈	—	5	3	no	—
105	C₃×D₄×Q₈	—	5	6	no	—
106	C₃×D₄×Q₈	—	5	1	no	—
107	C₃×D₄×Q₈	—	5	3	no	—
108	C₃×D₄×Q₈	D₅	1	1	yes	characteristic, direct product factor
109	C₂×C₃×C₄⋊Q₈	—	5	3	no	—
110	C₂×C₃×C₂²⋊Q₈	—	5	6	no	—
111	C₂×C₃×C₄×Q₈	—	5	1	no	—
112	C₂×C₃×C₄×D₄	—	5	3	no	—
113	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
114	C₂×Q₈×D₅	—	2	16	no	—
115	C₂×Q₈×D₅	C₂²×C₃	1	6	yes	—
116	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
117	C₂×Q₈×D₅	C₂²×C₃	1	6	yes	complemented
118	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	complemented
119	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₄×D₅	C₂²×C₃	1	6	yes	—
121	C₂²×Dic₁₀	C₂²×C₃	1	6	yes	complemented
122	C₅×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
123	C₅×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
124	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₄×C₅×D₄	C₂²×C₃	1	3	yes	—
126	#4092	C₂²×C₃	1	6	yes	complemented
127	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
128	#4090	C₂²×C₃	1	6	yes	complemented
129	D₄×Dic₅	C₂²×C₃	1	3	yes	—
130	C₄×C₂²⋊D₅	C₂²×C₃	1	6	yes	—
131	#4070	C₂²×C₃	1	6	yes	complemented
132	#4043	C₂²×C₃	1	6	yes	complemented
133	#4042	C₂²×C₃	1	12	yes	complemented
134	#4039	C₂²×C₃	1	3	yes	—
135	D₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
136	D₅×C₄⋊C₄	C₂²×C₃	1	6	yes	—
137	D₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
138	#4034	C₂²×C₃	1	6	yes	complemented
139	#4034	C₂²×C₃	1	6	yes	complemented
140	#4033	C₂²×C₃	1	3	yes	complemented
141	#4027	C₂²×C₃	1	6	yes	—
142	D₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
143	#4024	C₂²×C₃	1	12	yes	complemented
144	C₄×D₂₀	C₂²×C₃	1	3	yes	—
145	C₄²×D₅	C₂²×C₃	1	3	yes	—
146	#4015	C₂²×C₃	1	3	yes	complemented
147	C₄×Dic₁₀	C₂²×C₃	1	3	yes	complemented
148	C₂×D₄×Q₈	—	5	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
150	C₂²×C₃×D₅	—	2	4	no	—
151	C₂²×C₃×D₅	—	2	4	no	—
152	C₂²×C₃×D₅	C₂×Q₈	1	8	yes	complemented
153	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
154	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
155	C₃×C₅×Q₈	—	2	12	no	—
156	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
157	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
158	C₂×C₃×C₄×C₅	—	2	12	no	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₂²⋊D₅	C₂×Q₈	1	8	yes	complemented
164	C₂×C₃×Dic₅	—	2	12	no	—
165	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
166	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
