Subgroups — C₅×#83614 #14458848

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5068	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5037	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5003	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5002	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3297	—	3	1	no	maximal, Hall
17	C₂×C₅×#235	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₃×C₅×#126	—	2	1	no	—
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#123	—	2	1	no	—
22	C₃×C₅×#121	—	2	1	no	—
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₄	—	2	1	no	—
26	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×#937	—	2	1	no	—
31	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#213	C₂²	1	1	yes	characteristic
33	C₂×C₅×#213	C₂²	1	1	yes	characteristic
34	C₅×#930	C₂²	1	1	yes	characteristic
35	C₅×#924	C₂²	1	1	yes	characteristic
36	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×#894	—	2	1	no	—
39	C₅×#884	—	2	1	no	—
40	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
41	C₅×#875	C₂²	1	1	yes	characteristic
42	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
43	C₅×#832	C₂²	1	1	yes	characteristic, complemented
44	C₅×#830	C₂²	1	1	yes	characteristic
45	C₅×#830	C₂²	1	1	yes	characteristic, complemented
46	C₅×#810	C₂²	1	1	yes	characteristic, complemented
47	C₅×#810	C₂²	1	1	yes	characteristic, complemented
48	C₅×#810	C₂²	1	1	yes	characteristic, complemented
49	C₅×#809	C₂²	1	1	yes	characteristic
50	C₅×#809	C₂²	1	1	yes	characteristic
51	C₅×#809	C₂²	1	1	yes	characteristic
52	C₅×#809	C₂²	1	1	yes	characteristic
53	C₅×#809	C₂²	1	1	yes	characteristic
54	C₅×#809	C₂²	1	1	yes	characteristic
55	C₅×#808	C₂²	1	1	yes	characteristic, complemented
56	C₅×#807	C₂²	1	1	yes	characteristic, complemented
57	C₅×#807	C₂²	1	1	yes	characteristic, complemented
58	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#83614	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#553	D₃	1	1	yes	characteristic, complemented
62	C₅×#546	—	3	1	no	—
63	C₅×#488	—	3	1	no	—
64	C₅×#484	—	3	1	no	—
65	C₅×#482	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#466	—	3	1	no	—
68	C₅×#465	—	3	1	no	—
69	C₅×#463	—	3	1	no	—
70	C₅×#449	—	3	1	no	—
71	C₅×#447	—	3	1	no	—
72	C₄×C₅×D₈	—	3	1	no	—
73	C₅×C₈×D₄	—	3	1	no	—
74	C₅×#416	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂×C₃×C₅×D₄	—	2	1	no	—
78	C₂×C₃×C₅×D₄	—	2	1	no	—
79	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	—	2	1	no	—
82	C₂²×C₃×C₄×C₅	—	2	1	no	—
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	1	no	—
87	C₅×#235	—	2	2	no	—
88	C₅×#235	—	4	1	no	—
89	C₂×C₅×D₁₂	—	2	2	no	—
90	C₂×C₅×D₁₂	—	2	1	no	—
91	C₂×C₅×D₁₂	—	4	1	no	—
92	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
93	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
94	C₂×C₄×C₅×D₃	—	2	1	no	—
95	C₂×C₄×C₅×D₃	—	2	1	no	—
