Subgroups — C₂×C₃×#66061 #14482906

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 448 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4092	C₂	1	2	yes	maximal, complemented
4	C₃×#66061	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4042	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4039	C₂	1	2	yes	maximal
7	C₂×C₃×#4034	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×#66061	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂×C₃×Q₈×D₅	—	2	16	no	—
13	C₂×C₃×Q₈×D₅	C₂²	1	16	yes	complemented
14	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
17	C₂²×C₃×Dic₁₀	C₂²	1	4	yes	—
18	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×#4092	C₂²	1	16	yes	complemented
24	C₂×C₃×#685	C₂²	1	4	yes	—
25	C₂×C₃×#685	C₂²	1	2	yes	—
26	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×#683	C₂²	1	4	yes	—
29	C₂×C₃×#683	C₂²	1	2	yes	—
30	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
31	C₃×#4042	C₂²	1	32	yes	complemented
32	C₃×#4039	C₂²	1	16	yes	—
33	C₃×#4034	C₂²	1	16	yes	complemented
34	C₃×C₄×D₂₀	C₂²	1	8	yes	—
35	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
36	C₂×C₃×D₄×Q₈	—	5	1	no	maximal, Hall
37	C₂²×Q₈×D₅	C₂×C₃	1	2	yes	complemented
38	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#4092	C₂×C₃	1	2	yes	complemented
40	#66061	C₂×C₃	1	16	yes	direct product factor
41	C₂×#4042	C₂×C₃	1	4	yes	complemented
42	C₂×#4039	C₂×C₃	1	2	yes	—
43	C₂×#4034	C₂×C₃	1	2	yes	complemented
44	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
45	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂³×C₃×D₅	C₂³	1	2	yes	—
47	C₂×C₃×C₅×Q₈	—	2	8	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	8	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	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
56	C₃×Q₈×D₅	—	2	64	no	—
57	C₂×C₃×D₂₀	Q₈	1	8	yes	complemented
58	C₂×C₃×D₂₀	C₂³	1	4	yes	—
59	C₂×C₃×C₄×D₅	—	2	8	no	—
60	C₂×C₃×C₄×D₅	—	2	16	no	—
61	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
62	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
63	C₂×C₃×Dic₁₀	—	2	16	no	—
64	C₂×C₃×Dic₁₀	D₄	1	8	yes	complemented
65	C₂×C₃×Dic₁₀	C₂³	1	16	yes	—
66	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
69	C₃×C₄²×C₅	C₂³	1	4	yes	—
70	C₃×#685	C₂³	1	16	yes	—
71	C₃×#685	C₂³	1	8	yes	—
72	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
73	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
74	C₃×#683	C₂³	1	16	yes	—
75	C₃×#683	C₂³	1	8	yes	—
76	C₃×C₄×Dic₅	C₂³	1	8	yes	—
77	C₂³×C₃×Q₈	—	5	2	no	—
78	C₃×D₄×Q₈	—	5	16	no	—
79	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
80	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
81	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
82	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
83	C₂×C₃×C₄×Q₈	—	5	1	no	—
84	C₂×C₃×C₄×D₄	—	5	2	no	—
85	C₂×C₃×C₄×D₄	—	5	1	no	—
86	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
87	C₂×Q₈×D₅	—	2	16	no	—
88	C₂×Q₈×D₅	C₂²×C₃	1	16	yes	complemented
89	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
91	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
92	C₂²×Dic₁₀	C₂²×C₃	1	4	yes	—
93	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
94	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	#4092	C₂²×C₃	1	16	yes	complemented
99	C₂×#685	C₂²×C₃	1	2	yes	—
100	C₂×#685	C₂²×C₃	1	4	yes	—
101	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
103	C₂×#683	C₂²×C₃	1	2	yes	—
