Subgroups — C₅×#83528 #14454456

Order 1920.

956 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5552	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5239	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5090	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5086	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5051	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5050	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5049	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5047	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5018	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5016	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3269	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₅×#235	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#123	—	2	1	no	—
23	C₃×C₅×#123	—	2	1	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	—	2	1	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
30	C₅×#951	—	2	4	no	—
31	C₅×#950	—	2	4	no	—
32	C₂×C₅×#216	C₂²	1	1	yes	characteristic
33	C₂×C₅×#216	C₂²	1	1	yes	characteristic
34	C₂×C₅×#216	C₂²	1	1	yes	characteristic
35	C₂×C₅×#216	C₂²	1	1	yes	characteristic
36	C₂×C₅×#215	C₂²	1	1	yes	characteristic
37	C₂×C₅×#215	C₂²	1	1	yes	characteristic
38	C₅×#939	—	2	1	no	—
39	C₂×C₅×#214	C₂²	1	1	yes	characteristic
40	C₂×C₅×#214	C₂²	1	1	yes	characteristic
41	C₂×C₅×#213	C₂²	1	1	yes	characteristic
42	C₅×#930	C₂²	1	1	yes	characteristic
43	C₅×#924	C₂²	1	1	yes	characteristic
44	C₂×C₅×#208	C₂²	1	1	yes	characteristic
45	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×#896	—	2	1	no	—
47	C₅×#885	—	2	1	no	—
48	C₅×#67⋊C₄	—	2	1	no	—
49	C₅×#875	C₂²	1	1	yes	characteristic
50	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
51	C₅×#835	C₂²	1	1	yes	characteristic
52	C₅×#835	C₂²	1	1	yes	characteristic
53	C₅×#832	C₂²	1	1	yes	characteristic
54	C₅×#830	C₂²	1	1	yes	characteristic
55	C₅×#830	C₂²	1	1	yes	characteristic
56	C₅×#810	C₂²	1	1	yes	characteristic
57	C₅×#810	C₂²	1	1	yes	characteristic
58	C₅×#809	C₂²	1	1	yes	characteristic
59	C₅×#807	C₂²	1	1	yes	characteristic
60	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
61	C₅×#803	C₂²	1	1	yes	characteristic
62	#83528	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#137	—	3	1	no	—
64	C₂×C₅×#135	—	3	1	no	—
65	C₅×#548	—	3	1	no	—
66	C₅×#547	D₃	1	1	yes	characteristic, complemented
67	C₅×#497	—	3	1	no	—
68	C₅×#468	—	3	1	no	—
69	C₅×#467	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#462	—	3	1	no	—
72	C₅×#452	—	3	1	no	—
73	C₅×#452	—	3	1	no	—
74	C₅×#451	—	3	1	no	—
75	C₅×#449	—	3	1	no	—
76	C₅×#440	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₃×C₅×#41	—	2	2	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	4	1	no	—
81	C₃×C₅×#41	—	4	1	no	—
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₅×#67	—	2	1	no	—
94	C₂×C₅×#67	—	2	1	no	—
95	C₂²×C₅×Dic₃	—	2	1	no	—