96	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₄⋊C₄	—	2	1	no	—
98	C₃×C₅×C₄⋊C₄	—	2	1	no	—
99	C₃×C₅×C₄⋊C₄	—	2	1	no	—
100	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₃×C₄²×C₅	—	2	1	no	—
111	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₅×#217	—	2	1	no	—
113	C₅×#214	—	4	1	no	—
114	C₅×#213	—	2	2	no	—
115	C₅×#213	—	4	1	no	—
116	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
117	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
118	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
121	C₅×Dic₃⋊C₄	—	2	1	no	—
122	C₂×C₅×C₃⋊C₈	—	4	1	no	—
123	C₂×C₅×C₃⋊C₈	—	4	1	no	—
124	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₃×#553	C₂×C₅	1	1	yes	characteristic, complemented
129	#5550	C₂×C₅	1	1	yes	characteristic, complemented
130	#5068	C₂×C₅	1	1	yes	characteristic, complemented
131	#5066	C₂×C₅	1	1	yes	characteristic, complemented
132	#5041	C₂×C₅	1	1	yes	characteristic, complemented
133	#5038	C₂×C₅	1	1	yes	characteristic, complemented
134	#5037	C₂×C₅	1	1	yes	characteristic, complemented
135	#5036	C₂×C₅	1	1	yes	characteristic, complemented
136	#5016	C₂×C₅	1	1	yes	characteristic, complemented
137	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
138	D₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
139	#5003	C₂×C₅	1	1	yes	characteristic, complemented
140	#5002	C₂×C₅	1	1	yes	characteristic, complemented
141	#4970	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	—	3	1	no	—
144	C₂²×C₅×D₄	—	3	1	no	—
145	C₂×C₅×SD₁₆	—	3	1	no	—
146	C₂×C₅×D₈	—	3	1	no	—
147	C₂×C₅×D₈	—	3	1	no	—
148	C₂²×C₅×C₈	—	3	1	no	—
149	C₂²×C₅×C₈	—	3	1	no	—
150	C₅×#126	—	2	1	no	—
151	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
152	C₅×#124	—	3	1	no	—
153	C₅×#123	—	2	1	no	—
154	C₅×#123	—	6	1	no	—
155	C₅×C₂²⋊Q₈	—	3	1	no	—
156	C₅×#121	—	2	1	no	—
157	C₅×#121	—	3	1	no	—
158	C₅×#121	—	6	1	no	—
159	C₅×#121	C₂×D₃	1	1	yes	characteristic
160	C₅×#121	C₂×D₃	1	1	yes	characteristic, complemented
161	C₅×#120	—	6	1	no	—
162	C₄×C₅×D₄	—	2	1	no	—
163	C₄×C₅×D₄	—	3	1	no	—
164	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
166	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
167	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
168	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
169	C₅×#107	—	3	1	no	—
170	C₅×#107	—	3	1	no	—
171	C₅×#106	—	3	1	no	—
172	C₅×C₄⋊C₈	—	3	1	no	—
173	C₅×#103	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#103	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₅×#102	—	3	1	no	—
178	C₅×#102	—	3	1	no	—
179	C₅×#102	—	3	1	no	—
180	C₅×#102	—	3	1	no	—
181	C₅×#102	—	3	1	no	—
182	C₅×#102	—	3	1	no	—
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₄×C₅×C₈	—	3	1	no	—
186	#3297	—	3	1	no	Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₂²×C₅×D₃	—	2	1	no	—
192	C₂²×C₅×D₃	—	4	2	no	—
193	C₂²×C₅×D₃	—	4	2	no	—
