Subgroups — C₅×#83598 #14458593

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5550	C₂	1	1	yes	maximal, characteristic
3	C₅×#5068	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5051	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5048	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5047	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5028	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#215	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×#4971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3296	—	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	—	2	1	no	—
21	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#123	—	2	1	no	—
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×#117	—	2	1	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#215	C₂²	1	1	yes	characteristic
32	C₂×C₅×#215	C₂²	1	1	yes	characteristic
33	C₅×#937	—	2	1	no	—
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×#835	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×#808	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	#83598	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#552	D₃	1	1	yes	characteristic, complemented
62	C₅×#546	—	3	1	no	—
63	C₅×#488	—	3	1	no	—
64	C₅×#483	—	3	1	no	—
65	C₅×#482	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#467	—	3	1	no	—
68	C₅×#465	—	3	1	no	—
69	C₅×#464	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#450	—	3	1	no	—
72	C₄×C₅×SD₁₆	—	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×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	—	2	1	no	—
83	C₂×C₅×#67	—	2	1	no	—
84	C₅×#235	—	2	2	no	—
85	C₅×#235	—	4	1	no	—
86	C₂×C₅×D₁₂	—	2	2	no	—
87	C₂×C₅×D₁₂	—	2	1	no	—
88	C₂×C₅×D₁₂	—	4	1	no	—
89	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
90	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
91	C₂×C₄×C₅×D₃	—	2	1	no	—
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₄⋊C₄	—	2	1	no	—
95	C₃×C₅×C₄⋊C₄	—	2	1	no	—
96	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
108	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₃×C₄²×C₅	—	2	1	no	—
110	C₃×C₄²×C₅	—	2	1	no	—
111	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₅×#217	—	2	1	no	—
113	C₅×#216	—	4	1	no	—
114	C₅×#215	—	2	2	no	—
115	C₅×#215	—	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×#552	C₂×C₅	1	1	yes	characteristic, complemented
129	#5550	C₂×C₅	1	1	yes	characteristic
130	#5068	C₂×C₅	1	1	yes	characteristic, complemented
131	#5066	C₂×C₅	1	1	yes	characteristic, complemented
132	#5051	C₂×C₅	1	1	yes	characteristic, complemented
133	#5048	C₂×C₅	1	1	yes	characteristic, complemented
134	#5047	C₂×C₅	1	1	yes	characteristic, complemented
135	#5046	C₂×C₅	1	1	yes	characteristic, complemented
136	#5028	C₂×C₅	1	1	yes	characteristic, complemented
137	C₄×#215	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	#4971	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×Q₁₆	—	3	1	no	—
146	C₂×C₅×SD₁₆	—	3	1	no	—