167	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
168	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
169	C₃×D₂₀	C₂×Q₈	1	4	yes	complemented
170	C₃×C₄×D₅	—	2	12	no	—
171	C₃×C₄×D₅	—	2	6	no	—
172	C₃×C₄×D₅	—	2	12	no	—
173	C₃×C₄×D₅	—	2	12	no	—
174	C₃×C₄×D₅	C₂×D₄	1	12	yes	—
175	C₃×C₄×D₅	C₂×Q₈	1	4	yes	complemented
176	C₃×Dic₁₀	—	2	12	no	—
177	C₃×Dic₁₀	—	2	24	no	—
178	C₃×Dic₁₀	C₂×D₄	1	12	yes	complemented
179	C₂²×C₃×Q₈	—	5	1	no	—
180	C₂²×C₃×Q₈	—	5	6	no	—
181	C₂²×C₃×Q₈	—	5	6	no	—
182	C₂²×C₃×Q₈	—	5	2	no	—
183	C₂²×C₃×Q₈	—	5	6	no	—
184	C₂²×C₃×Q₈	—	10	16	no	—
185	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	complemented
186	C₂²×C₃×D₄	—	5	1	no	—
187	C₂³×C₃×C₄	—	5	6	no	—
188	C₃×C₄⋊Q₈	—	5	6	no	—
189	C₃×C₄⋊Q₈	—	5	6	no	—
190	C₃×C₄⋊Q₈	—	5	6	no	—
191	C₃×C₄⋊Q₈	—	5	3	no	—
192	C₃×C₄⋊Q₈	C₂×D₅	1	3	yes	complemented
193	C₃×C₂²⋊Q₈	—	5	6	no	—
194	C₃×C₂²⋊Q₈	—	5	6	no	—
195	C₃×C₂²⋊Q₈	—	5	12	no	—
196	C₃×C₂²⋊Q₈	—	5	6	no	—
197	C₃×C₂²⋊Q₈	—	5	12	no	—
198	C₃×C₂²⋊Q₈	C₂×D₅	1	6	yes	complemented
199	C₃×C₄×Q₈	—	5	1	no	—
200	C₃×C₄×Q₈	—	5	3	no	—
201	C₃×C₄×Q₈	—	5	3	no	—
202	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
203	C₃×C₄×D₄	—	5	3	no	—
204	C₃×C₄×D₄	—	5	6	no	—
205	C₃×C₄×D₄	—	5	3	no	—
206	C₃×C₄×D₄	—	5	6	no	—
207	C₃×C₄×D₄	—	5	3	no	—
208	C₃×C₄×D₄	C₂×D₅	1	3	yes	—
209	C₂×C₃×C₄⋊C₄	—	5	3	no	—
210	C₂×C₃×C₄⋊C₄	—	5	3	no	—
211	C₂×C₃×C₄⋊C₄	—	5	6	no	—
212	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
213	C₂×C₃×C₄²	—	5	3	no	—
214	C₂³×D₅	C₂³×C₃	1	2	yes	—
215	C₂×C₅×Q₈	—	2	8	no	—
216	C₂×C₅×Q₈	C₂³×C₃	1	6	yes	—
217	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
220	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
221	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
222	Q₈×D₅	—	2	8	no	—
223	Q₈×D₅	—	2	24	no	—
224	Q₈×D₅	—	2	24	no	—
225	Q₈×D₅	C₃×D₄	1	8	yes	direct product factor
226	D₄×D₅	C₃×Q₈	1	8	yes	direct product factor
227	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
228	C₂×C₄×D₅	—	2	24	no	—
229	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
230	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
231	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
232	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
233	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
234	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
235	C₂×Dic₁₀	—	2	24	no	—
236	C₂×Dic₁₀	C₂³×C₃	1	6	yes	—
237	C₂×Dic₁₀	C₂³×C₃	1	12	yes	—