194	C₂²×C₅×D₃	—	8	1	no	—
195	C₃×C₅×D₄	—	2	2	no	—
196	C₃×C₅×D₄	—	2	1	no	—
197	C₃×C₅×D₄	—	2	1	no	—
198	C₃×C₅×D₄	—	4	2	no	—
199	C₃×C₅×D₄	—	8	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	8	1	no	—
208	C₂×C₃×C₄×C₅	—	8	1	no	—
209	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₅×#67	—	4	2	no	—
215	C₅×#67	—	8	1	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₅×D₁₂	—	2	1	no	—
219	C₅×D₁₂	—	2	1	no	—
220	C₅×D₁₂	—	2	1	no	—
221	C₅×D₁₂	—	4	2	no	—
222	C₅×D₁₂	#41	1	2	yes	—
223	C₄×C₅×D₃	—	4	2	no	—
224	C₄×C₅×D₃	—	8	1	no	—
225	C₅×Dic₆	—	2	1	no	—
226	C₅×Dic₆	—	2	1	no	—
227	C₅×C₃⋊C₈	—	2	1	no	—
228	C₅×C₃⋊C₈	—	2	1	no	—
229	C₅×C₃⋊C₈	—	2	1	no	—
230	C₅×C₃⋊C₈	—	2	1	no	—
231	C₂×#235	C₂²×C₅	1	1	yes	characteristic
232	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
233	C₃×#126	—	2	1	no	—
234	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₃×#123	—	2	1	no	—
236	C₃×#121	—	2	1	no	—
237	C₃×#121	C₂²×C₅	1	1	yes	characteristic
238	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₃×C₄×D₄	—	2	1	no	—
240	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	#937	—	2	1	no	—
245	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₂×#213	C₂²×C₅	1	1	yes	characteristic
247	C₂×#213	C₂²×C₅	1	1	yes	characteristic
248	#930	C₂²×C₅	1	1	yes	characteristic
249	#924	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
252	#894	—	2	1	no	—
253	#884	—	2	1	no	—
254	D₃×C₂²⋊C₄	—	2	1	no	—
255	#875	C₂²×C₅	1	1	yes	characteristic
256	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
257	#832	C₂²×C₅	1	1	yes	characteristic, complemented
258	#830	C₂²×C₅	1	1	yes	characteristic
259	#830	C₂²×C₅	1	1	yes	characteristic, complemented
260	#810	C₂²×C₅	1	1	yes	characteristic, complemented
261	#810	C₂²×C₅	1	1	yes	characteristic, complemented
262	#810	C₂²×C₅	1	1	yes	characteristic, complemented
263	#809	C₂²×C₅	1	1	yes	characteristic
264	#809	C₂²×C₅	1	1	yes	characteristic
265	#809	C₂²×C₅	1	1	yes	characteristic
266	#809	C₂²×C₅	1	1	yes	characteristic
267	#809	C₂²×C₅	1	1	yes	characteristic
268	#809	C₂²×C₅	1	1	yes	characteristic
269	#808	C₂²×C₅	1	1	yes	characteristic, complemented
270	#807	C₂²×C₅	1	1	yes	characteristic, complemented
271	#807	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂⁴×C₅	—	6	1	no	—
275	C₅×#41	—	6	2	no	—
276	C₅×#41	—	12	1	no	—
277	C₂×C₅×Q₈	—	3	1	no	—
278	C₂×C₅×D₄	—	2	1	no	—
279	C₂×C₅×D₄	—	2	1	no	—
280	C₂×C₅×D₄	—	3	1	no	—
281	C₂×C₅×D₄	—	3	1	no	—
282	C₂×C₅×D₄	—	6	2	no	—
283	C₂×C₅×D₄	—	6	1	no	—
284	C₂×C₅×D₄	—	6	1	no	—
285	C₂×C₅×D₄	—	6	1	no	—
286	C₂×C₅×D₄	—	12	1	no	—
287	C₂×C₅×D₄	#67	1	1	yes	characteristic
288	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	—	2	1	no	—
291	C₂²×C₄×C₅	—	6	1	no	—
292	C₂²×C₄×C₅	—	6	1	no	—
293	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
295	C₅×SD₁₆	—	12	1	no	—
296	C₅×D₈	—	6	2	no	—
297	C₅×D₈	—	12	1	no	—
