Subgroups — C₅×#84086 #14321163

Order 1920.

1872 conjugacy classes of subgroups.

The subgroup lattice has 440 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	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5229	C₂	1	2	yes	maximal, complemented
5	C₅×#5221	C₂	1	2	yes	maximal, complemented
6	C₅×#5220	C₂	1	4	yes	maximal, complemented
7	C₄×C₅×#217	C₂	1	4	yes	maximal, complemented
8	C₅×#2297	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	—	2	4	no	—
10	C₂×C₃×C₅×#41	—	2	4	no	—
11	C₂×C₃×C₅×#41	C₄	1	8	yes	complemented
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×#217	C₂²	1	8	yes	—
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₅×#926	—	2	4	no	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Dic₃	—	2	4	no	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
26	C₅×C₃⋊#95	C₂²	1	8	yes	—
27	#84086	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×#41	D₃	1	1	yes	characteristic
29	C₂×C₅×#117	—	3	1	no	—
30	C₂²×C₄²×C₅	—	3	1	no	—
31	C₅×#391	—	3	2	no	—
32	C₅×#390	—	3	2	no	—
33	C₅×#386	—	3	4	no	—
34	C₄×C₅×C₂²⋊C₄	—	3	4	no	—
35	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
36	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
37	C₃×C₅×#41	—	2	32	no	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	—
46	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
51	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
52	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	—	2	4	no	—
57	C₂²×C₅×Dic₃	—	2	8	no	—
58	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
59	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
60	C₅×#217	—	2	4	no	—
61	C₅×#217	—	2	16	no	—
62	C₅×C₄⋊Dic₃	—	2	4	no	—
63	C₄×C₅×Dic₃	—	2	4	no	—
64	C₄×C₅×Dic₃	—	2	4	no	—
65	C₄×C₅×Dic₃	—	2	4	no	—
66	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic
67	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
69	#5229	C₂×C₅	1	2	yes	complemented
70	#5221	C₂×C₅	1	2	yes	complemented
71	#5220	C₂×C₅	1	4	yes	complemented
72	C₄×#217	C₂×C₅	1	4	yes	complemented
73	C₂×C₅×#41	—	2	4	no	—
74	C₂×C₅×#41	—	2	4	no	—
75	C₂×C₅×#41	Dic₃	1	8	yes	complemented
76	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
78	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
79	C₂³×C₄×C₅	—	3	2	no	—
80	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
81	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
82	C₅×#117	—	6	4	no	—
83	C₂×C₅×C₄⋊C₄	—	3	2	no	—
84	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
85	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
86	C₂×C₄²×C₅	—	3	2	no	—
87	C₂×C₄²×C₅	—	3	2	no	—
88	C₂×C₄²×C₅	—	3	2	no	—
89	C₂×C₄²×C₅	—	6	4	no	—
90	C₅×#95	—	3	8	no	—
91	#2297	—	3	1	no	Sylow
92	C₂³×C₃×C₅	—	2	4	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	8	no	—
96	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
97	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
98	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
99	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	2	8	no	—
102	C₃×C₅×D₄	—	2	16	no	—
103	C₃×C₅×D₄	—	2	8	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	16	no	—
107	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₅×Dic₃	—	2	16	no	—
116	C₂×C₅×Dic₃	—	2	4	no	—
117	C₂×C₅×Dic₃	—	2	4	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	—	2	8	no	—
120	C₂×C₅×Dic₃	#41	1	8	yes	complemented
121	C₂×C₃×#41	—	2	4	no	—
122	C₂×C₃×#41	—	2	4	no	—
123	C₂×C₃×#41	C₄×C₅	1	8	yes	complemented
124	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
125	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
126	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
128	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
130	C₂×#217	C₂²×C₅	1	8	yes	—
131	C₂×#217	C₂²×C₅	1	2	yes	—
