Subgroups — C₅×#85735 #14480650

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 448 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	2	yes	maximal, complemented
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5526	C₂	1	4	yes	maximal, complemented
4	C₅×#5525	C₂	1	4	yes	maximal, complemented
5	C₅×#5524	C₂	1	8	yes	maximal, complemented
6	C₅×#5510	C₂	1	4	yes	maximal, complemented
7	C₅×#5493	C₂	1	4	yes	maximal, complemented
8	C₅×#5477	C₂	1	4	yes	maximal, complemented
9	C₅×#3449	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₂²	1	4	yes	—
12	C₂×C₅×#235	—	2	16	no	—
13	C₂×C₅×#235	C₂²	1	4	yes	—
14	C₂×C₅×#235	C₂²	1	4	yes	—
15	C₂×C₅×#235	C₂²	1	4	yes	complemented
16	C₂×C₅×#235	C₂²	1	4	yes	complemented
17	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
18	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	complemented
19	C₂²×C₅×Dic₆	C₂²	1	2	yes	complemented
20	C₃×C₅×#117	C₂²	1	4	yes	complemented
21	C₃×C₅×#117	C₂²	1	4	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
25	C₅×#930	C₂²	1	16	yes	complemented
26	C₅×#897	C₂²	1	16	yes	complemented
27	C₅×#895	C₂²	1	16	yes	complemented
28	C₅×#886	C₂²	1	16	yes	complemented
29	C₅×#882	C₂²	1	16	yes	complemented
30	C₅×#875	C₂²	1	8	yes	complemented
31	C₅×#874	C₂²	1	4	yes	complemented
32	C₄×C₅×D₁₂	C₂²	1	16	yes	complemented
33	C₅×#869	C₂²	1	4	yes	complemented
34	#85735	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₅×#41	—	3	2	no	—
36	C₅×#537	—	3	4	no	—
37	C₅×#536	—	3	4	no	—
38	C₅×#535	—	3	4	no	—
39	C₅×#534	—	3	4	no	—
40	C₅×#532	—	3	4	no	—
41	C₅×#525	—	3	8	no	—
42	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
43	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
44	C₂³×C₅×D₃	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	—	2	16	no	—
52	C₂×C₅×#67	C₂³	1	8	yes	—
53	C₂×C₅×#67	C₂³	1	8	yes	—
54	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
55	C₅×#235	—	2	16	no	—
56	C₅×#235	—	2	16	no	—
57	C₅×#235	—	2	16	no	—
58	C₅×#235	—	2	16	no	—
59	C₂×C₅×D₁₂	—	2	8	no	—
60	C₂×C₅×D₁₂	C₂³	1	4	yes	—
61	C₂×C₅×D₁₂	C₂³	1	4	yes	—
62	C₂×C₅×D₁₂	C₂³	1	16	yes	—
63	C₂×C₄×C₅×D₃	—	2	16	no	—
64	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
65	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
66	C₂×C₅×Dic₆	—	2	8	no	—
67	C₂×C₅×Dic₆	C₂³	1	4	yes	—
68	C₂×C₅×Dic₆	C₂³	1	4	yes	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
70	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₃×C₄²×C₅	C₂³	1	4	yes	—
72	C₃×C₄²×C₅	C₂³	1	4	yes	—
73	C₅×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
74	C₅×C₄⋊Dic₃	C₂³	1	16	yes	—
75	C₂²×#235	C₂×C₅	1	2	yes	complemented
76	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
77	#5526	C₂×C₅	1	4	yes	complemented
78	#5525	C₂×C₅	1	4	yes	complemented
79	#5524	C₂×C₅	1	8	yes	complemented
80	#5510	C₂×C₅	1	4	yes	complemented
81	#5493	C₂×C₅	1	4	yes	complemented
82	#5477	C₂×C₅	1	4	yes	complemented
83	C₂×C₅×#41	—	3	4	no	—
84	C₂×C₅×#41	—	3	4	no	—
85	C₂×C₅×#41	—	3	4	no	—
86	C₂×C₅×#41	—	3	4	no	—
87	C₂×C₅×#41	—	6	16	no	—
88	C₂²×C₅×Q₈	—	3	2	no	—
89	C₂²×C₅×D₄	—	3	4	no	—
90	C₂²×C₅×D₄	—	3	2	no	—
91	C₂³×C₄×C₅	—	3	4	no	—
92	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	—	3	4	no	—
94	C₅×#127	—	3	4	no	—
95	C₅×#124	—	3	8	no	—
96	C₅×#123	—	3	16	no	—
97	C₅×C₂²⋊Q₈	—	3	16	no	—
98	C₅×#121	—	3	16	no	—
99	C₅×#121	—	3	16	no	—