147	C₂×C₅×SD₁₆	—	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	—	2	1	no	—
152	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
153	C₅×#124	—	3	1	no	—
154	C₅×#123	—	2	1	no	—
155	C₅×#123	—	6	1	no	—
156	C₅×C₂²⋊Q₈	—	3	1	no	—
157	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
158	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
159	C₅×#121	—	3	1	no	—
160	C₅×#121	—	6	1	no	—
161	C₅×#120	—	6	1	no	—
162	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
163	C₄×C₅×D₄	—	3	1	no	—
164	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
165	C₅×#117	—	2	1	no	—
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×#106	—	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×#103	—	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	#3296	—	3	1	no	Sylow
187	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₅×D₃	—	2	1	no	—
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₂²×C₅×D₃	—	4	2	no	—
192	C₂²×C₅×D₃	—	4	2	no	—
193	C₂²×C₅×D₃	—	8	1	no	—
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×D₄	—	2	2	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	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	—	4	2	no	—
206	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₅×#67	—	4	2	no	—
212	C₅×#67	—	8	1	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	2	1	no	—
215	C₅×D₁₂	—	2	1	no	—
216	C₅×D₁₂	—	2	1	no	—
217	C₅×D₁₂	—	2	1	no	—
218	C₅×D₁₂	—	4	2	no	—
219	C₅×D₁₂	#41	1	2	yes	—
220	C₄×C₅×D₃	—	4	2	no	—
221	C₄×C₅×D₃	—	8	1	no	—
222	C₅×Dic₆	—	2	1	no	—
223	C₅×Dic₆	—	2	1	no	—
224	C₅×C₃⋊C₈	—	2	1	no	—
225	C₅×C₃⋊C₈	—	2	1	no	—
226	C₅×C₃⋊C₈	—	2	1	no	—
227	C₅×C₃⋊C₈	—	2	1	no	—
228	C₂×#235	C₂²×C₅	1	1	yes	characteristic
229	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
230	C₃×#126	—	2	1	no	—
231	C₃×#125	—	2	1	no	—
232	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₃×#123	—	2	1	no	—
234	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
236	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
237	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
238	C₃×#117	—	2	1	no	—
239	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
240	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₂×#215	C₂²×C₅	1	1	yes	characteristic
243	C₂×#215	C₂²×C₅	1	1	yes	characteristic
244	#937	—	2	1	no	—
245	#930	C₂²×C₅	1	1	yes	characteristic
246	#924	C₂²×C₅	1	1	yes	characteristic
247	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
249	#894	—	2	1	no	—
250	#884	—	2	1	no	—
251	D₃×C₂²⋊C₄	—	2	1	no	—
252	#875	C₂²×C₅	1	1	yes	characteristic
253	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
254	#835	C₂²×C₅	1	1	yes	characteristic, complemented
255	#830	C₂²×C₅	1	1	yes	characteristic
256	#830	C₂²×C₅	1	1	yes	characteristic, complemented
257	#810	C₂²×C₅	1	1	yes	characteristic, complemented
258	#810	C₂²×C₅	1	1	yes	characteristic, complemented
259	#810	C₂²×C₅	1	1	yes	characteristic, complemented
260	#809	C₂²×C₅	1	1	yes	characteristic
261	#809	C₂²×C₅	1	1	yes	characteristic
262	#809	C₂²×C₅	1	1	yes	characteristic
