Subgroups — C₅×#80680 #14458437

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5635	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5609	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5169	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5163	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×C₈×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4807	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4760	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3295	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	—	2	1	no	—
18	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₅×#946	C₂²	1	1	yes	characteristic, complemented
25	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#215	C₂²	1	1	yes	characteristic
27	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
28	C₅×#940	C₂²	1	1	yes	characteristic
29	C₅×#937	—	2	1	no	—
30	C₄×C₅×#67	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#897	—	2	1	no	—
34	C₅×#895	C₂²	1	1	yes	characteristic
35	C₅×#893	C₂²	1	1	yes	characteristic
36	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₅×#889	—	2	1	no	—
38	C₅×#888	C₂²	1	1	yes	characteristic, complemented
39	C₅×#884	—	2	1	no	—
40	C₅×#882	—	2	1	no	—
41	C₅×#67⋊C₄	—	2	1	no	—
42	C₅×#878	—	2	1	no	—
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
46	C₅×#832	C₂²	1	1	yes	characteristic, complemented
47	C₅×#832	C₂²	1	1	yes	characteristic, complemented
48	C₅×#830	C₂²	1	1	yes	characteristic, complemented
49	C₅×#821	C₂²	1	1	yes	characteristic
50	C₅×#821	C₂²	1	1	yes	characteristic
51	C₅×#821	C₂²	1	1	yes	characteristic, complemented
52	C₅×#821	C₂²	1	1	yes	characteristic, complemented
53	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
56	C₅×#809	C₂²	1	1	yes	characteristic
57	C₅×#809	C₂²	1	1	yes	characteristic, complemented
58	C₅×#808	C₂²	1	1	yes	characteristic, complemented
59	C₅×#808	C₂²	1	1	yes	characteristic, complemented
60	#80680	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#554	—	3	1	no	—
62	C₅×D₄²	—	3	1	no	—
63	C₅×#486	—	3	1	no	—
64	C₅×#481	—	3	1	no	—
65	C₅×#481	—	3	1	no	—
66	C₅×#476	—	3	1	no	—
67	C₅×#465	—	3	1	no	—
68	C₅×#465	D₃	1	1	yes	characteristic, complemented
69	C₅×#460	—	3	1	no	—
70	C₅×#450	—	3	1	no	—
71	C₅×#450	—	3	1	no	—
72	C₄×C₅×SD₁₆	—	3	1	no	—
73	C₅×C₈×D₄	—	3	1	no	—
74	C₂×C₅×#102	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂³×C₅×D₃	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	1	no	—
80	C₂×C₃×C₅×D₄	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	C₂×C₅×#67	—	2	1	no	—
85	C₂×C₅×#67	D₄	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	—	2	1	no	—
87	C₅×D₃×D₄	—	2	2	no	—
88	C₅×D₃×D₄	—	4	1	no	—
89	C₅×D₃×D₄	—	4	4	no	—
90	C₂×C₅×D₁₂	—	2	2	no	—
91	C₂×C₅×D₁₂	—	2	1	no	—
92	C₂×C₅×D₁₂	—	2	1	no	—
93	C₂×C₅×D₁₂	—	4	1	no	—
94	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
95	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	—	2	1	no	—
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₅×Dic₆	—	2	1	no	—
100	C₃×C₅×SD₁₆	—	4	1	no	—
101	C₂×C₃×C₅×C₈	—	4	1	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₅×#217	D₄	1	1	yes	characteristic
110	C₅×#215	—	2	2	no	—