132	#926	—	2	4	no	—
133	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
134	C₂×C₄×Dic₃	—	2	4	no	—
135	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
136	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
137	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
138	C₃⋊#95	C₂²×C₅	1	8	yes	—
139	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
140	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
141	C₅×#41	—	2	32	no	—
142	C₂×C₅×Q₈	—	2	2	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	C₂×Dic₃	1	4	yes	complemented
145	C₂×C₅×D₄	—	2	4	no	—
146	C₂×C₅×D₄	—	2	4	no	—
147	C₂×C₅×D₄	—	2	2	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	C₂×Dic₃	1	8	yes	—
150	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	complemented
151	C₂²×C₄×C₅	—	2	4	no	—
152	C₂²×C₄×C₅	—	2	4	no	—
153	C₂²×C₄×C₅	—	3	4	no	—
154	C₂²×C₄×C₅	—	3	4	no	—
155	C₂²×C₄×C₅	—	6	8	no	—
156	C₂²×C₄×C₅	—	6	4	no	—
157	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
158	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	complemented
159	C₂²×C₄×C₅	#67	1	4	yes	—
160	C₂²×C₄×C₅	#67	1	4	yes	—
161	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	6	4	no	—
165	C₅×C₂²⋊C₄	—	6	16	no	—
166	C₅×C₂²⋊C₄	—	6	4	no	—
167	C₄²×C₅	—	6	4	no	—
168	C₄²×C₅	—	6	4	no	—
169	C₄²×C₅	—	6	4	no	—
170	C₂²×#41	C₅×D₃	1	1	yes	characteristic
171	C₂×#117	—	3	1	no	—
172	C₂²×C₄²	—	3	1	no	—
173	#391	—	3	2	no	—
174	#390	—	3	2	no	—
175	#386	—	3	4	no	—
176	C₄×C₂²⋊C₄	—	3	4	no	—
177	C₂²×C₃×C₅	—	2	4	no	—
178	C₂²×C₃×C₅	—	2	4	no	—
179	C₂²×C₃×C₅	—	2	4	no	—
180	C₂²×C₃×C₅	—	2	4	no	—
181	C₂²×C₃×C₅	—	2	8	no	—
182	C₂²×C₃×C₅	—	4	4	no	—
183	C₂²×C₃×C₅	—	4	4	no	—
184	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
191	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
192	C₅×Dic₃	—	2	8	no	—
193	C₅×Dic₃	—	4	4	no	—
194	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
195	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
196	C₃×#41	—	2	32	no	—
197	C₂×C₃×Q₈	—	2	2	no	—
198	C₂×C₃×Q₈	—	2	2	no	—
199	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
200	C₂×C₃×D₄	—	2	4	no	—
201	C₂×C₃×D₄	—	2	4	no	—
202	C₂×C₃×D₄	—	2	2	no	—
203	C₂×C₃×D₄	—	2	2	no	—
204	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	—
205	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
206	C₂²×C₃×C₄	—	2	4	no	—
207	C₂²×C₃×C₄	—	2	4	no	—
208	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
209	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	complemented
210	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
211	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂²×Dic₃	—	2	4	no	—
216	C₂²×Dic₃	—	2	8	no	—
217	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
218	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
219	#217	—	2	4	no	—
220	#217	—	2	16	no	—
221	C₄⋊Dic₃	—	2	4	no	—
222	C₄×Dic₃	—	2	4	no	—
223	C₄×Dic₃	—	2	4	no	—
224	C₄×Dic₃	—	2	4	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	2	8	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
230	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
231	C₂³×C₅	C₂×#67	1	2	yes	—
232	C₂³×C₅	C₂×#67	1	2	yes	—
233	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
234	C₅×Q₈	—	2	8	no	—
235	C₅×D₄	—	2	16	no	—
236	C₅×D₄	—	2	8	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	16	no	—
240	C₂×C₄×C₅	—	3	8	no	—
241	C₂×C₄×C₅	—	6	16	no	—
242	C₂×C₄×C₅	—	6	4	no	—
243	C₂×C₄×C₅	—	6	4	no	—
244	C₂×C₄×C₅	—	6	8	no	—
245	C₂×C₄×C₅	—	6	4	no	—
246	C₂×C₄×C₅	#217	1	16	yes	complemented
247	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
248	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
249	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
250	C₂×C₄×C₅	C₂×#67	1	2	yes	—
