Subgroups — C₂×C₃×#66064 #14483809

Order 1920.

2400 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4092	C₂	1	4	yes	maximal, complemented
3	C₃×#66064	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4043	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4039	C₂	1	2	yes	maximal
6	C₂×C₃×D₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4036	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66064	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
15	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×#4092	C₂²	1	32	yes	complemented
21	C₂×C₃×#685	C₂²	1	4	yes	—
22	C₂×C₃×#685	C₂²	1	2	yes	—
23	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
24	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×#683	C₂²	1	2	yes	—
27	C₂×C₃×#683	C₂²	1	4	yes	—
28	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
29	C₃×#4043	C₂²	1	16	yes	complemented
30	C₃×#4039	C₂²	1	16	yes	—
31	C₃×D₅×C₄⋊C₄	C₂²	1	16	yes	complemented
32	C₃×#4036	C₂²	1	16	yes	complemented
33	C₃×C₄×D₂₀	C₂²	1	8	yes	—
34	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
35	C₂×C₃×#554	—	5	1	no	maximal, Hall
36	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4092	C₂×C₃	1	4	yes	complemented
38	#66064	C₂×C₃	1	16	yes	direct product factor
39	C₂×#4043	C₂×C₃	1	2	yes	complemented
40	C₂×#4039	C₂×C₃	1	2	yes	—
41	C₂×D₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
42	C₂×#4036	C₂×C₃	1	2	yes	complemented
43	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
44	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×D₅	C₂³	1	2	yes	—
46	C₂×C₃×C₅×Q₈	—	4	4	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
53	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂×C₃×D₂₀	Q₈	1	8	yes	complemented
56	C₂×C₃×D₂₀	C₂³	1	4	yes	—
57	C₂×C₃×C₄×D₅	—	2	8	no	—
58	C₂×C₃×C₄×D₅	—	4	8	no	—
59	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
60	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
61	C₂×C₃×Dic₁₀	—	2	4	no	—
62	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
65	C₃×C₄²×C₅	C₂³	1	4	yes	—
66	C₃×#685	C₂³	1	8	yes	—
67	C₃×#685	C₂³	1	16	yes	—
68	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
69	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
70	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
71	C₃×#683	C₂³	1	8	yes	—
72	C₃×#683	C₂³	1	16	yes	—
73	C₃×C₄×Dic₅	C₂³	1	8	yes	—
74	C₃×#554	—	5	16	no	—
75	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
76	C₂×C₃×#125	—	5	2	no	—
77	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
78	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
79	C₂×C₃×C₄×Q₈	—	5	1	no	—
80	C₂×C₃×C₄×D₄	—	5	2	no	—
81	C₂×C₃×C₄×D₄	—	5	1	no	—
82	C₂²×C₃×C₄⋊C₄	—	5	2	no	—
83	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
84	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
86	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
87	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
88	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
92	#4092	C₂²×C₃	1	32	yes	complemented
93	C₂×#685	C₂²×C₃	1	2	yes	—
94	C₂×#685	C₂²×C₃	1	4	yes	—
95	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