111	C₅×#215	—	4	1	no	—
112	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
113	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
114	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
115	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
116	C₅×C₄⋊Dic₃	—	2	1	no	—
117	C₅×C₄⋊Dic₃	—	2	1	no	—
118	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
120	C₅×Dic₃⋊C₄	—	2	1	no	—
121	C₅×Dic₃⋊C₄	—	2	1	no	—
122	C₅×Dic₃⋊C₄	—	2	1	no	—
123	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
124	C₄×C₅×Dic₃	—	2	1	no	—
125	C₄×C₅×Dic₃	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	C₅×D₃×C₈	—	4	1	no	—
129	#5635	C₂×C₅	1	1	yes	characteristic, complemented
130	#5609	C₂×C₅	1	1	yes	characteristic
131	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
132	#5169	C₂×C₅	1	1	yes	characteristic, complemented
133	#5163	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
135	C₈×#67	C₂×C₅	1	1	yes	characteristic, complemented
136	#5046	C₂×C₅	1	1	yes	characteristic, complemented
137	#5034	C₂×C₅	1	1	yes	characteristic, complemented
138	#4870	C₂×C₅	1	1	yes	characteristic, complemented
139	#4863	C₂×C₅	1	1	yes	characteristic, complemented
140	#4807	C₂×C₅	1	1	yes	characteristic, complemented
141	#4788	C₂×C₅	1	1	yes	characteristic, complemented
142	D₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
143	#4760	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₅×D₄	—	3	1	no	—
145	C₂²×C₅×D₄	—	3	1	no	—
146	C₂²×C₅×D₄	—	6	1	no	—
147	C₂×C₅×SD₁₆	—	3	1	no	—
148	C₂×C₅×SD₁₆	—	3	1	no	—
149	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
150	C₂²×C₅×C₈	—	3	1	no	—
151	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
152	C₅×C₄⋊Q₈	—	3	1	no	—
153	C₅×#127	—	3	1	no	—
154	C₅×#125	—	6	1	no	—
155	C₅×C₂²⋊Q₈	—	3	1	no	—
156	C₅×C₂²⋊Q₈	—	6	1	no	—
157	C₅×C₂²⋊Q₈	—	6	1	no	—
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×#121	C₂×D₃	1	1	yes	characteristic
162	C₅×#120	—	6	1	no	—
163	C₅×#120	—	6	1	no	—
164	C₄×C₅×Q₈	—	3	1	no	—
165	C₄×C₅×D₄	—	3	1	no	—
166	C₄×C₅×D₄	—	3	1	no	—
167	C₄×C₅×D₄	—	6	1	no	—
168	C₂×C₅×C₄⋊C₄	—	3	1	no	—
169	C₂×C₅×C₄⋊C₄	—	3	1	no	—
170	C₅×#106	—	3	1	no	—
171	C₅×#106	—	3	1	no	—
172	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
173	C₅×C₄⋊C₈	—	3	1	no	—
174	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
175	C₅×#102	—	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×#102	C₂×D₃	1	1	yes	characteristic, complemented
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₅×C₂²⋊C₈	—	3	1	no	—
186	C₄×C₅×C₈	—	3	1	no	—
187	#3295	—	3	1	no	Sylow
188	C₂³×C₃×C₅	—	2	1	no	—
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	—	4	2	no	—
195	C₂²×C₅×D₃	—	4	2	no	—
196	C₂²×C₅×D₃	—	8	1	no	—
197	C₂²×C₅×D₃	—	8	1	no	—
198	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×D₄	—	2	1	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	—	4	2	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	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
213	C₅×#67	—	8	1	no	—
214	C₅×#67	SD₁₆	1	4	yes	complemented
215	C₂×C₅×Dic₃	—	2	1	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	8	1	no	—
218	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