96	C₅×#235	—	2	2	no	—
97	C₅×#235	—	4	1	no	—
98	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
99	C₂×C₄×C₅×D₃	—	2	1	no	—
100	C₂×C₅×Dic₆	—	2	2	no	—
101	C₂×C₅×Dic₆	—	2	1	no	—
102	C₂×C₅×Dic₆	—	4	1	no	—
103	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
104	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₄⋊C₄	—	2	1	no	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	—	2	1	no	—
109	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₅×#217	—	2	1	no	—
118	C₅×#216	—	2	2	no	—
119	C₅×#216	—	2	2	no	—
120	C₅×#216	—	2	2	no	—
121	C₅×#216	—	4	1	no	—
122	C₅×#215	—	2	2	no	—
123	C₅×#215	—	4	1	no	—
124	C₅×#214	—	2	2	no	—
125	C₅×#214	D₄	1	4	yes	complemented
126	C₅×#213	—	2	2	no	—
127	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
128	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
129	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
130	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
131	C₅×Dic₃⋊C₄	—	2	1	no	—
132	C₅×Dic₃⋊C₄	—	2	1	no	—
133	C₄×C₅×Dic₃	—	2	1	no	—
134	C₅×#208	—	2	2	no	—
135	C₂×C₅×C₃⋊C₈	—	2	2	no	—
136	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
138	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
139	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
140	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#951	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
143	#5552	C₂×C₅	1	1	yes	characteristic, complemented
144	#5239	C₂×C₅	1	1	yes	characteristic, complemented
145	#5238	C₂×C₅	1	1	yes	characteristic, complemented
146	#5090	C₂×C₅	1	1	yes	characteristic, complemented
147	#5086	C₂×C₅	1	1	yes	characteristic, complemented
148	#5051	C₂×C₅	1	1	yes	characteristic, complemented
149	#5050	C₂×C₅	1	1	yes	characteristic, complemented
150	#5049	C₂×C₅	1	1	yes	characteristic, complemented
151	#5047	C₂×C₅	1	1	yes	characteristic, complemented
152	#5018	C₂×C₅	1	1	yes	characteristic, complemented
153	#5016	C₂×C₅	1	1	yes	characteristic, complemented
154	#5011	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	—	3	1	no	—
156	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
157	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
158	C₂²×C₅×Q₈	—	3	1	no	—
159	C₅×#137	—	6	4	no	—
160	C₅×#135	—	6	4	no	—
161	C₂×C₅×Q₁₆	—	3	1	no	—
162	C₂×C₅×Q₁₆	—	3	1	no	—
163	C₂×C₅×Q₁₆	—	3	1	no	—
164	C₂×C₅×Q₁₆	—	3	1	no	—
165	C₂×C₅×SD₁₆	—	3	1	no	—
166	C₂×C₅×SD₁₆	—	3	1	no	—
167	C₂×C₅×SD₁₆	—	3	1	no	—
168	C₂×C₅×SD₁₆	—	3	1	no	—
169	C₂×C₅×D₈	—	3	1	no	—
170	C₂×C₅×M₁₆	—	3	1	no	—
171	C₂²×C₅×C₈	—	3	1	no	—
172	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
173	C₅×#124	—	3	1	no	—
174	C₅×#124	—	6	1	no	—
175	C₅×#123	—	2	1	no	—
176	C₅×#123	—	2	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×C₂²⋊Q₈	—	6	1	no	—
179	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
180	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
181	C₅×#121	—	2	1	no	—
182	C₅×#121	—	3	1	no	—
