Subgroups — C₅×#81302 #14458287

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5609	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4890	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4883	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4882	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4786	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4760	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4732	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3294	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	—	2	1	no	—
18	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×#235	—	2	1	no	—
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₃×C₅×#121	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₅×#940	C₂²	1	1	yes	characteristic
24	C₅×#937	—	2	1	no	—
25	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
26	C₅×#930	C₂²	1	1	yes	characteristic, complemented
27	C₅×#929	—	2	1	no	—
28	C₄×C₅×#67	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#896	—	2	1	no	—
34	C₅×#895	C₂²	1	1	yes	characteristic
35	C₅×#895	C₂²	1	1	yes	characteristic, complemented
36	C₅×#894	—	2	1	no	—
37	C₅×#893	C₂²	1	1	yes	characteristic
38	C₅×#893	C₂²	1	1	yes	characteristic, complemented
39	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₅×#888	C₂²	1	1	yes	characteristic, complemented
41	C₅×#884	—	2	1	no	—
42	C₅×#882	—	2	1	no	—
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₅×#832	C₂²	1	1	yes	characteristic, complemented
49	C₅×#821	C₂²	1	1	yes	characteristic
50	C₅×#821	C₂²	1	1	yes	characteristic, complemented
51	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₅×#809	C₂²	1	1	yes	characteristic
55	C₅×#809	C₂²	1	1	yes	characteristic
56	C₅×#809	C₂²	1	1	yes	characteristic, complemented
57	C₅×#809	C₂²	1	1	yes	characteristic, complemented
58	C₅×#809	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	#81302	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#547	—	3	1	no	—
62	C₅×D₄²	—	3	1	no	—
63	C₅×#486	—	3	1	no	—
64	C₅×#480	—	3	1	no	—
65	C₅×#480	D₃	1	1	yes	characteristic, complemented
66	C₅×#474	—	3	1	no	—
67	C₅×#466	—	3	1	no	—
68	C₅×#466	—	3	1	no	—
69	C₅×#459	—	3	1	no	—
70	C₅×#447	—	3	1	no	—
71	C₅×#447	—	3	1	no	—
72	C₄×C₅×D₈	—	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×D₄	—	2	1	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
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	—	2	1	no	—
86	C₂×C₅×#67	D₄	1	1	yes	characteristic
87	C₅×D₃×D₄	—	2	2	no	—
88	C₅×D₃×D₄	—	4	1	no	—
89	C₅×D₃×D₄	—	4	4	no	—
90	C₅×#235	—	4	4	no	—
91	C₂×C₅×D₁₂	—	2	2	no	—
92	C₂×C₅×D₁₂	—	2	1	no	—
93	C₂×C₅×D₁₂	—	2	1	no	—
94	C₂×C₅×D₁₂	—	2	1	no	—
95	C₂×C₅×D₁₂	—	4	1	no	—
96	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
97	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
98	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
99	C₂×C₄×C₅×D₃	—	2	1	no	—
100	C₂×C₄×C₅×D₃	—	2	1	no	—
101	C₂×C₄×C₅×D₃	—	2	1	no	—
102	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
103	C₂×C₅×Dic₆	—	2	1	no	—
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₅×#217	D₄	1	1	yes	characteristic
112	C₅×#213	—	4	1	no	—
113	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