220	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
221	C₅×D₁₂	—	2	1	no	—
222	C₅×D₁₂	—	2	1	no	—
223	C₅×D₁₂	—	2	1	no	—
224	C₅×D₁₂	—	4	2	no	—
225	C₅×D₁₂	—	4	2	no	—
226	C₅×D₁₂	#41	1	2	yes	—
227	C₄×C₅×D₃	—	2	1	no	—
228	C₄×C₅×D₃	—	2	1	no	—
229	C₄×C₅×D₃	—	4	2	no	—
230	C₄×C₅×D₃	—	8	1	no	—
231	C₅×Dic₆	—	8	1	no	—
232	C₃×C₅×C₈	—	2	1	no	—
233	C₃×C₅×C₈	—	2	1	no	—
234	C₅×C₃⋊C₈	—	2	1	no	—
235	C₅×C₃⋊C₈	—	2	1	no	—
236	C₂×D₃×D₄	—	2	1	no	—
237	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
238	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
240	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₃×#121	C₂²×C₅	1	1	yes	characteristic
243	#946	C₂²×C₅	1	1	yes	characteristic, complemented
244	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₂×#215	C₂²×C₅	1	1	yes	characteristic
246	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
247	#940	C₂²×C₅	1	1	yes	characteristic
248	#937	—	2	1	no	—
249	C₄×#67	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
252	#897	—	2	1	no	—
253	#895	C₂²×C₅	1	1	yes	characteristic
254	#893	C₂²×C₅	1	1	yes	characteristic
255	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
256	#889	—	2	1	no	—
257	#888	C₂²×C₅	1	1	yes	characteristic, complemented
258	#884	—	2	1	no	—
259	#882	—	2	1	no	—
260	#67⋊C₄	—	2	1	no	—
261	#878	—	2	1	no	—
262	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
265	#832	C₂²×C₅	1	1	yes	characteristic, complemented
266	#832	C₂²×C₅	1	1	yes	characteristic, complemented
267	#830	C₂²×C₅	1	1	yes	characteristic, complemented
268	#821	C₂²×C₅	1	1	yes	characteristic
269	#821	C₂²×C₅	1	1	yes	characteristic
270	#821	C₂²×C₅	1	1	yes	characteristic, complemented
271	#821	C₂²×C₅	1	1	yes	characteristic, complemented
272	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
273	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
275	#809	C₂²×C₅	1	1	yes	characteristic
276	#809	C₂²×C₅	1	1	yes	characteristic, complemented
277	#808	C₂²×C₅	1	1	yes	characteristic, complemented
278	#808	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	—	6	1	no	—
280	C₂⁴×C₅	—	6	1	no	—
281	C₂×C₅×Q₈	—	6	1	no	—
282	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₅×D₄	—	2	1	no	—
284	C₂×C₅×D₄	—	3	1	no	—
285	C₂×C₅×D₄	—	3	1	no	—
286	C₂×C₅×D₄	—	3	1	no	—
287	C₂×C₅×D₄	—	6	2	no	—
288	C₂×C₅×D₄	—	6	1	no	—
289	C₂×C₅×D₄	—	6	1	no	—
290	C₂×C₅×D₄	—	6	1	no	—
291	C₂×C₅×D₄	—	6	1	no	—
292	C₂×C₅×D₄	—	6	2	no	—
293	C₂×C₅×D₄	—	6	1	no	—
294	C₂×C₅×D₄	—	12	1	no	—
295	C₂×C₅×D₄	—	12	1	no	—
296	C₂×C₅×D₄	—	12	4	no	—
297	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	6	1	no	—
300	C₂²×C₄×C₅	—	6	1	no	—
301	C₂²×C₄×C₅	—	6	1	no	—
302	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
303	C₅×SD₁₆	—	4	1	no	—
304	C₅×SD₁₆	—	6	2	no	—
305	C₅×SD₁₆	—	12	1	no	—
306	C₂×C₅×C₈	—	3	1	no	—
307	C₂×C₅×C₈	—	3	1	no	—
308	C₂×C₅×C₈	—	4	1	no	—
309	C₂×C₅×C₈	—	12	1	no	—
310	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
311	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
312	C₅×C₄⋊C₄	—	2	1	no	—
313	C₅×C₄⋊C₄	—	3	1	no	—
314	C₅×C₄⋊C₄	—	3	1	no	—
315	C₅×C₄⋊C₄	—	3	1	no	—
316	C₅×C₄⋊C₄	—	6	1	no	—
317	C₅×C₄⋊C₄	—	6	1	no	—
