Subgroups — C₂×C₅×#5129 #14411686

Order 1920.

1584 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	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5129	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#408	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×#67	C₄	1	2	yes	—
9	C₂×C₅×#235	—	2	4	no	—
10	C₂×C₅×#235	—	2	4	no	—
11	C₂×C₅×#235	C₄	1	4	yes	—
12	C₂×C₅×#235	C₂²	1	4	yes	—
13	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
15	C₂²×C₅×Dic₆	C₄	1	1	yes	characteristic
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	—
19	C₂²×C₅×C₃⋊C₈	—	2	4	no	—
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
22	C₅×(C₂×D₃)⋊C₈	C₂²	1	16	yes	complemented
23	C₂×#5129	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×#41	—	3	1	no	—
25	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂³×C₅×C₈	—	3	1	no	—
27	C₅×#408	—	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	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	—	2	8	no	—
38	C₂×C₅×#67	C₂×C₄	1	8	yes	—
39	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
40	C₅×#235	—	2	16	no	—
41	C₅×#235	—	2	8	no	—
42	C₅×#235	—	2	8	no	—
43	C₂×C₅×D₁₂	—	2	4	no	—
44	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
45	C₂×C₄×C₅×D₃	—	2	4	no	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
48	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
49	C₂×C₅×Dic₆	—	2	4	no	—
50	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
51	C₃×C₅×M₁₆	—	2	8	no	—
52	C₂×C₃×C₅×C₈	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₂×C₅×C₃⋊C₈	—	2	4	no	—
55	C₂×C₅×C₃⋊C₈	—	2	8	no	—
56	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
57	C₂²×#235	C₂×C₅	1	1	yes	characteristic
58	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂³×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
60	#5129	C₂×C₅	1	8	yes	direct product factor
61	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	4	yes	complemented
62	C₂×C₅×#41	—	3	4	no	—
63	C₂×C₅×#41	—	3	4	no	—
64	C₂×C₅×#41	—	6	4	no	—
65	C₂×C₅×#41	—	6	4	no	—
66	C₂²×C₅×Q₈	—	3	1	no	—
67	C₂²×C₅×D₄	—	3	2	no	—
68	C₂²×C₅×D₄	—	3	1	no	—
69	C₂³×C₄×C₅	—	3	2	no	—
70	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
71	C₂×C₅×M₁₆	—	2	4	no	—
72	C₂×C₅×M₁₆	C₂×D₃	1	4	yes	complemented
73	C₂²×C₅×C₈	—	3	4	no	—
74	C₂²×C₅×C₈	—	3	2	no	—
75	C₂²×C₅×C₈	—	6	4	no	—
76	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
77	C₅×C₂²⋊C₈	—	3	16	no	—
78	C₂×#408	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
81	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₅×D₃	—	2	4	no	—
84	C₂²×C₅×D₃	—	2	8	no	—
85	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	8	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
95	C₅×#67	—	2	16	no	—
96	C₂×C₅×Dic₃	—	2	4	no	—
97	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
98	C₅×D₁₂	—	2	8	no	—
99	C₄×C₅×D₃	—	2	8	no	—
100	C₄×C₅×D₃	—	2	4	no	—
101	C₄×C₅×D₃	—	2	4	no	—
102	C₅×Dic₆	—	2	8	no	—
103	C₃×C₅×C₈	—	2	4	no	—
104	C₅×C₃⋊C₈	—	2	4	no	—
105	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂²×#67	C₄×C₅	1	2	yes	—
107	C₂×#235	—	2	4	no	—
108	C₂×#235	—	2	4	no	—
109	C₂×#235	C₄×C₅	1	4	yes	—
110	C₂×#235	C₂²×C₅	1	4	yes	—
111	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
112	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
113	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic
114	C₂×C₃×M₁₆	—	2	4	no	—
115	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	complemented
116	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
117	C₂²×C₃⋊C₈	—	2	4	no	—
118	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
119	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
120	(C₂×D₃)⋊C₈	C₂²×C₅	1	16	yes	complemented
121	C₂⁴×C₅	—	3	2	no	—
122	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
123	C₅×#41	—	6	16	no	—
124	C₅×#41	—	6	8	no	—
125	C₅×#41	—	6	8	no	—
126	C₂×C₅×Q₈	—	3	4	no	—
127	C₂×C₅×Q₈	—	6	4	no	—
128	C₂×C₅×D₄	—	3	8	no	—
129	C₂×C₅×D₄	—	3	4	no	—
130	C₂×C₅×D₄	—	6	8	no	—
131	C₂×C₅×D₄	—	6	4	no	—
132	C₂²×C₄×C₅	—	3	2	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	4	no	—
137	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
139	C₂²×C₄×C₅	D₁₂	1	4	yes	—
140	C₂²×C₄×C₅	#67	1	4	yes	—
141	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
142	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
143	C₅×M₁₆	—	2	8	no	—
144	C₂×C₅×C₈	—	2	4	no	—
145	C₂×C₅×C₈	—	3	4	no	—
146	C₂×C₅×C₈	—	6	4	no	—
147	C₂×C₅×C₈	—	6	8	no	—
148	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
149	C₂²×#41	—	3	1	no	—
150	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
151	C₂³×C₈	—	3	1	no	—
152	#408	—	3	8	no	—