298	C₂×C₅×C₈	—	3	1	no	—
299	C₂×C₅×C₈	—	3	1	no	—
300	C₂×C₅×C₈	—	3	1	no	—
301	C₂×C₅×C₈	—	3	1	no	—
302	C₂×C₅×C₈	—	12	1	no	—
303	C₂×C₅×C₈	—	12	1	no	—
304	C₅×C₄⋊C₄	—	2	1	no	—
305	C₅×C₄⋊C₄	—	2	1	no	—
306	C₅×C₄⋊C₄	—	2	1	no	—
307	C₅×C₄⋊C₄	—	3	1	no	—
308	C₅×C₄⋊C₄	—	6	1	no	—
309	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
310	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
311	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
312	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	—	6	1	no	—
318	C₅×C₂²⋊C₄	—	6	1	no	—
319	C₅×C₂²⋊C₄	—	6	1	no	—
320	C₅×C₂²⋊C₄	—	6	1	no	—
321	C₅×C₂²⋊C₄	—	6	1	no	—
322	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
324	C₄²×C₅	—	2	1	no	—
325	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
326	#553	C₅×D₃	1	1	yes	characteristic, complemented
327	#546	—	3	1	no	—
328	#488	—	3	1	no	—
329	#484	—	3	1	no	—
330	#482	—	3	1	no	—
331	#478	—	3	1	no	—
332	#466	—	3	1	no	—
333	#465	—	3	1	no	—
334	#463	—	3	1	no	—
335	#449	—	3	1	no	—
336	#447	—	3	1	no	—
337	C₄×D₈	—	3	1	no	—
338	C₈×D₄	—	3	1	no	—
339	#416	—	3	1	no	—
340	C₂×#102	—	3	1	no	—
341	C₂²×C₃×C₅	—	2	1	no	—
342	C₂²×C₃×C₅	—	2	1	no	—
343	C₂²×C₃×C₅	—	2	1	no	—
344	C₂²×C₃×C₅	—	2	1	no	—
345	C₂²×C₃×C₅	—	2	1	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	#135	1	2	yes	—
350	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₅×D₃	—	2	2	no	—
352	C₂×C₅×D₃	—	4	1	no	—
353	C₂×C₅×D₃	—	4	1	no	—
354	C₂×C₅×D₃	—	4	1	no	—
355	C₂×C₅×D₃	—	4	1	no	—
356	C₂×C₅×D₃	—	4	1	no	—
357	C₂×C₅×D₃	—	8	4	no	—
358	C₃×C₄×C₅	—	2	1	no	—
359	C₃×C₄×C₅	—	2	1	no	—
360	C₃×C₄×C₅	—	2	1	no	—
361	C₃×C₄×C₅	—	2	1	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
366	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
367	C₅×Dic₃	—	4	1	no	—
368	C₅×Dic₃	—	4	1	no	—
369	C₂³×D₃	—	2	1	no	—
370	C₂×C₃×D₄	—	2	1	no	—
371	C₂×C₃×D₄	—	2	1	no	—
372	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
373	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₃×C₄	—	2	1	no	—
375	C₂²×C₃×C₄	—	2	1	no	—
376	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂×#67	—	2	1	no	—
379	C₂×#67	—	2	1	no	—
380	#235	—	2	2	no	—
381	#235	—	4	1	no	—
382	C₂×D₁₂	—	2	2	no	—
383	C₂×D₁₂	—	2	1	no	—
384	C₂×D₁₂	—	4	1	no	—
385	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
386	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₄×D₃	—	2	1	no	—
388	C₂×C₄×D₃	—	2	1	no	—
389	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	—	2	1	no	—
393	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
394	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
396	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
397	C₃×C₂²⋊C₄	—	2	1	no	—
398	C₃×C₂²⋊C₄	—	2	1	no	—
399	C₃×C₂²⋊C₄	—	2	1	no	—
400	C₃×C₂²⋊C₄	—	2	1	no	—
401	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
402	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
