Subgroups — C₂×C₅×#5237 #14412106

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	2	yes	maximal, complemented
3	C₅×#5237	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₅×#836	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#833	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#413	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	—	2	2	no	—
8	C₂×C₃×C₅×#41	—	2	2	no	—
9	C₂×C₃×C₅×#41	—	2	4	no	—
10	C₂×C₃×C₅×#41	C₄	1	4	yes	—
11	C₂×C₃×C₅×#41	C₂²	1	4	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₄	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₄	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×#208	—	2	2	no	—
18	C₂×C₅×#208	—	2	4	no	—
19	C₂×C₅×#208	C₂²	1	4	yes	—
20	C₂×C₅×#208	C₂²	1	8	yes	complemented
21	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
22	C₅×#836	C₂²	1	8	yes	complemented
23	C₅×#833	C₂²	1	8	yes	complemented
24	C₂×#5237	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×#41	D₃	1	1	yes	characteristic
26	C₂²×C₅×M₁₆	—	3	2	no	—
27	C₅×#413	—	3	8	no	—
28	C₂×C₅×#101	—	3	2	no	—
29	C₂×C₅×#100	—	3	2	no	—
30	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
31	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
32	C₃×C₅×#41	—	2	8	no	—
33	C₃×C₅×#41	—	2	8	no	—
34	C₃×C₅×#41	—	2	8	no	—
35	C₃×C₅×#41	—	2	8	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
55	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
56	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₅×#208	—	2	4	no	—
60	C₅×#208	—	2	8	no	—
61	C₅×#208	C₂³	1	8	yes	—
62	C₂×C₅×C₃⋊C₈	—	2	4	no	—
63	C₂×C₅×C₃⋊C₈	—	2	8	no	—
64	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic
65	C₂²×#208	C₂×C₅	1	2	yes	complemented
66	#5237	C₂×C₅	1	8	yes	direct product factor
67	C₂×#836	C₂×C₅	1	2	yes	complemented
68	C₂×#833	C₂×C₅	1	2	yes	complemented
69	C₂×C₅×#41	—	2	2	no	—
70	C₂×C₅×#41	—	2	4	no	—
71	C₂×C₅×#41	—	2	2	no	—
72	C₂×C₅×#41	Dic₃	1	4	yes	—
73	C₂×C₅×#41	C₂×D₃	1	4	yes	—
74	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₅×D₄	Dic₃	1	2	yes	—
76	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
77	C₂³×C₄×C₅	Dic₃	1	2	yes	—
78	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	3	4	no	—
80	C₂×C₅×M₁₆	—	3	8	no	—
81	C₂×C₅×M₁₆	—	6	2	no	—
82	C₂×C₅×M₁₆	—	6	4	no	—
83	C₂²×C₅×C₈	—	6	2	no	—
84	C₅×#101	—	3	8	no	—
85	C₅×#100	—	3	8	no	—
86	C₂×#413	—	3	1	no	Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	4	2	no	—
90	C₂³×C₃×C₅	—	4	4	no	—
91	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
92	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
93	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
95	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
96	C₃×C₅×Q₈	—	2	4	no	—
97	C₃×C₅×Q₈	—	2	4	no	—
98	C₃×C₅×D₄	—	2	16	no	—
99	C₃×C₅×D₄	—	2	4	no	—
100	C₃×C₅×D₄	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	8	no	—
104	C₂×C₃×C₄×C₅	—	2	8	no	—
105	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×C₃⋊C₈	—	2	8	no	—
119	C₂×C₃×#41	—	2	2	no	—
120	C₂×C₃×#41	—	2	2	no	—
121	C₂×C₃×#41	—	2	4	no	—
122	C₂×C₃×#41	C₄×C₅	1	4	yes	—
123	C₂×C₃×#41	C₂²×C₅	1	4	yes	—
124	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
125	C₂²×C₃×D₄	C₄×C₅	1	2	yes	—
126	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₄×C₅	1	2	yes	—
128	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×#208	—	2	2	no	—
130	C₂×#208	—	2	4	no	—
131	C₂×#208	C₂²×C₅	1	4	yes	—
132	C₂×#208	C₂²×C₅	1	8	yes	complemented
133	C₂²×C₃⋊C₈	—	2	2	no	—
134	#836	C₂²×C₅	1	8	yes	complemented
135	#833	C₂²×C₅	1	8	yes	complemented
136	C₂⁴×C₅	C₂×Dic₃	1	2	yes	—
137	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
138	C₅×#41	—	2	8	no	—
139	C₅×#41	—	2	8	no	—
140	C₅×#41	—	2	8	no	—
141	C₅×#41	—	2	8	no	—
142	C₂×C₅×Q₈	—	2	2	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
145	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
146	C₂×C₅×D₄	—	2	4	no	—
147	C₂×C₅×D₄	—	2	4	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	C₂×Dic₃	1	8	yes	—
151	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
152	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
153	C₂²×C₄×C₅	—	2	4	no	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	—
158	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	#67	1	2	yes	—
161	C₂²×C₄×C₅	#67	1	4	yes	—
162	C₂²×C₄×C₅	#67	1	2	yes	—
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
165	C₅×M₁₆	—	3	8	no	—
166	C₅×M₁₆	—	6	4	no	—
167	C₅×M₁₆	—	6	8	no	—
168	C₂×C₅×C₈	—	6	4	no	—
169	C₂×C₅×C₈	—	6	8	no	—
170	C₂²×#41	C₅×D₃	1	1	yes	characteristic
171	C₂²×M₁₆	—	3	2	no	—