183	C₅×#121	—	6	1	no	—
184	C₄×C₅×Q₈	—	3	1	no	—
185	C₄×C₅×D₄	—	6	1	no	—
186	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
187	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
188	C₂×C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×#107	—	3	1	no	—
190	C₅×C₄⋊C₈	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#103	—	3	1	no	—
194	C₅×#103	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	—	3	1	no	—
197	C₅×C₂²⋊C₈	—	3	1	no	—
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×#97	—	3	1	no	—
200	#3269	—	3	1	no	Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	—	2	1	no	—
208	C₃×C₅×Q₈	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	4	1	no	—
211	C₃×C₅×D₄	—	4	2	no	—
212	C₃×C₅×D₄	—	4	2	no	—
213	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	4	2	no	—
222	C₂×C₃×C₄×C₅	—	4	2	no	—
223	C₂×C₃×C₄×C₅	—	4	2	no	—
224	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₅×#67	—	4	2	no	—
230	C₅×#67	—	4	2	no	—
231	C₂×C₅×Dic₃	—	2	1	no	—
232	C₂×C₅×Dic₃	—	2	1	no	—
233	C₂×C₅×Dic₃	—	2	1	no	—
234	C₂×C₅×Dic₃	—	4	2	no	—
235	C₅×D₁₂	—	2	1	no	—
236	C₅×D₁₂	—	2	1	no	—
237	C₄×C₅×D₃	—	4	2	no	—
238	C₅×Dic₆	—	2	1	no	—
239	C₅×Dic₆	—	2	1	no	—
240	C₅×Dic₆	—	2	1	no	—
241	C₅×Dic₆	—	4	2	no	—
242	C₅×Dic₆	C₂×D₄	1	2	yes	—
243	C₅×C₃⋊C₈	—	2	1	no	—
244	C₅×C₃⋊C₈	—	2	1	no	—
245	C₅×C₃⋊C₈	—	2	1	no	—
246	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
247	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
249	C₂×#235	C₂²×C₅	1	1	yes	characteristic
250	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
251	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₃×#123	—	2	1	no	—
253	C₃×#123	—	2	1	no	—
254	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
255	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
256	C₃×#121	—	2	1	no	—
257	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
258	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×C₄⋊C₄	—	2	1	no	—
260	#951	—	2	4	no	—
261	#950	—	2	4	no	—
262	C₂×#216	C₂²×C₅	1	1	yes	characteristic
263	C₂×#216	C₂²×C₅	1	1	yes	characteristic
264	C₂×#216	C₂²×C₅	1	1	yes	characteristic
265	C₂×#216	C₂²×C₅	1	1	yes	characteristic
266	C₂×#215	C₂²×C₅	1	1	yes	characteristic
267	C₂×#215	C₂²×C₅	1	1	yes	characteristic
268	#939	—	2	1	no	—
269	C₂×#214	C₂²×C₅	1	1	yes	characteristic
270	C₂×#214	C₂²×C₅	1	1	yes	characteristic
271	C₂×#213	C₂²×C₅	1	1	yes	characteristic
272	#930	C₂²×C₅	1	1	yes	characteristic
273	#924	C₂²×C₅	1	1	yes	characteristic
274	C₂×#208	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	#896	—	2	1	no	—
277	#885	—	2	1	no	—
278	#67⋊C₄	—	2	1	no	—
279	#875	C₂²×C₅	1	1	yes	characteristic
280	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
281	#835	C₂²×C₅	1	1	yes	characteristic
282	#835	C₂²×C₅	1	1	yes	characteristic
283	#832	C₂²×C₅	1	1	yes	characteristic
284	#830	C₂²×C₅	1	1	yes	characteristic
285	#830	C₂²×C₅	1	1	yes	characteristic