100	C₅×#120	—	3	16	no	—
101	C₄×C₅×D₄	—	3	16	no	—
102	C₅×#117	C₂×D₃	1	4	yes	complemented
103	C₅×#117	C₂×D₃	1	4	yes	complemented
104	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
105	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
106	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
107	#3449	—	3	1	no	Sylow
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
110	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
111	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
112	C₂²×C₅×D₃	—	2	8	no	—
113	C₂²×C₅×D₃	—	4	8	no	—
114	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
115	C₂×C₃×C₄×C₅	—	4	4	no	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×#67	—	2	16	no	—
125	C₅×#67	—	2	16	no	—
126	C₂×C₅×Dic₃	—	2	8	no	—
127	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
128	C₅×D₁₂	—	2	8	no	—
129	C₅×D₁₂	—	2	8	no	—
130	C₅×D₁₂	—	4	16	no	—
131	C₄×C₅×D₃	—	2	16	no	—
132	C₄×C₅×D₃	—	2	16	no	—
133	C₅×Dic₆	—	2	8	no	—
134	C₅×Dic₆	—	2	8	no	—
135	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂²×#67	C₂²×C₅	1	4	yes	—
137	C₂×#235	—	2	16	no	—
138	C₂×#235	C₂²×C₅	1	4	yes	—
139	C₂×#235	C₂²×C₅	1	4	yes	—
140	C₂×#235	C₂²×C₅	1	4	yes	complemented
141	C₂×#235	C₂²×C₅	1	4	yes	complemented
142	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
143	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	complemented
144	C₂²×Dic₆	C₂²×C₅	1	2	yes	complemented
145	C₃×#117	C₂²×C₅	1	4	yes	complemented
146	C₃×#117	C₂²×C₅	1	4	yes	complemented
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
148	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
150	#930	C₂²×C₅	1	16	yes	complemented
151	#897	C₂²×C₅	1	16	yes	complemented
152	#895	C₂²×C₅	1	16	yes	complemented
153	#886	C₂²×C₅	1	16	yes	complemented
154	#882	C₂²×C₅	1	16	yes	complemented
155	#875	C₂²×C₅	1	8	yes	complemented
156	#874	C₂²×C₅	1	4	yes	complemented
157	C₄×D₁₂	C₂²×C₅	1	16	yes	complemented
158	#869	C₂²×C₅	1	4	yes	complemented
159	C₂⁴×C₅	—	3	4	no	—
160	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₅×#41	—	6	16	no	—
162	C₅×#41	—	6	16	no	—
163	C₅×#41	—	6	16	no	—
164	C₅×#41	—	6	16	no	—
165	C₂×C₅×Q₈	—	3	4	no	—
166	C₂×C₅×Q₈	—	3	4	no	—
167	C₂×C₅×Q₈	—	6	8	no	—
168	C₂×C₅×D₄	—	3	8	no	—
169	C₂×C₅×D₄	—	3	8	no	—
170	C₂×C₅×D₄	—	3	4	no	—
171	C₂×C₅×D₄	—	3	4	no	—
172	C₂×C₅×D₄	—	3	16	no	—
173	C₂×C₅×D₄	—	6	16	no	—
174	C₂×C₅×D₄	—	6	8	no	—
175	C₂²×C₄×C₅	—	3	4	no	—
176	C₂²×C₄×C₅	—	3	8	no	—
177	C₂²×C₄×C₅	—	3	8	no	—
178	C₂²×C₄×C₅	—	6	16	no	—
179	C₂²×C₄×C₅	D₁₂	1	8	yes	complemented
180	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
181	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
183	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
185	C₅×C₄⋊C₄	—	3	16	no	—
186	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
187	C₅×C₂²⋊C₄	—	3	32	no	—
188	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
189	C₄²×C₅	C₂²×D₃	1	4	yes	—
190	C₄²×C₅	C₂²×D₃	1	4	yes	—
191	C₂²×#41	—	3	2	no	—
192	#537	—	3	4	no	—
193	#536	—	3	4	no	—
194	#535	—	3	4	no	—
195	#534	—	3	4	no	—
196	#532	—	3	4	no	—
197	#525	—	3	8	no	—
198	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
199	C₂²×C₃×C₅	—	2	2	no	—
200	C₂²×C₃×C₅	—	2	4	no	—
201	C₂²×C₃×C₅	—	4	4	no	—
202	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
203	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