114	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
115	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
116	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
117	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
118	C₅×(C₂×D₃)⋊C₄	D₄	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	D₄	1	1	yes	characteristic
123	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₂×C₅×C₃⋊C₈	—	4	1	no	—
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×D₂₄	—	2	2	no	—
128	C₅×D₂₄	—	4	1	no	—
129	C₅×D₃×C₈	—	4	1	no	—
130	#5609	C₂×C₅	1	1	yes	characteristic, complemented
131	#5507	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
133	#5038	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
135	#4890	C₂×C₅	1	1	yes	characteristic, complemented
136	#4883	C₂×C₅	1	1	yes	characteristic, complemented
137	#4882	C₂×C₅	1	1	yes	characteristic, complemented
138	#4872	C₂×C₅	1	1	yes	characteristic, complemented
139	#4786	C₂×C₅	1	1	yes	characteristic, complemented
140	#4773	C₂×C₅	1	1	yes	characteristic, complemented
141	D₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
142	#4760	C₂×C₅	1	1	yes	characteristic, complemented
143	#4732	C₂×C₅	1	1	yes	characteristic, complemented
144	#67⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×C₅×#41	—	6	1	no	—
146	C₂²×C₅×D₄	—	3	1	no	—
147	C₂²×C₅×D₄	—	3	1	no	—
148	C₂²×C₅×D₄	—	6	1	no	—
149	C₂×C₅×D₈	—	3	1	no	—
150	C₂×C₅×D₈	—	3	1	no	—
151	C₂×C₅×D₈	—	3	1	no	—
152	C₂²×C₅×C₈	—	3	1	no	—
153	C₂²×C₅×C₈	—	3	1	no	—
154	C₅×C₄⋊Q₈	—	3	1	no	—
155	C₅×#127	—	3	1	no	—
156	C₅×#123	—	6	1	no	—
157	C₅×#123	—	6	1	no	—
158	C₅×C₂²⋊Q₈	—	6	1	no	—
159	C₅×#121	—	3	1	no	—
160	C₅×#121	—	3	1	no	—
161	C₅×#121	—	3	1	no	—
162	C₅×#121	—	6	1	no	—
163	C₅×#121	C₂×D₃	1	1	yes	characteristic
164	C₅×#120	—	6	1	no	—
165	C₅×#120	—	6	1	no	—
166	C₄×C₅×D₄	—	3	1	no	—
167	C₄×C₅×D₄	—	3	1	no	—
168	C₄×C₅×D₄	—	3	1	no	—
169	C₂×C₅×C₄⋊C₄	—	3	1	no	—
170	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
171	C₅×#107	—	3	1	no	—
172	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
173	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
174	C₅×C₄⋊C₈	—	3	1	no	—
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×#102	C₂×D₃	1	1	yes	characteristic, complemented
185	C₅×C₂²⋊C₈	—	3	1	no	—
186	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
187	C₄×C₅×C₈	—	3	1	no	—
188	#3294	—	3	1	no	Sylow
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₅×D₃	—	2	1	no	—
192	C₂²×C₅×D₃	—	2	1	no	—
193	C₂²×C₅×D₃	—	2	1	no	—
194	C₂²×C₅×D₃	—	4	2	no	—
195	C₂²×C₅×D₃	—	4	2	no	—
196	C₂²×C₅×D₃	—	4	2	no	—
197	C₂²×C₅×D₃	—	4	2	no	—
198	C₂²×C₅×D₃	—	8	1	no	—
199	C₂²×C₅×D₃	—	8	1	no	—
200	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
210	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₅×#67	—	4	2	no	—
213	C₅×#67	—	4	2	no	—
214	C₅×#67	—	4	2	no	—
215	C₅×#67	—	8	1	no	—
216	C₅×#67	D₈	1	4	yes	complemented
217	C₂×C₅×Dic₃	—	2	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	—	2	1	no	—
225	C₅×D₁₂	—	2	1	no	—
226	C₅×D₁₂	—	4	2	no	—
227	C₅×D₁₂	—	4	2	no	—
228	C₅×D₁₂	—	4	2	no	—
229	C₅×D₁₂	#41	1	2	yes	complemented
230	C₄×C₅×D₃	—	2	1	no	—
231	C₄×C₅×D₃	—	2	1	no	—
232	C₄×C₅×D₃	—	4	2	no	—
233	C₄×C₅×D₃	—	4	2	no	—
234	C₄×C₅×D₃	—	4	2	no	—
235	C₅×Dic₆	—	4	2	no	—
236	C₃×C₅×C₈	—	2	1	no	—
