Subgroups — C₅×#83762 #14411749

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 492 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	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5129	C₂	1	4	yes	maximal, complemented
5	C₅×#5126	C₂	1	4	yes	maximal, complemented
6	C₅×#5110	C₂	1	4	yes	maximal, complemented
7	C₅×#2879	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₅×#67	C₄	1	2	yes	—
10	C₂×C₅×#235	—	2	4	no	—
11	C₂×C₅×#235	—	2	4	no	—
12	C₂×C₅×#235	C₄	1	2	yes	—
13	C₂×C₅×#235	C₄	1	2	yes	—
14	C₂×C₅×#235	C₂²	1	2	yes	—
15	C₂×C₅×#235	C₂²	1	2	yes	—
16	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
18	C₂²×C₅×Dic₆	C₄	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	—	2	4	no	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
23	C₂×C₅×#208	—	2	4	no	—
24	C₂×C₅×#208	C₂²	1	2	yes	—
25	C₂×C₅×#208	C₂²	1	2	yes	complemented
26	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
27	C₅×(C₂×D₃)⋊C₈	C₂²	1	16	yes	complemented
28	#83762	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂²×C₅×#41	—	3	1	no	—
30	C₂²×C₅×M₁₆	—	3	1	no	—
31	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
32	C₅×#408	—	3	4	no	—
33	C₅×#408	—	3	4	no	—
34	C₅×#407	—	3	4	no	—
35	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×#67	—	2	8	no	—
46	C₂×C₅×#67	C₂×C₄	1	4	yes	—
47	C₂×C₅×#67	C₂×C₄	1	4	yes	—
48	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
49	C₅×#235	—	2	8	no	—
50	C₅×#235	—	2	8	no	—
51	C₅×#235	—	2	4	no	—
52	C₅×#235	—	2	4	no	—
53	C₅×#235	—	2	4	no	—
54	C₅×#235	—	2	4	no	—
55	C₂×C₅×D₁₂	—	2	4	no	—
56	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
57	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
58	C₂×C₄×C₅×D₃	—	2	4	no	—
59	C₂×C₄×C₅×D₃	—	2	4	no	—
60	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
62	C₂×C₅×Dic₆	—	2	4	no	—
63	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
64	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
65	C₃×C₅×M₁₆	—	2	4	no	—
66	C₃×C₅×M₁₆	—	2	4	no	—
67	C₂×C₃×C₅×C₈	—	2	4	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
69	C₅×#208	—	2	4	no	—
70	C₅×#208	—	2	4	no	—
71	C₂×C₅×C₃⋊C₈	—	2	4	no	—
72	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
73	C₂²×#235	C₂×C₅	1	1	yes	characteristic
74	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
76	#5129	C₂×C₅	1	4	yes	complemented
77	#5126	C₂×C₅	1	4	yes	complemented
78	#5110	C₂×C₅	1	4	yes	complemented
79	C₂×C₅×#41	—	3	2	no	—
80	C₂×C₅×#41	—	3	2	no	—
81	C₂×C₅×#41	—	3	2	no	—
82	C₂×C₅×#41	—	3	2	no	—
83	C₂×C₅×#41	—	6	4	no	—
84	C₂×C₅×#41	—	6	4	no	—
85	C₂²×C₅×Q₈	—	3	1	no	—
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	1	no	—
88	C₂³×C₄×C₅	—	3	2	no	—
89	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×M₁₆	—	2	4	no	—
91	C₂×C₅×M₁₆	—	3	2	no	—
92	C₂×C₅×M₁₆	—	3	2	no	—
93	C₂×C₅×M₁₆	—	6	4	no	—
94	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
95	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
96	C₂²×C₅×C₈	—	3	2	no	—
97	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
98	C₅×C₂²⋊C₈	—	3	16	no	—
99	#2879	—	3	1	no	Sylow
100	C₂³×C₃×C₅	—	4	2	no	—
101	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
102	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₅×D₃	—	2	4	no	—
106	C₂²×C₅×D₃	—	4	4	no	—
107	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₅×#67	—	2	8	no	—
122	C₅×#67	—	2	8	no	—
123	C₂×C₅×Dic₃	—	2	4	no	—
124	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
125	C₅×D₁₂	—	2	4	no	—
126	C₅×D₁₂	—	2	4	no	—
127	C₄×C₅×D₃	—	2	8	no	—
128	C₄×C₅×D₃	—	2	4	no	—
129	C₄×C₅×D₃	—	2	4	no	—
130	C₅×Dic₆	—	2	4	no	—
131	C₅×Dic₆	—	2	4	no	—
132	C₃×C₅×C₈	—	2	4	no	—
133	C₅×C₃⋊C₈	—	2	4	no	—
134	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂²×#67	C₄×C₅	1	2	yes	—
136	C₂×#235	—	2	4	no	—
137	C₂×#235	—	2	4	no	—
138	C₂×#235	C₄×C₅	1	2	yes	—
139	C₂×#235	C₄×C₅	1	2	yes	—
140	C₂×#235	C₂²×C₅	1	2	yes	—
141	C₂×#235	C₂²×C₅	1	2	yes	—
142	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
143	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