153	C₂×C₂²⋊C₈	—	3	4	no	—
154	C₂²×C₃×C₅	—	2	4	no	—
155	C₂²×C₃×C₅	—	2	8	no	—
156	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂²×C₃×C₅	#131	1	4	yes	—
159	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₅×D₃	—	2	4	no	—
161	C₂×C₅×D₃	—	2	8	no	—
162	C₂×C₅×D₃	—	4	8	no	—
163	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
164	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
165	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₅×Dic₃	—	2	4	no	—
168	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
169	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
170	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
172	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
173	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
176	C₂×#67	—	2	8	no	—
177	C₂×#67	C₂×C₄×C₅	1	8	yes	—
178	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
179	#235	—	2	16	no	—
180	#235	—	2	8	no	—
181	#235	—	2	8	no	—
182	C₂×D₁₂	—	2	4	no	—
183	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
184	C₂×C₄×D₃	—	2	4	no	—
185	C₂×C₄×D₃	—	2	4	no	—
186	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
187	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
188	C₂×Dic₆	—	2	4	no	—
189	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
190	C₃×M₁₆	—	2	8	no	—
191	C₂×C₃×C₈	—	2	4	no	—
192	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
193	C₂×C₃⋊C₈	—	2	4	no	—
194	C₂×C₃⋊C₈	—	2	8	no	—
195	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	3	4	no	—
198	C₂³×C₅	—	6	8	no	—
199	C₂³×C₅	—	6	4	no	—
200	C₂³×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
201	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
202	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
203	C₅×Q₈	—	6	8	no	—
204	C₅×D₄	—	6	16	no	—
205	C₅×D₄	—	6	8	no	—
206	C₂×C₄×C₅	—	3	4	no	—
207	C₂×C₄×C₅	—	6	4	no	—
208	C₂×C₄×C₅	—	6	8	no	—
209	C₂×C₄×C₅	—	6	4	no	—
210	C₂×C₄×C₅	—	6	4	no	—
211	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
212	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	8	yes	—
213	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
215	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
216	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
217	C₂×C₄×C₅	C₂×#67	1	2	yes	—
218	C₂×C₄×C₅	C₂×#67	1	4	yes	—
219	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
220	C₅×C₈	—	2	4	no	—
221	C₅×C₈	—	6	4	no	—
222	C₂×#41	—	3	4	no	—
223	C₂×#41	—	3	4	no	—
224	C₂×#41	—	6	4	no	—
225	C₂×#41	—	6	4	no	—
226	C₂²×Q₈	—	3	1	no	—
227	C₂²×D₄	—	3	2	no	—
228	C₂²×D₄	—	3	1	no	—
229	C₂³×C₄	—	3	2	no	—
230	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
231	C₂×M₁₆	—	2	4	no	—
232	C₂×M₁₆	C₂×C₅×D₃	1	4	yes	complemented
233	C₂²×C₈	—	3	2	no	—
234	C₂²×C₈	—	3	4	no	—
235	C₂²×C₈	—	6	4	no	—
236	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
237	C₂²⋊C₈	—	3	16	no	—
238	C₂×C₃×C₅	—	2	4	no	—
239	C₂×C₃×C₅	#408	1	4	yes	complemented
240	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#131	1	2	yes	—
242	C₅×D₃	—	4	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	C₅×C₂²⋊C₄	1	4	yes	—
245	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
246	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
247	C₂²×D₃	—	2	4	no	—
248	C₂²×D₃	—	2	8	no	—
249	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
250	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
251	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	8	yes	—
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
253	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
258	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
259	#67	—	2	16	no	—
260	C₂×Dic₃	—	2	4	no	—
261	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
262	D₁₂	—	2	8	no	—
263	C₄×D₃	—	2	8	no	—
264	C₄×D₃	—	2	4	no	—
265	C₄×D₃	—	2	4	no	—
266	Dic₆	—	2	8	no	—
267	C₃×C₈	—	2	4	no	—
268	C₃⋊C₈	—	2	4	no	—
269	C₂²×C₅	—	2	8	no	—
270	C₂²×C₅	—	2	4	no	—
271	C₂²×C₅	—	6	8	no	—
272	C₂²×C₅	—	6	4	no	—
273	C₂²×C₅	—	12	8	no	—
274	C₂²×C₅	#907	1	4	yes	—
275	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
276	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
277	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
278	C₄×C₅	—	6	4	no	—
279	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
280	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
281	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
282	C₄×C₅	C₂²×#67	1	1	yes	characteristic
283	C₂⁴	—	3	2	no	—
284	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
285	#41	—	6	16	no	—
286	#41	—	6	8	no	—
287	#41	—	6	8	no	—
288	C₂×Q₈	—	3	4	no	—
289	C₂×Q₈	—	6	4	no	—