286	#810	C₂²×C₅	1	1	yes	characteristic
287	#810	C₂²×C₅	1	1	yes	characteristic
288	#809	C₂²×C₅	1	1	yes	characteristic
289	#807	C₂²×C₅	1	1	yes	characteristic
290	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
291	#803	C₂²×C₅	1	1	yes	characteristic
292	C₅×#41	—	2	2	no	—
293	C₅×#41	—	2	2	no	—
294	C₅×#41	—	4	1	no	—
295	C₅×#41	—	4	1	no	—
296	C₅×#41	—	6	2	no	—
297	C₅×#41	—	12	1	no	—
298	C₂×C₅×Q₈	—	3	1	no	—
299	C₂×C₅×Q₈	—	3	1	no	—
300	C₂×C₅×Q₈	—	6	2	no	—
301	C₂×C₅×Q₈	—	6	1	no	—
302	C₂×C₅×Q₈	—	12	1	no	—
303	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₅×D₄	—	2	1	no	—
306	C₂×C₅×D₄	—	2	1	no	—
307	C₂×C₅×D₄	—	3	1	no	—
308	C₂×C₅×D₄	—	6	1	no	—
309	C₂×C₅×D₄	—	6	1	no	—
310	C₂×C₅×D₄	#67	1	1	yes	characteristic
311	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	—	2	1	no	—
313	C₂²×C₄×C₅	—	2	1	no	—
314	C₂²×C₄×C₅	—	2	1	no	—
315	C₂²×C₄×C₅	—	6	1	no	—
316	C₂²×C₄×C₅	—	6	1	no	—
317	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₅×Q₁₆	—	6	2	no	—
320	C₅×Q₁₆	—	6	2	no	—
321	C₅×Q₁₆	—	6	2	no	—
322	C₅×Q₁₆	—	12	1	no	—
323	C₅×SD₁₆	—	3	4	no	—
324	C₅×SD₁₆	—	6	2	no	—
325	C₅×SD₁₆	—	6	2	no	—
326	C₅×SD₁₆	—	12	1	no	—
327	C₅×D₈	—	6	2	no	—
328	C₅×M₁₆	—	6	2	no	—
329	C₂×C₅×C₈	—	3	1	no	—
330	C₂×C₅×C₈	—	3	1	no	—
331	C₂×C₅×C₈	—	3	1	no	—
332	C₂×C₅×C₈	—	3	1	no	—
333	C₂×C₅×C₈	—	6	2	no	—
334	C₅×C₄⋊C₄	—	2	1	no	—
335	C₅×C₄⋊C₄	—	2	1	no	—
336	C₅×C₄⋊C₄	—	2	1	no	—
337	C₅×C₄⋊C₄	—	2	1	no	—
338	C₅×C₄⋊C₄	—	3	1	no	—
339	C₅×C₄⋊C₄	—	6	1	no	—
340	C₅×C₄⋊C₄	—	6	1	no	—
341	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
342	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
343	C₅×C₂²⋊C₄	—	2	1	no	—
344	C₅×C₂²⋊C₄	—	2	1	no	—
345	C₅×C₂²⋊C₄	—	2	1	no	—
346	C₅×C₂²⋊C₄	—	6	1	no	—
347	C₅×C₂²⋊C₄	—	6	1	no	—
348	C₅×C₂²⋊C₄	—	6	1	no	—
349	C₅×C₂²⋊C₄	—	6	1	no	—
350	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
351	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
352	C₄²×C₅	—	6	1	no	—
353	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
354	C₂×#137	—	3	1	no	—
355	C₂×#135	—	3	1	no	—
356	#548	—	3	1	no	—
357	#547	C₅×D₃	1	1	yes	characteristic, complemented
358	#497	—	3	1	no	—
359	#468	—	3	1	no	—
360	#467	—	3	1	no	—
361	#463	—	3	1	no	—
362	#462	—	3	1	no	—
363	#452	—	3	1	no	—
364	#452	—	3	1	no	—
365	#451	—	3	1	no	—
366	#449	—	3	1	no	—
367	#440	—	3	1	no	—
368	#435	—	3	1	no	—
369	C₂²×C₃×C₅	—	2	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	2	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	—	4	1	no	—
377	C₂²×C₃×C₅	—	4	1	no	—
378	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₅×D₃	—	4	1	no	—
380	C₂×C₅×D₃	—	4	1	no	—
381	C₂×C₅×D₃	—	4	1	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	—	2	1	no	—
385	C₃×C₄×C₅	—	2	1	no	—
386	C₃×C₄×C₅	—	4	1	no	—
387	C₃×C₄×C₅	—	4	1	no	—
388	C₃×C₄×C₅	—	4	1	no	—
389	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
391	C₅×Dic₃	—	2	2	no	—
392	C₅×Dic₃	—	4	1	no	—
