Subgroups — C₂×C₅×#5126 #14411627

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 408 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	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5126	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#407	—	3	1	no	maximal, Hall
7	C₂⁴×C₅×D₃	C₄	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₅×Dic₃	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	2	4	no	—
11	C₂²×C₄×C₅×D₃	—	2	4	no	—
12	C₂²×C₄×C₅×D₃	C₄	1	4	yes	—
13	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
16	C₂×C₃×C₅×M₁₆	—	2	4	no	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	complemented
18	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
19	C₂×C₅×#208	—	2	4	no	—
20	C₂×C₅×#208	C₂²	1	4	yes	complemented
21	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
22	C₅×(C₂×D₃)⋊C₈	C₂²	1	16	yes	complemented
23	C₂×#5126	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂⁴×C₄×C₅	—	3	1	no	—
25	C₂²×C₅×M₁₆	—	3	1	no	—
26	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
27	C₅×#407	—	3	8	no	—
28	C₂×C₅×C₂²⋊C₈	—	3	4	no	—
29	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₅×D₃	—	2	4	no	—
31	C₂³×C₅×D₃	—	2	8	no	—
32	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
33	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	4	no	—
41	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
42	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	—	2	16	no	—
44	C₂×C₄×C₅×D₃	—	2	8	no	—
45	C₂×C₄×C₅×D₃	—	2	4	no	—
46	C₂×C₄×C₅×D₃	—	2	8	no	—
47	C₂×C₄×C₅×D₃	—	2	4	no	—
48	C₂×C₄×C₅×D₃	—	2	8	no	—
49	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
50	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
51	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
52	C₃×C₅×M₁₆	—	2	8	no	—
53	C₂×C₃×C₅×C₈	—	2	4	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	4	yes	complemented
55	C₅×#208	—	2	8	no	—
56	C₂×C₅×C₃⋊C₈	—	2	4	no	—
57	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	complemented
58	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
59	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
61	#5126	C₂×C₅	1	8	yes	direct product factor
62	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	4	yes	complemented
63	C₂⁵×C₅	—	3	1	no	—
64	C₂³×C₄×C₅	—	3	1	no	—
65	C₂³×C₄×C₅	—	3	2	no	—
66	C₂³×C₄×C₅	—	3	4	no	—
67	C₂³×C₄×C₅	—	3	4	no	—
68	C₂³×C₄×C₅	—	3	2	no	—
69	C₂³×C₄×C₅	—	6	4	no	—
70	C₂³×C₄×C₅	—	6	4	no	—
71	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂×C₅×M₁₆	—	2	4	no	—
73	C₂×C₅×M₁₆	—	3	4	no	—
74	C₂×C₅×M₁₆	—	6	4	no	—
75	C₂×C₅×M₁₆	C₂×D₃	1	4	yes	complemented
76	C₂²×C₅×C₈	—	3	2	no	—
77	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
78	C₅×C₂²⋊C₈	—	3	16	no	—
79	C₂×#407	—	3	1	no	Sylow
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
82	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₅×D₃	—	2	32	no	—
85	C₂²×C₅×D₃	—	2	8	no	—
86	C₂²×C₅×D₃	—	2	4	no	—
87	C₂²×C₅×D₃	—	2	4	no	—
88	C₂²×C₅×D₃	—	2	16	no	—
89	C₂²×C₅×D₃	M₁₆	1	8	yes	complemented
90	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	8	yes	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₅×Dic₃	—	2	8	no	—
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
103	C₄×C₅×D₃	—	2	8	no	—
104	C₄×C₅×D₃	—	2	16	no	—
105	C₄×C₅×D₃	—	2	4	no	—
106	C₄×C₅×D₃	—	2	4	no	—
107	C₃×C₅×C₈	—	2	4	no	—
108	C₅×C₃⋊C₈	—	2	4	no	—
109	C₂⁴×D₃	C₄×C₅	1	1	yes	characteristic
110	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂³×Dic₃	C₄×C₅	1	1	yes	characteristic
112	C₂²×C₄×D₃	—	2	4	no	—
113	C₂²×C₄×D₃	—	2	4	no	—
114	C₂²×C₄×D₃	C₄×C₅	1	4	yes	—
115	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
116	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
117	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