237	C₃×C₅×C₈	—	2	1	no	—
238	C₅×C₃⋊C₈	—	2	1	no	—
239	C₅×C₃⋊C₈	—	2	1	no	—
240	C₂×D₃×D₄	—	2	1	no	—
241	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×#235	—	2	1	no	—
243	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
244	C₃×#121	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
246	#940	C₂²×C₅	1	1	yes	characteristic
247	#937	—	2	1	no	—
248	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
249	#930	C₂²×C₅	1	1	yes	characteristic, complemented
250	#929	—	2	1	no	—
251	C₄×#67	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
256	#896	—	2	1	no	—
257	#895	C₂²×C₅	1	1	yes	characteristic
258	#895	C₂²×C₅	1	1	yes	characteristic, complemented
259	#894	—	2	1	no	—
260	#893	C₂²×C₅	1	1	yes	characteristic
261	#893	C₂²×C₅	1	1	yes	characteristic, complemented
262	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
263	#888	C₂²×C₅	1	1	yes	characteristic, complemented
264	#884	—	2	1	no	—
265	#882	—	2	1	no	—
266	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	#832	C₂²×C₅	1	1	yes	characteristic, complemented
272	#821	C₂²×C₅	1	1	yes	characteristic
273	#821	C₂²×C₅	1	1	yes	characteristic, complemented
274	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
275	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
277	#809	C₂²×C₅	1	1	yes	characteristic
278	#809	C₂²×C₅	1	1	yes	characteristic
279	#809	C₂²×C₅	1	1	yes	characteristic, complemented
280	#809	C₂²×C₅	1	1	yes	characteristic, complemented
281	#809	C₂²×C₅	1	1	yes	characteristic, complemented
282	#807	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₂⁴×C₅	—	6	1	no	—
284	C₂⁴×C₅	—	6	1	no	—
285	C₅×#41	—	12	4	no	—
286	C₂×C₅×Q₈	—	6	1	no	—
287	C₂×C₅×D₄	—	2	1	no	—
288	C₂×C₅×D₄	—	3	1	no	—
289	C₂×C₅×D₄	—	3	1	no	—
290	C₂×C₅×D₄	—	3	1	no	—
291	C₂×C₅×D₄	—	3	1	no	—
292	C₂×C₅×D₄	—	6	2	no	—
293	C₂×C₅×D₄	—	6	1	no	—
294	C₂×C₅×D₄	—	6	1	no	—
295	C₂×C₅×D₄	—	6	1	no	—
296	C₂×C₅×D₄	—	6	1	no	—
297	C₂×C₅×D₄	—	6	1	no	—
298	C₂×C₅×D₄	—	6	2	no	—
299	C₂×C₅×D₄	—	6	1	no	—
300	C₂×C₅×D₄	—	6	1	no	—
301	C₂×C₅×D₄	—	12	1	no	—
302	C₂×C₅×D₄	—	12	1	no	—
303	C₂×C₅×D₄	—	12	4	no	—
304	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	—	2	1	no	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	6	1	no	—
308	C₂²×C₄×C₅	—	6	1	no	—
309	C₂²×C₄×C₅	—	6	1	no	—
310	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
311	C₅×D₈	—	6	2	no	—
312	C₅×D₈	—	12	1	no	—
313	C₅×D₈	—	12	1	no	—
314	C₂×C₅×C₈	—	3	1	no	—
315	C₂×C₅×C₈	—	3	1	no	—
316	C₂×C₅×C₈	—	12	1	no	—
317	C₂×C₅×C₈	—	12	1	no	—
318	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
320	C₅×C₄⋊C₄	—	2	1	no	—
321	C₅×C₄⋊C₄	—	3	1	no	—
322	C₅×C₄⋊C₄	—	3	1	no	—
323	C₅×C₄⋊C₄	—	6	1	no	—
324	C₅×C₄⋊C₄	—	6	1	no	—
325	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
326	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
327	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
328	C₅×C₂²⋊C₄	—	2	1	no	—
329	C₅×C₂²⋊C₄	—	3	1	no	—
330	C₅×C₂²⋊C₄	—	3	1	no	—
331	C₅×C₂²⋊C₄	—	6	1	no	—
332	C₅×C₂²⋊C₄	—	6	1	no	—
333	C₅×C₂²⋊C₄	—	6	1	no	—
334	C₅×C₂²⋊C₄	—	6	1	no	—
335	C₅×C₂²⋊C₄	—	6	1	no	—
336	C₄²×C₅	—	3	1	no	—
337	#547	—	3	1	no	—
338	D₄²	—	3	1	no	—
339	#486	—	3	1	no	—
340	#480	—	3	1	no	—
341	#480	C₅×D₃	1	1	yes	characteristic, complemented