318	C₅×C₄⋊C₄	—	6	1	no	—
319	C₅×C₄⋊C₄	—	6	1	no	—
320	C₅×C₄⋊C₄	—	6	1	no	—
321	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
322	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	—	2	1	no	—
324	C₅×C₂²⋊C₄	—	2	1	no	—
325	C₅×C₂²⋊C₄	—	3	1	no	—
326	C₅×C₂²⋊C₄	—	3	1	no	—
327	C₅×C₂²⋊C₄	—	6	1	no	—
328	C₅×C₂²⋊C₄	—	6	1	no	—
329	C₅×C₂²⋊C₄	—	6	1	no	—
330	C₄²×C₅	—	3	1	no	—
331	C₄²×C₅	—	6	1	no	—
332	#554	—	3	1	no	—
333	D₄²	—	3	1	no	—
334	#486	—	3	1	no	—
335	#481	—	3	1	no	—
336	#481	—	3	1	no	—
337	#476	—	3	1	no	—
338	#465	—	3	1	no	—
339	#465	C₅×D₃	1	1	yes	characteristic, complemented
340	#460	—	3	1	no	—
341	#450	—	3	1	no	—
342	#450	—	3	1	no	—
343	C₄×SD₁₆	—	3	1	no	—
344	C₈×D₄	—	3	1	no	—
345	C₂×#102	—	3	1	no	—
346	C₂×#102	—	3	1	no	—
347	C₂²×C₃×C₅	—	2	1	no	—
348	C₂²×C₃×C₅	—	2	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
353	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₅×D₃	—	2	1	no	—
355	C₂×C₅×D₃	—	2	1	no	—
356	C₂×C₅×D₃	—	2	2	no	—
357	C₂×C₅×D₃	—	4	1	no	—
358	C₂×C₅×D₃	—	4	1	no	—
359	C₂×C₅×D₃	—	4	1	no	—
360	C₂×C₅×D₃	—	4	1	no	—
361	C₂×C₅×D₃	—	4	1	no	—
362	C₂×C₅×D₃	—	8	4	no	—
363	C₂×C₅×D₃	—	8	4	no	—
364	C₂×C₅×D₃	C₂×SD₁₆	1	2	yes	—
365	C₃×C₄×C₅	—	2	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₃×C₄×C₅	—	4	1	no	—
368	C₃×C₄×C₅	—	4	1	no	—
369	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
370	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
371	C₅×Dic₃	—	2	1	no	—
372	C₅×Dic₃	—	2	1	no	—
373	C₅×Dic₃	—	4	1	no	—
374	C₅×Dic₃	—	4	1	no	—
375	C₅×Dic₃	C₂×SD₁₆	1	2	yes	—
376	C₂³×D₃	—	2	1	no	—
377	C₂³×D₃	—	2	1	no	—
378	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×D₄	—	2	1	no	—
380	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂×#67	—	2	1	no	—
383	C₂×#67	—	2	1	no	—
384	C₂×#67	—	2	1	no	—
385	C₂×#67	C₅×D₄	1	1	yes	characteristic
386	C₂²×Dic₃	—	2	1	no	—
387	D₃×D₄	—	2	2	no	—
388	D₃×D₄	—	4	1	no	—
389	D₃×D₄	—	4	4	no	—
390	C₂×D₁₂	—	2	2	no	—
391	C₂×D₁₂	—	2	1	no	—
392	C₂×D₁₂	—	2	1	no	—
393	C₂×D₁₂	—	4	1	no	—
394	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
395	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₄×D₃	—	2	1	no	—
397	C₂×C₄×D₃	—	2	1	no	—
398	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
399	C₂×Dic₆	—	2	1	no	—
400	C₃×SD₁₆	—	4	1	no	—
401	C₂×C₃×C₈	—	4	1	no	—
402	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₃×C₄⋊C₄	—	2	1	no	—
405	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₃×C₂²⋊C₄	—	2	1	no	—
408	C₃×C₂²⋊C₄	—	2	1	no	—
409	#217	C₅×D₄	1	1	yes	characteristic
410	#215	—	2	2	no	—
411	#215	—	4	1	no	—
412	(C₂×D₃)⋊C₄	—	2	1	no	—
413	(C₂×D₃)⋊C₄	—	2	1	no	—
414	(C₂×D₃)⋊C₄	—	2	1	no	—
415	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
416	C₄⋊Dic₃	—	2	1	no	—
417	C₄⋊Dic₃	—	2	1	no	—
418	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
419	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
420	Dic₃⋊C₄	—	2	1	no	—
421	Dic₃⋊C₄	—	2	1	no	—
422	Dic₃⋊C₄	—	2	1	no	—
423	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
424	C₄×Dic₃	—	2	1	no	—
425	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
428	D₃×C₈	—	4	1	no	—
429	C₂³×C₅	—	2	1	no	—
430	C₂³×C₅	—	3	1	no	—
431	C₂³×C₅	—	6	1	no	—
