Subgroups — C₂²×C₅×#896 #14479417

Order 1920.

3680 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#896	C₂	1	24	yes	maximal, direct product factor
9	C₂²×C₅×C₂²⋊Q₈	—	3	1	no	maximal, Hall
10	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	—	2	8	no	—
18	C₂²×C₄×C₅×D₃	C₂²	1	12	yes	—
19	C₂²×C₅×Dic₆	—	2	8	no	—
20	C₂²×C₅×Dic₆	C₂²	1	12	yes	complemented
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	12	yes	complemented
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	12	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	12	yes	—
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	12	yes	complemented
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	12	yes	complemented
26	C₅×#896	C₂²	1	64	yes	direct product factor
27	C₂²×#896	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂³×C₅×Q₈	—	3	1	no	—
29	C₂⁴×C₄×C₅	—	3	1	no	—
30	C₂×C₅×C₂²⋊Q₈	—	3	24	no	—
31	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
32	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
33	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
34	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
35	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
36	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
37	C₂³×C₅×D₃	—	2	4	no	—
38	C₂³×C₅×D₃	—	2	4	no	—
39	C₂³×C₅×D₃	Q₈	1	8	yes	complemented
40	C₂³×C₅×D₃	C₂³	1	6	yes	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
47	C₂²×C₅×Dic₃	—	2	4	no	—
48	C₂²×C₅×Dic₃	—	2	4	no	—
49	C₂²×C₅×Dic₃	D₄	1	8	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
52	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
53	C₂×C₄×C₅×D₃	—	2	48	no	—
54	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
55	C₂×C₅×Dic₆	—	2	48	no	—
56	C₂×C₅×Dic₆	C₂³	1	16	yes	complemented
57	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	complemented
58	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
59	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
60	C₅×Dic₃⋊C₄	C₂³	1	16	yes	complemented
61	C₅×Dic₃⋊C₄	C₂³	1	16	yes	complemented
62	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
63	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
66	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
67	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#896	C₂×C₅	1	24	yes	direct product factor
70	C₂⁵×C₅	—	3	1	no	—
71	C₂²×C₅×Q₈	—	3	12	no	—
72	C₂²×C₅×Q₈	—	6	8	no	—
73	C₂³×C₄×C₅	—	3	1	no	—
74	C₂³×C₄×C₅	—	3	1	no	—
75	C₂³×C₄×C₅	—	3	1	no	—
76	C₂³×C₄×C₅	—	3	12	no	—
77	C₂³×C₄×C₅	—	6	8	no	—
78	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
81	C₅×C₂²⋊Q₈	—	3	64	no	—
82	C₂×C₅×C₄⋊C₄	—	3	12	no	—
83	C₂×C₅×C₄⋊C₄	—	3	12	no	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	12	yes	complemented
85	C₂×C₅×C₂²⋊C₄	—	3	12	no	—
86	C₂×C₅×C₂²⋊C₄	—	3	12	no	—
87	C₂²×C₂²⋊Q₈	—	3	1	no	Sylow
88	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
89	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
90	C₂³×C₃×C₅	#41	1	4	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