98	C₂×#683	C₂²×C₃	1	2	yes	—
99	C₂×#683	C₂²×C₃	1	4	yes	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
101	#4043	C₂²×C₃	1	16	yes	complemented
102	#4039	C₂²×C₃	1	16	yes	—
103	D₅×C₄⋊C₄	C₂²×C₃	1	16	yes	complemented
104	#4036	C₂²×C₃	1	16	yes	complemented
105	C₄×D₂₀	C₂²×C₃	1	8	yes	—
106	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
107	C₂×#554	—	5	1	no	Sylow
108	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
109	C₂²×C₃×D₅	—	2	4	no	—
110	C₂²×C₃×D₅	—	2	4	no	—
111	C₂²×C₃×D₅	C₂×Q₈	1	8	yes	—
112	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
113	C₃×C₅×Q₈	—	4	8	no	—
114	C₂×C₃×C₄×C₅	—	2	8	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
117	C₂×C₃×C₄×C₅	#41	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
122	C₂×C₃×Dic₅	—	2	4	no	—
123	C₂×C₃×Dic₅	—	2	4	no	—
124	C₂×C₃×Dic₅	—	2	4	no	—
125	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
126	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
127	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
128	C₃×D₂₀	C₂×Q₈	1	16	yes	complemented
129	C₃×C₄×D₅	—	2	16	no	—
130	C₃×C₄×D₅	—	4	16	no	—
131	C₃×Dic₁₀	—	2	8	no	—
132	C₂²×C₃×Q₈	—	5	1	no	—
133	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
134	C₂²×C₃×D₄	—	5	1	no	—
135	C₂³×C₃×C₄	—	5	2	no	—
136	C₂³×C₃×C₄	—	5	4	no	—
137	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
138	C₃×#125	—	5	16	no	—
139	C₃×C₂²⋊Q₈	—	5	32	no	—
140	C₃×C₂²⋊Q₈	—	5	16	no	—
141	C₃×C₄×Q₈	—	5	8	no	—
142	C₃×C₄×D₄	—	5	16	no	—
143	C₃×C₄×D₄	—	5	8	no	—
144	C₂×C₃×C₄⋊C₄	—	5	1	no	—
145	C₂×C₃×C₄⋊C₄	—	5	4	no	—
146	C₂×C₃×C₄⋊C₄	—	5	1	no	—
147	C₂×C₃×C₄⋊C₄	—	5	2	no	—
148	C₂×C₃×C₄⋊C₄	—	5	4	no	—
149	C₂×C₃×C₄⋊C₄	—	5	16	no	—
150	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
152	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
153	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
154	C₂×C₃×C₄²	—	5	2	no	—
155	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
156	C₂³×D₅	C₂³×C₃	1	2	yes	—
157	C₂×C₅×Q₈	—	4	4	no	—
158	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
164	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
165	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
166	C₂×D₂₀	C₃×Q₈	1	8	yes	complemented
167	C₂×D₂₀	C₂³×C₃	1	4	yes	—
168	C₂×C₄×D₅	—	2	8	no	—
169	C₂×C₄×D₅	—	4	8	no	—
170	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
171	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
172	C₂×Dic₁₀	—	2	4	no	—
173	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
174	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
175	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
176	C₄²×C₅	C₂³×C₃	1	4	yes	—
177	#685	C₂³×C₃	1	8	yes	—
178	#685	C₂³×C₃	1	16	yes	—
179	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
180	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
181	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
182	#683	C₂³×C₃	1	8	yes	—
183	#683	C₂³×C₃	1	16	yes	—
184	C₄×Dic₅	C₂³×C₃	1	8	yes	—
185	#554	—	5	16	no	—
186	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
187	C₂×#125	—	5	2	no	—
188	C₂×C₂²⋊Q₈	—	5	4	no	—
189	C₂×C₂²⋊Q₈	—	5	2	no	—
190	C₂×C₄×Q₈	—	5	1	no	—
191	C₂×C₄×D₄	—	5	2	no	—