238	C₂×Dic₁₀	C₂³×C₃	1	3	yes	—
239	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
240	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
241	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
242	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
243	C₄²×C₅	C₂³×C₃	1	3	yes	—
244	C₂²⋊Dic₅	C₂³×C₃	1	6	yes	—
245	#685	C₂³×C₃	1	6	yes	—
246	#685	C₂³×C₃	1	6	yes	—
247	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
248	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
249	C₄⋊Dic₅	C₂³×C₃	1	6	yes	—
250	#683	C₂³×C₃	1	6	yes	—
251	#683	C₂³×C₃	1	12	yes	—
252	#683	C₂³×C₃	1	6	yes	—
253	C₄×Dic₅	C₂³×C₃	1	3	yes	—
254	C₄×Dic₅	C₂³×C₃	1	3	yes	—
255	C₄×Dic₅	C₂³×C₃	1	3	yes	—
256	C₂³×Q₈	—	5	2	no	—
257	D₄×Q₈	—	5	2	no	—
258	D₄×Q₈	—	5	3	no	—
259	D₄×Q₈	—	5	6	no	—
260	D₄×Q₈	—	5	1	no	—
261	D₄×Q₈	—	5	3	no	—
262	D₄×Q₈	C₃×D₅	1	1	yes	characteristic, direct product factor
263	C₂×C₄⋊Q₈	—	5	3	no	—
264	C₂×C₂²⋊Q₈	—	5	6	no	—
265	C₂×C₄×Q₈	—	5	1	no	—
266	C₂×C₄×D₄	—	5	3	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	complemented
270	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
271	C₂×C₃×D₅	—	2	2	no	—
272	C₂×C₃×D₅	—	2	2	no	—
273	C₂×C₃×D₅	—	2	16	no	—
274	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
275	C₂×C₃×D₅	C₂²×Q₈	1	2	yes	—
276	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	complemented
277	C₂×C₃×D₅	2₋¹⁺⁴	1	2	yes	—
278	C₃×C₄×C₅	—	2	6	no	—
279	C₃×C₄×C₅	—	2	3	no	—
280	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
281	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	complemented
282	C₃×Dic₅	—	2	6	no	—
283	C₃×Dic₅	—	2	3	no	—
284	C₃×Dic₅	C₂²×D₄	1	6	yes	—
285	C₃×Dic₅	C₂²×Q₈	1	2	yes	complemented
286	C₂⁴×C₃	—	5	2	no	—
287	C₂×C₃×Q₈	—	2	8	no	—
288	C₂×C₃×Q₈	—	5	8	no	—
289	C₂×C₃×Q₈	—	5	3	no	—
290	C₂×C₃×Q₈	—	5	12	no	—
291	C₂×C₃×Q₈	—	5	6	no	—
292	C₂×C₃×Q₈	—	10	24	no	—
293	C₂×C₃×Q₈	—	10	24	no	—
294	C₂×C₃×Q₈	—	10	24	no	—
295	C₂×C₃×Q₈	—	10	8	no	—
296	C₂×C₃×Q₈	C₂²×D₅	1	6	yes	—
297	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
298	C₂×C₃×D₄	—	5	2	no	—
299	C₂×C₃×D₄	—	5	8	no	—
300	C₂×C₃×D₄	—	5	1	no	—
301	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
302	C₂²×C₃×C₄	—	5	1	no	—
303	C₂²×C₃×C₄	—	5	3	no	—
304	C₂²×C₃×C₄	—	5	6	no	—
305	C₂²×C₃×C₄	—	5	3	no	—
306	C₂²×C₃×C₄	—	5	6	no	—
307	C₂²×C₃×C₄	—	5	6	no	—
308	C₂²×C₃×C₄	—	5	6	no	—
309	C₂²×C₃×C₄	—	10	24	no	—
310	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