432	C₂³×C₅	—	6	1	no	—
433	C₂³×C₅	—	12	2	no	—
434	C₂³×C₅	—	12	2	no	—
435	C₂³×C₅	—	12	2	no	—
436	C₂³×C₅	—	12	2	no	—
437	C₂³×C₅	—	24	1	no	—
438	C₂³×C₅	—	24	1	no	—
439	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
440	C₅×Q₈	—	2	1	no	—
441	C₅×Q₈	—	2	1	no	—
442	C₅×Q₈	—	24	1	no	—
443	C₅×D₄	—	2	1	no	—
444	C₅×D₄	—	2	1	no	—
445	C₅×D₄	—	3	4	no	—
446	C₅×D₄	—	3	2	no	—
447	C₅×D₄	—	4	2	no	—
448	C₅×D₄	—	6	1	no	—
449	C₅×D₄	—	6	1	no	—
450	C₅×D₄	—	6	1	no	—
451	C₅×D₄	—	12	2	no	—
452	C₅×D₄	—	12	2	no	—
453	C₅×D₄	—	12	2	no	—
454	C₅×D₄	—	12	2	no	—
455	C₅×D₄	—	24	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	3	1	no	—
462	C₂×C₄×C₅	—	3	1	no	—
463	C₂×C₄×C₅	—	3	1	no	—
464	C₂×C₄×C₅	—	6	1	no	—
465	C₂×C₄×C₅	—	6	1	no	—
466	C₂×C₄×C₅	—	6	1	no	—
467	C₂×C₄×C₅	—	6	1	no	—
468	C₂×C₄×C₅	—	12	2	no	—
469	C₂×C₄×C₅	—	24	1	no	—
470	C₂×C₄×C₅	—	24	1	no	—
471	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
472	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
473	C₅×C₈	—	2	1	no	—
474	C₅×C₈	—	2	1	no	—
475	C₅×C₈	—	6	1	no	—
476	C₅×C₈	—	6	1	no	—
477	C₂²×D₄	—	3	1	no	—
478	C₂²×D₄	—	3	1	no	—
479	C₂²×D₄	—	6	1	no	—
480	C₂×SD₁₆	—	3	1	no	—
481	C₂×SD₁₆	—	3	1	no	—
482	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
483	C₂²×C₈	—	3	1	no	—
484	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
485	C₄⋊Q₈	—	3	1	no	—
486	#127	—	3	1	no	—
487	#125	—	6	1	no	—
488	C₂²⋊Q₈	—	3	1	no	—
489	C₂²⋊Q₈	—	6	1	no	—
490	C₂²⋊Q₈	—	6	1	no	—
491	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
492	#121	—	3	1	no	—
493	#121	—	6	1	no	—
494	#121	C₂×C₅×D₃	1	1	yes	characteristic
495	#120	—	6	1	no	—
496	#120	—	6	1	no	—
497	C₄×Q₈	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	6	1	no	—
501	C₂×C₄⋊C₄	—	3	1	no	—
502	C₂×C₄⋊C₄	—	3	1	no	—
503	#106	—	3	1	no	—
504	#106	—	3	1	no	—
505	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
506	C₄⋊C₈	—	3	1	no	—
507	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
508	#102	—	3	1	no	—
509	#102	—	3	1	no	—
510	#102	—	3	1	no	—
511	#102	—	3	1	no	—
512	#102	—	3	1	no	—
513	#102	—	3	1	no	—
514	#102	—	3	1	no	—
515	#102	—	3	1	no	—
516	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
517	C₂²⋊C₈	—	3	1	no	—
518	C₂²⋊C₈	—	3	1	no	—
519	C₄×C₈	—	3	1	no	—
520	C₂×C₃×C₅	—	2	2	no	—
521	C₂×C₃×C₅	—	8	1	no	—
522	C₂×C₃×C₅	#546	1	1	yes	characteristic
523	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
524	C₂×C₃×C₅	#576	1	1	yes	characteristic
525	C₅×D₃	—	2	2	no	—
526	C₅×D₃	—	4	2	no	—
527	C₅×D₃	—	8	1	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂²×D₃	—	2	1	no	—
531	C₂²×D₃	—	2	1	no	—
532	C₂²×D₃	—	4	2	no	—
533	C₂²×D₃	—	4	2	no	—
534	C₂²×D₃	—	4	2	no	—
535	C₂²×D₃	—	4	2	no	—
536	C₂²×D₃	—	8	1	no	—
537	C₂²×D₃	—	8	1	no	—
538	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
539	C₃×Q₈	—	2	1	no	—
540	C₃×Q₈	—	2	1	no	—
541	C₃×D₄	—	2	1	no	—
542	C₃×D₄	—	2	1	no	—
543	C₃×D₄	—	4	2	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
551	#67	—	4	2	no	—
552	#67	—	4	2	no	—
553	#67	—	8	1	no	—
554	#67	C₅×SD₁₆	1	4	yes	complemented
555	C₂×Dic₃	—	2	1	no	—
556	C₂×Dic₃	—	2	1	no	—
557	C₂×Dic₃	—	8	1	no	—
558	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