204	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
205	C₂×C₅×D₃	—	2	8	no	—
206	C₂×C₅×D₃	—	2	16	no	—
207	C₂×C₅×D₃	—	4	16	no	—
208	C₃×C₄×C₅	—	2	8	no	—
209	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
211	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
212	C₅×Dic₃	—	2	8	no	—
213	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
214	C₂³×D₃	C₂³×C₅	1	4	yes	—
215	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
216	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
221	C₂×#67	—	2	16	no	—
222	C₂×#67	C₂³×C₅	1	8	yes	—
223	C₂×#67	C₂³×C₅	1	8	yes	—
224	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
225	#235	—	2	16	no	—
226	#235	—	2	16	no	—
227	#235	—	2	16	no	—
228	#235	—	2	16	no	—
229	C₂×D₁₂	—	2	8	no	—
230	C₂×D₁₂	C₂³×C₅	1	4	yes	—
231	C₂×D₁₂	C₂³×C₅	1	4	yes	—
232	C₂×D₁₂	C₂³×C₅	1	16	yes	—
233	C₂×C₄×D₃	—	2	16	no	—
234	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
235	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
236	C₂×Dic₆	—	2	8	no	—
237	C₂×Dic₆	C₂³×C₅	1	4	yes	—
238	C₂×Dic₆	C₂³×C₅	1	4	yes	—
239	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
240	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
241	C₃×C₄²	C₂³×C₅	1	4	yes	—
242	C₃×C₄²	C₂³×C₅	1	4	yes	—
243	(C₂×D₃)⋊C₄	C₂³×C₅	1	32	yes	—
244	C₄⋊Dic₃	C₂³×C₅	1	16	yes	—
245	C₂³×C₅	—	3	8	no	—
246	C₂³×C₅	—	4	2	no	—
247	C₂³×C₅	—	6	8	no	—
248	C₂³×C₅	—	12	8	no	—
249	C₂³×C₅	C₂×D₁₂	1	4	yes	—
250	C₂³×C₅	C₂³×D₃	1	2	yes	—
251	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
252	C₅×Q₈	—	6	8	no	—
253	C₅×Q₈	—	6	8	no	—
254	C₅×D₄	—	6	16	no	—
255	C₅×D₄	—	6	16	no	—
256	C₅×D₄	—	6	8	no	—
257	C₅×D₄	—	6	8	no	—
258	C₅×D₄	—	12	16	no	—
259	C₂×C₄×C₅	—	3	8	no	—
260	C₂×C₄×C₅	—	4	4	no	—
261	C₂×C₄×C₅	—	6	8	no	—
262	C₂×C₄×C₅	—	6	16	no	—
263	C₂×C₄×C₅	—	6	16	no	—
264	C₂×C₄×C₅	C₂×D₁₂	1	8	yes	—
265	C₂×C₄×C₅	C₂×D₁₂	1	8	yes	—
266	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
267	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
268	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
269	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₂×#41	—	3	4	no	—
273	C₂×#41	—	3	4	no	—
274	C₂×#41	—	3	4	no	—
275	C₂×#41	—	3	4	no	—
276	C₂×#41	—	6	16	no	—
277	C₂²×Q₈	—	3	2	no	—
278	C₂²×D₄	—	3	4	no	—
279	C₂²×D₄	—	3	2	no	—
280	C₂³×C₄	—	3	4	no	—
281	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
282	C₄⋊Q₈	—	3	4	no	—
283	#127	—	3	4	no	—
284	#124	—	3	8	no	—
285	#123	—	3	16	no	—
286	C₂²⋊Q₈	—	3	16	no	—
287	#121	—	3	16	no	—
288	#121	—	3	16	no	—
289	#120	—	3	16	no	—
290	C₄×D₄	—	3	16	no	—
291	#117	C₂×C₅×D₃	1	4	yes	complemented
292	#117	C₂×C₅×D₃	1	4	yes	complemented
293	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
294	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
295	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
296	C₂×C₃×C₅	—	2	4	no	—
297	C₂×C₃×C₅	—	2	2	no	—
298	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
299	C₂×C₃×C₅	#585	1	2	yes	—
300	C₅×D₃	—	4	8	no	—
301	C₂³×C₃	—	4	2	no	—
302	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
303	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
304	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
305	C₂²×D₃	—	2	8	no	—
306	C₂²×D₃	—	4	8	no	—
307	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
308	C₂×C₃×C₄	—	4	4	no	—