311	C₃×C₄⋊C₄	—	5	6	no	—
312	C₃×C₄⋊C₄	—	5	6	no	—
313	C₃×C₄⋊C₄	—	5	12	no	—
314	C₃×C₄⋊C₄	—	5	3	no	—
315	C₃×C₄⋊C₄	—	5	3	no	—
316	C₃×C₄⋊C₄	—	5	6	no	—
317	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
318	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
319	C₃×C₄⋊C₄	C₂²×D₅	1	6	yes	—
320	C₃×C₂²⋊C₄	—	5	6	no	—
321	C₃×C₂²⋊C₄	—	5	6	no	—
322	C₃×C₂²⋊C₄	—	5	6	no	—
323	C₃×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
324	C₃×C₄²	—	5	3	no	—
325	C₃×C₄²	—	5	3	no	—
326	C₃×C₄²	—	5	3	no	—
327	C₃×C₄²	C₂²×D₅	1	3	yes	—
328	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
329	C₂²×D₅	—	2	4	no	—
330	C₂²×D₅	—	2	4	no	—
331	C₂²×D₅	C₂×C₃×Q₈	1	8	yes	complemented
332	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
333	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
334	C₅×Q₈	—	2	12	no	—
335	C₅×Q₈	C₂×C₃×D₄	1	4	yes	complemented
336	C₅×D₄	C₂×C₃×Q₈	1	4	yes	complemented
337	C₂×C₄×C₅	—	2	12	no	—
338	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
339	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
340	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
341	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
342	C₂²⋊D₅	C₂×C₃×Q₈	1	8	yes	complemented
343	C₂×Dic₅	—	2	12	no	—
344	C₂×Dic₅	C₂⁴×C₃	1	3	yes	—
345	C₂×Dic₅	C₂⁴×C₃	1	6	yes	—
346	C₂×Dic₅	C₂⁴×C₃	1	3	yes	—
347	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
348	D₂₀	C₂×C₃×Q₈	1	4	yes	complemented
349	C₄×D₅	—	2	12	no	—
350	C₄×D₅	—	2	6	no	—
351	C₄×D₅	—	2	12	no	—
352	C₄×D₅	—	2	12	no	—
353	C₄×D₅	C₂×C₃×D₄	1	12	yes	—
354	C₄×D₅	C₂×C₃×Q₈	1	4	yes	complemented
355	Dic₁₀	—	2	12	no	—
356	Dic₁₀	—	2	24	no	—
357	Dic₁₀	C₂×C₃×D₄	1	12	yes	complemented
358	C₂²×Q₈	—	5	1	no	—
359	C₂²×Q₈	—	5	6	no	—
360	C₂²×Q₈	—	5	6	no	—
361	C₂²×Q₈	—	5	2	no	—
362	C₂²×Q₈	—	5	6	no	—
363	C₂²×Q₈	—	10	16	no	—
364	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	complemented
365	C₂²×D₄	—	5	1	no	—
366	C₂³×C₄	—	5	6	no	—
367	C₄⋊Q₈	—	5	6	no	—
368	C₄⋊Q₈	—	5	6	no	—
369	C₄⋊Q₈	—	5	6	no	—
370	C₄⋊Q₈	—	5	3	no	—
371	C₄⋊Q₈	C₂×C₃×D₅	1	3	yes	complemented
372	C₂²⋊Q₈	—	5	6	no	—
373	C₂²⋊Q₈	—	5	6	no	—
374	C₂²⋊Q₈	—	5	12	no	—
375	C₂²⋊Q₈	—	5	6	no	—
376	C₂²⋊Q₈	—	5	12	no	—
377	C₂²⋊Q₈	C₂×C₃×D₅	1	6	yes	complemented
378	C₄×Q₈	—	5	1	no	—
379	C₄×Q₈	—	5	3	no	—
380	C₄×Q₈	—	5	3	no	—
381	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
382	C₄×D₄	—	5	3	no	—
383	C₄×D₄	—	5	6	no	—
384	C₄×D₄	—	5	3	no	—
385	C₄×D₄	—	5	6	no	—
386	C₄×D₄	—	5	3	no	—