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	#808	C₂²×C₅	1	1	yes	characteristic, complemented
267	#808	C₂²×C₅	1	1	yes	characteristic, complemented
268	#807	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂⁴×C₅	—	6	1	no	—
272	C₅×#41	—	6	2	no	—
273	C₅×#41	—	12	1	no	—
274	C₂×C₅×Q₈	—	3	1	no	—
275	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×D₄	—	3	1	no	—
277	C₂×C₅×D₄	—	3	1	no	—
278	C₂×C₅×D₄	—	6	2	no	—
279	C₂×C₅×D₄	—	6	1	no	—
280	C₂×C₅×D₄	—	6	1	no	—
281	C₂×C₅×D₄	—	6	1	no	—
282	C₂×C₅×D₄	—	12	1	no	—
283	C₂×C₅×D₄	#67	1	1	yes	characteristic
284	C₂²×C₄×C₅	—	2	1	no	—
285	C₂²×C₄×C₅	—	6	1	no	—
286	C₂²×C₄×C₅	—	6	1	no	—
287	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
289	C₅×Q₁₆	—	12	1	no	—
290	C₅×SD₁₆	—	6	2	no	—
291	C₅×SD₁₆	—	12	1	no	—
292	C₂×C₅×C₈	—	3	1	no	—
293	C₂×C₅×C₈	—	3	1	no	—
294	C₂×C₅×C₈	—	3	1	no	—
295	C₂×C₅×C₈	—	3	1	no	—
296	C₂×C₅×C₈	—	12	1	no	—
297	C₂×C₅×C₈	—	12	1	no	—
298	C₅×C₄⋊C₄	—	2	1	no	—
299	C₅×C₄⋊C₄	—	2	1	no	—
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	—	2	1	no	—
303	C₅×C₄⋊C₄	—	2	1	no	—
304	C₅×C₄⋊C₄	—	3	1	no	—
305	C₅×C₄⋊C₄	—	6	1	no	—
306	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
307	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
308	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
309	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
310	C₅×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	6	1	no	—
314	C₅×C₂²⋊C₄	—	6	1	no	—
315	C₅×C₂²⋊C₄	—	6	1	no	—
316	C₅×C₂²⋊C₄	—	6	1	no	—
317	C₅×C₂²⋊C₄	—	6	1	no	—
318	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
319	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
320	C₄²×C₅	—	2	1	no	—
321	C₄²×C₅	—	2	1	no	—
322	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
323	#552	C₅×D₃	1	1	yes	characteristic, complemented
324	#546	—	3	1	no	—
325	#488	—	3	1	no	—
326	#483	—	3	1	no	—
327	#482	—	3	1	no	—
328	#478	—	3	1	no	—
329	#467	—	3	1	no	—
330	#465	—	3	1	no	—
331	#464	—	3	1	no	—
332	#452	—	3	1	no	—
333	#450	—	3	1	no	—
334	C₄×SD₁₆	—	3	1	no	—
335	C₈×D₄	—	3	1	no	—
336	#416	—	3	1	no	—
337	C₂×#102	—	3	1	no	—
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	—	2	1	no	—
340	C₂²×C₃×C₅	—	2	1	no	—
341	C₂²×C₃×C₅	—	2	1	no	—
342	C₂²×C₃×C₅	—	2	1	no	—
343	C₂²×C₃×C₅	#135	1	2	yes	—
344	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₅×D₃	—	2	2	no	—
346	C₂×C₅×D₃	—	4	1	no	—
347	C₂×C₅×D₃	—	4	1	no	—
348	C₂×C₅×D₃	—	4	1	no	—
349	C₂×C₅×D₃	—	4	1	no	—
350	C₂×C₅×D₃	—	4	1	no	—
351	C₂×C₅×D₃	—	8	4	no	—
352	C₃×C₄×C₅	—	2	1	no	—
353	C₃×C₄×C₅	—	2	1	no	—
354	C₃×C₄×C₅	—	2	1	no	—
355	C₃×C₄×C₅	—	2	1	no	—
356	C₃×C₄×C₅	—	4	1	no	—
357	C₃×C₄×C₅	—	4	1	no	—
358	C₃×C₄×C₅	—	4	1	no	—
359	C₃×C₄×C₅	—	4	1	no	—
360	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
361	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
362	C₅×Dic₃	—	4	1	no	—
363	C₅×Dic₃	—	4	1	no	—
364	C₂³×D₃	—	2	1	no	—
365	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
367	C₂²×C₃×C₄	—	2	1	no	—