342	#474	—	3	1	no	—
343	#466	—	3	1	no	—
344	#466	—	3	1	no	—
345	#459	—	3	1	no	—
346	#447	—	3	1	no	—
347	#447	—	3	1	no	—
348	C₄×D₈	—	3	1	no	—
349	C₈×D₄	—	3	1	no	—
350	C₂×#102	—	3	1	no	—
351	C₂×#102	—	3	1	no	—
352	C₂²×C₃×C₅	—	2	1	no	—
353	C₂²×C₃×C₅	—	2	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	1	no	—
356	C₂²×C₃×C₅	—	4	1	no	—
357	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
358	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₅×D₃	—	2	1	no	—
360	C₂×C₅×D₃	—	2	1	no	—
361	C₂×C₅×D₃	—	2	2	no	—
362	C₂×C₅×D₃	—	4	1	no	—
363	C₂×C₅×D₃	—	4	1	no	—
364	C₂×C₅×D₃	—	4	1	no	—
365	C₂×C₅×D₃	—	4	1	no	—
366	C₂×C₅×D₃	—	4	1	no	—
367	C₂×C₅×D₃	—	4	1	no	—
368	C₂×C₅×D₃	—	4	1	no	—
369	C₂×C₅×D₃	—	4	1	no	—
370	C₂×C₅×D₃	—	8	4	no	—
371	C₂×C₅×D₃	—	8	4	no	—
372	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
373	C₃×C₄×C₅	—	2	1	no	—
374	C₃×C₄×C₅	—	4	1	no	—
375	C₃×C₄×C₅	—	4	1	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
378	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
379	C₅×Dic₃	—	2	1	no	—
380	C₅×Dic₃	—	2	1	no	—
381	C₅×Dic₃	—	4	1	no	—
382	C₅×Dic₃	C₂×D₈	1	2	yes	—
383	C₂³×D₃	—	2	1	no	—
384	C₂³×D₃	—	2	1	no	—
385	C₂×C₃×D₄	—	2	1	no	—
386	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₃×C₄	—	2	1	no	—
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×#67	—	2	1	no	—
390	C₂×#67	—	2	1	no	—
391	C₂×#67	—	2	1	no	—
392	C₂×#67	—	2	1	no	—
393	C₂×#67	C₅×D₄	1	1	yes	characteristic
394	D₃×D₄	—	2	2	no	—
395	D₃×D₄	—	4	1	no	—
396	D₃×D₄	—	4	4	no	—
397	#235	—	4	4	no	—
398	C₂×D₁₂	—	2	2	no	—
399	C₂×D₁₂	—	2	1	no	—
400	C₂×D₁₂	—	2	1	no	—
401	C₂×D₁₂	—	2	1	no	—
402	C₂×D₁₂	—	4	1	no	—
403	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
404	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
405	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄×D₃	—	2	1	no	—
407	C₂×C₄×D₃	—	2	1	no	—
408	C₂×C₄×D₃	—	2	1	no	—
409	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
410	C₂×Dic₆	—	2	1	no	—
411	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
413	C₃×C₄⋊C₄	—	2	1	no	—
414	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
415	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
416	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
417	C₃×C₂²⋊C₄	—	2	1	no	—
418	#217	C₅×D₄	1	1	yes	characteristic
419	#213	—	4	1	no	—
420	(C₂×D₃)⋊C₄	—	2	1	no	—
421	(C₂×D₃)⋊C₄	—	2	1	no	—
422	(C₂×D₃)⋊C₄	—	2	1	no	—
423	(C₂×D₃)⋊C₄	—	2	1	no	—
424	(C₂×D₃)⋊C₄	—	2	1	no	—
425	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
426	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
427	Dic₃⋊C₄	—	2	1	no	—
428	Dic₃⋊C₄	—	2	1	no	—
429	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
430	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₃⋊C₈	—	4	1	no	—
432	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
433	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
434	D₂₄	—	2	2	no	—
435	D₂₄	—	4	1	no	—
436	D₃×C₈	—	4	1	no	—
437	C₂³×C₅	—	2	1	no	—
438	C₂³×C₅	—	3	1	no	—
439	C₂³×C₅	—	6	1	no	—
440	C₂³×C₅	—	6	1	no	—
441	C₂³×C₅	—	6	1	no	—
442	C₂³×C₅	—	12	2	no	—
443	C₂³×C₅	—	12	2	no	—
444	C₂³×C₅	—	12	2	no	—
445	C₂³×C₅	—	12	2	no	—
446	C₂³×C₅	—	24	1	no	—
447	C₂³×C₅	—	24	1	no	—
448	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