387	C₄×D₄	C₂×C₃×D₅	1	3	yes	—
388	C₂×C₄⋊C₄	—	5	3	no	—
389	C₂×C₄⋊C₄	—	5	3	no	—
390	C₂×C₄⋊C₄	—	5	6	no	—
391	C₂×C₂²⋊C₄	—	5	6	no	—
392	C₂×C₄²	—	5	3	no	—
393	C₂×C₃×C₅	—	2	4	no	—
394	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
395	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
396	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	C₃×D₅	—	2	4	no	—
398	C₃×D₅	D₄×Q₈	1	4	yes	direct product factor
399	C₂³×C₃	—	5	1	no	—
400	C₂³×C₃	—	5	8	no	—
401	C₂³×C₃	—	5	2	no	—
402	C₂³×C₃	—	10	4	no	—
403	C₂³×C₃	—	10	4	no	—
404	C₂³×C₃	C₂³×D₅	1	2	yes	—
405	C₃×Q₈	—	2	12	no	—
406	C₃×Q₈	—	5	12	no	—
407	C₃×Q₈	—	10	24	no	—
408	C₃×Q₈	—	10	12	no	—
409	C₃×Q₈	D₄×D₅	1	4	yes	direct product factor
410	C₃×D₄	—	5	8	no	—
411	C₃×D₄	—	5	4	no	—
412	C₃×D₄	Q₈×D₅	1	4	yes	direct product factor
413	C₂×C₃×C₄	—	2	12	no	—
414	C₂×C₃×C₄	—	5	1	no	—
415	C₂×C₃×C₄	—	5	3	no	—
416	C₂×C₃×C₄	—	5	12	no	—
417	C₂×C₃×C₄	—	5	4	no	—
418	C₂×C₃×C₄	—	5	3	no	—
419	C₂×C₃×C₄	—	5	6	no	—
420	C₂×C₃×C₄	—	10	12	no	—
421	C₂×C₃×C₄	—	10	6	no	—
422	C₂×C₃×C₄	—	10	12	no	—
423	C₂×C₃×C₄	—	10	12	no	—
424	C₂×C₃×C₄	—	10	12	no	—
425	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
426	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
427	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
428	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	C₂²×C₃×Q₈	1	4	yes	complemented
432	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
433	C₂×D₅	—	2	2	no	—
434	C₂×D₅	—	2	2	no	—
435	C₂×D₅	—	2	16	no	—
436	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
437	C₂×D₅	C₂²×C₃×Q₈	1	2	yes	—
438	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	complemented
439	C₂×D₅	C₃×2₋¹⁺⁴	1	2	yes	—
440	C₄×C₅	—	2	6	no	—
441	C₄×C₅	—	2	3	no	—
442	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
443	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	complemented
444	Dic₅	—	2	6	no	—
445	Dic₅	—	2	3	no	—
446	Dic₅	C₂²×C₃×D₄	1	6	yes	—
447	Dic₅	C₂²×C₃×Q₈	1	2	yes	complemented
448	C₂⁴	—	5	2	no	—
449	C₂×Q₈	—	2	8	no	—
450	C₂×Q₈	—	5	8	no	—
451	C₂×Q₈	—	5	3	no	—
452	C₂×Q₈	—	5	12	no	—
453	C₂×Q₈	—	5	6	no	—
454	C₂×Q₈	—	10	24	no	—
455	C₂×Q₈	—	10	24	no	—
456	C₂×Q₈	—	10	24	no	—
457	C₂×Q₈	—	10	8	no	—
458	C₂×Q₈	C₂²×C₃×D₅	1	6	yes	—
459	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
460	C₂×D₄	—	5	2	no	—
461	C₂×D₄	—	5	8	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
464	C₂²×C₄	—	5	1	no	—
465	C₂²×C₄	—	5	3	no	—