368	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂×#67	—	2	1	no	—
371	C₂×#67	—	2	1	no	—
372	#235	—	2	2	no	—
373	#235	—	4	1	no	—
374	C₂×D₁₂	—	2	2	no	—
375	C₂×D₁₂	—	2	1	no	—
376	C₂×D₁₂	—	4	1	no	—
377	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
378	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄×D₃	—	2	1	no	—
380	C₂×C₄×D₃	—	2	1	no	—
381	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
382	C₃×C₄⋊C₄	—	2	1	no	—
383	C₃×C₄⋊C₄	—	2	1	no	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	—	2	1	no	—
386	C₃×C₄⋊C₄	—	2	1	no	—
387	C₃×C₄⋊C₄	—	2	1	no	—
388	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
389	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
390	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
391	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
392	C₃×C₂²⋊C₄	—	2	1	no	—
393	C₃×C₂²⋊C₄	—	2	1	no	—
394	C₃×C₂²⋊C₄	—	2	1	no	—
395	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
396	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
397	C₃×C₄²	—	2	1	no	—
398	C₃×C₄²	—	2	1	no	—
399	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
400	#217	—	2	1	no	—
401	#216	—	4	1	no	—
402	#215	—	2	2	no	—
403	#215	—	4	1	no	—
404	(C₂×D₃)⋊C₄	—	2	1	no	—
405	(C₂×D₃)⋊C₄	—	2	1	no	—
406	(C₂×D₃)⋊C₄	—	2	1	no	—
407	(C₂×D₃)⋊C₄	—	2	1	no	—
408	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
409	Dic₃⋊C₄	—	2	1	no	—
410	C₂×C₃⋊C₈	—	4	1	no	—
411	C₂×C₃⋊C₈	—	4	1	no	—
412	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
416	C₂³×C₅	—	6	1	no	—
417	C₂³×C₅	—	6	1	no	—
418	C₂³×C₅	—	12	2	no	—
419	C₂³×C₅	—	12	2	no	—
420	C₂³×C₅	—	24	1	no	—
421	C₂³×C₅	C₂×#67	1	1	yes	characteristic
422	C₂³×C₅	C₂×#67	1	1	yes	characteristic
423	C₅×Q₈	—	2	1	no	—
424	C₅×Q₈	—	2	1	no	—
425	C₅×Q₈	—	6	1	no	—
426	C₅×Q₈	—	6	1	no	—
427	C₅×D₄	—	2	2	no	—
428	C₅×D₄	—	3	2	no	—
429	C₅×D₄	—	6	1	no	—
430	C₅×D₄	—	6	1	no	—
431	C₅×D₄	—	6	1	no	—
432	C₅×D₄	—	12	2	no	—
433	C₅×D₄	—	12	2	no	—
434	C₅×D₄	—	24	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	4	2	no	—
444	C₂×C₄×C₅	—	6	1	no	—
445	C₂×C₄×C₅	—	6	1	no	—
446	C₂×C₄×C₅	—	12	2	no	—
447	C₂×C₄×C₅	—	24	1	no	—
448	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
449	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
450	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
451	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
452	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
453	C₅×C₈	—	6	1	no	—
454	C₅×C₈	—	6	1	no	—
455	C₅×C₈	—	6	1	no	—
456	C₅×C₈	—	6	1	no	—
457	C₂×#41	—	3	1	no	—
458	C₂²×D₄	—	3	1	no	—
459	C₂×Q₁₆	—	3	1	no	—
460	C₂×SD₁₆	—	3	1	no	—
461	C₂×SD₁₆	—	3	1	no	—
462	C₂²×C₈	—	3	1	no	—
463	C₂²×C₈	—	3	1	no	—
464	#126	—	2	1	no	—
465	#125	—	2	1	no	—
466	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
467	#124	—	3	1	no	—
468	#123	—	2	1	no	—
469	#123	—	6	1	no	—
470	C₂²⋊Q₈	—	3	1	no	—
471	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
472	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
473	#121	—	3	1	no	—
474	#121	—	6	1	no	—