251	C₂×C₄×C₅	C₂×#67	1	2	yes	—
252	C₂×C₄×C₅	C₂×#67	1	2	yes	—
253	C₂×C₄×C₅	C₂×#67	1	2	yes	—
254	C₂×#41	—	2	4	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	C₅×Dic₃	1	8	yes	complemented
257	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
258	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
259	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂³×C₄	—	3	2	no	—
261	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
262	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	#117	—	6	4	no	—
264	C₂×C₄⋊C₄	—	3	2	no	—
265	C₂×C₂²⋊C₄	—	3	2	no	—
266	C₂×C₂²⋊C₄	—	3	8	no	—
267	C₂×C₄²	—	3	2	no	—
268	C₂×C₄²	—	3	2	no	—
269	C₂×C₄²	—	3	2	no	—
270	C₂×C₄²	—	6	4	no	—
271	#95	—	3	8	no	—
272	C₂×C₃×C₅	—	2	4	no	—
273	C₂×C₃×C₅	—	4	4	no	—
274	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₃×C₅	C₄×#41	1	2	yes	—
276	C₂×C₃×C₅	#525	1	2	yes	—
277	C₂×C₃×C₅	#532	1	2	yes	—
278	C₂³×C₃	—	2	4	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	8	no	—
282	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
283	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
284	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
285	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
286	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
287	C₃×Q₈	—	2	8	no	—
288	C₃×D₄	—	2	16	no	—
289	C₃×D₄	—	2	8	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	16	no	—
293	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	16	yes	complemented
294	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
295	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
296	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂×Dic₃	—	2	16	no	—
302	C₂×Dic₃	—	2	4	no	—
303	C₂×Dic₃	—	2	4	no	—
304	C₂×Dic₃	—	2	4	no	—
305	C₂×Dic₃	—	2	8	no	—
306	C₂×Dic₃	C₅×#41	1	8	yes	complemented
307	C₂²×C₅	—	2	4	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	4	no	—
310	C₂²×C₅	—	2	8	no	—
311	C₂²×C₅	—	2	4	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	C₂×#217	1	4	yes	—
315	C₂²×C₅	D₃×#41	1	4	yes	—
316	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
317	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
318	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
319	C₄×C₅	—	2	4	no	—
320	C₄×C₅	—	6	8	no	—
321	C₄×C₅	—	12	4	no	—
322	C₄×C₅	C₂×#217	1	4	yes	—
323	C₄×C₅	C₂×#217	1	4	yes	—
324	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
325	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
326	#41	—	2	32	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂×C₅×Dic₃	1	4	yes	complemented
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	C₂×C₅×Dic₃	1	8	yes	—
335	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	complemented
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	3	4	no	—
339	C₂²×C₄	—	3	4	no	—
340	C₂²×C₄	—	6	8	no	—
341	C₂²×C₄	—	6	4	no	—
342	C₂²×C₄	C₂×C₅×Dic₃	1	4	yes	—
343	C₂²×C₄	C₂×C₅×Dic₃	1	8	yes	complemented
344	C₂²×C₄	C₅×#67	1	4	yes	—
345	C₂²×C₄	C₅×#67	1	4	yes	—
346	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
347	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
349	C₄⋊C₄	—	6	4	no	—
350	C₂²⋊C₄	—	6	16	no	—
351	C₂²⋊C₄	—	6	4	no	—
352	C₄²	—	6	4	no	—
353	C₄²	—	6	4	no	—
354	C₄²	—	6	4	no	—
355	C₃×C₅	#2297	1	1	yes	characteristic, complemented, Hall
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	4	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	2	4	no	—
360	C₂²×C₃	—	2	8	no	—
361	C₂²×C₃	—	4	4	no	—
362	C₂²×C₃	—	4	4	no	—
363	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
364	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
365	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
368	C₃×C₄	—	2	4	no	—
369	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