466	C₂²×C₄	—	5	6	no	—
467	C₂²×C₄	—	5	3	no	—
468	C₂²×C₄	—	5	6	no	—
469	C₂²×C₄	—	5	6	no	—
470	C₂²×C₄	—	5	6	no	—
471	C₂²×C₄	—	10	24	no	—
472	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
473	C₄⋊C₄	—	5	6	no	—
474	C₄⋊C₄	—	5	3	no	—
475	C₄⋊C₄	—	5	6	no	—
476	C₄⋊C₄	—	5	3	no	—
477	C₄⋊C₄	—	5	12	no	—
478	C₄⋊C₄	—	5	6	no	—
479	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
480	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
481	C₄⋊C₄	C₂²×C₃×D₅	1	6	yes	—
482	C₂²⋊C₄	—	5	6	no	—
483	C₂²⋊C₄	—	5	6	no	—
484	C₂²⋊C₄	—	5	6	no	—
485	C₂²⋊C₄	C₂²×C₃×D₅	1	6	yes	—
486	C₄²	—	5	3	no	—
487	C₄²	—	5	3	no	—
488	C₄²	—	5	3	no	—
489	C₄²	C₂²×C₃×D₅	1	3	yes	—
490	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	—	5	2	no	—
494	C₂²×C₃	—	5	2	no	—
495	C₂²×C₃	—	5	2	no	—
496	C₂²×C₃	—	5	4	no	—
497	C₂²×C₃	—	10	16	no	—
498	C₂²×C₃	—	10	2	no	—
499	C₂²×C₃	—	10	2	no	—
500	C₂²×C₃	C₂×Q₈×D₅	1	4	yes	complemented
501	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
502	C₃×C₄	—	2	6	no	—
503	C₃×C₄	—	2	3	no	—
504	C₃×C₄	—	5	6	no	—
505	C₃×C₄	—	5	2	no	—
506	C₃×C₄	—	10	6	no	—
507	C₃×C₄	—	10	3	no	—
508	C₃×C₄	C₂×D₄×D₅	1	6	yes	—
509	C₃×C₄	C₂×Q₈×D₅	1	2	yes	complemented
510	C₂×C₅	—	2	4	no	—
511	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
512	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
513	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
514	D₅	—	2	4	no	—
515	D₅	C₃×D₄×Q₈	1	4	yes	direct product factor
516	C₂³	—	5	1	no	—
517	C₂³	—	5	8	no	—
518	C₂³	—	5	2	no	—
519	C₂³	—	10	4	no	—
520	C₂³	—	10	4	no	—
521	C₂³	C₂³×C₃×D₅	1	2	yes	—
522	Q₈	—	2	12	no	—
523	Q₈	—	5	12	no	—
524	Q₈	—	10	24	no	—
525	Q₈	—	10	12	no	—
526	Q₈	C₃×D₄×D₅	1	4	yes	direct product factor
527	D₄	—	5	8	no	—
528	D₄	—	5	4	no	—
529	D₄	C₃×Q₈×D₅	1	4	yes	direct product factor
530	C₂×C₄	—	2	12	no	—
531	C₂×C₄	—	5	1	no	—
532	C₂×C₄	—	5	3	no	—
533	C₂×C₄	—	5	12	no	—
534	C₂×C₄	—	5	4	no	—
535	C₂×C₄	—	5	3	no	—
536	C₂×C₄	—	5	6	no	—
537	C₂×C₄	—	10	12	no	—
538	C₂×C₄	—	10	12	no	—
539	C₂×C₄	—	10	6	no	—
540	C₂×C₄	—	10	12	no	—
541	C₂×C₄	—	10	12	no	—
542	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
543	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
544	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
545	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
546	C₂×C₃	—	2	4	no	—
547	C₂×C₃	—	5	4	no	—
548	C₂×C₃	—	10	4	no	—
549	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