192	C₂×C₄×D₄	—	5	1	no	—
193	C₂²×C₄⋊C₄	—	5	2	no	—
194	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
195	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
196	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
197	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
198	C₂×C₃×D₅	—	2	16	no	—
199	C₂×C₃×D₅	—	2	4	no	—
200	C₂×C₃×D₅	—	2	4	no	—
201	C₂×C₃×D₅	C₂²×Q₈	1	8	yes	—
202	C₃×C₄×C₅	—	2	8	no	—
203	C₃×C₄×C₅	—	2	2	no	—
204	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	—
205	C₃×C₄×C₅	C₂×#41	1	4	yes	—
206	C₃×Dic₅	—	2	4	no	—
207	C₃×Dic₅	—	2	4	no	—
208	C₃×Dic₅	—	2	4	no	—
209	C₂⁴×C₃	—	5	2	no	—
210	C₂×C₃×Q₈	—	4	4	no	—
211	C₂×C₃×Q₈	—	5	4	no	—
212	C₂×C₃×Q₈	—	10	4	no	—
213	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
214	C₂×C₃×D₄	—	5	8	no	—
215	C₂×C₃×D₄	—	5	4	no	—
216	C₂²×C₃×C₄	—	5	2	no	—
217	C₂²×C₃×C₄	—	5	2	no	—
218	C₂²×C₃×C₄	—	5	2	no	—
219	C₂²×C₃×C₄	—	5	8	no	—
220	C₂²×C₃×C₄	—	5	16	no	—
221	C₂²×C₃×C₄	—	10	8	no	—
222	C₂²×C₃×C₄	—	20	8	no	—
223	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
225	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	5	16	no	—
228	C₃×C₄⋊C₄	—	5	8	no	—
229	C₃×C₄⋊C₄	—	5	4	no	—
230	C₃×C₄⋊C₄	—	5	4	no	—
231	C₃×C₄⋊C₄	—	5	16	no	—
232	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
233	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
234	C₃×C₂²⋊C₄	—	5	16	no	—
235	C₃×C₂²⋊C₄	—	5	8	no	—
236	C₃×C₄²	—	5	8	no	—
237	C₃×C₄²	C₂²×D₅	1	4	yes	—
238	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
239	C₂²×D₅	—	2	4	no	—
240	C₂²×D₅	—	2	4	no	—
241	C₂²×D₅	C₂×C₃×Q₈	1	8	yes	—
242	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
243	C₅×Q₈	—	4	8	no	—
244	C₂×C₄×C₅	—	2	8	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
247	C₂×C₄×C₅	C₃×#41	1	4	yes	—
248	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
249	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
250	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
251	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
252	C₂×Dic₅	—	2	4	no	—
253	C₂×Dic₅	—	2	4	no	—
254	C₂×Dic₅	—	2	4	no	—
255	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
256	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
257	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
258	D₂₀	C₂×C₃×Q₈	1	16	yes	complemented
259	C₄×D₅	—	2	16	no	—
260	C₄×D₅	—	4	16	no	—
261	Dic₁₀	—	2	8	no	—
262	C₂²×Q₈	—	5	1	no	—
263	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
264	C₂²×D₄	—	5	1	no	—
265	C₂³×C₄	—	5	2	no	—
266	C₂³×C₄	—	5	4	no	—
267	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
268	#125	—	5	16	no	—
269	C₂²⋊Q₈	—	5	32	no	—
270	C₂²⋊Q₈	—	5	16	no	—
271	C₄×Q₈	—	5	8	no	—
272	C₄×D₄	—	5	16	no	—
273	C₄×D₄	—	5	8	no	—
274	C₂×C₄⋊C₄	—	5	1	no	—
275	C₂×C₄⋊C₄	—	5	4	no	—
276	C₂×C₄⋊C₄	—	5	1	no	—
277	C₂×C₄⋊C₄	—	5	2	no	—
278	C₂×C₄⋊C₄	—	5	4	no	—
279	C₂×C₄⋊C₄	—	5	16	no	—
280	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
282	C₂×C₂²⋊C₄	—	5	4	no	—
283	C₂×C₂²⋊C₄	—	5	2	no	—
284	C₂×C₄²	—	5	2	no	—
285	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
286	C₂×C₃×C₅	#554	1	4	yes	complemented
287	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₃×D₅	—	2	8	no	—