393	C₅×Dic₃	—	4	1	no	—
394	C₃×#41	—	2	2	no	—
395	C₃×#41	—	2	2	no	—
396	C₃×#41	—	4	1	no	—
397	C₃×#41	—	4	1	no	—
398	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₃×D₄	—	2	1	no	—
401	C₂×C₃×D₄	—	2	1	no	—
402	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
403	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	—	2	1	no	—
405	C₂²×C₃×C₄	—	2	1	no	—
406	C₂²×C₃×C₄	—	2	1	no	—
407	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂×#67	—	2	1	no	—
410	C₂×#67	—	2	1	no	—
411	C₂²×Dic₃	—	2	1	no	—
412	#235	—	2	2	no	—
413	#235	—	4	1	no	—
414	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄×D₃	—	2	1	no	—
416	C₂×Dic₆	—	2	2	no	—
417	C₂×Dic₆	—	2	1	no	—
418	C₂×Dic₆	—	4	1	no	—
419	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
420	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
421	C₃×C₄⋊C₄	—	2	1	no	—
422	C₃×C₄⋊C₄	—	2	1	no	—
423	C₃×C₄⋊C₄	—	2	1	no	—
424	C₃×C₄⋊C₄	—	2	1	no	—
425	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
426	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
427	C₃×C₂²⋊C₄	—	2	1	no	—
428	C₃×C₂²⋊C₄	—	2	1	no	—
429	C₃×C₂²⋊C₄	—	2	1	no	—
430	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
431	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
432	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
433	#217	—	2	1	no	—
434	#216	—	2	2	no	—
435	#216	—	2	2	no	—
436	#216	—	2	2	no	—
437	#216	—	4	1	no	—
438	#215	—	2	2	no	—
439	#215	—	4	1	no	—
440	#214	—	2	2	no	—
441	#214	C₅×D₄	1	4	yes	complemented
442	#213	—	2	2	no	—
443	(C₂×D₃)⋊C₄	—	2	1	no	—
444	(C₂×D₃)⋊C₄	—	2	1	no	—
445	(C₂×D₃)⋊C₄	—	2	1	no	—
446	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
447	Dic₃⋊C₄	—	2	1	no	—
448	Dic₃⋊C₄	—	2	1	no	—
449	C₄×Dic₃	—	2	1	no	—
450	#208	—	2	2	no	—
451	C₂×C₃⋊C₈	—	2	2	no	—
452	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	—	6	1	no	—
458	C₂³×C₅	C₂×#67	1	1	yes	characteristic
459	C₂³×C₅	C₂×#67	1	1	yes	characteristic
460	C₅×Q₈	—	2	1	no	—
461	C₅×Q₈	—	2	1	no	—
462	C₅×Q₈	—	2	1	no	—
463	C₅×Q₈	—	2	1	no	—
464	C₅×Q₈	—	3	2	no	—
465	C₅×Q₈	—	6	1	no	—
466	C₅×Q₈	—	6	1	no	—
467	C₅×Q₈	—	6	1	no	—
468	C₅×Q₈	—	12	2	no	—
469	C₅×D₄	—	2	1	no	—
470	C₅×D₄	—	4	1	no	—
471	C₅×D₄	—	4	2	no	—
472	C₅×D₄	—	4	2	no	—
473	C₅×D₄	—	6	1	no	—
474	C₅×D₄	—	6	1	no	—
475	C₅×D₄	—	12	2	no	—
476	C₅×D₄	—	12	2	no	—
477	C₅×D₄	D₃×D₄	1	2	yes	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	4	2	no	—
486	C₂×C₄×C₅	—	4	2	no	—
487	C₂×C₄×C₅	—	4	2	no	—
488	C₂×C₄×C₅	—	6	1	no	—
489	C₂×C₄×C₅	—	6	1	no	—
490	C₂×C₄×C₅	—	6	1	no	—
491	C₂×C₄×C₅	—	12	2	no	—
492	C₂×C₄×C₅	—	12	2	no	—
493	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
494	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
495	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
496	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
497	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
498	C₅×C₈	—	3	2	no	—
499	C₅×C₈	—	6	1	no	—