104	C₂×#683	C₂²×C₃	1	4	yes	—
105	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
106	#4042	C₂²×C₃	1	32	yes	complemented
107	#4039	C₂²×C₃	1	16	yes	—
108	#4034	C₂²×C₃	1	16	yes	complemented
109	C₄×D₂₀	C₂²×C₃	1	8	yes	—
110	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
111	C₂×D₄×Q₈	—	5	1	no	Sylow
112	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
113	C₂²×C₃×D₅	—	2	4	no	—
114	C₂²×C₃×D₅	—	2	4	no	—
115	C₂²×C₃×D₅	C₂×Q₈	1	8	yes	complemented
116	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
117	C₃×C₅×Q₈	—	2	16	no	—
118	C₂×C₃×C₄×C₅	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂×C₃×Dic₅	—	2	4	no	—
127	C₂×C₃×Dic₅	—	2	4	no	—
128	C₂×C₃×Dic₅	C₂×D₄	1	8	yes	—
129	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
130	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
131	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
132	C₃×D₂₀	C₂×Q₈	1	16	yes	complemented
133	C₃×C₄×D₅	—	2	16	no	—
134	C₃×C₄×D₅	—	2	32	no	—
135	C₃×Dic₁₀	—	2	32	no	—
136	C₃×Dic₁₀	C₂×D₄	1	16	yes	complemented
137	C₂²×C₃×Q₈	—	5	16	no	—
138	C₂²×C₃×Q₈	—	5	1	no	—
139	C₂²×C₃×Q₈	—	5	4	no	—
140	C₂²×C₃×Q₈	—	10	16	no	—
141	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
142	C₂²×C₃×D₄	—	5	1	no	—
143	C₂³×C₃×C₄	—	5	4	no	—
144	C₂³×C₃×C₄	—	5	2	no	—
145	C₃×C₄⋊Q₈	—	5	16	no	—
146	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
147	C₃×C₂²⋊Q₈	—	5	16	no	—
148	C₃×C₂²⋊Q₈	—	5	32	no	—
149	C₃×C₄×Q₈	—	5	8	no	—
150	C₃×C₄×D₄	—	5	16	no	—
151	C₃×C₄×D₄	—	5	8	no	—
152	C₂×C₃×C₄⋊C₄	—	5	1	no	—
153	C₂×C₃×C₄⋊C₄	—	5	2	no	—
154	C₂×C₃×C₄⋊C₄	—	5	1	no	—
155	C₂×C₃×C₄⋊C₄	—	5	4	no	—
156	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
159	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
160	C₂×C₃×C₄²	—	5	2	no	—
161	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
162	C₂³×D₅	C₂³×C₃	1	2	yes	—
163	C₂×C₅×Q₈	—	2	8	no	—
164	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
170	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
171	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
172	Q₈×D₅	—	2	64	no	—
173	C₂×D₂₀	C₃×Q₈	1	8	yes	complemented
174	C₂×D₂₀	C₂³×C₃	1	4	yes	—
175	C₂×C₄×D₅	—	2	8	no	—
176	C₂×C₄×D₅	—	2	16	no	—
177	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
178	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
179	C₂×Dic₁₀	—	2	16	no	—
180	C₂×Dic₁₀	C₃×D₄	1	8	yes	complemented
181	C₂×Dic₁₀	C₂³×C₃	1	16	yes	—
182	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
183	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
184	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
185	C₄²×C₅	C₂³×C₃	1	4	yes	—
186	#685	C₂³×C₃	1	8	yes	—
187	#685	C₂³×C₃	1	16	yes	—
188	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
189	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
190	#683	C₂³×C₃	1	8	yes	—
191	#683	C₂³×C₃	1	16	yes	—
192	C₄×Dic₅	C₂³×C₃	1	8	yes	—
193	C₂³×Q₈	—	5	2	no	—
194	D₄×Q₈	—	5	16	no	—
195	C₂×C₄⋊Q₈	—	5	2	no	—
196	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
197	C₂×C₂²⋊Q₈	—	5	2	no	—
198	C₂×C₂²⋊Q₈	—	5	4	no	—
199	C₂×C₄×Q₈	—	5	1	no	—
200	C₂×C₄×D₄	—	5	2	no	—
201	C₂×C₄×D₄	—	5	1	no	—
202	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
203	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
204	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
205	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
206	C₂×C₃×D₅	—	2	16	no	—
207	C₂×C₃×D₅	—	2	4	no	—