92	C₂²×C₅×D₃	—	2	32	no	—
93	C₂²×C₅×D₃	—	2	12	no	—
94	C₂²×C₅×D₃	—	2	12	no	—
95	C₂²×C₅×D₃	C₂×Q₈	1	24	yes	complemented
96	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
97	C₂×C₃×C₄×C₅	—	2	12	no	—
98	C₂×C₃×C₄×C₅	—	2	12	no	—
99	C₂×C₃×C₄×C₅	—	2	12	no	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
103	C₂×C₅×Dic₃	—	2	12	no	—
104	C₂×C₅×Dic₃	—	2	12	no	—
105	C₂×C₅×Dic₃	C₂×D₄	1	24	yes	—
106	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
107	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
108	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
109	C₄×C₅×D₃	—	2	32	no	—
110	C₅×Dic₆	—	2	32	no	—
111	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
112	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
113	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
115	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
116	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
117	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
118	C₂²×C₄×D₃	—	2	8	no	—
119	C₂²×C₄×D₃	C₂²×C₅	1	12	yes	—
120	C₂²×Dic₆	—	2	8	no	—
121	C₂²×Dic₆	C₂²×C₅	1	12	yes	complemented
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	12	yes	complemented
123	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	12	yes	—
124	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	12	yes	—
125	C₂×Dic₃⋊C₄	C₂²×C₅	1	12	yes	complemented
126	C₂×Dic₃⋊C₄	C₂²×C₅	1	12	yes	complemented
127	#896	C₂²×C₅	1	64	yes	direct product factor
128	C₂⁴×C₅	—	3	8	no	—
129	C₂⁴×C₅	—	3	6	no	—
130	C₂⁴×C₅	—	6	4	no	—
131	C₂⁴×C₅	—	6	4	no	—
132	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₂×C₅×Q₈	—	3	16	no	—
134	C₂×C₅×Q₈	—	6	48	no	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	—	2	4	no	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	3	8	no	—
139	C₂²×C₄×C₅	—	3	6	no	—
140	C₂²×C₄×C₅	—	3	6	no	—
141	C₂²×C₄×C₅	—	3	6	no	—
142	C₂²×C₄×C₅	—	3	16	no	—
143	C₂²×C₄×C₅	—	6	48	no	—
144	C₂²×C₄×C₅	—	6	4	no	—
145	C₂²×C₄×C₅	—	6	4	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
147	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
148	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
149	C₅×C₄⋊C₄	—	3	16	no	—
150	C₅×C₄⋊C₄	—	3	16	no	—
151	C₅×C₄⋊C₄	C₂²×D₃	1	16	yes	complemented
152	C₅×C₂²⋊C₄	—	3	16	no	—
153	C₅×C₂²⋊C₄	—	3	16	no	—
154	C₂³×Q₈	—	3	1	no	—
155	C₂⁴×C₄	—	3	1	no	—
156	C₂×C₂²⋊Q₈	—	3	24	no	—
157	C₂²×C₄⋊C₄	—	3	1	no	—
158	C₂²×C₄⋊C₄	—	3	1	no	—
159	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
160	C₂²×C₂²⋊C₄	—	3	1	no	—
161	C₂²×C₂²⋊C₄	—	3	1	no	—
162	C₂²×C₃×C₅	C₂²⋊Q₈	1	16	yes	complemented
163	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
164	C₂²×C₃×C₅	C₂²×Q₈	1	6	yes	—
165	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
166	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
167	C₂×C₅×D₃	—	2	48	no	—
168	C₂×C₅×D₃	—	2	4	no	—
169	C₂×C₅×D₃	—	2	4	no	—
170	C₂×C₅×D₃	C₂²×Q₈	1	8	yes	complemented
171	C₃×C₄×C₅	—	2	4	no	—
172	C₃×C₄×C₅	—	2	4	no	—
173	C₃×C₄×C₅	—	2	4	no	—
174	C₅×Dic₃	—	2	4	no	—