449	C₅×Q₈	—	12	2	no	—
450	C₅×D₄	—	2	1	no	—
451	C₅×D₄	—	2	1	no	—
452	C₅×D₄	—	3	4	no	—
453	C₅×D₄	—	3	2	no	—
454	C₅×D₄	—	4	2	no	—
455	C₅×D₄	—	6	1	no	—
456	C₅×D₄	—	6	1	no	—
457	C₅×D₄	—	6	1	no	—
458	C₅×D₄	—	6	1	no	—
459	C₅×D₄	—	6	1	no	—
460	C₅×D₄	—	12	2	no	—
461	C₅×D₄	—	12	2	no	—
462	C₅×D₄	—	12	2	no	—
463	C₅×D₄	—	12	2	no	—
464	C₅×D₄	—	12	2	no	—
465	C₅×D₄	—	12	2	no	—
466	C₅×D₄	—	24	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	3	1	no	—
473	C₂×C₄×C₅	—	3	1	no	—
474	C₂×C₄×C₅	—	3	1	no	—
475	C₂×C₄×C₅	—	4	2	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	12	2	no	—
480	C₂×C₄×C₅	—	12	2	no	—
481	C₂×C₄×C₅	—	12	2	no	—
482	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
484	C₅×C₈	—	2	1	no	—
485	C₅×C₈	—	2	1	no	—
486	C₅×C₈	—	6	1	no	—
487	C₅×C₈	—	6	1	no	—
488	C₂×#41	—	6	1	no	—
489	C₂²×D₄	—	3	1	no	—
490	C₂²×D₄	—	3	1	no	—
491	C₂²×D₄	—	6	1	no	—
492	C₂×D₈	—	3	1	no	—
493	C₂×D₈	—	3	1	no	—
494	C₂×D₈	—	3	1	no	—
495	C₂²×C₈	—	3	1	no	—
496	C₂²×C₈	—	3	1	no	—
497	C₄⋊Q₈	—	3	1	no	—
498	#127	—	3	1	no	—
499	#123	—	6	1	no	—
500	#123	—	6	1	no	—
501	C₂²⋊Q₈	—	6	1	no	—
502	#121	—	3	1	no	—
503	#121	—	3	1	no	—
504	#121	—	3	1	no	—
505	#121	—	6	1	no	—
506	#121	C₂×C₅×D₃	1	1	yes	characteristic
507	#120	—	6	1	no	—
508	#120	—	6	1	no	—
509	C₄×D₄	—	3	1	no	—
510	C₄×D₄	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₂×C₄⋊C₄	—	3	1	no	—
513	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
514	#107	—	3	1	no	—
515	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
516	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
517	C₄⋊C₈	—	3	1	no	—
518	#102	—	3	1	no	—
519	#102	—	3	1	no	—
520	#102	—	3	1	no	—
521	#102	—	3	1	no	—
522	#102	—	3	1	no	—
523	#102	—	3	1	no	—
524	#102	—	3	1	no	—
525	#102	—	3	1	no	—
526	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
527	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
528	C₂²⋊C₈	—	3	1	no	—
529	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
530	C₄×C₈	—	3	1	no	—
531	C₂×C₃×C₅	—	2	2	no	—
532	C₂×C₃×C₅	—	8	1	no	—
533	C₂×C₃×C₅	#546	1	1	yes	characteristic
534	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
535	C₂×C₃×C₅	#577	1	1	yes	characteristic
536	C₅×D₃	—	2	2	no	—
537	C₅×D₃	—	4	2	no	—
538	C₅×D₃	—	8	1	no	—
539	C₅×D₃	—	8	1	no	—
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂²×D₃	—	2	1	no	—
543	C₂²×D₃	—	2	1	no	—
544	C₂²×D₃	—	2	1	no	—
545	C₂²×D₃	—	4	2	no	—
546	C₂²×D₃	—	4	2	no	—
547	C₂²×D₃	—	4	2	no	—
548	C₂²×D₃	—	4	2	no	—
549	C₂²×D₃	—	8	1	no	—
550	C₂²×D₃	—	8	1	no	—
551	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
552	C₃×D₄	—	2	1	no	—
553	C₃×D₄	—	2	1	no	—
554	C₃×D₄	—	4	2	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	4	2	no	—
561	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
563	#67	—	4	2	no	—
564	#67	—	4	2	no	—
565	#67	—	4	2	no	—
566	#67	—	8	1	no	—
567	#67	C₅×D₈	1	4	yes	complemented
568	C₂×Dic₃	—	2	1	no	—
569	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
570	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
571	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
572	D₁₂	—	2	1	no	—
573	D₁₂	—	2	1	no	—
574	D₁₂	—	2	1	no	—
575	D₁₂	—	2	1	no	—
576	D₁₂	—	2	1	no	—
577	D₁₂	—	4	2	no	—
578	D₁₂	—	4	2	no	—
579	D₁₂	—	4	2	no	—
580	D₁₂	C₅×#41	1	2	yes	complemented