500	C₅×C₈	—	6	1	no	—
501	C₅×C₈	—	6	1	no	—
502	C₂×#41	—	3	1	no	—
503	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
504	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
505	C₂²×Q₈	—	3	1	no	—
506	#137	—	6	4	no	—
507	#135	—	6	4	no	—
508	C₂×Q₁₆	—	3	1	no	—
509	C₂×Q₁₆	—	3	1	no	—
510	C₂×Q₁₆	—	3	1	no	—
511	C₂×Q₁₆	—	3	1	no	—
512	C₂×SD₁₆	—	3	1	no	—
513	C₂×SD₁₆	—	3	1	no	—
514	C₂×SD₁₆	—	3	1	no	—
515	C₂×SD₁₆	—	3	1	no	—
516	C₂×D₈	—	3	1	no	—
517	C₂×M₁₆	—	3	1	no	—
518	C₂²×C₈	—	3	1	no	—
519	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
520	#124	—	3	1	no	—
521	#124	—	6	1	no	—
522	#123	—	2	1	no	—
523	#123	—	2	1	no	—
524	C₂²⋊Q₈	—	3	1	no	—
525	C₂²⋊Q₈	—	6	1	no	—
526	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
527	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
528	#121	—	2	1	no	—
529	#121	—	3	1	no	—
530	#121	—	6	1	no	—
531	C₄×Q₈	—	3	1	no	—
532	C₄×D₄	—	6	1	no	—
533	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
534	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	2	1	no	—
536	#107	—	3	1	no	—
537	C₄⋊C₈	—	3	1	no	—
538	#103	—	3	1	no	—
539	#103	—	3	1	no	—
540	#103	—	3	1	no	—
541	#103	—	3	1	no	—
542	#102	—	3	1	no	—
543	#102	—	3	1	no	—
544	C₂²⋊C₈	—	3	1	no	—
545	C₂²⋊C₈	—	3	1	no	—
546	#97	—	3	1	no	—
547	C₂×C₃×C₅	—	4	1	no	—
548	C₂×C₃×C₅	—	4	1	no	—
549	C₂×C₃×C₅	—	4	2	no	—
550	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
551	C₂×C₃×C₅	#575	1	1	yes	characteristic
552	C₂×C₃×C₅	#578	1	1	yes	characteristic
553	C₅×D₃	—	8	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
557	C₂²×D₃	—	2	1	no	—
558	C₃×Q₈	—	2	1	no	—
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	2	1	no	—
561	C₃×Q₈	—	2	1	no	—
562	C₃×D₄	—	2	1	no	—
563	C₃×D₄	—	4	1	no	—
564	C₃×D₄	—	4	2	no	—
565	C₃×D₄	—	4	2	no	—
566	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	4	2	no	—
575	C₂×C₃×C₄	—	4	2	no	—
576	C₂×C₃×C₄	—	4	2	no	—
577	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
582	#67	—	4	2	no	—
583	#67	—	4	2	no	—
584	C₂×Dic₃	—	2	1	no	—
585	C₂×Dic₃	—	2	1	no	—
586	C₂×Dic₃	—	2	1	no	—
587	C₂×Dic₃	—	4	2	no	—
588	D₁₂	—	2	1	no	—
589	D₁₂	—	2	1	no	—
590	C₄×D₃	—	4	2	no	—
591	Dic₆	—	2	1	no	—
592	Dic₆	—	2	1	no	—
593	Dic₆	—	2	1	no	—
594	Dic₆	—	4	2	no	—
595	Dic₆	C₂×C₅×D₄	1	2	yes	—
596	C₃⋊C₈	—	2	1	no	—
597	C₃⋊C₈	—	2	1	no	—
598	C₃⋊C₈	—	2	1	no	—
599	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	2	no	—
603	C₂²×C₅	—	2	1	no	—
604	C₂²×C₅	—	2	1	no	—
605	C₂²×C₅	—	2	1	no	—
606	C₂²×C₅	—	2	1	no	—
607	C₂²×C₅	—	4	1	no	—
608	C₂²×C₅	—	4	1	no	—
609	C₂²×C₅	—	12	1	no	—
610	C₂²×C₅	—	12	1	no	—
611	C₂²×C₅	—	12	1	no	—
612	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
613	C₄×C₅	—	2	1	no	—
614	C₄×C₅	—	2	1	no	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	—	4	1	no	—
618	C₄×C₅	—	4	1	no	—
619	C₄×C₅	—	4	1	no	—
620	C₄×C₅	—	6	2	no	—
621	C₄×C₅	—	12	1	no	—
622	C₄×C₅	—	12	1	no	—
623	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