475	#120	—	6	1	no	—
476	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
477	C₄×D₄	—	3	1	no	—
478	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
479	#117	—	2	1	no	—
480	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
481	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	—	6	1	no	—
483	#107	—	3	1	no	—
484	#106	—	3	1	no	—
485	#106	—	3	1	no	—
486	C₄⋊C₈	—	3	1	no	—
487	#103	—	3	1	no	—
488	#103	—	3	1	no	—
489	#103	—	3	1	no	—
490	#103	—	3	1	no	—
491	#102	—	3	1	no	—
492	#102	—	3	1	no	—
493	#102	—	3	1	no	—
494	#102	—	3	1	no	—
495	#102	—	3	1	no	—
496	#102	—	3	1	no	—
497	C₂²⋊C₈	—	3	1	no	—
498	C₂²⋊C₈	—	3	1	no	—
499	C₄×C₈	—	3	1	no	—
500	C₂×C₃×C₅	—	2	2	no	—
501	C₂×C₃×C₅	—	4	1	no	—
502	C₂×C₃×C₅	#546	1	1	yes	characteristic
503	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
504	C₂×C₃×C₅	#577	1	1	yes	characteristic
505	C₅×D₃	—	4	2	no	—
506	C₅×D₃	—	8	1	no	—
507	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
509	C₂²×D₃	—	2	1	no	—
510	C₂²×D₃	—	2	1	no	—
511	C₂²×D₃	—	4	2	no	—
512	C₂²×D₃	—	4	2	no	—
513	C₂²×D₃	—	8	1	no	—
514	C₃×Q₈	—	2	1	no	—
515	C₃×Q₈	—	2	1	no	—
516	C₃×D₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	4	2	no	—
526	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
531	#67	—	4	2	no	—
532	#67	—	8	1	no	—
533	C₂×Dic₃	—	2	1	no	—
534	C₂×Dic₃	—	2	1	no	—
535	D₁₂	—	2	1	no	—
536	D₁₂	—	2	1	no	—
537	D₁₂	—	2	1	no	—
538	D₁₂	—	4	2	no	—
539	D₁₂	C₅×#41	1	2	yes	—
540	C₄×D₃	—	4	2	no	—
541	C₄×D₃	—	8	1	no	—
542	Dic₆	—	2	1	no	—
543	Dic₆	—	2	1	no	—
544	C₃⋊C₈	—	2	1	no	—
545	C₃⋊C₈	—	2	1	no	—
546	C₃⋊C₈	—	2	1	no	—
547	C₃⋊C₈	—	2	1	no	—
548	C₂²×C₅	—	2	1	no	—
549	C₂²×C₅	—	2	1	no	—
550	C₂²×C₅	—	2	1	no	—
551	C₂²×C₅	—	2	1	no	—
552	C₂²×C₅	—	2	1	no	—
553	C₂²×C₅	—	6	2	no	—
554	C₂²×C₅	—	12	1	no	—
555	C₂²×C₅	—	12	1	no	—
556	C₂²×C₅	—	12	1	no	—
557	C₂²×C₅	—	12	1	no	—
558	C₂²×C₅	—	12	1	no	—
559	C₂²×C₅	—	24	4	no	—
560	C₂²×C₅	#950	1	2	yes	—
561	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
562	C₄×C₅	—	2	1	no	—
563	C₄×C₅	—	2	1	no	—
564	C₄×C₅	—	2	1	no	—
565	C₄×C₅	—	2	1	no	—
566	C₄×C₅	—	4	1	no	—
567	C₄×C₅	—	4	1	no	—
568	C₄×C₅	—	4	1	no	—
569	C₄×C₅	—	4	1	no	—
570	C₄×C₅	—	12	1	no	—
571	C₄×C₅	—	12	1	no	—
572	C₄×C₅	D₃×#41	1	1	yes	characteristic
573	C₄×C₅	#1009	1	1	yes	characteristic
574	C₂⁴	—	6	1	no	—
575	#41	—	6	2	no	—
576	#41	—	12	1	no	—
577	C₂×Q₈	—	3	1	no	—
578	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
579	C₂×D₄	—	3	1	no	—
580	C₂×D₄	—	3	1	no	—
581	C₂×D₄	—	6	2	no	—
582	C₂×D₄	—	6	1	no	—
583	C₂×D₄	—	6	1	no	—
584	C₂×D₄	—	6	1	no	—
585	C₂×D₄	—	12	1	no	—
586	C₂×D₄	C₅×#67	1	1	yes	characteristic
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	6	1	no	—
589	C₂²×C₄	—	6	1	no	—
590	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
592	Q₁₆	—	12	1	no	—
593	SD₁₆	—	6	2	no	—
594	SD₁₆	—	12	1	no	—
595	C₂×C₈	—	3	1	no	—
596	C₂×C₈	—	3	1	no	—
597	C₂×C₈	—	3	1	no	—
598	C₂×C₈	—	3	1	no	—
599	C₂×C₈	—	12	1	no	—
600	C₂×C₈	—	12	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	3	1	no	—