175	C₅×Dic₃	—	2	4	no	—
176	C₅×Dic₃	C₂²×D₄	1	8	yes	—
177	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
178	C₂³×D₃	—	2	4	no	—
179	C₂³×D₃	—	2	4	no	—
180	C₂³×D₃	C₅×Q₈	1	8	yes	complemented
181	C₂³×D₃	C₂³×C₅	1	6	yes	—
182	C₂²×C₃×C₄	—	2	4	no	—
183	C₂²×C₃×C₄	—	2	4	no	—
184	C₂²×C₃×C₄	—	2	4	no	—
185	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
187	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
188	C₂²×Dic₃	—	2	4	no	—
189	C₂²×Dic₃	—	2	4	no	—
190	C₂²×Dic₃	C₅×D₄	1	8	yes	—
191	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
192	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
193	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
194	C₂×C₄×D₃	—	2	48	no	—
195	C₂×C₄×D₃	C₂³×C₅	1	16	yes	—
196	C₂×Dic₆	—	2	48	no	—
197	C₂×Dic₆	C₂³×C₅	1	16	yes	complemented
198	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	complemented
199	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
200	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
201	Dic₃⋊C₄	C₂³×C₅	1	16	yes	complemented
202	Dic₃⋊C₄	C₂³×C₅	1	16	yes	complemented
203	C₂³×C₅	—	3	24	no	—
204	C₂³×C₅	—	3	4	no	—
205	C₂³×C₅	—	6	32	no	—
206	C₂³×C₅	—	6	12	no	—
207	C₂³×C₅	—	6	12	no	—
208	C₂³×C₅	#235	1	4	yes	—
209	C₂³×C₅	D₃×D₄	1	4	yes	—
210	C₂³×C₅	D₃×Q₈	1	4	yes	—
211	C₂³×C₅	C₂³×D₃	1	3	yes	—
212	C₅×Q₈	—	6	32	no	—
213	C₂×C₄×C₅	—	2	12	no	—
214	C₂×C₄×C₅	—	2	12	no	—
215	C₂×C₄×C₅	—	2	12	no	—
216	C₂×C₄×C₅	—	3	24	no	—
217	C₂×C₄×C₅	—	3	4	no	—
218	C₂×C₄×C₅	—	3	4	no	—
219	C₂×C₄×C₅	—	3	4	no	—
220	C₂×C₄×C₅	—	6	32	no	—
221	C₂×C₄×C₅	—	6	12	no	—
222	C₂×C₄×C₅	—	6	12	no	—
223	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
224	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
225	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
226	C₂⁵	—	3	1	no	—
227	C₂²×Q₈	—	3	12	no	—
228	C₂²×Q₈	—	6	8	no	—
229	C₂³×C₄	—	3	1	no	—
230	C₂³×C₄	—	3	1	no	—
231	C₂³×C₄	—	3	1	no	—
232	C₂³×C₄	—	3	12	no	—
233	C₂³×C₄	—	6	8	no	—
234	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
237	C₂²⋊Q₈	—	3	64	no	—
238	C₂×C₄⋊C₄	—	3	12	no	—
239	C₂×C₄⋊C₄	—	3	12	no	—
240	C₂×C₄⋊C₄	C₂×C₅×D₃	1	12	yes	complemented
241	C₂×C₂²⋊C₄	—	3	12	no	—
242	C₂×C₂²⋊C₄	—	3	12	no	—
243	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	12	yes	complemented
244	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
247	C₅×D₃	—	2	8	no	—
248	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
249	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
250	C₂³×C₃	C₅×#41	1	4	yes	—
251	C₂³×C₃	C₂⁴×C₅	1	3	yes	—
252	C₂²×D₃	—	2	32	no	—
253	C₂²×D₃	—	2	12	no	—
254	C₂²×D₃	—	2	12	no	—
255	C₂²×D₃	C₂×C₅×Q₈	1	24	yes	complemented
256	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
257	C₂×C₃×C₄	—	2	12	no	—
258	C₂×C₃×C₄	—	2	12	no	—
259	C₂×C₃×C₄	—	2	12	no	—
260	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
261	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
262	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
263	C₂×Dic₃	—	2	12	no	—
264	C₂×Dic₃	—	2	12	no	—
265	C₂×Dic₃	C₂×C₅×D₄	1	24	yes	—