208	C₂×C₃×D₅	—	2	4	no	—
209	C₂×C₃×D₅	C₂²×Q₈	1	8	yes	complemented
210	C₃×C₄×C₅	—	2	8	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
213	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	complemented
214	C₃×Dic₅	—	2	4	no	—
215	C₃×Dic₅	—	2	4	no	—
216	C₃×Dic₅	C₂²×D₄	1	8	yes	—
217	C₂⁴×C₃	—	5	2	no	—
218	C₂×C₃×Q₈	—	2	8	no	—
219	C₂×C₃×Q₈	—	5	8	no	—
220	C₂×C₃×Q₈	—	5	4	no	—
221	C₂×C₃×Q₈	—	5	16	no	—
222	C₂×C₃×Q₈	—	10	16	no	—
223	C₂×C₃×Q₈	—	10	64	no	—
224	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
225	C₂×C₃×D₄	—	5	8	no	—
226	C₂×C₃×D₄	—	5	4	no	—
227	C₂²×C₃×C₄	—	5	2	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	—	5	2	no	—
230	C₂²×C₃×C₄	—	5	16	no	—
231	C₂²×C₃×C₄	—	5	8	no	—
232	C₂²×C₃×C₄	—	10	16	no	—
233	C₂²×C₃×C₄	—	10	8	no	—
234	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
236	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₃×C₄⋊C₄	—	5	8	no	—
239	C₃×C₄⋊C₄	—	5	16	no	—
240	C₃×C₄⋊C₄	—	5	4	no	—
241	C₃×C₄⋊C₄	—	5	4	no	—
242	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
243	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
244	C₃×C₂²⋊C₄	—	5	16	no	—
245	C₃×C₂²⋊C₄	—	5	8	no	—
246	C₃×C₄²	—	5	8	no	—
247	C₃×C₄²	C₂²×D₅	1	4	yes	—
248	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
249	C₂²×D₅	—	2	4	no	—
250	C₂²×D₅	—	2	4	no	—
251	C₂²×D₅	C₂×C₃×Q₈	1	8	yes	complemented
252	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
253	C₅×Q₈	—	2	16	no	—
254	C₂×C₄×C₅	—	2	8	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
257	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	complemented
258	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
259	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
260	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
261	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
262	C₂×Dic₅	—	2	4	no	—
263	C₂×Dic₅	—	2	4	no	—
264	C₂×Dic₅	C₂×C₃×D₄	1	8	yes	—
265	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
266	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
267	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
268	D₂₀	C₂×C₃×Q₈	1	16	yes	complemented
269	C₄×D₅	—	2	16	no	—
270	C₄×D₅	—	2	32	no	—
271	Dic₁₀	—	2	32	no	—
272	Dic₁₀	C₂×C₃×D₄	1	16	yes	complemented
273	C₂²×Q₈	—	5	16	no	—
274	C₂²×Q₈	—	5	1	no	—
275	C₂²×Q₈	—	5	4	no	—
276	C₂²×Q₈	—	10	16	no	—
277	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
278	C₂²×D₄	—	5	1	no	—
279	C₂³×C₄	—	5	4	no	—
280	C₂³×C₄	—	5	2	no	—
281	C₄⋊Q₈	—	5	16	no	—
282	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
283	C₂²⋊Q₈	—	5	16	no	—
284	C₂²⋊Q₈	—	5	32	no	—
285	C₄×Q₈	—	5	8	no	—
286	C₄×D₄	—	5	16	no	—
287	C₄×D₄	—	5	8	no	—
288	C₂×C₄⋊C₄	—	5	1	no	—
289	C₂×C₄⋊C₄	—	5	2	no	—
290	C₂×C₄⋊C₄	—	5	1	no	—
291	C₂×C₄⋊C₄	—	5	4	no	—
292	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
294	C₂×C₂²⋊C₄	—	5	4	no	—
295	C₂×C₂²⋊C₄	—	5	2	no	—
296	C₂×C₄²	—	5	2	no	—
297	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
299	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₃×D₅	—	2	8	no	—
303	C₂³×C₃	—	5	8	no	—
304	C₂³×C₃	—	5	4	no	—
305	C₂³×C₃	—	10	4	no	—
306	C₂³×C₃	—	10	4	no	—
307	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
308	C₃×Q₈	—	2	16	no	—
309	C₃×Q₈	—	5	16	no	—
310	C₃×Q₈	—	10	32	no	—
311	C₃×D₄	—	5	16	no	—
312	C₂×C₃×C₄	—	2	8	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	5	8	no	—
315	C₂×C₃×C₄	—	5	4	no	—
316	C₂×C₃×C₄	—	5	4	no	—
317	C₂×C₃×C₄	—	5	4	no	—
318	C₂×C₃×C₄	—	10	32	no	—