118	C₂×C₃×M₁₆	—	2	4	no	—
119	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	complemented
120	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
121	C₂×#208	—	2	4	no	—
122	C₂×#208	C₂²×C₅	1	4	yes	complemented
123	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
124	(C₂×D₃)⋊C₈	C₂²×C₅	1	16	yes	complemented
125	C₂⁴×C₅	—	3	2	no	—
126	C₂⁴×C₅	—	3	4	no	—
127	C₂⁴×C₅	—	6	8	no	—
128	C₂⁴×C₅	—	6	4	no	—
129	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	—	3	4	no	—
131	C₂²×C₄×C₅	—	3	2	no	—
132	C₂²×C₄×C₅	—	3	8	no	—
133	C₂²×C₄×C₅	—	3	4	no	—
134	C₂²×C₄×C₅	—	3	4	no	—
135	C₂²×C₄×C₅	—	6	4	no	—
136	C₂²×C₄×C₅	—	6	16	no	—
137	C₂²×C₄×C₅	—	6	8	no	—
138	C₂²×C₄×C₅	—	6	4	no	—
139	C₂²×C₄×C₅	—	6	8	no	—
140	C₂²×C₄×C₅	—	6	4	no	—
141	C₂²×C₄×C₅	—	6	8	no	—
142	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
144	C₂²×C₄×C₅	D₁₂	1	4	yes	—
145	C₂²×C₄×C₅	#67	1	4	yes	—
146	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₅×M₁₆	—	2	8	no	—
149	C₅×M₁₆	—	6	8	no	—
150	C₂×C₅×C₈	—	2	4	no	—
151	C₂×C₅×C₈	—	3	4	no	—
152	C₂×C₅×C₈	—	6	4	no	—
153	C₂×C₅×C₈	C₂²×D₃	1	4	yes	complemented
154	C₂⁴×C₄	—	3	1	no	—
155	C₂²×M₁₆	—	3	1	no	—
156	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
157	#407	—	3	8	no	—
158	C₂×C₂²⋊C₈	—	3	4	no	—
159	C₂²×C₃×C₅	—	2	4	no	—
160	C₂²×C₃×C₅	—	2	8	no	—
161	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
164	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₅×D₃	—	2	32	no	—
166	C₂×C₅×D₃	—	2	4	no	—
167	C₂×C₅×D₃	—	2	4	no	—
168	C₂×C₅×D₃	—	2	16	no	—
169	C₂×C₅×D₃	C₂×M₁₆	1	8	yes	complemented
170	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
171	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
172	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₅×Dic₃	—	2	4	no	—
175	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂³×D₃	—	2	4	no	—
177	C₂³×D₃	—	2	8	no	—
178	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
179	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
180	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
183	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₂²×Dic₃	—	2	4	no	—
187	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
188	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
189	C₂×C₄×D₃	—	2	16	no	—
190	C₂×C₄×D₃	—	2	8	no	—
191	C₂×C₄×D₃	—	2	4	no	—
192	C₂×C₄×D₃	—	2	8	no	—
193	C₂×C₄×D₃	—	2	4	no	—
194	C₂×C₄×D₃	—	2	8	no	—
195	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
196	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
197	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
198	C₃×M₁₆	—	2	8	no	—
199	C₂×C₃×C₈	—	2	4	no	—
200	C₂×C₃×C₈	C₂³×C₅	1	4	yes	complemented
201	#208	—	2	8	no	—
202	C₂×C₃⋊C₈	—	2	4	no	—
203	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
204	C₂³×C₅	—	2	4	no	—
205	C₂³×C₅	—	3	8	no	—
206	C₂³×C₅	—	3	4	no	—
207	C₂³×C₅	—	6	16	no	—
208	C₂³×C₅	—	6	32	no	—
209	C₂³×C₅	—	6	4	no	—
210	C₂³×C₅	—	6	8	no	—
211	C₂³×C₅	—	6	4	no	—
212	C₂³×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
213	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
214	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
215	C₂×C₄×C₅	—	3	4	no	—
216	C₂×C₄×C₅	—	6	8	no	—
217	C₂×C₄×C₅	—	6	4	no	—
218	C₂×C₄×C₅	—	6	16	no	—
219	C₂×C₄×C₅	—	6	8	no	—
220	C₂×C₄×C₅	—	6	4	no	—
221	C₂×C₄×C₅	—	6	4	no	—
222	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	8	yes	—
223	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
224	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
225	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
227	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
228	C₂×C₄×C₅	C₂×#67	1	2	yes	—
229	C₂×C₄×C₅	C₂×#67	1	4	yes	—
230	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