291	C₂³×C₃	—	5	8	no	—
292	C₂³×C₃	—	5	4	no	—
293	C₂³×C₃	—	10	4	no	—
294	C₂³×C₃	—	10	4	no	—
295	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
296	C₃×Q₈	—	4	8	no	—
297	C₃×Q₈	—	10	8	no	—
298	C₃×D₄	—	5	16	no	—
299	C₂×C₃×C₄	—	2	8	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	5	4	no	—
302	C₂×C₃×C₄	—	5	4	no	—
303	C₂×C₃×C₄	—	5	4	no	—
304	C₂×C₃×C₄	—	10	4	no	—
305	C₂×C₃×C₄	—	10	4	no	—
306	C₂×C₃×C₄	—	10	4	no	—
307	C₂×C₃×C₄	—	10	16	no	—
308	C₂×C₃×C₄	—	20	16	no	—
309	C₂×C₃×C₄	Q₈×D₅	1	4	yes	—
310	C₂×C₃×C₄	#713	1	4	yes	—
311	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
312	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
313	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
314	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
315	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
316	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
317	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
319	C₂×D₅	—	2	4	no	—
320	C₂×D₅	—	2	4	no	—
321	C₂×D₅	—	2	16	no	—
322	C₂×D₅	C₂²×C₃×Q₈	1	8	yes	—
323	C₄×C₅	—	2	8	no	—
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	C₂²×C₃×Q₈	1	4	yes	—
326	C₄×C₅	C₂×C₃×#41	1	4	yes	—
327	Dic₅	—	2	4	no	—
328	Dic₅	—	2	4	no	—
329	Dic₅	—	2	4	no	—
330	C₂⁴	—	5	2	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	—	5	4	no	—
333	C₂×Q₈	—	10	4	no	—
334	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
335	C₂×D₄	—	5	8	no	—
336	C₂×D₄	—	5	4	no	—
337	C₂²×C₄	—	5	2	no	—
338	C₂²×C₄	—	5	2	no	—
339	C₂²×C₄	—	5	2	no	—
340	C₂²×C₄	—	5	8	no	—
341	C₂²×C₄	—	5	16	no	—
342	C₂²×C₄	—	10	8	no	—
343	C₂²×C₄	—	20	8	no	—
344	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
346	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
348	C₄⋊C₄	—	5	4	no	—
349	C₄⋊C₄	—	5	16	no	—
350	C₄⋊C₄	—	5	4	no	—
351	C₄⋊C₄	—	5	8	no	—
352	C₄⋊C₄	—	5	16	no	—
353	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
354	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
355	C₂²⋊C₄	—	5	16	no	—
356	C₂²⋊C₄	—	5	8	no	—
357	C₄²	—	5	8	no	—
358	C₄²	C₂²×C₃×D₅	1	4	yes	—
359	C₃×C₅	C₂×#554	1	1	yes	characteristic, complemented, Hall
360	C₂²×C₃	—	5	8	no	—
361	C₂²×C₃	—	10	16	no	—
362	C₂²×C₃	—	10	4	no	—
363	C₂²×C₃	—	10	4	no	—
364	C₂²×C₃	#4144	1	2	yes	—
365	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
366	C₂²×C₃	C₂×#713	1	2	yes	—
367	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
368	C₃×C₄	—	2	8	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	10	4	no	—
371	C₃×C₄	—	10	4	no	—
372	C₃×C₄	—	10	4	no	—
373	C₃×C₄	C₂×Q₈×D₅	1	4	yes	—
374	C₃×C₄	C₂×#713	1	4	yes	—
375	C₂×C₅	C₃×#554	1	4	yes	complemented
376	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
377	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
378	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
379	D₅	—	2	8	no	—
380	C₂³	—	5	8	no	—
381	C₂³	—	5	4	no	—
382	C₂³	—	10	4	no	—
383	C₂³	—	10	4	no	—
384	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
385	Q₈	—	4	8	no	—
386	Q₈	—	10	8	no	—
387	D₄	—	5	16	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	5	4	no	—
391	C₂×C₄	—	5	4	no	—
392	C₂×C₄	—	5	4	no	—
393	C₂×C₄	—	10	4	no	—