266	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
267	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
268	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
269	C₄×D₃	—	2	32	no	—
270	Dic₆	—	2	32	no	—
271	C₂²×C₅	—	3	8	no	—
272	C₂²×C₅	—	6	4	no	—
273	C₂²×C₅	—	6	4	no	—
274	C₂²×C₅	—	6	48	no	—
275	C₂²×C₅	#896	1	16	yes	direct product factor
276	C₂²×C₅	C₂×#235	1	6	yes	—
277	C₂²×C₅	C₂×D₃×D₄	1	6	yes	—
278	C₂²×C₅	C₂×D₃×Q₈	1	6	yes	—
279	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	2	4	no	—
282	C₄×C₅	—	2	4	no	—
283	C₄×C₅	—	3	8	no	—
284	C₄×C₅	—	6	4	no	—
285	C₄×C₅	—	6	4	no	—
286	C₂⁴	—	3	8	no	—
287	C₂⁴	—	3	6	no	—
288	C₂⁴	—	6	4	no	—
289	C₂⁴	—	6	4	no	—
290	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
291	C₂×Q₈	—	3	16	no	—
292	C₂×Q₈	—	6	48	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	3	8	no	—
297	C₂²×C₄	—	3	6	no	—
298	C₂²×C₄	—	3	6	no	—
299	C₂²×C₄	—	3	6	no	—
300	C₂²×C₄	—	3	16	no	—
301	C₂²×C₄	—	6	48	no	—
302	C₂²×C₄	—	6	4	no	—
303	C₂²×C₄	—	6	4	no	—
304	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
305	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
306	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
307	C₄⋊C₄	—	3	16	no	—
308	C₄⋊C₄	—	3	16	no	—
309	C₄⋊C₄	C₂²×C₅×D₃	1	16	yes	complemented
310	C₂²⋊C₄	—	3	16	no	—
311	C₂²⋊C₄	—	3	16	no	—
312	C₃×C₅	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	C₅×C₂²⋊Q₈	1	16	yes	complemented
314	C₂²×C₃	C₂²×C₅×D₄	1	6	yes	—
315	C₂²×C₃	C₂²×C₅×Q₈	1	6	yes	—
316	C₂²×C₃	C₂×C₅×#41	1	6	yes	—
317	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
318	C₂×D₃	—	2	48	no	—
319	C₂×D₃	—	2	4	no	—
320	C₂×D₃	—	2	4	no	—
321	C₂×D₃	C₂²×C₅×Q₈	1	8	yes	complemented
322	C₃×C₄	—	2	4	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	4	no	—
325	Dic₃	—	2	4	no	—
326	Dic₃	—	2	4	no	—
327	Dic₃	C₂²×C₅×D₄	1	8	yes	—
328	C₂×C₅	—	6	8	no	—
329	C₂×C₅	C₂×#896	1	12	yes	direct product factor
330	C₂×C₅	C₂²×#235	1	1	yes	characteristic
331	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
332	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
333	C₂³	—	3	24	no	—
334	C₂³	—	3	4	no	—
335	C₂³	—	6	32	no	—
336	C₂³	—	6	12	no	—
337	C₂³	—	6	12	no	—
338	C₂³	C₅×#235	1	4	yes	—
339	C₂³	C₅×D₃×D₄	1	4	yes	—
340	C₂³	C₅×D₃×Q₈	1	4	yes	—
341	C₂³	C₂³×C₅×D₃	1	3	yes	—
342	Q₈	—	6	32	no	—
343	C₂×C₄	—	2	12	no	—
344	C₂×C₄	—	2	12	no	—
345	C₂×C₄	—	2	12	no	—
346	C₂×C₄	—	3	24	no	—
347	C₂×C₄	—	3	4	no	—
348	C₂×C₄	—	3	4	no	—
349	C₂×C₄	—	3	4	no	—
350	C₂×C₄	—	6	32	no	—
351	C₂×C₄	—	6	12	no	—
352	C₂×C₄	—	6	12	no	—
353	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
354	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
355	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
356	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	12	yes	complemented
357	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
358	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
359	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
360	D₃	—	2	8	no	—