550	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
551	C₂×C₃	D₅×2₋¹⁺⁴	1	1	yes	characteristic
552	C₅	C₂×C₃×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	5	2	no	—
556	C₂²	—	5	2	no	—
557	C₂²	—	5	2	no	—
558	C₂²	—	5	4	no	—
559	C₂²	—	10	16	no	—
560	C₂²	—	10	2	no	—
561	C₂²	—	10	2	no	—
562	C₂²	C₂×C₃×Q₈×D₅	1	4	yes	complemented
563	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
564	C₄	—	2	6	no	—
565	C₄	—	2	3	no	—
566	C₄	—	5	6	no	—
567	C₄	—	5	2	no	—
568	C₄	—	10	6	no	—
569	C₄	—	10	3	no	—
570	C₄	C₂×C₃×D₄×D₅	1	6	yes	—
571	C₄	C₂×C₃×Q₈×D₅	1	2	yes	complemented
572	C₃	D₄×Q₈×D₅	1	1	yes	characteristic, direct product factor, Sylow
573	C₂	—	2	4	no	—
574	C₂	—	5	4	no	—
575	C₂	—	10	4	no	—
576	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
577	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
578	C₂	C₃×D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×D₄×Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₃×D₄×D₅	C₂²
hypercenter	C₃×D₄×Q₈	D₅
hypocenter	C₅	C₂×C₃×D₄×Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×D₅	C₂	semidirect
2. C₃×C₅×D₄×Q₈	C₂	semidirect
3. C₃×Q₈×C₂²⋊D₅	C₂	semidirect
4. C₃×#66061	C₂	semidirect
5. C₃×D₅×C₄⋊Q₈	C₂	semidirect
6. C₃×#65966	C₂	semidirect
7. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
8. C₃×Q₈×D₂₀	C₂	semidirect
9. C₃×C₄×Q₈×D₅	C₂	semidirect
11. C₃×D₄×Dic₁₀	C₂	semidirect
12. D₄×Q₈×D₅	C₃	direct (N × H)
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×C₃×Q₈×D₅	C₂²	semidirect
18. C₂×C₃×Q₈×D₅	C₂²	semidirect
21. C₂²×C₃×Dic₁₀	C₂²	semidirect
22. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₃×#4092	C₂²	semidirect
27. C₃×Q₈×Dic₅	C₂²	semidirect
28. C₃×#4090	C₂²	semidirect
31. C₃×#4070	C₂²	semidirect
32. C₃×#4043	C₂²	semidirect
33. C₃×#4042	C₂²	semidirect
38. C₃×#4034	C₂²	semidirect
39. C₃×#4034	C₂²	semidirect
40. C₃×#4033	C₂²	semidirect
43. C₃×#4024	C₂²	semidirect
46. C₃×#4015	C₂²	semidirect
47. C₃×C₄×Dic₁₀	C₂²	semidirect
49. C₂²×Q₈×D₅	C₂×C₃	semidirect
50. C₅×D₄×Q₈	C₂×C₃	semidirect
51. Q₈×C₂²⋊D₅	C₂×C₃	semidirect
52. #66061	C₂×C₃	semidirect
53. D₅×C₄⋊Q₈	C₂×C₃	semidirect
54. #65966	C₂×C₃	semidirect
55. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
56. Q₈×D₂₀	C₂×C₃	semidirect
57. C₄×Q₈×D₅	C₂×C₃	semidirect
59. D₄×Dic₁₀	C₂×C₃	semidirect
71. C₃×Q₈×D₅	D₄	direct (N × H)
72. C₃×D₄×D₅	Q₈	direct (N × H)
108. C₃×D₄×Q₈	D₅	direct (N × H)
113. C₂²×C₅×Q₈	C₂²×C₃	semidirect
117. C₂×Q₈×D₅	C₂²×C₃	semidirect