624	C₄×C₅	#1004	1	1	yes	characteristic
625	#41	—	2	2	no	—
626	#41	—	2	2	no	—
627	#41	—	4	1	no	—
628	#41	—	4	1	no	—
629	#41	—	6	2	no	—
630	#41	—	12	1	no	—
631	C₂×Q₈	—	3	1	no	—
632	C₂×Q₈	—	3	1	no	—
633	C₂×Q₈	—	6	2	no	—
634	C₂×Q₈	—	6	1	no	—
635	C₂×Q₈	—	12	1	no	—
636	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	6	1	no	—
642	C₂×D₄	—	6	1	no	—
643	C₂×D₄	C₅×#67	1	1	yes	characteristic
644	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	6	1	no	—
649	C₂²×C₄	—	6	1	no	—
650	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
651	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
652	Q₁₆	—	6	2	no	—
653	Q₁₆	—	6	2	no	—
654	Q₁₆	—	6	2	no	—
655	Q₁₆	—	12	1	no	—
656	SD₁₆	—	3	4	no	—
657	SD₁₆	—	6	2	no	—
658	SD₁₆	—	6	2	no	—
659	SD₁₆	—	12	1	no	—
660	D₈	—	6	2	no	—
661	M₁₆	—	6	2	no	—
662	C₂×C₈	—	3	1	no	—
663	C₂×C₈	—	3	1	no	—
664	C₂×C₈	—	3	1	no	—
665	C₂×C₈	—	3	1	no	—
666	C₂×C₈	—	6	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	3	1	no	—
672	C₄⋊C₄	—	6	1	no	—
673	C₄⋊C₄	—	6	1	no	—
674	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
675	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	6	1	no	—
680	C₂²⋊C₄	—	6	1	no	—
681	C₂²⋊C₄	—	6	1	no	—
682	C₂²⋊C₄	—	6	1	no	—
683	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
684	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
685	C₄²	—	6	1	no	—
686	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
687	C₃×C₅	#3269	1	1	yes	characteristic, complemented, Hall
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	2	no	—
691	C₂²×C₃	—	2	1	no	—
692	C₂²×C₃	—	2	1	no	—
693	C₂²×C₃	—	2	1	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	4	1	no	—
696	C₂²×C₃	—	4	1	no	—
697	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
698	C₂×D₃	—	4	1	no	—
699	C₂×D₃	—	4	1	no	—
700	C₂×D₃	—	4	1	no	—
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	2	1	no	—
705	C₃×C₄	—	4	1	no	—
706	C₃×C₄	—	4	1	no	—
707	C₃×C₄	—	4	1	no	—
708	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
709	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
710	Dic₃	—	2	2	no	—
711	Dic₃	—	4	1	no	—
712	Dic₃	—	4	1	no	—
713	C₂×C₅	—	4	1	no	—
714	C₂×C₅	—	4	1	no	—
715	C₂×C₅	—	4	2	no	—
716	C₂×C₅	—	24	1	no	—
717	C₂×C₅	D₄×#67	1	1	yes	characteristic
718	C₂×C₅	#5822	1	1	yes	characteristic
719	C₂×C₅	#5838	1	1	yes	characteristic
720	C₂³	—	2	1	no	—
721	C₂³	—	6	1	no	—
722	C₂³	C₂×C₅×#67	1	1	yes	characteristic
723	C₂³	C₂×C₅×#67	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	3	2	no	—
729	Q₈	—	6	1	no	—
730	Q₈	—	6	1	no	—
731	Q₈	—	6	1	no	—
732	Q₈	—	12	2	no	—
733	D₄	—	2	1	no	—
734	D₄	—	4	1	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	6	1	no	—
738	D₄	—	6	1	no	—
739	D₄	—	12	2	no	—
740	D₄	—	12	2	no	—
741	D₄	C₅×D₃×D₄	1	2	yes	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	6	1	no	—
753	C₂×C₄	—	6	1	no	—
754	C₂×C₄	—	6	1	no	—
755	C₂×C₄	—	12	2	no	—
756	C₂×C₄	—	12	2	no	—