144	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic
145	C₂×C₃×M₁₆	—	2	4	no	—
146	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
147	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
148	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
149	C₂×#208	—	2	4	no	—
150	C₂×#208	C₂²×C₅	1	2	yes	—
151	C₂×#208	C₂²×C₅	1	2	yes	complemented
152	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
153	(C₂×D₃)⋊C₈	C₂²×C₅	1	16	yes	complemented
154	C₂⁴×C₅	—	3	2	no	—
155	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
156	C₅×#41	—	6	8	no	—
157	C₅×#41	—	6	8	no	—
158	C₅×#41	—	6	4	no	—
159	C₅×#41	—	6	4	no	—
160	C₅×#41	—	6	4	no	—
161	C₅×#41	—	6	4	no	—
162	C₂×C₅×Q₈	—	3	2	no	—
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	4	no	—
165	C₂×C₅×D₄	—	3	4	no	—
166	C₂×C₅×D₄	—	3	4	no	—
167	C₂×C₅×D₄	—	3	2	no	—
168	C₂×C₅×D₄	—	3	2	no	—
169	C₂×C₅×D₄	—	6	8	no	—
170	C₂×C₅×D₄	—	6	4	no	—
171	C₂²×C₄×C₅	—	3	2	no	—
172	C₂²×C₄×C₅	—	3	4	no	—
173	C₂²×C₄×C₅	—	3	4	no	—
174	C₂²×C₄×C₅	—	6	4	no	—
175	C₂²×C₄×C₅	—	6	4	no	—
176	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
179	C₂²×C₄×C₅	D₁₂	1	4	yes	—
180	C₂²×C₄×C₅	#67	1	4	yes	—
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
184	C₅×M₁₆	—	2	4	no	—
185	C₅×M₁₆	—	2	4	no	—
186	C₅×M₁₆	—	6	4	no	—
187	C₅×M₁₆	—	6	4	no	—
188	C₂×C₅×C₈	—	2	4	no	—
189	C₂×C₅×C₈	—	3	4	no	—
190	C₂×C₅×C₈	—	6	4	no	—
191	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
192	C₂²×#41	—	3	1	no	—
193	C₂²×M₁₆	—	3	1	no	—
194	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
195	#408	—	3	4	no	—
196	#408	—	3	4	no	—
197	#407	—	3	4	no	—
198	C₂²×C₃×C₅	—	2	2	no	—
199	C₂²×C₃×C₅	—	2	2	no	—
200	C₂²×C₃×C₅	—	2	2	no	—
201	C₂²×C₃×C₅	—	4	4	no	—
202	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₅×D₃	—	2	4	no	—
207	C₂×C₅×D₃	—	2	8	no	—
208	C₂×C₅×D₃	—	4	8	no	—
209	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
210	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
211	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
212	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₅×Dic₃	—	2	4	no	—
215	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
221	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂×#67	—	2	8	no	—
226	C₂×#67	C₂×C₄×C₅	1	4	yes	—
227	C₂×#67	C₂×C₄×C₅	1	4	yes	—
228	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
229	#235	—	2	8	no	—
230	#235	—	2	8	no	—
231	#235	—	2	4	no	—
232	#235	—	2	4	no	—
233	#235	—	2	4	no	—
234	#235	—	2	4	no	—
235	C₂×D₁₂	—	2	4	no	—
236	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
237	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₄×D₃	—	2	4	no	—
239	C₂×C₄×D₃	—	2	4	no	—
240	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
241	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
242	C₂×Dic₆	—	2	4	no	—
243	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
244	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
245	C₃×M₁₆	—	2	4	no	—
246	C₃×M₁₆	—	2	4	no	—
247	C₂×C₃×C₈	—	2	4	no	—
248	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
249	#208	—	2	4	no	—
250	#208	—	2	4	no	—
251	C₂×C₃⋊C₈	—	2	4	no	—
252	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
253	C₂³×C₅	—	3	4	no	—
254	C₂³×C₅	—	4	2	no	—
255	C₂³×C₅	—	6	4	no	—
256	C₂³×C₅	—	12	4	no	—
257	C₂³×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
258	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₅×Q₈	—	6	4	no	—
262	C₅×Q₈	—	6	4	no	—
263	C₅×D₄	—	6	8	no	—
264	C₅×D₄	—	6	8	no	—
265	C₅×D₄	—	6	4	no	—
266	C₅×D₄	—	6	4	no	—
267	C₂×C₄×C₅	—	3	4	no	—
268	C₂×C₄×C₅	—	6	4	no	—
269	C₂×C₄×C₅	—	6	8	no	—
270	C₂×C₄×C₅	—	6	4	no	—
271	C₂×C₄×C₅	—	6	4	no	—
272	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
273	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
274	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
275	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
279	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
280	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
281	C₂×C₄×C₅	C₂×#67	1	2	yes	—