403	C₃×C₄²	—	2	1	no	—
404	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
405	#217	—	2	1	no	—
406	#214	—	4	1	no	—
407	#213	—	2	2	no	—
408	#213	—	4	1	no	—
409	(C₂×D₃)⋊C₄	—	2	1	no	—
410	(C₂×D₃)⋊C₄	—	2	1	no	—
411	(C₂×D₃)⋊C₄	—	2	1	no	—
412	(C₂×D₃)⋊C₄	—	2	1	no	—
413	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
414	Dic₃⋊C₄	—	2	1	no	—
415	C₂×C₃⋊C₈	—	4	1	no	—
416	C₂×C₃⋊C₈	—	4	1	no	—
417	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	—	6	1	no	—
423	C₂³×C₅	—	6	1	no	—
424	C₂³×C₅	—	12	2	no	—
425	C₂³×C₅	—	12	2	no	—
426	C₂³×C₅	—	24	1	no	—
427	C₂³×C₅	C₂×#67	1	1	yes	characteristic
428	C₂³×C₅	C₂×#67	1	1	yes	characteristic
429	C₅×Q₈	—	6	1	no	—
430	C₅×Q₈	—	6	1	no	—
431	C₅×D₄	—	2	2	no	—
432	C₅×D₄	—	2	1	no	—
433	C₅×D₄	—	2	1	no	—
434	C₅×D₄	—	3	2	no	—
435	C₅×D₄	—	4	2	no	—
436	C₅×D₄	—	6	1	no	—
437	C₅×D₄	—	6	1	no	—
438	C₅×D₄	—	6	1	no	—
439	C₅×D₄	—	8	1	no	—
440	C₅×D₄	—	12	2	no	—
441	C₅×D₄	—	12	2	no	—
442	C₅×D₄	—	24	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	6	1	no	—
451	C₂×C₄×C₅	—	6	1	no	—
452	C₂×C₄×C₅	—	8	1	no	—
453	C₂×C₄×C₅	—	8	1	no	—
454	C₂×C₄×C₅	—	12	2	no	—
455	C₂×C₄×C₅	—	24	1	no	—
456	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
457	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
458	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
459	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
460	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
461	C₅×C₈	—	6	1	no	—
462	C₅×C₈	—	6	1	no	—
463	C₅×C₈	—	6	1	no	—
464	C₅×C₈	—	6	1	no	—
465	C₂×#41	—	3	1	no	—
466	C₂²×D₄	—	3	1	no	—
467	C₂×SD₁₆	—	3	1	no	—
468	C₂×D₈	—	3	1	no	—
469	C₂×D₈	—	3	1	no	—
470	C₂²×C₈	—	3	1	no	—
471	C₂²×C₈	—	3	1	no	—
472	#126	—	2	1	no	—
473	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
474	#124	—	3	1	no	—
475	#123	—	2	1	no	—
476	#123	—	6	1	no	—
477	C₂²⋊Q₈	—	3	1	no	—
478	#121	—	2	1	no	—
479	#121	—	3	1	no	—
480	#121	—	6	1	no	—
481	#121	C₂×C₅×D₃	1	1	yes	characteristic
482	#121	C₂×C₅×D₃	1	1	yes	characteristic, complemented
483	#120	—	6	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
487	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
488	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
489	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	—	6	1	no	—
491	#107	—	3	1	no	—
492	#107	—	3	1	no	—
493	#106	—	3	1	no	—
494	C₄⋊C₈	—	3	1	no	—
495	#103	—	3	1	no	—
496	#103	—	3	1	no	—
497	#103	—	3	1	no	—
498	#102	—	3	1	no	—
499	#102	—	3	1	no	—
500	#102	—	3	1	no	—
501	#102	—	3	1	no	—
502	#102	—	3	1	no	—
503	#102	—	3	1	no	—
504	#102	—	3	1	no	—
505	C₂²⋊C₈	—	3	1	no	—
506	C₂²⋊C₈	—	3	1	no	—
507	C₄×C₈	—	3	1	no	—
508	C₂×C₃×C₅	—	2	2	no	—
509	C₂×C₃×C₅	—	4	1	no	—
510	C₂×C₃×C₅	—	8	1	no	—
511	C₂×C₃×C₅	#546	1	1	yes	characteristic
512	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
513	C₂×C₃×C₅	#576	1	1	yes	characteristic
514	C₅×D₃	—	4	2	no	—