394	C₂×C₄	—	10	4	no	—
395	C₂×C₄	—	10	4	no	—
396	C₂×C₄	—	10	16	no	—
397	C₂×C₄	—	20	16	no	—
398	C₂×C₄	C₃×Q₈×D₅	1	4	yes	—
399	C₂×C₄	C₃×#713	1	4	yes	—
400	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
401	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
402	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
403	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
404	C₂×C₃	—	10	8	no	—
405	C₂×C₃	#66064	1	4	yes	direct product factor
406	C₂×C₃	C₂×#4144	1	1	yes	characteristic
407	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
408	C₂×C₃	C₂²×#713	1	1	yes	characteristic
409	C₅	C₂×C₃×#554	1	1	yes	characteristic, complemented, Sylow
410	C₂²	—	5	8	no	—
411	C₂²	—	10	4	no	—
412	C₂²	—	10	4	no	—
413	C₂²	—	10	16	no	—
414	C₂²	C₃×#4144	1	2	yes	—
415	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
416	C₂²	C₂×C₃×#713	1	2	yes	—
417	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
418	C₄	—	2	8	no	—
419	C₄	—	2	2	no	—
420	C₄	—	10	4	no	—
421	C₄	—	10	4	no	—
422	C₄	—	10	4	no	—
423	C₄	C₂×C₃×Q₈×D₅	1	4	yes	—
424	C₄	C₂×C₃×#713	1	4	yes	—
425	C₃	C₂×#66064	1	1	yes	characteristic, direct product factor, Sylow
426	C₂	—	10	8	no	—
427	C₂	C₃×#66064	1	4	yes	direct product factor
428	C₂	C₂×C₃×#4144	1	1	yes	characteristic
429	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
430	C₂	C₂²×C₃×#713	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#554
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
2. C₂×C₃×#4092	C₂	semidirect
3. C₃×#66064	C₂	direct (N × H)
4. C₂×C₃×#4043	C₂	semidirect
6. C₂×C₃×D₅×C₄⋊C₄	C₂	semidirect
7. C₂×C₃×#4036	C₂	semidirect
9. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
10. C₂×#66064	C₃	direct (N × H)
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×#4092	C₂²	semidirect
29. C₃×#4043	C₂²	semidirect
31. C₃×D₅×C₄⋊C₄	C₂²	semidirect
32. C₃×#4036	C₂²	semidirect
34. C₃×C₄×Dic₁₀	C₂²	semidirect
36. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
37. C₂×#4092	C₂×C₃	semidirect
38. #66064	C₂×C₃	direct (N × H)
39. C₂×#4043	C₂×C₃	semidirect
41. C₂×D₅×C₄⋊C₄	C₂×C₃	semidirect
42. C₂×#4036	C₂×C₃	semidirect
44. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
55. C₂×C₃×D₂₀	Q₈	semidirect
75. C₂×C₃×C₄⋊Q₈	D₅	semidirect
88. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
92. #4092	C₂²×C₃	semidirect
101. #4043	C₂²×C₃	semidirect
103. D₅×C₄⋊C₄	C₂²×C₃	semidirect
104. #4036	C₂²×C₃	semidirect
106. C₄×Dic₁₀	C₂²×C₃	semidirect
128. C₃×D₂₀	C₂×Q₈	semidirect
137. C₃×C₄⋊Q₈	C₂×D₅	semidirect
166. C₂×D₂₀	C₃×Q₈	semidirect
186. C₂×C₄⋊Q₈	C₃×D₅	semidirect
258. D₂₀	C₂×C₃×Q₈	semidirect
267. C₄⋊Q₈	C₂×C₃×D₅	semidirect
286. C₂×C₃×C₅	#554	semidirect
359. C₃×C₅	C₂×#554	semidirect
375. C₂×C₅	C₃×#554	semidirect
405. C₂×C₃	#66064	direct (N × H)
409. C₅	C₂×C₃×#554	semidirect
425. C₃	C₂×#66064	direct (N × H)
427. C₂	C₃×#66064	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×#4092	2
C₃×#66064	2
C₂×C₃×#4043	2
C₂×C₃×#4039	2
C₂×C₃×D₅×C₄⋊C₄	2
C₂×C₃×#4036	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#66064	3
C₂×C₃×#554	5

Subgroups — C2×C3×#66064 #14483809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66064 #14483809