319	C₂×C₃×C₄	—	10	4	no	—
320	C₂×C₃×C₄	—	10	4	no	—
321	C₂×C₃×C₄	—	10	16	no	—
322	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
323	C₂×C₃×C₄	Q₈×D₅	1	4	yes	complemented
324	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
326	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
327	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
328	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
329	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
330	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
331	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
332	C₂×D₅	—	2	4	no	—
333	C₂×D₅	—	2	4	no	—
334	C₂×D₅	—	2	16	no	—
335	C₂×D₅	C₂²×C₃×Q₈	1	8	yes	complemented
336	C₄×C₅	—	2	8	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
339	C₄×C₅	C₂²×C₃×Q₈	1	4	yes	complemented
340	Dic₅	—	2	4	no	—
341	Dic₅	—	2	4	no	—
342	Dic₅	C₂²×C₃×D₄	1	8	yes	—
343	C₂⁴	—	5	2	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂×Q₈	—	5	8	no	—
346	C₂×Q₈	—	5	4	no	—
347	C₂×Q₈	—	5	16	no	—
348	C₂×Q₈	—	10	16	no	—
349	C₂×Q₈	—	10	64	no	—
350	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
351	C₂×D₄	—	5	8	no	—
352	C₂×D₄	—	5	4	no	—
353	C₂²×C₄	—	5	2	no	—
354	C₂²×C₄	—	5	2	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	—	5	16	no	—
357	C₂²×C₄	—	5	8	no	—
358	C₂²×C₄	—	10	16	no	—
359	C₂²×C₄	—	10	8	no	—
360	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
362	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
364	C₄⋊C₄	—	5	4	no	—
365	C₄⋊C₄	—	5	8	no	—
366	C₄⋊C₄	—	5	4	no	—
367	C₄⋊C₄	—	5	16	no	—
368	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
369	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
370	C₂²⋊C₄	—	5	16	no	—
371	C₂²⋊C₄	—	5	8	no	—
372	C₄²	—	5	8	no	—
373	C₄²	C₂²×C₃×D₅	1	4	yes	—
374	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	5	8	no	—
376	C₂²×C₃	—	10	16	no	—
377	C₂²×C₃	—	10	4	no	—
378	C₂²×C₃	—	10	4	no	—
379	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
380	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
381	C₂²×C₃	#4147	1	2	yes	—
382	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
383	C₃×C₄	—	2	8	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	5	8	no	—
386	C₃×C₄	—	10	4	no	—
387	C₃×C₄	—	10	4	no	—
388	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
389	C₃×C₄	C₂×Q₈×D₅	1	4	yes	complemented
390	C₂×C₅	C₃×D₄×Q₈	1	4	yes	complemented
391	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
392	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
393	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
394	D₅	—	2	8	no	—
395	C₂³	—	5	8	no	—
396	C₂³	—	5	4	no	—
397	C₂³	—	10	4	no	—
398	C₂³	—	10	4	no	—
399	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
400	Q₈	—	2	16	no	—
401	Q₈	—	5	16	no	—
402	Q₈	—	10	32	no	—
403	D₄	—	5	16	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	5	8	no	—
407	C₂×C₄	—	5	4	no	—
408	C₂×C₄	—	5	4	no	—
409	C₂×C₄	—	5	4	no	—
410	C₂×C₄	—	10	32	no	—
411	C₂×C₄	—	10	4	no	—
412	C₂×C₄	—	10	4	no	—
413	C₂×C₄	—	10	16	no	—
414	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
415	C₂×C₄	C₃×Q₈×D₅	1	4	yes	complemented
416	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
417	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
418	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
419	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
420	C₂×C₃	—	10	8	no	—
421	C₂×C₃	#66061	1	4	yes	direct product factor