515	C₅×D₃	—	8	1	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂²×D₃	—	2	1	no	—
520	C₂²×D₃	—	2	1	no	—
521	C₂²×D₃	—	4	2	no	—
522	C₂²×D₃	—	4	2	no	—
523	C₂²×D₃	—	8	1	no	—
524	C₃×D₄	—	2	2	no	—
525	C₃×D₄	—	2	1	no	—
526	C₃×D₄	—	2	1	no	—
527	C₃×D₄	—	4	2	no	—
528	C₃×D₄	—	8	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	8	1	no	—
537	C₂×C₃×C₄	—	8	1	no	—
538	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
543	#67	—	4	2	no	—
544	#67	—	8	1	no	—
545	C₂×Dic₃	—	2	1	no	—
546	C₂×Dic₃	—	2	1	no	—
547	D₁₂	—	2	1	no	—
548	D₁₂	—	2	1	no	—
549	D₁₂	—	2	1	no	—
550	D₁₂	—	4	2	no	—
551	D₁₂	C₅×#41	1	2	yes	—
552	C₄×D₃	—	4	2	no	—
553	C₄×D₃	—	8	1	no	—
554	Dic₆	—	2	1	no	—
555	Dic₆	—	2	1	no	—
556	C₃⋊C₈	—	2	1	no	—
557	C₃⋊C₈	—	2	1	no	—
558	C₃⋊C₈	—	2	1	no	—
559	C₃⋊C₈	—	2	1	no	—
560	C₂²×C₅	—	2	1	no	—
561	C₂²×C₅	—	2	1	no	—
562	C₂²×C₅	—	2	1	no	—
563	C₂²×C₅	—	2	1	no	—
564	C₂²×C₅	—	2	1	no	—
565	C₂²×C₅	—	4	1	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	—	4	1	no	—
568	C₂²×C₅	—	6	2	no	—
569	C₂²×C₅	—	12	1	no	—
570	C₂²×C₅	—	12	1	no	—
571	C₂²×C₅	—	12	1	no	—
572	C₂²×C₅	—	12	1	no	—
573	C₂²×C₅	—	12	1	no	—
574	C₂²×C₅	—	24	4	no	—
575	C₂²×C₅	#950	1	2	yes	—
576	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
577	C₄×C₅	—	2	1	no	—
578	C₄×C₅	—	2	1	no	—
579	C₄×C₅	—	2	1	no	—
580	C₄×C₅	—	2	1	no	—
581	C₄×C₅	—	4	1	no	—
582	C₄×C₅	—	4	1	no	—
583	C₄×C₅	—	4	1	no	—
584	C₄×C₅	—	12	1	no	—
585	C₄×C₅	—	12	1	no	—
586	C₄×C₅	D₃×#41	1	1	yes	characteristic
587	C₄×C₅	#1009	1	1	yes	characteristic
588	C₂⁴	—	6	1	no	—
589	#41	—	6	2	no	—
590	#41	—	12	1	no	—
591	C₂×Q₈	—	3	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	3	1	no	—
595	C₂×D₄	—	3	1	no	—
596	C₂×D₄	—	6	2	no	—
597	C₂×D₄	—	6	1	no	—
598	C₂×D₄	—	6	1	no	—
599	C₂×D₄	—	6	1	no	—
600	C₂×D₄	—	12	1	no	—
601	C₂×D₄	C₅×#67	1	1	yes	characteristic
602	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	6	1	no	—
606	C₂²×C₄	—	6	1	no	—
607	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
608	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
609	SD₁₆	—	12	1	no	—
610	D₈	—	6	2	no	—
611	D₈	—	12	1	no	—
612	C₂×C₈	—	3	1	no	—
613	C₂×C₈	—	3	1	no	—
614	C₂×C₈	—	3	1	no	—
615	C₂×C₈	—	3	1	no	—
616	C₂×C₈	—	12	1	no	—
617	C₂×C₈	—	12	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	3	1	no	—
622	C₄⋊C₄	—	6	1	no	—
623	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
624	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
625	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	6	1	no	—
632	C₂²⋊C₄	—	6	1	no	—
633	C₂²⋊C₄	—	6	1	no	—
634	C₂²⋊C₄	—	6	1	no	—
635	C₂²⋊C₄	—	6	1	no	—
636	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
637	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
638	C₄²	—	2	1	no	—
639	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
640	C₃×C₅	#3297	1	1	yes	characteristic, complemented, Hall
641	C₂²×C₃	—	2	1	no	—