231	C₅×C₈	—	2	4	no	—
232	C₅×C₈	—	6	4	no	—
233	C₂⁵	—	3	1	no	—
234	C₂³×C₄	—	3	1	no	—
235	C₂³×C₄	—	3	2	no	—
236	C₂³×C₄	—	3	4	no	—
237	C₂³×C₄	—	3	2	no	—
238	C₂³×C₄	—	3	4	no	—
239	C₂³×C₄	—	6	4	no	—
240	C₂³×C₄	—	6	4	no	—
241	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	3	4	no	—
244	C₂×M₁₆	—	6	4	no	—
245	C₂×M₁₆	C₂×C₅×D₃	1	4	yes	complemented
246	C₂²×C₈	—	3	2	no	—
247	C₂²×C₈	C₂×C₅×D₃	1	2	yes	complemented
248	C₂²⋊C₈	—	3	16	no	—
249	C₂×C₃×C₅	—	2	4	no	—
250	C₂×C₃×C₅	#407	1	4	yes	complemented
251	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
253	C₅×D₃	—	2	8	no	—
254	C₂³×C₃	—	2	4	no	—
255	C₂³×C₃	C₅×C₂²⋊C₄	1	4	yes	—
256	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
257	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂²×D₃	—	2	32	no	—
259	C₂²×D₃	—	2	8	no	—
260	C₂²×D₃	—	2	4	no	—
261	C₂²×D₃	—	2	4	no	—
262	C₂²×D₃	—	2	16	no	—
263	C₂²×D₃	C₅×M₁₆	1	8	yes	complemented
264	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
265	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	8	yes	—
266	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
271	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
273	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
274	C₂×Dic₃	—	2	8	no	—
275	C₂×Dic₃	—	2	4	no	—
276	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
277	C₄×D₃	—	2	8	no	—
278	C₄×D₃	—	2	16	no	—
279	C₄×D₃	—	2	4	no	—
280	C₄×D₃	—	2	4	no	—
281	C₃×C₈	—	2	4	no	—
282	C₃⋊C₈	—	2	4	no	—
283	C₂²×C₅	—	2	8	no	—
284	C₂²×C₅	—	2	4	no	—
285	C₂²×C₅	—	3	8	no	—
286	C₂²×C₅	—	6	32	no	—
287	C₂²×C₅	—	6	16	no	—
288	C₂²×C₅	—	6	4	no	—
289	C₂²×C₅	—	6	4	no	—
290	C₂²×C₅	D₃×M₁₆	1	4	yes	—
291	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
292	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
293	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
294	C₄×C₅	—	6	4	no	—
295	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
296	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
297	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
298	C₄×C₅	C₂²×#67	1	1	yes	characteristic
299	C₂⁴	—	3	2	no	—
300	C₂⁴	—	3	4	no	—
301	C₂⁴	—	6	8	no	—
302	C₂⁴	—	6	4	no	—
303	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
304	C₂²×C₄	—	3	4	no	—
305	C₂²×C₄	—	3	2	no	—
306	C₂²×C₄	—	3	4	no	—
307	C₂²×C₄	—	3	8	no	—
308	C₂²×C₄	—	3	4	no	—
309	C₂²×C₄	—	6	4	no	—
310	C₂²×C₄	—	6	16	no	—
311	C₂²×C₄	—	6	8	no	—
312	C₂²×C₄	—	6	4	no	—
313	C₂²×C₄	—	6	8	no	—
314	C₂²×C₄	—	6	4	no	—
315	C₂²×C₄	—	6	8	no	—
316	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
317	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
318	C₂²×C₄	C₅×D₁₂	1	4	yes	—
319	C₂²×C₄	C₅×#67	1	4	yes	—
320	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
322	M₁₆	—	2	8	no	—
323	M₁₆	—	6	8	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	3	4	no	—
326	C₂×C₈	—	6	4	no	—
327	C₂×C₈	C₂²×C₅×D₃	1	4	yes	complemented
328	C₃×C₅	C₂×#407	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
332	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
333	C₂²×C₃	C₂×C₅×M₁₆	1	4	yes	—
334	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
335	C₂×D₃	—	2	32	no	—
336	C₂×D₃	—	2	16	no	—
337	C₂×D₃	—	2	4	no	—
338	C₂×D₃	—	2	4	no	—
339	C₂×D₃	C₂×C₅×M₁₆	1	8	yes	complemented
340	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
341	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
342	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
343	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
344	Dic₃	—	2	4	no	—
345	C₂×C₅	—	2	4	no	—
346	C₂×C₅	—	6	8	no	—
347	C₂×C₅	#5126	1	4	yes	direct product factor
348	C₂×C₅	C₂×D₃×M₁₆	1	2	yes	—
349	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
350	C₂³	—	2	4	no	—
351	C₂³	—	3	8	no	—
352	C₂³	—	3	4	no	—
353	C₂³	—	6	16	no	—