118. C₂×Q₈×D₅	C₂²×C₃	semidirect
121. C₂²×Dic₁₀	C₂²×C₃	semidirect
122. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
123. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
124. C₄×C₅×Q₈	C₂²×C₃	semidirect
126. #4092	C₂²×C₃	semidirect
127. Q₈×Dic₅	C₂²×C₃	semidirect
128. #4090	C₂²×C₃	semidirect
131. #4070	C₂²×C₃	semidirect
132. #4043	C₂²×C₃	semidirect
133. #4042	C₂²×C₃	semidirect
138. #4034	C₂²×C₃	semidirect
139. #4034	C₂²×C₃	semidirect
140. #4033	C₂²×C₃	semidirect
143. #4024	C₂²×C₃	semidirect
146. #4015	C₂²×C₃	semidirect
147. C₄×Dic₁₀	C₂²×C₃	semidirect
152. C₂²×C₃×D₅	C₂×Q₈	semidirect
156. C₃×C₅×Q₈	C₂×D₄	semidirect
157. C₃×C₅×D₄	C₂×Q₈	semidirect
163. C₃×C₂²⋊D₅	C₂×Q₈	semidirect
169. C₃×D₂₀	C₂×Q₈	semidirect
175. C₃×C₄×D₅	C₂×Q₈	semidirect
178. C₃×Dic₁₀	C₂×D₄	semidirect
185. C₂²×C₃×Q₈	C₂×D₅	semidirect
192. C₃×C₄⋊Q₈	C₂×D₅	semidirect
198. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
202. C₃×C₄×Q₈	C₂×D₅	semidirect
225. Q₈×D₅	C₃×D₄	direct (N × H)
226. D₄×D₅	C₃×Q₈	direct (N × H)
262. D₄×Q₈	C₃×D₅	direct (N × H)
269. C₂²×C₃×C₅	C₂²×Q₈	semidirect
276. C₂×C₃×D₅	C₂²×Q₈	semidirect
281. C₃×C₄×C₅	C₂²×Q₈	semidirect
285. C₃×Dic₅	C₂²×Q₈	semidirect
331. C₂²×D₅	C₂×C₃×Q₈	semidirect
335. C₅×Q₈	C₂×C₃×D₄	semidirect
336. C₅×D₄	C₂×C₃×Q₈	semidirect
342. C₂²⋊D₅	C₂×C₃×Q₈	semidirect
348. D₂₀	C₂×C₃×Q₈	semidirect
354. C₄×D₅	C₂×C₃×Q₈	semidirect
357. Dic₁₀	C₂×C₃×D₄	semidirect
364. C₂²×Q₈	C₂×C₃×D₅	semidirect
371. C₄⋊Q₈	C₂×C₃×D₅	semidirect
377. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
381. C₄×Q₈	C₂×C₃×D₅	semidirect
398. C₃×D₅	D₄×Q₈	direct (N × H)
409. C₃×Q₈	D₄×D₅	direct (N × H)
412. C₃×D₄	Q₈×D₅	direct (N × H)
431. C₂²×C₅	C₂²×C₃×Q₈	semidirect
438. C₂×D₅	C₂²×C₃×Q₈	semidirect
443. C₄×C₅	C₂²×C₃×Q₈	semidirect
447. Dic₅	C₂²×C₃×Q₈	semidirect
490. C₃×C₅	C₂×D₄×Q₈	semidirect
500. C₂²×C₃	C₂×Q₈×D₅	semidirect
509. C₃×C₄	C₂×Q₈×D₅	semidirect
515. D₅	C₃×D₄×Q₈	direct (N × H)
526. Q₈	C₃×D₄×D₅	direct (N × H)
529. D₄	C₃×Q₈×D₅	direct (N × H)
552. C₅	C₂×C₃×D₄×Q₈	semidirect
562. C₂²	C₂×C₃×Q₈×D₅	semidirect
571. C₄	C₂×C₃×Q₈×D₅	semidirect
572. C₃	D₄×Q₈×D₅	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×Q₈×D₅	2
C₃×C₅×D₄×Q₈	2
C₃×Q₈×C₂²⋊D₅	2
C₃×#66061	2
C₃×D₅×C₄⋊Q₈	2
C₃×#65966	2
C₃×D₅×C₂²⋊Q₈	2
C₃×Q₈×D₂₀	2
C₃×C₄×Q₈×D₅	2
C₃×C₄×D₄×D₅	2
C₃×D₄×Dic₁₀	2
D₄×Q₈×D₅	3
C₂×C₃×D₄×Q₈	5

Subgroups — C3×D4×Q8×D5 #14482897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×Q₈×D₅ #14482897