282	C₂×C₄×C₅	C₂×#67	1	2	yes	—
283	C₂×C₄×C₅	C₂×#67	1	2	yes	—
284	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
285	C₅×C₈	—	2	4	no	—
286	C₅×C₈	—	6	4	no	—
287	C₂×#41	—	3	2	no	—
288	C₂×#41	—	3	2	no	—
289	C₂×#41	—	3	2	no	—
290	C₂×#41	—	3	2	no	—
291	C₂×#41	—	6	4	no	—
292	C₂×#41	—	6	4	no	—
293	C₂²×Q₈	—	3	1	no	—
294	C₂²×D₄	—	3	2	no	—
295	C₂²×D₄	—	3	1	no	—
296	C₂³×C₄	—	3	2	no	—
297	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	3	2	no	—
300	C₂×M₁₆	—	3	2	no	—
301	C₂×M₁₆	—	6	4	no	—
302	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
303	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
304	C₂²×C₈	—	3	2	no	—
305	C₂²×C₈	C₂×C₅×D₃	1	2	yes	complemented
306	C₂²⋊C₈	—	3	16	no	—
307	C₂×C₃×C₅	—	2	2	no	—
308	C₂×C₃×C₅	—	2	2	no	—
309	C₂×C₃×C₅	—	2	2	no	—
310	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₃×C₅	#568	1	2	yes	—
312	C₅×D₃	—	4	4	no	—
313	C₂³×C₃	—	4	2	no	—
314	C₂³×C₃	C₅×C₂²⋊C₄	1	4	yes	—
315	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
316	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×D₃	—	2	4	no	—
319	C₂²×D₃	—	4	4	no	—
320	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
321	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
322	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
323	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
324	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
328	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
329	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
330	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
333	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
334	#67	—	2	8	no	—
335	#67	—	2	8	no	—
336	C₂×Dic₃	—	2	4	no	—
337	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
338	D₁₂	—	2	4	no	—
339	D₁₂	—	2	4	no	—
340	C₄×D₃	—	2	8	no	—
341	C₄×D₃	—	2	4	no	—
342	C₄×D₃	—	2	4	no	—
343	Dic₆	—	2	4	no	—
344	Dic₆	—	2	4	no	—
345	C₃×C₈	—	2	4	no	—
346	C₃⋊C₈	—	2	4	no	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	2	2	no	—
350	C₂²×C₅	—	4	4	no	—
351	C₂²×C₅	—	6	8	no	—
352	C₂²×C₅	—	6	4	no	—
353	C₂²×C₅	—	12	8	no	—
354	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
355	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
356	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
357	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
358	C₄×C₅	—	6	4	no	—
359	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
360	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
361	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
362	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
363	C₄×C₅	C₂²×#67	1	1	yes	characteristic
364	C₂⁴	—	3	2	no	—
365	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
366	#41	—	6	8	no	—
367	#41	—	6	8	no	—
368	#41	—	6	4	no	—
369	#41	—	6	4	no	—
370	#41	—	6	4	no	—
371	#41	—	6	4	no	—
372	C₂×Q₈	—	3	2	no	—
373	C₂×Q₈	—	3	2	no	—
374	C₂×Q₈	—	6	4	no	—
375	C₂×D₄	—	3	4	no	—
376	C₂×D₄	—	3	4	no	—
377	C₂×D₄	—	3	2	no	—
378	C₂×D₄	—	3	2	no	—
379	C₂×D₄	—	6	8	no	—
380	C₂×D₄	—	6	4	no	—
381	C₂²×C₄	—	3	2	no	—
382	C₂²×C₄	—	3	4	no	—
383	C₂²×C₄	—	3	4	no	—
384	C₂²×C₄	—	6	4	no	—
385	C₂²×C₄	—	6	4	no	—
386	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
387	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
388	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
389	C₂²×C₄	C₅×D₁₂	1	4	yes	—
390	C₂²×C₄	C₅×#67	1	4	yes	—
391	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
394	M₁₆	—	2	4	no	—
395	M₁₆	—	2	4	no	—
396	M₁₆	—	6	4	no	—
397	M₁₆	—	6	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	3	4	no	—
400	C₂×C₈	—	6	4	no	—
401	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
402	C₃×C₅	#2879	1	1	yes	characteristic, complemented, Hall
403	C₂²×C₃	—	2	2	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	4	4	no	—
407	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
408	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
409	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
410	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