172	#413	—	3	8	no	—
173	C₂×#101	—	3	2	no	—
174	C₂×#100	—	3	2	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	4	no	—
177	C₂²×C₃×C₅	—	2	4	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	4	no	—
181	C₂²×C₃×C₅	—	4	4	no	—
182	C₂²×C₃×C₅	—	4	4	no	—
183	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₃×C₄×C₅	—	2	4	no	—
188	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
189	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
190	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
191	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
192	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
193	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
194	C₃×#41	—	2	8	no	—
195	C₃×#41	—	2	8	no	—
196	C₃×#41	—	2	8	no	—
197	C₃×#41	—	2	8	no	—
198	C₂×C₃×Q₈	—	2	2	no	—
199	C₂×C₃×Q₈	—	2	2	no	—
200	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
201	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
202	C₂×C₃×D₄	—	2	4	no	—
203	C₂×C₃×D₄	—	2	4	no	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	—	2	2	no	—
206	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	—
207	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	—	2	4	no	—
210	C₂²×C₃×C₄	—	2	2	no	—
211	C₂²×C₃×C₄	—	2	2	no	—
212	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
214	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
216	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
217	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
218	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
221	#208	—	2	4	no	—
222	#208	—	2	8	no	—
223	#208	C₂³×C₅	1	8	yes	—
224	C₂×C₃⋊C₈	—	2	4	no	—
225	C₂×C₃⋊C₈	—	2	8	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	4	2	no	—
229	C₂³×C₅	—	4	4	no	—
230	C₂³×C₅	#217	1	2	yes	—
231	C₂³×C₅	#217	1	2	yes	—
232	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
233	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
234	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
235	C₅×Q₈	—	2	4	no	—
236	C₅×Q₈	—	2	4	no	—
237	C₅×D₄	—	2	16	no	—
238	C₅×D₄	—	2	4	no	—
239	C₅×D₄	—	2	4	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	8	no	—
243	C₂×C₄×C₅	—	2	8	no	—
244	C₂×C₄×C₅	#217	1	1	yes	characteristic
245	C₂×C₄×C₅	#217	1	2	yes	—
246	C₂×C₄×C₅	#217	1	4	yes	—
247	C₂×C₄×C₅	#217	1	4	yes	—
248	C₂×C₄×C₅	#217	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
250	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
251	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#67	1	2	yes	—
253	C₂×C₄×C₅	C₂×#67	1	4	yes	—
254	C₂×C₄×C₅	C₂×#67	1	2	yes	—
255	C₂×C₄×C₅	C₂×#67	1	4	yes	—
256	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
257	C₅×C₈	—	6	8	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	4	no	—
261	C₂×#41	C₅×Dic₃	1	4	yes	—
262	C₂×#41	C₂×C₅×D₃	1	4	yes	—
263	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂²×D₄	C₅×Dic₃	1	2	yes	—
265	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
266	C₂³×C₄	C₅×Dic₃	1	2	yes	—
267	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
268	C₂×M₁₆	—	3	4	no	—
269	C₂×M₁₆	—	3	8	no	—
270	C₂×M₁₆	—	6	2	no	—
271	C₂×M₁₆	—	6	4	no	—
272	C₂²×C₈	—	6	2	no	—
273	#101	—	3	8	no	—
274	#100	—	3	8	no	—
275	C₂×C₃×C₅	—	2	1	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	4	no	—
278	C₂×C₃×C₅	—	4	4	no	—
279	C₂×C₃×C₅	#413	1	2	yes	complemented
280	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	4	2	no	—
284	C₂³×C₃	—	4	4	no	—
285	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
286	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
287	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
289	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
290	C₃×Q₈	—	2	4	no	—
291	C₃×Q₈	—	2	4	no	—
292	C₃×D₄	—	2	16	no	—
293	C₃×D₄	—	2	4	no	—
294	C₃×D₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	8	no	—
298	C₂×C₃×C₄	—	2	8	no	—
299	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
300	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
303	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
304	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
305	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
306	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
309	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
310	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
311	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
312	C₃⋊C₈	—	2	8	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	2	4	no	—
315	C₂²×C₅	—	2	4	no	—
316	C₂²×C₅	—	4	2	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	—	4	4	no	—