290	C₂×D₄	—	3	8	no	—
291	C₂×D₄	—	3	4	no	—
292	C₂×D₄	—	6	8	no	—
293	C₂×D₄	—	6	4	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	—	3	4	no	—
296	C₂²×C₄	—	3	4	no	—
297	C₂²×C₄	—	6	4	no	—
298	C₂²×C₄	—	6	4	no	—
299	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
300	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
301	C₂²×C₄	C₅×D₁₂	1	4	yes	—
302	C₂²×C₄	C₅×#67	1	4	yes	—
303	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
305	M₁₆	—	2	8	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	3	4	no	—
308	C₂×C₈	—	6	4	no	—
309	C₂×C₈	—	6	8	no	—
310	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
311	C₃×C₅	C₂×#408	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	8	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
315	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
316	C₂²×C₃	C₅×#131	1	4	yes	—
317	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
318	C₂×D₃	—	2	4	no	—
319	C₂×D₃	—	2	8	no	—
320	C₂×D₃	—	4	8	no	—
321	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
322	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
323	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
324	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
325	Dic₃	—	2	4	no	—
326	C₂×C₅	—	2	4	no	—
327	C₂×C₅	—	12	4	no	—
328	C₂×C₅	#5129	1	4	yes	direct product factor
329	C₂×C₅	C₂×#907	1	2	yes	—
330	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
331	C₂³	—	2	4	no	—
332	C₂³	—	3	4	no	—
333	C₂³	—	6	8	no	—
334	C₂³	—	6	4	no	—
335	C₂³	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
336	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
337	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
338	Q₈	—	6	8	no	—
339	D₄	—	6	16	no	—
340	D₄	—	6	8	no	—
341	C₂×C₄	—	3	4	no	—
342	C₂×C₄	—	6	4	no	—
343	C₂×C₄	—	6	8	no	—
344	C₂×C₄	—	6	4	no	—
345	C₂×C₄	—	6	4	no	—
346	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
347	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	8	yes	—
348	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
350	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
351	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
352	C₂×C₄	C₂×C₅×#67	1	2	yes	—
353	C₂×C₄	C₂×C₅×#67	1	4	yes	—
354	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
355	C₈	—	2	4	no	—
356	C₈	—	6	4	no	—
357	C₂×C₃	—	2	4	no	—
358	C₂×C₃	C₅×#408	1	4	yes	complemented
359	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₃	C₂×C₅×#131	1	2	yes	—
361	D₃	—	4	4	no	—
362	C₅	C₂×#5129	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	4	no	—
364	C₂²	—	2	8	no	—
365	C₂²	—	6	8	no	—
366	C₂²	—	6	4	no	—
367	C₂²	—	12	8	no	—
368	C₂²	C₅×#907	1	4	yes	—
369	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
370	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
371	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
372	C₄	—	6	4	no	—
373	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
374	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
375	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
376	C₄	C₂²×C₅×#67	1	1	yes	characteristic
377	C₃	C₂×C₅×#408	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	2	4	no	—
379	C₂	—	12	4	no	—
380	C₂	C₅×#5129	1	4	yes	direct product factor
381	C₂	C₂×C₅×#907	1	2	yes	—
382	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	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₂×C₅×#408
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. C₂³×C₅×C₃⋊C₈	C₂	semidirect
4. C₅×#5129	C₂	direct (N × H)
5. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
21. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
22. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
23. C₂×#5129	C₅	direct (N × H)
25. C₂²×C₅×M₁₆	D₃	semidirect
58. C₂²×C₃×M₁₆	C₂×C₅	semidirect
59. C₂³×C₃⋊C₈	C₂×C₅	semidirect
60. #5129	C₂×C₅	direct (N × H)
61. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
72. C₂×C₅×M₁₆	C₂×D₃	semidirect
115. C₂×C₃×M₁₆	C₂²×C₅	semidirect
119. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
120. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
150. C₂²×M₁₆	C₅×D₃	semidirect
232. C₂×M₁₆	C₂×C₅×D₃	semidirect
239. C₂×C₃×C₅	#408	semidirect
311. C₃×C₅	C₂×#408	semidirect
328. C₂×C₅	#5129	direct (N × H)
358. C₂×C₃	C₅×#408	semidirect
362. C₅	C₂×#5129	direct (N × H)
377. C₃	C₂×C₅×#408	semidirect
380. C₂	C₅×#5129	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×C₅×#235	2
C₂²×C₃×C₅×M₁₆	2
C₂³×C₅×C₃⋊C₈	2
C₅×#5129	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#408	3
C₂×#5129	5

Subgroups — C2×C5×#5129 #14411686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5129 #14411686