581	C₄×D₃	—	2	1	no	—
582	C₄×D₃	—	2	1	no	—
583	C₄×D₃	—	4	2	no	—
584	C₄×D₃	—	4	2	no	—
585	C₄×D₃	—	4	2	no	—
586	Dic₆	—	4	2	no	—
587	C₃×C₈	—	2	1	no	—
588	C₃×C₈	—	2	1	no	—
589	C₃⋊C₈	—	2	1	no	—
590	C₃⋊C₈	—	2	1	no	—
591	C₂²×C₅	—	2	1	no	—
592	C₂²×C₅	—	2	1	no	—
593	C₂²×C₅	—	3	2	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	—	4	1	no	—
597	C₂²×C₅	—	6	1	no	—
598	C₂²×C₅	—	6	1	no	—
599	C₂²×C₅	—	6	2	no	—
600	C₂²×C₅	—	12	1	no	—
601	C₂²×C₅	—	12	1	no	—
602	C₂²×C₅	—	12	1	no	—
603	C₂²×C₅	—	12	1	no	—
604	C₂²×C₅	—	12	1	no	—
605	C₂²×C₅	—	12	1	no	—
606	C₂²×C₅	—	12	1	no	—
607	C₂²×C₅	—	12	1	no	—
608	C₂²×C₅	—	24	4	no	—
609	C₂²×C₅	—	24	4	no	—
610	C₂²×C₅	D₃×D₈	1	2	yes	—
611	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
612	C₄×C₅	—	2	1	no	—
613	C₄×C₅	—	3	2	no	—
614	C₄×C₅	—	4	1	no	—
615	C₄×C₅	—	4	1	no	—
616	C₄×C₅	—	4	1	no	—
617	C₄×C₅	—	6	1	no	—
618	C₄×C₅	—	6	1	no	—
619	C₄×C₅	—	12	1	no	—
620	C₄×C₅	D₃×#41	1	1	yes	characteristic
621	C₄×C₅	#1009	1	1	yes	characteristic
622	C₂⁴	—	6	1	no	—
623	C₂⁴	—	6	1	no	—
624	#41	—	12	4	no	—
625	C₂×Q₈	—	6	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	3	1	no	—
628	C₂×D₄	—	3	1	no	—
629	C₂×D₄	—	3	1	no	—
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	6	2	no	—
632	C₂×D₄	—	6	1	no	—
633	C₂×D₄	—	6	1	no	—
634	C₂×D₄	—	6	1	no	—
635	C₂×D₄	—	6	1	no	—
636	C₂×D₄	—	6	1	no	—
637	C₂×D₄	—	6	2	no	—
638	C₂×D₄	—	6	1	no	—
639	C₂×D₄	—	6	1	no	—
640	C₂×D₄	—	12	1	no	—
641	C₂×D₄	—	12	1	no	—
642	C₂×D₄	—	12	4	no	—
643	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	3	1	no	—
646	C₂²×C₄	—	6	1	no	—
647	C₂²×C₄	—	6	1	no	—
648	C₂²×C₄	—	6	1	no	—
649	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
650	D₈	—	6	2	no	—
651	D₈	—	12	1	no	—
652	D₈	—	12	1	no	—
653	C₂×C₈	—	3	1	no	—
654	C₂×C₈	—	3	1	no	—
655	C₂×C₈	—	12	1	no	—
656	C₂×C₈	—	12	1	no	—
657	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
658	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	3	1	no	—
661	C₄⋊C₄	—	3	1	no	—
662	C₄⋊C₄	—	6	1	no	—
663	C₄⋊C₄	—	6	1	no	—
664	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
666	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	3	1	no	—
669	C₂²⋊C₄	—	3	1	no	—
670	C₂²⋊C₄	—	6	1	no	—
671	C₂²⋊C₄	—	6	1	no	—
672	C₂²⋊C₄	—	6	1	no	—
673	C₂²⋊C₄	—	6	1	no	—
674	C₂²⋊C₄	—	6	1	no	—
675	C₄²	—	3	1	no	—
676	C₃×C₅	#3294	1	1	yes	characteristic, complemented, Hall
677	C₂²×C₃	—	2	1	no	—
678	C₂²×C₃	—	2	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	—	4	1	no	—
682	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
683	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
684	C₂×D₃	—	2	1	no	—
685	C₂×D₃	—	2	1	no	—
686	C₂×D₃	—	2	2	no	—
687	C₂×D₃	—	4	1	no	—
688	C₂×D₃	—	4	1	no	—
689	C₂×D₃	—	4	1	no	—
690	C₂×D₃	—	4	1	no	—
691	C₂×D₃	—	4	1	no	—
692	C₂×D₃	—	4	1	no	—
693	C₂×D₃	—	4	1	no	—
694	C₂×D₃	—	4	1	no	—
695	C₂×D₃	—	8	4	no	—
696	C₂×D₃	—	8	4	no	—
697	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
698	C₃×C₄	—	2	1	no	—
699	C₃×C₄	—	4	1	no	—
700	C₃×C₄	—	4	1	no	—
701	C₃×C₄	—	4	1	no	—
702	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
703	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
704	Dic₃	—	2	1	no	—
705	Dic₃	—	2	1	no	—
706	Dic₃	—	4	1	no	—
707	Dic₃	C₂×C₅×D₈	1	2	yes	—
708	C₂×C₅	—	2	2	no	—