559	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
560	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
561	D₁₂	—	2	1	no	—
562	D₁₂	—	2	1	no	—
563	D₁₂	—	2	1	no	—
564	D₁₂	—	4	2	no	—
565	D₁₂	—	4	2	no	—
566	D₁₂	C₅×#41	1	2	yes	—
567	C₄×D₃	—	2	1	no	—
568	C₄×D₃	—	2	1	no	—
569	C₄×D₃	—	4	2	no	—
570	C₄×D₃	—	8	1	no	—
571	Dic₆	—	8	1	no	—
572	C₃×C₈	—	2	1	no	—
573	C₃×C₈	—	2	1	no	—
574	C₃⋊C₈	—	2	1	no	—
575	C₃⋊C₈	—	2	1	no	—
576	C₂²×C₅	—	2	1	no	—
577	C₂²×C₅	—	2	1	no	—
578	C₂²×C₅	—	3	2	no	—
579	C₂²×C₅	—	4	1	no	—
580	C₂²×C₅	—	4	1	no	—
581	C₂²×C₅	—	4	1	no	—
582	C₂²×C₅	—	6	1	no	—
583	C₂²×C₅	—	6	1	no	—
584	C₂²×C₅	—	6	2	no	—
585	C₂²×C₅	—	12	1	no	—
586	C₂²×C₅	—	12	1	no	—
587	C₂²×C₅	—	12	1	no	—
588	C₂²×C₅	—	12	1	no	—
589	C₂²×C₅	—	12	1	no	—
590	C₂²×C₅	—	24	4	no	—
591	C₂²×C₅	—	24	4	no	—
592	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
593	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
594	C₄×C₅	—	2	1	no	—
595	C₄×C₅	—	3	2	no	—
596	C₄×C₅	—	4	1	no	—
597	C₄×C₅	—	4	1	no	—
598	C₄×C₅	—	4	1	no	—
599	C₄×C₅	—	6	1	no	—
600	C₄×C₅	—	6	1	no	—
601	C₄×C₅	—	12	1	no	—
602	C₄×C₅	—	12	1	no	—
603	C₄×C₅	#1004	1	1	yes	characteristic
604	C₄×C₅	D₃×#41	1	1	yes	characteristic
605	C₂⁴	—	6	1	no	—
606	C₂⁴	—	6	1	no	—
607	C₂×Q₈	—	6	1	no	—
608	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	3	1	no	—
611	C₂×D₄	—	3	1	no	—
612	C₂×D₄	—	3	1	no	—
613	C₂×D₄	—	6	2	no	—
614	C₂×D₄	—	6	1	no	—
615	C₂×D₄	—	6	1	no	—
616	C₂×D₄	—	6	1	no	—
617	C₂×D₄	—	6	1	no	—
618	C₂×D₄	—	6	2	no	—
619	C₂×D₄	—	6	1	no	—
620	C₂×D₄	—	12	1	no	—
621	C₂×D₄	—	12	1	no	—
622	C₂×D₄	—	12	4	no	—
623	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	6	1	no	—
626	C₂²×C₄	—	6	1	no	—
627	C₂²×C₄	—	6	1	no	—
628	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
629	SD₁₆	—	4	1	no	—
630	SD₁₆	—	6	2	no	—
631	SD₁₆	—	12	1	no	—
632	C₂×C₈	—	3	1	no	—
633	C₂×C₈	—	3	1	no	—
634	C₂×C₈	—	4	1	no	—
635	C₂×C₈	—	12	1	no	—
636	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	3	1	no	—
640	C₄⋊C₄	—	3	1	no	—
641	C₄⋊C₄	—	3	1	no	—
642	C₄⋊C₄	—	6	1	no	—
643	C₄⋊C₄	—	6	1	no	—
644	C₄⋊C₄	—	6	1	no	—
645	C₄⋊C₄	—	6	1	no	—
646	C₄⋊C₄	—	6	1	no	—
647	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
648	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	3	1	no	—
652	C₂²⋊C₄	—	3	1	no	—
653	C₂²⋊C₄	—	6	1	no	—
654	C₂²⋊C₄	—	6	1	no	—
655	C₂²⋊C₄	—	6	1	no	—
656	C₄²	—	3	1	no	—
657	C₄²	—	6	1	no	—
658	C₃×C₅	#3295	1	1	yes	characteristic, complemented, Hall
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	1	no	—
661	C₂²×C₃	—	4	1	no	—
662	C₂²×C₃	—	4	1	no	—
663	C₂²×C₃	—	4	1	no	—
664	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
665	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
666	C₂×D₃	—	2	1	no	—
667	C₂×D₃	—	2	1	no	—
668	C₂×D₃	—	2	2	no	—
669	C₂×D₃	—	4	1	no	—
670	C₂×D₃	—	4	1	no	—
671	C₂×D₃	—	4	1	no	—
672	C₂×D₃	—	4	1	no	—
673	C₂×D₃	—	4	1	no	—
674	C₂×D₃	—	8	4	no	—
675	C₂×D₃	—	8	4	no	—
676	C₂×D₃	C₂×C₅×SD₁₆	1	2	yes	—
677	C₃×C₄	—	2	1	no	—
678	C₃×C₄	—	4	1	no	—
679	C₃×C₄	—	4	1	no	—
680	C₃×C₄	—	4	1	no	—
681	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
682	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
683	Dic₃	—	2	1	no	—