757	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
758	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
759	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
760	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
761	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
762	C₈	—	3	2	no	—
763	C₈	—	6	1	no	—
764	C₈	—	6	1	no	—
765	C₈	—	6	1	no	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	1	no	—
768	C₂×C₃	—	4	2	no	—
769	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
770	C₂×C₃	C₅×#575	1	1	yes	characteristic
771	C₂×C₃	C₅×#578	1	1	yes	characteristic
772	D₃	—	8	1	no	—
773	C₅	#83528	1	1	yes	characteristic, direct product factor, Sylow
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	12	1	no	—
784	C₂²	—	12	1	no	—
785	C₂²	—	12	1	no	—
786	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	6	2	no	—
795	C₄	—	12	1	no	—
796	C₄	—	12	1	no	—
797	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
798	C₄	C₅×#1004	1	1	yes	characteristic
799	C₃	C₅×#3269	1	1	yes	characteristic, complemented, Sylow
800	C₂	—	4	1	no	—
801	C₂	—	4	1	no	—
802	C₂	—	4	2	no	—
803	C₂	—	24	1	no	—
804	C₂	C₅×D₄×#67	1	1	yes	characteristic
805	C₂	C₅×#5822	1	1	yes	characteristic
806	C₂	C₅×#5838	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#547	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#547	D₃
hypocenter	C₃	C₅×#3269
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×#547

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#547	C₂	semidirect
2. C₂×C₅×#951	C₂	semidirect
3. C₂×C₅×#950	C₂	semidirect
4. C₅×#5552	C₂	semidirect
5. C₅×#5239	C₂	semidirect
6. C₅×#5238	C₂	semidirect
7. C₅×#5090	C₂	semidirect
8. C₅×#5086	C₂	semidirect
9. C₅×#5051	C₂	semidirect
10. C₅×#5050	C₂	semidirect
11. C₅×#5049	C₂	semidirect
12. C₅×#5047	C₂	semidirect
13. C₅×#5018	C₂	semidirect
14. C₅×#5016	C₂	semidirect
15. C₅×#5011	C₂	semidirect
62. #83528	C₅	direct (N × H)
66. C₅×#547	D₃	semidirect
125. C₅×#214	D₄	semidirect
140. C₃×#547	C₂×C₅	semidirect
141. C₂×#951	C₂×C₅	semidirect
142. C₂×#950	C₂×C₅	semidirect
143. #5552	C₂×C₅	semidirect
144. #5239	C₂×C₅	semidirect
145. #5238	C₂×C₅	semidirect
146. #5090	C₂×C₅	semidirect
147. #5086	C₂×C₅	semidirect
148. #5051	C₂×C₅	semidirect
149. #5050	C₂×C₅	semidirect
150. #5049	C₂×C₅	semidirect
151. #5047	C₂×C₅	semidirect
152. #5018	C₂×C₅	semidirect
153. #5016	C₂×C₅	semidirect
154. #5011	C₂×C₅	semidirect
357. #547	C₅×D₃	semidirect
441. #214	C₅×D₄	semidirect
687. C₃×C₅	#3269	semidirect
773. C₅	#83528	direct (N × H)
799. C₃	C₅×#3269	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#547	2
C₂×C₅×#951	2
C₂×C₅×#950	2
C₅×#5552	2
C₅×#5239	2
C₅×#5238	2
C₅×#5090	2
C₅×#5086	2
C₅×#5051	2
C₅×#5050	2
C₅×#5049	2
C₅×#5047	2
C₅×#5018	2
C₅×#5016	2
C₅×#5011	2
C₅×#3269	3
#83528	5

Subgroups — C5×#83528 #14454456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83528 #14454456