422	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
423	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
424	C₂×C₃	C₂×#4147	1	1	yes	characteristic
425	C₅	C₂×C₃×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
426	C₂²	—	5	8	no	—
427	C₂²	—	10	4	no	—
428	C₂²	—	10	4	no	—
429	C₂²	—	10	16	no	—
430	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
431	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
432	C₂²	C₃×#4147	1	2	yes	—
433	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
434	C₄	—	2	8	no	—
435	C₄	—	2	2	no	—
436	C₄	—	5	8	no	—
437	C₄	—	10	4	no	—
438	C₄	—	10	4	no	—
439	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
440	C₄	C₂×C₃×Q₈×D₅	1	4	yes	complemented
441	C₃	C₂×#66061	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	10	8	no	—
443	C₂	C₃×#66061	1	4	yes	direct product factor
444	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
445	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
446	C₂	C₂×C₃×#4147	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×D₄×Q₈
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. C₂²×C₃×Q₈×D₅	C₂	semidirect
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃×#4092	C₂	semidirect
4. C₃×#66061	C₂	direct (N × H)
5. C₂×C₃×#4042	C₂	semidirect
7. C₂×C₃×#4034	C₂	semidirect
9. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
10. C₂×#66061	C₃	direct (N × H)
13. C₂×C₃×Q₈×D₅	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×#4092	C₂²	semidirect
31. C₃×#4042	C₂²	semidirect
33. C₃×#4034	C₂²	semidirect
35. C₃×C₄×Dic₁₀	C₂²	semidirect
37. C₂²×Q₈×D₅	C₂×C₃	semidirect
38. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
39. C₂×#4092	C₂×C₃	semidirect
40. #66061	C₂×C₃	direct (N × H)
41. C₂×#4042	C₂×C₃	semidirect
43. C₂×#4034	C₂×C₃	semidirect
45. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
57. C₂×C₃×D₂₀	Q₈	semidirect
64. C₂×C₃×Dic₁₀	D₄	semidirect
80. C₂×C₃×C₄⋊Q₈	D₅	semidirect
88. C₂×Q₈×D₅	C₂²×C₃	semidirect
94. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
98. #4092	C₂²×C₃	semidirect
106. #4042	C₂²×C₃	semidirect
108. #4034	C₂²×C₃	semidirect
110. C₄×Dic₁₀	C₂²×C₃	semidirect
115. C₂²×C₃×D₅	C₂×Q₈	semidirect
121. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
132. C₃×D₂₀	C₂×Q₈	semidirect
136. C₃×Dic₁₀	C₂×D₄	semidirect
146. C₃×C₄⋊Q₈	C₂×D₅	semidirect
173. C₂×D₂₀	C₃×Q₈	semidirect
180. C₂×Dic₁₀	C₃×D₄	semidirect
196. C₂×C₄⋊Q₈	C₃×D₅	semidirect
209. C₂×C₃×D₅	C₂²×Q₈	semidirect
213. C₃×C₄×C₅	C₂²×Q₈	semidirect
251. C₂²×D₅	C₂×C₃×Q₈	semidirect
257. C₂×C₄×C₅	C₂×C₃×Q₈	semidirect
268. D₂₀	C₂×C₃×Q₈	semidirect
272. Dic₁₀	C₂×C₃×D₄	semidirect
282. C₄⋊Q₈	C₂×C₃×D₅	semidirect
298. C₂×C₃×C₅	D₄×Q₈	semidirect
323. C₂×C₃×C₄	Q₈×D₅	semidirect
335. C₂×D₅	C₂²×C₃×Q₈	semidirect
339. C₄×C₅	C₂²×C₃×Q₈	semidirect
374. C₃×C₅	C₂×D₄×Q₈	semidirect
389. C₃×C₄	C₂×Q₈×D₅	semidirect
390. C₂×C₅	C₃×D₄×Q₈	semidirect
415. C₂×C₄	C₃×Q₈×D₅	semidirect
421. C₂×C₃	#66061	direct (N × H)
425. C₅	C₂×C₃×D₄×Q₈	semidirect
440. C₄	C₂×C₃×Q₈×D₅	semidirect
441. C₃	C₂×#66061	direct (N × H)
443. C₂	C₃×#66061	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
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×#4092	2
C₃×#66061	2
C₂×C₃×#4042	2
C₂×C₃×#4039	2
C₂×C₃×#4034	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#66061	3
C₂×C₃×D₄×Q₈	5

Subgroups — C2×C3×#66061 #14482906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66061 #14482906