642	C₂²×C₃	—	2	1	no	—
643	C₂²×C₃	—	2	1	no	—
644	C₂²×C₃	—	2	1	no	—
645	C₂²×C₃	—	2	1	no	—
646	C₂²×C₃	—	4	1	no	—
647	C₂²×C₃	—	4	1	no	—
648	C₂²×C₃	—	4	1	no	—
649	C₂²×C₃	C₅×#135	1	2	yes	—
650	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
651	C₂×D₃	—	2	2	no	—
652	C₂×D₃	—	4	1	no	—
653	C₂×D₃	—	4	1	no	—
654	C₂×D₃	—	4	1	no	—
655	C₂×D₃	—	4	1	no	—
656	C₂×D₃	—	4	1	no	—
657	C₂×D₃	—	8	4	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	4	1	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
666	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
667	Dic₃	—	4	1	no	—
668	Dic₃	—	4	1	no	—
669	C₂×C₅	—	2	2	no	—
670	C₂×C₅	—	4	1	no	—
671	C₂×C₅	—	8	1	no	—
672	C₂×C₅	—	12	2	no	—
673	C₂×C₅	—	24	1	no	—
674	C₂×C₅	C₂×#950	1	1	yes	characteristic
675	C₂×C₅	#5829	1	1	yes	characteristic
676	C₂×C₅	#5835	1	1	yes	characteristic
677	C₂³	—	2	1	no	—
678	C₂³	—	6	1	no	—
679	C₂³	—	6	1	no	—
680	C₂³	—	12	2	no	—
681	C₂³	—	12	2	no	—
682	C₂³	—	24	1	no	—
683	C₂³	C₂×C₅×#67	1	1	yes	characteristic
684	C₂³	C₂×C₅×#67	1	1	yes	characteristic
685	Q₈	—	6	1	no	—
686	Q₈	—	6	1	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	1	no	—
689	D₄	—	2	1	no	—
690	D₄	—	3	2	no	—
691	D₄	—	4	2	no	—
692	D₄	—	6	1	no	—
693	D₄	—	6	1	no	—
694	D₄	—	6	1	no	—
695	D₄	—	8	1	no	—
696	D₄	—	12	2	no	—
697	D₄	—	12	2	no	—
698	D₄	—	24	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	6	1	no	—
707	C₂×C₄	—	6	1	no	—
708	C₂×C₄	—	8	1	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	12	2	no	—
711	C₂×C₄	—	24	1	no	—
712	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
713	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
714	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
715	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
716	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
717	C₈	—	6	1	no	—
718	C₈	—	6	1	no	—
719	C₈	—	6	1	no	—
720	C₈	—	6	1	no	—
721	C₂×C₃	—	2	2	no	—
722	C₂×C₃	—	4	1	no	—
723	C₂×C₃	—	8	1	no	—
724	C₂×C₃	C₅×#546	1	1	yes	characteristic
725	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
726	C₂×C₃	C₅×#576	1	1	yes	characteristic
727	D₃	—	4	2	no	—
728	D₃	—	8	1	no	—
729	C₅	#83614	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	6	2	no	—
739	C₂²	—	12	1	no	—
740	C₂²	—	12	1	no	—
741	C₂²	—	12	1	no	—
742	C₂²	—	12	1	no	—
743	C₂²	—	12	1	no	—
744	C₂²	—	24	4	no	—
745	C₂²	C₅×#950	1	2	yes	—
746	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	12	1	no	—
755	C₄	—	12	1	no	—
756	C₄	C₅×D₃×#41	1	1	yes	characteristic
757	C₄	C₅×#1009	1	1	yes	characteristic
758	C₃	C₅×#3297	1	1	yes	characteristic, complemented, Sylow
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	8	1	no	—
762	C₂	—	12	2	no	—
763	C₂	—	24	1	no	—
764	C₂	C₂×C₅×#950	1	1	yes	characteristic
765	C₂	C₅×#5829	1	1	yes	characteristic
766	C₂	C₅×#5835	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×#553	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#553	D₃