684	Dic₃	—	2	1	no	—
685	Dic₃	—	4	1	no	—
686	Dic₃	—	4	1	no	—
687	Dic₃	C₂×C₅×SD₁₆	1	2	yes	—
688	C₂×C₅	—	2	2	no	—
689	C₂×C₅	—	6	2	no	—
690	C₂×C₅	—	8	1	no	—
691	C₂×C₅	—	12	2	no	—
692	C₂×C₅	—	24	1	no	—
693	C₂×C₅	#5610	1	1	yes	characteristic
694	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
695	C₂×C₅	#5769	1	1	yes	characteristic
696	C₂³	—	2	1	no	—
697	C₂³	—	3	1	no	—
698	C₂³	—	6	1	no	—
699	C₂³	—	6	1	no	—
700	C₂³	—	12	2	no	—
701	C₂³	—	12	2	no	—
702	C₂³	—	12	2	no	—
703	C₂³	—	12	2	no	—
704	C₂³	—	24	1	no	—
705	C₂³	—	24	1	no	—
706	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
707	Q₈	—	2	1	no	—
708	Q₈	—	2	1	no	—
709	Q₈	—	24	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	3	4	no	—
713	D₄	—	3	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	6	1	no	—
716	D₄	—	6	1	no	—
717	D₄	—	6	1	no	—
718	D₄	—	12	2	no	—
719	D₄	—	12	2	no	—
720	D₄	—	12	2	no	—
721	D₄	—	12	2	no	—
722	D₄	—	24	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	3	1	no	—
729	C₂×C₄	—	3	1	no	—
730	C₂×C₄	—	3	1	no	—
731	C₂×C₄	—	6	1	no	—
732	C₂×C₄	—	6	1	no	—
733	C₂×C₄	—	6	1	no	—
734	C₂×C₄	—	6	1	no	—
735	C₂×C₄	—	12	2	no	—
736	C₂×C₄	—	24	1	no	—
737	C₂×C₄	—	24	1	no	—
738	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
740	C₈	—	2	1	no	—
741	C₈	—	2	1	no	—
742	C₈	—	6	1	no	—
743	C₈	—	6	1	no	—
744	C₂×C₃	—	2	2	no	—
745	C₂×C₃	—	8	1	no	—
746	C₂×C₃	C₅×#546	1	1	yes	characteristic
747	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
748	C₂×C₃	C₅×#576	1	1	yes	characteristic
749	D₃	—	2	2	no	—
750	D₃	—	4	2	no	—
751	D₃	—	8	1	no	—
752	C₅	#80680	1	1	yes	characteristic, direct product factor, Sylow
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	3	2	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	6	1	no	—
760	C₂²	—	6	1	no	—
761	C₂²	—	6	2	no	—
762	C₂²	—	12	1	no	—
763	C₂²	—	12	1	no	—
764	C₂²	—	12	1	no	—
765	C₂²	—	12	1	no	—
766	C₂²	—	12	1	no	—
767	C₂²	—	24	4	no	—
768	C₂²	—	24	4	no	—
769	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
770	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	3	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	1	no	—
776	C₄	—	6	1	no	—
777	C₄	—	6	1	no	—
778	C₄	—	12	1	no	—
779	C₄	—	12	1	no	—
780	C₄	C₅×#1004	1	1	yes	characteristic
781	C₄	C₅×D₃×#41	1	1	yes	characteristic
782	C₃	C₅×#3295	1	1	yes	characteristic, complemented, Sylow
783	C₂	—	2	2	no	—
784	C₂	—	6	2	no	—
785	C₂	—	8	1	no	—
786	C₂	—	12	2	no	—
787	C₂	—	24	1	no	—
788	C₂	C₅×#5610	1	1	yes	characteristic
789	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
790	C₂	C₅×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#465	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5609	C₂
hypercenter	C₅×#465	D₃
hypocenter	C₃	C₅×#3295
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#465

Complements

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

N	H ≅ G/N	type
1. C₅×#5635	C₂	semidirect
3. C₃×C₅×#465	C₂	semidirect
4. C₅×#5169	C₂	semidirect
5. C₅×#5163	C₂	semidirect
6. C₂×C₅×#821	C₂	semidirect
7. C₅×C₈×#67	C₂	semidirect
8. C₅×#5046	C₂	semidirect
9. C₅×#5034	C₂	semidirect
10. C₅×#4870	C₂	semidirect
11. C₅×#4863	C₂	semidirect
12. C₅×#4807	C₂	semidirect