411	C₂×D₃	—	2	4	no	—
412	C₂×D₃	—	2	8	no	—
413	C₂×D₃	—	4	8	no	—
414	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
415	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
416	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
417	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
418	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
419	Dic₃	—	2	4	no	—
420	C₂×C₅	—	2	2	no	—
421	C₂×C₅	—	2	2	no	—
422	C₂×C₅	—	2	2	no	—
423	C₂×C₅	—	12	4	no	—
424	C₂×C₅	#5745	1	2	yes	—
425	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
426	C₂³	—	3	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	6	4	no	—
429	C₂³	—	12	4	no	—
430	C₂³	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
431	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
432	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
433	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
434	Q₈	—	6	4	no	—
435	Q₈	—	6	4	no	—
436	D₄	—	6	8	no	—
437	D₄	—	6	8	no	—
438	D₄	—	6	4	no	—
439	D₄	—	6	4	no	—
440	C₂×C₄	—	3	4	no	—
441	C₂×C₄	—	6	4	no	—
442	C₂×C₄	—	6	8	no	—
443	C₂×C₄	—	6	4	no	—
444	C₂×C₄	—	6	4	no	—
445	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
446	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
447	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
448	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
449	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
452	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
453	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
454	C₂×C₄	C₂×C₅×#67	1	2	yes	—
455	C₂×C₄	C₂×C₅×#67	1	2	yes	—
456	C₂×C₄	C₂×C₅×#67	1	2	yes	—
457	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	6	4	no	—
460	C₂×C₃	—	2	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₃	C₅×#568	1	2	yes	—
465	D₃	—	4	4	no	—
466	C₅	#83762	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	6	8	no	—
472	C₂²	—	6	4	no	—
473	C₂²	—	12	8	no	—
474	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
475	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
476	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
477	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
478	C₄	—	6	4	no	—
479	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
480	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
481	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
482	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
483	C₄	C₂²×C₅×#67	1	1	yes	characteristic
484	C₃	C₅×#2879	1	1	yes	characteristic, complemented, Sylow
485	C₂	—	2	2	no	—
486	C₂	—	2	2	no	—
487	C₂	—	2	2	no	—
488	C₂	—	12	4	no	—
489	C₂	C₅×#5745	1	2	yes	—
490	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#2879
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×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×#5129	C₂	semidirect
5. C₅×#5126	C₂	semidirect
6. C₅×#5110	C₂	semidirect
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
22. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₂×C₅×#208	C₂²	semidirect
26. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
27. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
28. #83762	C₅	direct (N × H)
31. C₂²×C₅×M₁₆	D₃	semidirect
74. C₂²×C₃×M₁₆	C₂×C₅	semidirect
75. C₂²×#208	C₂×C₅	semidirect
76. #5129	C₂×C₅	semidirect
77. #5126	C₂×C₅	semidirect
78. #5110	C₂×C₅	semidirect
95. C₂×C₅×M₁₆	C₂×D₃	semidirect
97. C₂²×C₅×C₈	C₂×D₃	semidirect
147. C₂×C₃×M₁₆	C₂²×C₅	semidirect
148. C₂²×C₃×C₈	C₂²×C₅	semidirect
151. C₂×#208	C₂²×C₅	semidirect
152. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
153. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
194. C₂²×M₁₆	C₅×D₃	semidirect
303. C₂×M₁₆	C₂×C₅×D₃	semidirect
305. C₂²×C₈	C₂×C₅×D₃	semidirect
402. C₃×C₅	#2879	semidirect
466. C₅	#83762	direct (N × H)
484. C₃	C₅×#2879	semidirect

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
C₂²×C₅×#208	2
C₅×#5129	2
C₅×#5126	2
C₅×#5110	2
C₅×#2879	3
#83762	5

Subgroups — C5×#83762 #14411749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83762 #14411749