709	C₂×C₅	—	6	2	no	—
710	C₂×C₅	—	8	1	no	—
711	C₂×C₅	—	12	2	no	—
712	C₂×C₅	—	24	1	no	—
713	C₂×C₅	—	24	1	no	—
714	C₂×C₅	#5654	1	1	yes	characteristic
715	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
716	C₂×C₅	#5778	1	1	yes	characteristic
717	C₂³	—	2	1	no	—
718	C₂³	—	3	1	no	—
719	C₂³	—	6	1	no	—
720	C₂³	—	6	1	no	—
721	C₂³	—	6	1	no	—
722	C₂³	—	12	2	no	—
723	C₂³	—	12	2	no	—
724	C₂³	—	12	2	no	—
725	C₂³	—	12	2	no	—
726	C₂³	—	24	1	no	—
727	C₂³	—	24	1	no	—
728	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
729	Q₈	—	12	2	no	—
730	D₄	—	2	1	no	—
731	D₄	—	2	1	no	—
732	D₄	—	3	4	no	—
733	D₄	—	3	2	no	—
734	D₄	—	4	2	no	—
735	D₄	—	6	1	no	—
736	D₄	—	6	1	no	—
737	D₄	—	6	1	no	—
738	D₄	—	6	1	no	—
739	D₄	—	6	1	no	—
740	D₄	—	12	2	no	—
741	D₄	—	12	2	no	—
742	D₄	—	12	2	no	—
743	D₄	—	12	2	no	—
744	D₄	—	12	2	no	—
745	D₄	—	12	2	no	—
746	D₄	—	24	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	3	1	no	—
753	C₂×C₄	—	3	1	no	—
754	C₂×C₄	—	3	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	6	1	no	—
757	C₂×C₄	—	6	1	no	—
758	C₂×C₄	—	6	1	no	—
759	C₂×C₄	—	12	2	no	—
760	C₂×C₄	—	12	2	no	—
761	C₂×C₄	—	12	2	no	—
762	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
763	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
764	C₈	—	2	1	no	—
765	C₈	—	2	1	no	—
766	C₈	—	6	1	no	—
767	C₈	—	6	1	no	—
768	C₂×C₃	—	2	2	no	—
769	C₂×C₃	—	8	1	no	—
770	C₂×C₃	C₅×#546	1	1	yes	characteristic
771	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
772	C₂×C₃	C₅×#577	1	1	yes	characteristic
773	D₃	—	2	2	no	—
774	D₃	—	4	2	no	—
775	D₃	—	8	1	no	—
776	D₃	—	8	1	no	—
777	C₅	#81302	1	1	yes	characteristic, direct product factor, Sylow
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	3	2	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	6	1	no	—
785	C₂²	—	6	1	no	—
786	C₂²	—	6	2	no	—
787	C₂²	—	12	1	no	—
788	C₂²	—	12	1	no	—
789	C₂²	—	12	1	no	—
790	C₂²	—	12	1	no	—
791	C₂²	—	12	1	no	—
792	C₂²	—	12	1	no	—
793	C₂²	—	12	1	no	—
794	C₂²	—	12	1	no	—
795	C₂²	—	24	4	no	—
796	C₂²	—	24	4	no	—
797	C₂²	C₅×D₃×D₈	1	2	yes	—
798	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
799	C₄	—	2	1	no	—
800	C₄	—	3	2	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	6	1	no	—
805	C₄	—	6	1	no	—
806	C₄	—	12	1	no	—
807	C₄	C₅×D₃×#41	1	1	yes	characteristic
808	C₄	C₅×#1009	1	1	yes	characteristic
809	C₃	C₅×#3294	1	1	yes	characteristic, complemented, Sylow
810	C₂	—	2	2	no	—
811	C₂	—	6	2	no	—
812	C₂	—	8	1	no	—
813	C₂	—	12	2	no	—
814	C₂	—	24	1	no	—
815	C₂	—	24	1	no	—
816	C₂	C₅×#5654	1	1	yes	characteristic
817	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
818	C₂	C₅×#5778	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×#480	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#480	D₃
hypocenter	C₃	C₅×#3294
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#480

Complements

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

N	H ≅ G/N	type
1. C₅×#5609	C₂	semidirect
2. C₅×#5507	C₂	semidirect
3. C₃×C₅×#480	C₂	semidirect
4. C₅×#5038	C₂	semidirect
5. C₂×C₅×#809	C₂	semidirect
6. C₅×#4890	C₂	semidirect
7. C₅×#4883	C₂	semidirect
8. C₅×#4882	C₂	semidirect
9. C₅×#4872	C₂	semidirect
10. C₅×#4786	C₂	semidirect
11. C₅×#4773	C₂	semidirect
12. C₅×D₃×#102	C₂	semidirect