608	C₄⋊C₄	—	6	1	no	—
609	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
610	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
611	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
612	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	6	1	no	—
617	C₂²⋊C₄	—	6	1	no	—
618	C₂²⋊C₄	—	6	1	no	—
619	C₂²⋊C₄	—	6	1	no	—
620	C₂²⋊C₄	—	6	1	no	—
621	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
622	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
626	C₃×C₅	#3296	1	1	yes	characteristic, complemented, Hall
627	C₂²×C₃	—	2	1	no	—
628	C₂²×C₃	—	2	1	no	—
629	C₂²×C₃	—	2	1	no	—
630	C₂²×C₃	—	2	1	no	—
631	C₂²×C₃	—	2	1	no	—
632	C₂²×C₃	C₅×#135	1	2	yes	—
633	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
634	C₂×D₃	—	2	2	no	—
635	C₂×D₃	—	4	1	no	—
636	C₂×D₃	—	4	1	no	—
637	C₂×D₃	—	4	1	no	—
638	C₂×D₃	—	4	1	no	—
639	C₂×D₃	—	4	1	no	—
640	C₂×D₃	—	8	4	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	2	1	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
650	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
651	Dic₃	—	4	1	no	—
652	Dic₃	—	4	1	no	—
653	C₂×C₅	—	2	2	no	—
654	C₂×C₅	—	4	1	no	—
655	C₂×C₅	—	12	2	no	—
656	C₂×C₅	—	24	1	no	—
657	C₂×C₅	C₂×#950	1	1	yes	characteristic
658	C₂×C₅	#5829	1	1	yes	characteristic
659	C₂×C₅	#5837	1	1	yes	characteristic
660	C₂³	—	6	1	no	—
661	C₂³	—	6	1	no	—
662	C₂³	—	12	2	no	—
663	C₂³	—	12	2	no	—
664	C₂³	—	24	1	no	—
665	C₂³	C₂×C₅×#67	1	1	yes	characteristic
666	C₂³	C₂×C₅×#67	1	1	yes	characteristic
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	6	1	no	—
670	Q₈	—	6	1	no	—
671	D₄	—	2	2	no	—
672	D₄	—	3	2	no	—
673	D₄	—	6	1	no	—
674	D₄	—	6	1	no	—
675	D₄	—	6	1	no	—
676	D₄	—	12	2	no	—
677	D₄	—	12	2	no	—
678	D₄	—	24	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	6	1	no	—
689	C₂×C₄	—	6	1	no	—
690	C₂×C₄	—	12	2	no	—
691	C₂×C₄	—	24	1	no	—
692	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
693	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
694	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
695	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
696	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
697	C₈	—	6	1	no	—
698	C₈	—	6	1	no	—
699	C₈	—	6	1	no	—
700	C₈	—	6	1	no	—
701	C₂×C₃	—	2	2	no	—
702	C₂×C₃	—	4	1	no	—
703	C₂×C₃	C₅×#546	1	1	yes	characteristic
704	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
705	C₂×C₃	C₅×#577	1	1	yes	characteristic
706	D₃	—	4	2	no	—
707	D₃	—	8	1	no	—
708	C₅	#83598	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	6	2	no	—
715	C₂²	—	12	1	no	—
716	C₂²	—	12	1	no	—
717	C₂²	—	12	1	no	—
718	C₂²	—	12	1	no	—
719	C₂²	—	12	1	no	—
720	C₂²	—	24	4	no	—
721	C₂²	C₅×#950	1	2	yes	—
722	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	12	1	no	—
732	C₄	—	12	1	no	—
733	C₄	C₅×D₃×#41	1	1	yes	characteristic
734	C₄	C₅×#1009	1	1	yes	characteristic
735	C₃	C₅×#3296	1	1	yes	characteristic, complemented, Sylow
736	C₂	—	2	2	no	—
737	C₂	—	4	1	no	—
738	C₂	—	12	2	no	—
739	C₂	—	24	1	no	—