361	C₅	C₂²×#896	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	—	3	8	no	—
363	C₂²	—	6	4	no	—
364	C₂²	—	6	4	no	—
365	C₂²	—	6	48	no	—
366	C₂²	C₅×#896	1	16	yes	direct product factor
367	C₂²	C₂×C₅×#235	1	6	yes	—
368	C₂²	C₂×C₅×D₃×D₄	1	6	yes	—
369	C₂²	C₂×C₅×D₃×Q₈	1	6	yes	—
370	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	4	no	—
374	C₄	—	3	8	no	—
375	C₄	—	6	4	no	—
376	C₄	—	6	4	no	—
377	C₃	C₂²×C₅×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	6	8	no	—
379	C₂	C₂×C₅×#896	1	12	yes	direct product factor
380	C₂	C₂²×C₅×#235	1	1	yes	characteristic
381	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
382	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₅×D₃	C₂²
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂²×C₅×C₂²⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
6. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
7. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
8. C₂×C₅×#896	C₂	direct (N × H)
20. C₂²×C₅×Dic₆	C₂²	semidirect
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
25. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
26. C₅×#896	C₂²	direct (N × H)
27. C₂²×#896	C₅	direct (N × H)
33. C₂²×C₅×C₄⋊C₄	D₃	semidirect
39. C₂³×C₅×D₃	Q₈	semidirect
56. C₂×C₅×Dic₆	C₂³	semidirect
57. C₃×C₅×C₄⋊C₄	C₂³	semidirect
60. C₅×Dic₃⋊C₄	C₂³	semidirect
61. C₅×Dic₃⋊C₄	C₂³	semidirect
63. C₂³×Dic₆	C₂×C₅	semidirect
64. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
67. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
68. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
69. C₂×#896	C₂×C₅	direct (N × H)
84. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
95. C₂²×C₅×D₃	C₂×Q₈	semidirect
121. C₂²×Dic₆	C₂²×C₅	semidirect
122. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
125. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
126. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
127. #896	C₂²×C₅	direct (N × H)
151. C₅×C₄⋊C₄	C₂²×D₃	semidirect
159. C₂²×C₄⋊C₄	C₅×D₃	semidirect
162. C₂²×C₃×C₅	C₂²⋊Q₈	semidirect
170. C₂×C₅×D₃	C₂²×Q₈	semidirect
180. C₂³×D₃	C₅×Q₈	semidirect
197. C₂×Dic₆	C₂³×C₅	semidirect
198. C₃×C₄⋊C₄	C₂³×C₅	semidirect
201. Dic₃⋊C₄	C₂³×C₅	semidirect
202. Dic₃⋊C₄	C₂³×C₅	semidirect
240. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
243. C₂×C₃×C₅	C₂×C₂²⋊Q₈	semidirect
255. C₂²×D₃	C₂×C₅×Q₈	semidirect
275. C₂²×C₅	#896	direct (N × H)
309. C₄⋊C₄	C₂²×C₅×D₃	semidirect
312. C₃×C₅	C₂²×C₂²⋊Q₈	semidirect
313. C₂²×C₃	C₅×C₂²⋊Q₈	semidirect
321. C₂×D₃	C₂²×C₅×Q₈	semidirect
329. C₂×C₅	C₂×#896	direct (N × H)
356. C₂×C₃	C₂×C₅×C₂²⋊Q₈	semidirect
361. C₅	C₂²×#896	direct (N × H)
366. C₂²	C₅×#896	direct (N × H)
377. C₃	C₂²×C₅×C₂²⋊Q₈	semidirect
379. C₂	C₂×C₅×#896	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×C₄×C₅×D₃	2
C₂³×C₅×Dic₆	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₂²×C₅×Dic₃⋊C₄	2
C₂×C₅×#896	2
C₂²×C₅×C₂²⋊Q₈	3
C₂²×#896	5

Subgroups — C22×C5×#896 #14479417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#896 #14479417