13. C₅×#4788	C₂	semidirect
14. C₅×D₃×#102	C₂	semidirect
15. C₅×#4760	C₂	semidirect
20. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
21. C₂²×C₃×C₅×C₈	C₂²	semidirect
22. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
24. C₅×#946	C₂²	semidirect
25. C₅×Q₈×Dic₃	C₂²	semidirect
27. C₂×C₅×#215	C₂²	semidirect
31. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
32. C₂×C₅×D₃×C₈	C₂²	semidirect
36. C₅×D₃×C₄⋊C₄	C₂²	semidirect
38. C₅×#888	C₂²	semidirect
43. C₃×C₅×#106	C₂²	semidirect
44. C₃×C₅×#103	C₂²	semidirect
45. C₃×C₅×#102	C₂²	semidirect
46. C₅×#832	C₂²	semidirect
47. C₅×#832	C₂²	semidirect
48. C₅×#830	C₂²	semidirect
51. C₅×#821	C₂²	semidirect
52. C₅×#821	C₂²	semidirect
53. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
54. C₅×Dic₃⋊C₈	C₂²	semidirect
55. C₅×C₈×Dic₃	C₂²	semidirect
57. C₅×#809	C₂²	semidirect
58. C₅×#808	C₂²	semidirect
59. C₅×#808	C₂²	semidirect
60. #80680	C₅	direct (N × H)
68. C₅×#465	D₃	semidirect
129. #5635	C₂×C₅	semidirect
131. C₃×#465	C₂×C₅	semidirect
132. #5169	C₂×C₅	semidirect
133. #5163	C₂×C₅	semidirect
134. C₂×#821	C₂×C₅	semidirect
135. C₈×#67	C₂×C₅	semidirect
136. #5046	C₂×C₅	semidirect
137. #5034	C₂×C₅	semidirect
138. #4870	C₂×C₅	semidirect
139. #4863	C₂×C₅	semidirect
140. #4807	C₂×C₅	semidirect
141. #4788	C₂×C₅	semidirect
142. D₃×#102	C₂×C₅	semidirect
143. #4760	C₂×C₅	semidirect
149. C₂×C₅×SD₁₆	C₂×D₃	semidirect
151. C₂²×C₅×C₈	C₂×D₃	semidirect
158. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
172. C₅×#106	C₂×D₃	semidirect
174. C₅×#103	C₂×D₃	semidirect
183. C₅×#102	C₂×D₃	semidirect
214. C₅×#67	SD₁₆	semidirect
239. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
240. C₂²×C₃×C₈	C₂²×C₅	semidirect
241. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
243. #946	C₂²×C₅	semidirect
244. Q₈×Dic₃	C₂²×C₅	semidirect
246. C₂×#215	C₂²×C₅	semidirect
250. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
251. C₂×D₃×C₈	C₂²×C₅	semidirect
255. D₃×C₄⋊C₄	C₂²×C₅	semidirect
257. #888	C₂²×C₅	semidirect
262. C₃×#106	C₂²×C₅	semidirect
263. C₃×#103	C₂²×C₅	semidirect
264. C₃×#102	C₂²×C₅	semidirect
265. #832	C₂²×C₅	semidirect
266. #832	C₂²×C₅	semidirect
267. #830	C₂²×C₅	semidirect
270. #821	C₂²×C₅	semidirect
271. #821	C₂²×C₅	semidirect
272. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
273. Dic₃⋊C₈	C₂²×C₅	semidirect
274. C₈×Dic₃	C₂²×C₅	semidirect
276. #809	C₂²×C₅	semidirect
277. #808	C₂²×C₅	semidirect
278. #808	C₂²×C₅	semidirect
339. #465	C₅×D₃	semidirect
482. C₂×SD₁₆	C₂×C₅×D₃	semidirect
484. C₂²×C₈	C₂×C₅×D₃	semidirect
491. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
505. #106	C₂×C₅×D₃	semidirect
507. #103	C₂×C₅×D₃	semidirect
516. #102	C₂×C₅×D₃	semidirect
554. #67	C₅×SD₁₆	semidirect
658. C₃×C₅	#3295	semidirect
752. C₅	#80680	direct (N × H)
782. C₃	C₅×#3295	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5635	2
C₅×#5609	2
C₃×C₅×#465	2
C₅×#5169	2
C₅×#5163	2
C₂×C₅×#821	2
C₅×C₈×#67	2
C₅×#5046	2
C₅×#5034	2
C₅×#4870	2
C₅×#4863	2
C₅×#4807	2
C₅×#4788	2
C₅×D₃×#102	2
C₅×#4760	2
C₅×#3295	3
#80680	5

Subgroups — C5×#80680 #14458437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80680 #14458437