370	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
371	Dic₃	—	2	8	no	—
372	Dic₃	—	4	4	no	—
373	C₂×C₅	—	2	4	no	—
374	C₂×C₅	—	4	4	no	—
375	C₂×C₅	Dic₃×#41	1	2	yes	—
376	C₂×C₅	#5828	1	2	yes	—
377	C₂×C₅	#5832	1	2	yes	—
378	C₂×C₅	C₂²×#217	1	1	yes	characteristic
379	C₂³	—	2	4	no	—
380	C₂³	—	2	8	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
384	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
385	C₂³	C₂×C₅×#67	1	2	yes	—
386	C₂³	C₂×C₅×#67	1	2	yes	—
387	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	D₄	—	2	16	no	—
390	D₄	—	2	8	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	3	8	no	—
395	C₂×C₄	—	6	16	no	—
396	C₂×C₄	—	6	4	no	—
397	C₂×C₄	—	6	4	no	—
398	C₂×C₄	—	6	8	no	—
399	C₂×C₄	—	6	4	no	—
400	C₂×C₄	C₅×#217	1	16	yes	complemented
401	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
402	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
403	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
404	C₂×C₄	C₂×C₅×#67	1	2	yes	—
405	C₂×C₄	C₂×C₅×#67	1	2	yes	—
406	C₂×C₄	C₂×C₅×#67	1	2	yes	—
407	C₂×C₄	C₂×C₅×#67	1	2	yes	—
408	C₂×C₃	—	2	4	no	—
409	C₂×C₃	—	4	4	no	—
410	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₂×C₃	C₄×C₅×#41	1	2	yes	—
412	C₂×C₃	C₅×#525	1	2	yes	—
413	C₂×C₃	C₅×#532	1	2	yes	—
414	C₅	#84086	1	1	yes	characteristic, direct product factor, Sylow
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	C₂×C₅×#217	1	4	yes	—
423	C₂²	C₅×D₃×#41	1	4	yes	—
424	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
425	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
426	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
427	C₄	—	2	4	no	—
428	C₄	—	6	8	no	—
429	C₄	—	12	4	no	—
430	C₄	C₂×C₅×#217	1	4	yes	—
431	C₄	C₂×C₅×#217	1	4	yes	—
432	C₃	C₅×#2297	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	2	4	no	—
434	C₂	—	4	4	no	—
435	C₂	C₅×Dic₃×#41	1	2	yes	—
436	C₂	C₅×#5828	1	2	yes	—
437	C₂	C₅×#5832	1	2	yes	—
438	C₂	C₂²×C₅×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting, prime radical	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₅×#2297
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#926	C₂	semidirect
3. C₂²×C₄×C₅×Dic₃	C₂	semidirect
4. C₅×#5229	C₂	semidirect
5. C₅×#5221	C₂	semidirect
6. C₅×#5220	C₂	semidirect
7. C₄×C₅×#217	C₂	semidirect
11. C₂×C₃×C₅×#41	C₄	semidirect
27. #84086	C₅	direct (N × H)
40. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
46. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
50. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
67. C₂×#926	C₂×C₅	semidirect
68. C₂²×C₄×Dic₃	C₂×C₅	semidirect
69. #5229	C₂×C₅	semidirect
70. #5221	C₂×C₅	semidirect
71. #5220	C₂×C₅	semidirect
72. C₄×#217	C₂×C₅	semidirect
75. C₂×C₅×#41	Dic₃	semidirect
107. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
120. C₂×C₅×Dic₃	#41	semidirect
123. C₂×C₃×#41	C₄×C₅	semidirect
144. C₂×C₅×Q₈	C₂×Dic₃	semidirect
150. C₂×C₅×D₄	C₂×Dic₃	semidirect
158. C₂²×C₄×C₅	C₂×Dic₃	semidirect
199. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
205. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
209. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
246. C₂×C₄×C₅	#217	semidirect
256. C₂×#41	C₅×Dic₃	semidirect
293. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
306. C₂×Dic₃	C₅×#41	semidirect
329. C₂×Q₈	C₂×C₅×Dic₃	semidirect
335. C₂×D₄	C₂×C₅×Dic₃	semidirect
343. C₂²×C₄	C₂×C₅×Dic₃	semidirect
355. C₃×C₅	#2297	semidirect
400. C₂×C₄	C₅×#217	semidirect
414. C₅	#84086	direct (N × H)
432. C₃	C₅×#2297	semidirect

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
C₂×C₅×#926	2
C₂²×C₄×C₅×Dic₃	2
C₅×#5229	2
C₅×#5221	2
C₅×#5220	2
C₄×C₅×#217	2
C₅×#2297	3
#84086	5

Subgroups — C5×#84086 #14321163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#84086 #14321163