13. C₅×#4760	C₂	semidirect
14. C₅×#4732	C₂	semidirect
15. C₅×#67⋊C₈	C₂	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
25. C₂×C₅×#213	C₂²	semidirect
26. C₅×#930	C₂²	semidirect
29. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
31. C₂×C₅×D₂₄	C₂²	semidirect
32. C₂×C₅×D₃×C₈	C₂²	semidirect
35. C₅×#895	C₂²	semidirect
38. C₅×#893	C₂²	semidirect
39. C₅×D₃×C₄⋊C₄	C₂²	semidirect
40. C₅×#888	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#107	C₂²	semidirect
45. C₃×C₅×#102	C₂²	semidirect
46. C₃×C₅×#102	C₂²	semidirect
47. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
48. C₅×#832	C₂²	semidirect
50. C₅×#821	C₂²	semidirect
51. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
52. C₅×Dic₃⋊C₈	C₂²	semidirect
53. C₅×C₈×Dic₃	C₂²	semidirect
56. C₅×#809	C₂²	semidirect
57. C₅×#809	C₂²	semidirect
58. C₅×#809	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. #81302	C₅	direct (N × H)
65. C₅×#480	D₃	semidirect
130. #5609	C₂×C₅	semidirect
131. #5507	C₂×C₅	semidirect
132. C₃×#480	C₂×C₅	semidirect
133. #5038	C₂×C₅	semidirect
134. C₂×#809	C₂×C₅	semidirect
135. #4890	C₂×C₅	semidirect
136. #4883	C₂×C₅	semidirect
137. #4882	C₂×C₅	semidirect
138. #4872	C₂×C₅	semidirect
139. #4786	C₂×C₅	semidirect
140. #4773	C₂×C₅	semidirect
141. D₃×#102	C₂×C₅	semidirect
142. #4760	C₂×C₅	semidirect
143. #4732	C₂×C₅	semidirect
144. #67⋊C₈	C₂×C₅	semidirect
170. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
172. C₅×#107	C₂×D₃	semidirect
173. C₅×#107	C₂×D₃	semidirect
183. C₅×#102	C₂×D₃	semidirect
184. C₅×#102	C₂×D₃	semidirect
186. C₅×C₂²⋊C₈	C₂×D₃	semidirect
216. C₅×#67	D₈	semidirect
229. C₅×D₁₂	#41	semidirect
245. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
248. C₂×#213	C₂²×C₅	semidirect
249. #930	C₂²×C₅	semidirect
252. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
254. C₂×D₂₄	C₂²×C₅	semidirect
255. C₂×D₃×C₈	C₂²×C₅	semidirect
258. #895	C₂²×C₅	semidirect
261. #893	C₂²×C₅	semidirect
262. D₃×C₄⋊C₄	C₂²×C₅	semidirect
263. #888	C₂²×C₅	semidirect
266. C₃×#107	C₂²×C₅	semidirect
267. C₃×#107	C₂²×C₅	semidirect
268. C₃×#102	C₂²×C₅	semidirect
269. C₃×#102	C₂²×C₅	semidirect
270. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
271. #832	C₂²×C₅	semidirect
273. #821	C₂²×C₅	semidirect
274. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
275. Dic₃⋊C₈	C₂²×C₅	semidirect
276. C₈×Dic₃	C₂²×C₅	semidirect
279. #809	C₂²×C₅	semidirect
280. #809	C₂²×C₅	semidirect
281. #809	C₂²×C₅	semidirect
282. #807	C₂²×C₅	semidirect
341. #480	C₅×D₃	semidirect
513. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
515. #107	C₂×C₅×D₃	semidirect
516. #107	C₂×C₅×D₃	semidirect
526. #102	C₂×C₅×D₃	semidirect
527. #102	C₂×C₅×D₃	semidirect
529. C₂²⋊C₈	C₂×C₅×D₃	semidirect
567. #67	C₅×D₈	semidirect
580. D₁₂	C₅×#41	semidirect
676. C₃×C₅	#3294	semidirect
777. C₅	#81302	direct (N × H)
809. C₃	C₅×#3294	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5609	2
C₅×#5507	2
C₃×C₅×#480	2
C₅×#5038	2
C₂×C₅×#809	2
C₅×#4890	2
C₅×#4883	2
C₅×#4882	2
C₅×#4872	2
C₅×#4786	2
C₅×#4773	2
C₅×D₃×#102	2
C₅×#4760	2
C₅×#4732	2
C₅×#67⋊C₈	2
C₅×#3294	3
#81302	5

Subgroups — C5×#81302 #14458287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81302 #14458287