309	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
310	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
311	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
312	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
313	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
314	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
317	#67	—	2	16	no	—
318	#67	—	2	16	no	—
319	C₂×Dic₃	—	2	8	no	—
320	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
321	D₁₂	—	2	8	no	—
322	D₁₂	—	2	8	no	—
323	D₁₂	—	4	16	no	—
324	C₄×D₃	—	2	16	no	—
325	C₄×D₃	—	2	16	no	—
326	Dic₆	—	2	8	no	—
327	Dic₆	—	2	8	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	4	no	—
330	C₂²×C₅	—	4	4	no	—
331	C₂²×C₅	—	6	8	no	—
332	C₂²×C₅	—	6	16	no	—
333	C₂²×C₅	—	12	16	no	—
334	C₂²×C₅	C₂²×D₁₂	1	4	yes	—
335	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
336	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
337	C₄×C₅	—	2	8	no	—
338	C₄×C₅	—	6	8	no	—
339	C₄×C₅	C₂²×D₁₂	1	2	yes	—
340	C₄×C₅	C₂²×D₁₂	1	4	yes	—
341	C₄×C₅	C₂²×D₁₂	1	2	yes	—
342	C₂⁴	—	3	4	no	—
343	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
344	#41	—	6	16	no	—
345	#41	—	6	16	no	—
346	#41	—	6	16	no	—
347	#41	—	6	16	no	—
348	C₂×Q₈	—	3	4	no	—
349	C₂×Q₈	—	3	4	no	—
350	C₂×Q₈	—	6	8	no	—
351	C₂×D₄	—	3	8	no	—
352	C₂×D₄	—	3	8	no	—
353	C₂×D₄	—	3	4	no	—
354	C₂×D₄	—	3	4	no	—
355	C₂×D₄	—	3	16	no	—
356	C₂×D₄	—	6	16	no	—
357	C₂×D₄	—	6	8	no	—
358	C₂²×C₄	—	3	4	no	—
359	C₂²×C₄	—	3	8	no	—
360	C₂²×C₄	—	3	8	no	—
361	C₂²×C₄	—	6	16	no	—
362	C₂²×C₄	C₅×D₁₂	1	8	yes	complemented
363	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
364	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
367	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
368	C₄⋊C₄	—	3	16	no	—
369	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
370	C₂²⋊C₄	—	3	32	no	—
371	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
372	C₄²	C₂²×C₅×D₃	1	4	yes	—
373	C₄²	C₂²×C₅×D₃	1	4	yes	—
374	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	4	no	—
377	C₂²×C₃	—	4	4	no	—
378	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
379	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
380	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
381	C₂×D₃	—	2	8	no	—
382	C₂×D₃	—	2	16	no	—
383	C₂×D₃	—	4	16	no	—
384	C₃×C₄	—	2	8	no	—
385	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
386	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
387	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
388	Dic₃	—	2	8	no	—
389	C₂×C₅	—	2	4	no	—
390	C₂×C₅	—	2	2	no	—
391	C₂×C₅	—	12	8	no	—
392	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
393	C₂×C₅	#5964	1	2	yes	—
394	C₂³	—	3	8	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	6	8	no	—
397	C₂³	—	12	8	no	—
398	C₂³	C₂×C₅×D₁₂	1	4	yes	—
399	C₂³	C₂³×C₅×D₃	1	2	yes	—
400	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
401	Q₈	—	6	8	no	—
402	Q₈	—	6	8	no	—
403	D₄	—	6	16	no	—
404	D₄	—	6	16	no	—
405	D₄	—	6	8	no	—
406	D₄	—	6	8	no	—
407	D₄	—	12	16	no	—
408	C₂×C₄	—	3	8	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	6	8	no	—
411	C₂×C₄	—	6	16	no	—
412	C₂×C₄	—	6	16	no	—
413	C₂×C₄	C₂×C₅×D₁₂	1	8	yes	—
414	C₂×C₄	C₂×C₅×D₁₂	1	8	yes	—
415	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
416	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