354	C₂³	—	6	32	no	—
355	C₂³	—	6	4	no	—
356	C₂³	—	6	8	no	—
357	C₂³	—	6	4	no	—
358	C₂³	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
359	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
360	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
361	C₂×C₄	—	3	4	no	—
362	C₂×C₄	—	6	8	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	—	6	8	no	—
365	C₂×C₄	—	6	16	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	—	6	4	no	—
368	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	8	yes	—
369	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
370	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
372	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
373	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
374	C₂×C₄	C₂×C₅×#67	1	2	yes	—
375	C₂×C₄	C₂×C₅×#67	1	4	yes	—
376	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	6	4	no	—
379	C₂×C₃	—	2	4	no	—
380	C₂×C₃	C₅×#407	1	4	yes	complemented
381	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₃	C₂²×C₅×M₁₆	1	2	yes	—
383	D₃	—	2	8	no	—
384	C₅	C₂×#5126	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	2	4	no	—
386	C₂²	—	2	8	no	—
387	C₂²	—	3	8	no	—
388	C₂²	—	6	32	no	—
389	C₂²	—	6	4	no	—
390	C₂²	—	6	4	no	—
391	C₂²	—	6	16	no	—
392	C₂²	C₅×D₃×M₁₆	1	4	yes	—
393	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
394	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
395	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
396	C₄	—	6	4	no	—
397	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
398	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
399	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
400	C₄	C₂²×C₅×#67	1	1	yes	characteristic
401	C₃	C₂×C₅×#407	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	4	no	—
403	C₂	—	6	8	no	—
404	C₂	C₅×#5126	1	4	yes	direct product factor
405	C₂	C₂×C₅×D₃×M₁₆	1	2	yes	—
406	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₅×D₃	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₂×C₅×#407
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₅×#208	C₂	semidirect
4. C₅×#5126	C₂	direct (N × H)
5. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₂²×C₃×C₅×C₈	C₂²	semidirect
20. C₂×C₅×#208	C₂²	semidirect
21. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
22. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
23. C₂×#5126	C₅	direct (N × H)
26. C₂²×C₅×M₁₆	D₃	semidirect
54. C₂×C₃×C₅×C₈	C₂³	semidirect
57. C₂×C₅×C₃⋊C₈	C₂³	semidirect
59. C₂²×C₃×M₁₆	C₂×C₅	semidirect
60. C₂²×#208	C₂×C₅	semidirect
61. #5126	C₂×C₅	direct (N × H)
62. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
75. C₂×C₅×M₁₆	C₂×D₃	semidirect
77. C₂²×C₅×C₈	C₂×D₃	semidirect
89. C₂²×C₅×D₃	M₁₆	semidirect
119. C₂×C₃×M₁₆	C₂²×C₅	semidirect
120. C₂²×C₃×C₈	C₂²×C₅	semidirect
122. C₂×#208	C₂²×C₅	semidirect
123. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
124. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
153. C₂×C₅×C₈	C₂²×D₃	semidirect
156. C₂²×M₁₆	C₅×D₃	semidirect
169. C₂×C₅×D₃	C₂×M₁₆	semidirect
200. C₂×C₃×C₈	C₂³×C₅	semidirect
203. C₂×C₃⋊C₈	C₂³×C₅	semidirect
245. C₂×M₁₆	C₂×C₅×D₃	semidirect
247. C₂²×C₈	C₂×C₅×D₃	semidirect
250. C₂×C₃×C₅	#407	semidirect
263. C₂²×D₃	C₅×M₁₆	semidirect
327. C₂×C₈	C₂²×C₅×D₃	semidirect
328. C₃×C₅	C₂×#407	semidirect
339. C₂×D₃	C₂×C₅×M₁₆	semidirect
347. C₂×C₅	#5126	direct (N × H)
380. C₂×C₃	C₅×#407	semidirect
384. C₅	C₂×#5126	direct (N × H)
401. C₃	C₂×C₅×#407	semidirect
404. C₂	C₅×#5126	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
C₂²×C₃×C₅×M₁₆	2
C₂²×C₅×#208	2
C₅×#5126	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#407	3
C₂×#5126	5

Subgroups — C2×C5×#5126 #14411627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5126 #14411627