740	C₂	C₂×C₅×#950	1	1	yes	characteristic
741	C₂	C₅×#5829	1	1	yes	characteristic
742	C₂	C₅×#5837	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×#552	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5550	C₂
hypercenter	C₅×#552	D₃
hypocenter	C₃	C₅×#3296
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×#552

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#552	C₂	semidirect
3. C₅×#5068	C₂	semidirect
4. C₅×#5066	C₂	semidirect
5. C₅×#5051	C₂	semidirect
6. C₅×#5048	C₂	semidirect
7. C₅×#5047	C₂	semidirect
8. C₅×#5046	C₂	semidirect
9. C₅×#5028	C₂	semidirect
10. C₄×C₅×#215	C₂	semidirect
11. C₅×D₄×C₃⋊C₈	C₂	semidirect
12. C₅×#5003	C₂	semidirect
13. C₅×#5002	C₂	semidirect
14. C₅×#4971	C₂	semidirect
15. C₂×C₅×#809	C₂	semidirect
21. C₃×C₅×#125	C₂²	semidirect
24. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
25. C₃×C₄×C₅×Q₈	C₂²	semidirect
28. C₃×C₅×#117	C₂²	semidirect
30. C₂×C₅×#216	C₂²	semidirect
37. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
43. C₅×#835	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×#808	C₂²	semidirect
57. C₅×#807	C₂²	semidirect
58. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
59. C₄×C₅×C₃⋊C₈	C₂²	semidirect
60. #83598	C₅	direct (N × H)
61. C₅×#552	D₃	semidirect
128. C₃×#552	C₂×C₅	semidirect
130. #5068	C₂×C₅	semidirect
131. #5066	C₂×C₅	semidirect
132. #5051	C₂×C₅	semidirect
133. #5048	C₂×C₅	semidirect
134. #5047	C₂×C₅	semidirect
135. #5046	C₂×C₅	semidirect
136. #5028	C₂×C₅	semidirect
137. C₄×#215	C₂×C₅	semidirect
138. D₄×C₃⋊C₈	C₂×C₅	semidirect
139. #5003	C₂×C₅	semidirect
140. #5002	C₂×C₅	semidirect
141. #4971	C₂×C₅	semidirect
142. C₂×#809	C₂×C₅	semidirect
152. C₅×#125	C₂×D₃	semidirect
158. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
162. C₄×C₅×Q₈	C₂×D₃	semidirect
166. C₅×#117	C₂×D₃	semidirect
232. C₃×#125	C₂²×C₅	semidirect
235. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
236. C₃×C₄×Q₈	C₂²×C₅	semidirect
239. C₃×#117	C₂²×C₅	semidirect
241. C₂×#216	C₂²×C₅	semidirect
248. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
254. #835	C₂²×C₅	semidirect
256. #830	C₂²×C₅	semidirect
257. #810	C₂²×C₅	semidirect
258. #810	C₂²×C₅	semidirect
259. #810	C₂²×C₅	semidirect
266. #808	C₂²×C₅	semidirect
267. #808	C₂²×C₅	semidirect
268. #807	C₂²×C₅	semidirect
269. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
270. C₄×C₃⋊C₈	C₂²×C₅	semidirect
323. #552	C₅×D₃	semidirect
466. #125	C₂×C₅×D₃	semidirect
472. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
476. C₄×Q₈	C₂×C₅×D₃	semidirect
480. #117	C₂×C₅×D₃	semidirect
626. C₃×C₅	#3296	semidirect
708. C₅	#83598	direct (N × H)
735. C₃	C₅×#3296	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#552	2
C₅×#5550	2
C₅×#5068	2
C₅×#5066	2
C₅×#5051	2
C₅×#5048	2
C₅×#5047	2
C₅×#5046	2
C₅×#5028	2
C₄×C₅×#215	2
C₅×D₄×C₃⋊C₈	2
C₅×#5003	2
C₅×#5002	2
C₅×#4971	2
C₂×C₅×#809	2
C₅×#3296	3
#83598	5

Subgroups — C5×#83598 #14458593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83598 #14458593