417	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
418	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
421	C₂×C₃	—	2	4	no	—
422	C₂×C₃	—	2	2	no	—
423	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
424	C₂×C₃	C₅×#585	1	2	yes	—
425	D₃	—	4	8	no	—
426	C₅	#85735	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	6	8	no	—
431	C₂²	—	6	16	no	—
432	C₂²	—	12	16	no	—
433	C₂²	C₂²×C₅×D₁₂	1	4	yes	—
434	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
435	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
436	C₄	—	2	8	no	—
437	C₄	—	6	8	no	—
438	C₄	C₂²×C₅×D₁₂	1	2	yes	—
439	C₄	C₂²×C₅×D₁₂	1	4	yes	—
440	C₄	C₂²×C₅×D₁₂	1	2	yes	—
441	C₃	C₅×#3449	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	4	no	—
443	C₂	—	2	2	no	—
444	C₂	—	12	8	no	—
445	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
446	C₂	C₅×#5964	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#235	C₂	semidirect
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₅×#5526	C₂	semidirect
4. C₅×#5525	C₂	semidirect
5. C₅×#5524	C₂	semidirect
6. C₅×#5510	C₂	semidirect
7. C₅×#5493	C₂	semidirect
8. C₅×#5477	C₂	semidirect
15. C₂×C₅×#235	C₂²	semidirect
16. C₂×C₅×#235	C₂²	semidirect
17. C₂²×C₅×D₁₂	C₂²	semidirect
18. C₂²×C₄×C₅×D₃	C₂²	semidirect
19. C₂²×C₅×Dic₆	C₂²	semidirect
20. C₃×C₅×#117	C₂²	semidirect
21. C₃×C₅×#117	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₄²×C₅	C₂²	semidirect
25. C₅×#930	C₂²	semidirect
26. C₅×#897	C₂²	semidirect
27. C₅×#895	C₂²	semidirect
28. C₅×#886	C₂²	semidirect
29. C₅×#882	C₂²	semidirect
30. C₅×#875	C₂²	semidirect
31. C₅×#874	C₂²	semidirect
32. C₄×C₅×D₁₂	C₂²	semidirect
33. C₅×#869	C₂²	semidirect
34. #85735	C₅	direct (N × H)
42. C₂×C₅×#117	D₃	semidirect
45. C₂²×C₃×C₄×C₅	D₄	semidirect
75. C₂²×#235	C₂×C₅	semidirect
76. C₂×C₃×#117	C₂×C₅	semidirect
77. #5526	C₂×C₅	semidirect
78. #5525	C₂×C₅	semidirect
79. #5524	C₂×C₅	semidirect
80. #5510	C₂×C₅	semidirect
81. #5493	C₂×C₅	semidirect
82. #5477	C₂×C₅	semidirect
102. C₅×#117	C₂×D₃	semidirect
103. C₅×#117	C₂×D₃	semidirect
104. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
106. C₂×C₄²×C₅	C₂×D₃	semidirect
140. C₂×#235	C₂²×C₅	semidirect
141. C₂×#235	C₂²×C₅	semidirect
142. C₂²×D₁₂	C₂²×C₅	semidirect
143. C₂²×C₄×D₃	C₂²×C₅	semidirect
144. C₂²×Dic₆	C₂²×C₅	semidirect
145. C₃×#117	C₂²×C₅	semidirect
146. C₃×#117	C₂²×C₅	semidirect
147. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
149. C₂×C₃×C₄²	C₂²×C₅	semidirect
150. #930	C₂²×C₅	semidirect
151. #897	C₂²×C₅	semidirect
152. #895	C₂²×C₅	semidirect
153. #886	C₂²×C₅	semidirect
154. #882	C₂²×C₅	semidirect
155. #875	C₂²×C₅	semidirect
156. #874	C₂²×C₅	semidirect
157. C₄×D₁₂	C₂²×C₅	semidirect
158. #869	C₂²×C₅	semidirect
179. C₂²×C₄×C₅	D₁₂	semidirect
198. C₂×#117	C₅×D₃	semidirect
215. C₂²×C₃×C₄	C₅×D₄	semidirect
291. #117	C₂×C₅×D₃	semidirect
292. #117	C₂×C₅×D₃	semidirect
293. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
295. C₂×C₄²	C₂×C₅×D₃	semidirect
362. C₂²×C₄	C₅×D₁₂	semidirect
374. C₃×C₅	#3449	semidirect
426. C₅	#85735	direct (N × H)
441. C₃	C₅×#3449	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
C₂×C₃×C₅×#117	2
C₅×#5526	2
C₅×#5525	2
C₅×#5524	2
C₅×#5510	2
C₅×#5493	2
C₅×#5477	2
C₅×#3449	3
#85735	5

Subgroups — C5×#85735 #14480650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#85735 #14480650