hypocenter	C₃	C₅×#3297
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×#553

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#553	C₂	semidirect
2. C₅×#5550	C₂	semidirect
3. C₅×#5068	C₂	semidirect
4. C₅×#5066	C₂	semidirect
5. C₅×#5041	C₂	semidirect
6. C₅×#5038	C₂	semidirect
7. C₅×#5037	C₂	semidirect
8. C₅×#5036	C₂	semidirect
9. C₅×#5016	C₂	semidirect
10. C₄×C₅×#213	C₂	semidirect
11. C₅×D₄×C₃⋊C₈	C₂	semidirect
12. C₅×#5003	C₂	semidirect
13. C₅×#5002	C₂	semidirect
14. C₅×#4970	C₂	semidirect
15. C₂×C₅×#809	C₂	semidirect
20. C₃×C₅×#125	C₂²	semidirect
24. C₃×C₅×#121	C₂²	semidirect
27. C₃×C₄×C₅×D₄	C₂²	semidirect
28. C₃×C₅×#117	C₂²	semidirect
31. C₂×C₅×#214	C₂²	semidirect
37. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
43. C₅×#832	C₂²	semidirect
45. C₅×#830	C₂²	semidirect
46. C₅×#810	C₂²	semidirect
47. C₅×#810	C₂²	semidirect
48. C₅×#810	C₂²	semidirect
55. C₅×#808	C₂²	semidirect
56. C₅×#807	C₂²	semidirect
57. C₅×#807	C₂²	semidirect
58. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
59. C₄×C₅×C₃⋊C₈	C₂²	semidirect
60. #83614	C₅	direct (N × H)
61. C₅×#553	D₃	semidirect
128. C₃×#553	C₂×C₅	semidirect
129. #5550	C₂×C₅	semidirect
130. #5068	C₂×C₅	semidirect
131. #5066	C₂×C₅	semidirect
132. #5041	C₂×C₅	semidirect
133. #5038	C₂×C₅	semidirect
134. #5037	C₂×C₅	semidirect
135. #5036	C₂×C₅	semidirect
136. #5016	C₂×C₅	semidirect
137. C₄×#213	C₂×C₅	semidirect
138. D₄×C₃⋊C₈	C₂×C₅	semidirect
139. #5003	C₂×C₅	semidirect
140. #5002	C₂×C₅	semidirect
141. #4970	C₂×C₅	semidirect
142. C₂×#809	C₂×C₅	semidirect
151. C₅×#125	C₂×D₃	semidirect
160. C₅×#121	C₂×D₃	semidirect
165. C₄×C₅×D₄	C₂×D₃	semidirect
166. C₅×#117	C₂×D₃	semidirect
234. C₃×#125	C₂²×C₅	semidirect
238. C₃×#121	C₂²×C₅	semidirect
241. C₃×C₄×D₄	C₂²×C₅	semidirect
242. C₃×#117	C₂²×C₅	semidirect
245. C₂×#214	C₂²×C₅	semidirect
251. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
257. #832	C₂²×C₅	semidirect
259. #830	C₂²×C₅	semidirect
260. #810	C₂²×C₅	semidirect
261. #810	C₂²×C₅	semidirect
262. #810	C₂²×C₅	semidirect
269. #808	C₂²×C₅	semidirect
270. #807	C₂²×C₅	semidirect
271. #807	C₂²×C₅	semidirect
272. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
273. C₄×C₃⋊C₈	C₂²×C₅	semidirect
326. #553	C₅×D₃	semidirect
473. #125	C₂×C₅×D₃	semidirect
482. #121	C₂×C₅×D₃	semidirect
487. C₄×D₄	C₂×C₅×D₃	semidirect
488. #117	C₂×C₅×D₃	semidirect
640. C₃×C₅	#3297	semidirect
729. C₅	#83614	direct (N × H)
758. C₃	C₅×#3297	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#553	2
C₅×#5550	2
C₅×#5068	2
C₅×#5066	2
C₅×#5041	2
C₅×#5038	2
C₅×#5037	2
C₅×#5036	2
C₅×#5016	2
C₄×C₅×#213	2
C₅×D₄×C₃⋊C₈	2
C₅×#5003	2
C₅×#5002	2
C₅×#4970	2
C₂×C₅×#809	2
C₅×#3297	3
#83614	5

Subgroups — C5×#83614 #14458848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83614 #14458848