319	C₂²×C₅	—	4	4	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	C₂×#217	1	1	yes	characteristic
322	C₂²×C₅	C₂×#217	1	4	yes	—
323	C₂²×C₅	C₂×#217	1	1	yes	characteristic
324	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
325	C₄×C₅	—	2	4	no	—
326	C₄×C₅	C₂×#217	1	2	yes	—
327	C₄×C₅	C₂×#217	1	2	yes	—
328	C₄×C₅	C₂×#217	1	2	yes	—
329	C₄×C₅	C₂²×#67	1	2	yes	—
330	C₂⁴	C₂×C₅×Dic₃	1	2	yes	—
331	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
332	#41	—	2	8	no	—
333	#41	—	2	8	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
339	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂×C₅×Dic₃	1	8	yes	—
345	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
346	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
351	C₂²×C₄	C₂×C₅×Dic₃	1	8	yes	—
352	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
354	C₂²×C₄	C₅×#67	1	2	yes	—
355	C₂²×C₄	C₅×#67	1	2	yes	—
356	C₂²×C₄	C₅×#67	1	4	yes	—
357	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
359	M₁₆	—	3	8	no	—
360	M₁₆	—	6	4	no	—
361	M₁₆	—	6	8	no	—
362	C₂×C₈	—	6	4	no	—
363	C₂×C₈	—	6	8	no	—
364	C₃×C₅	C₂×#413	1	1	yes	characteristic, complemented, Hall
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	—	4	4	no	—
371	C₂²×C₃	—	4	4	no	—
372	C₂²×C₃	—	4	4	no	—
373	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
374	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
375	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
379	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
380	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
381	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	2	4	no	—
385	C₂×C₅	—	4	4	no	—
386	C₂×C₅	#5237	1	2	yes	direct product factor
387	C₂×C₅	C₂²×#217	1	1	yes	characteristic
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	4	no	—
392	C₂³	C₅×#217	1	2	yes	—
393	C₂³	C₅×#217	1	2	yes	—
394	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
395	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
396	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	D₄	—	2	16	no	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	C₅×#217	1	2	yes	—
407	C₂×C₄	C₅×#217	1	1	yes	characteristic
408	C₂×C₄	C₅×#217	1	1	yes	characteristic
409	C₂×C₄	C₅×#217	1	4	yes	—
410	C₂×C₄	C₅×#217	1	4	yes	—
411	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
412	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
413	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
414	C₂×C₄	C₂×C₅×#67	1	2	yes	—
415	C₂×C₄	C₂×C₅×#67	1	4	yes	—
416	C₂×C₄	C₂×C₅×#67	1	2	yes	—
417	C₂×C₄	C₂×C₅×#67	1	4	yes	—
418	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
419	C₈	—	6	8	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	4	no	—
423	C₂×C₃	—	4	4	no	—
424	C₂×C₃	C₅×#413	1	2	yes	complemented
425	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₅	C₂×#5237	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₂×C₅×#217	1	1	yes	characteristic
436	C₂²	C₂×C₅×#217	1	4	yes	—
437	C₂²	C₂×C₅×#217	1	1	yes	characteristic
438	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	C₂×C₅×#217	1	2	yes	—
441	C₄	C₂×C₅×#217	1	2	yes	—
442	C₄	C₂×C₅×#217	1	2	yes	—
443	C₄	C₂²×C₅×#67	1	2	yes	—
444	C₃	C₂×C₅×#413	1	1	yes	characteristic, complemented, Sylow
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	4	no	—
448	C₂	—	4	4	no	—
449	C₂	C₅×#5237	1	2	yes	direct product factor
450	C₂	C₂²×C₅×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#217
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂²×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₂×C₅×#413
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#208	C₂	semidirect
3. C₅×#5237	C₂	direct (N × H)
4. C₂×C₅×#836	C₂	semidirect
5. C₂×C₅×#833	C₂	semidirect
20. C₂×C₅×#208	C₂²	semidirect
22. C₅×#836	C₂²	semidirect
23. C₅×#833	C₂²	semidirect
24. C₂×#5237	C₅	direct (N × H)
65. C₂²×#208	C₂×C₅	semidirect
66. #5237	C₂×C₅	direct (N × H)
67. C₂×#836	C₂×C₅	semidirect
68. C₂×#833	C₂×C₅	semidirect
132. C₂×#208	C₂²×C₅	semidirect
134. #836	C₂²×C₅	semidirect
135. #833	C₂²×C₅	semidirect
279. C₂×C₃×C₅	#413	semidirect
364. C₃×C₅	C₂×#413	semidirect
386. C₂×C₅	#5237	direct (N × H)
424. C₂×C₃	C₅×#413	semidirect
426. C₅	C₂×#5237	direct (N × H)
444. C₃	C₂×C₅×#413	semidirect
449. C₂	C₅×#5237	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×C₅×#41	2
C₂²×C₅×#208	2
C₅×#5237	2
C₂×C₅×#836	2
C₂×C₅×#833	2
C₂×C₅×#413	3
C₂×#5237	5

Subgroups — C2×C5×#5237 #14412106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5237 #14412106