Subgroups — C₅×#80597 #14426223

Order 1920.

992 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	C₂×C₅×#919	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#916	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5668	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5182	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5163	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5028	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4844	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4818	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4804	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3035	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×C₅×#239	C₂²	1	1	yes	characteristic
19	C₂×C₅×#237	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₃×C₅×#124	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
25	C₅×#944	C₂²	1	1	yes	characteristic
26	C₂×C₅×#216	C₂²	1	1	yes	characteristic
27	C₂×C₅×#215	C₂²	1	1	yes	characteristic
28	C₂×C₅×#215	C₂²	1	1	yes	characteristic
29	C₅×#940	C₂²	1	1	yes	characteristic
30	C₂×C₅×#213	C₂²	1	1	yes	characteristic
31	C₅×#919	—	2	4	no	—
32	C₅×#916	—	2	4	no	—
33	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×#204	C₂²	1	1	yes	characteristic
35	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₅×#893	—	2	1	no	—
38	C₅×#893	C₂²	1	1	yes	characteristic
39	C₅×#892	—	2	1	no	—
40	C₅×#892	C₂²	1	1	yes	characteristic
41	C₅×#884	—	2	1	no	—
42	C₅×#884	—	2	1	no	—
43	C₅×#67⋊C₄	—	2	1	no	—
44	C₅×#67⋊C₄	—	2	1	no	—
45	C₅×#875	C₂²	1	1	yes	characteristic
46	C₄×C₅×D₁₂	—	2	1	no	—
47	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
48	C₄²×C₅×D₃	—	2	1	no	—
49	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₅×#835	C₂²	1	1	yes	characteristic
54	C₅×#832	C₂²	1	1	yes	characteristic
55	C₅×#821	C₂²	1	1	yes	characteristic
56	C₅×#816	C₂²	1	1	yes	characteristic
57	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×#810	C₂²	1	1	yes	characteristic
60	C₅×#809	C₂²	1	1	yes	characteristic
61	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
62	#80597	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#135	—	3	1	no	—
64	C₂×C₅×#135	—	3	1	no	—
65	C₅×#532	—	3	1	no	—
66	C₄×C₅×#41	—	3	1	no	—
67	C₅×#464	—	3	1	no	—
68	C₅×#464	D₃	1	1	yes	characteristic, complemented
69	C₅×#463	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#462	—	3	1	no	—
72	C₅×#461	—	3	1	no	—
73	C₅×#460	—	3	1	no	—
74	C₅×#459	—	3	1	no	—
75	C₂×C₅×C₄⋊C₈	—	3	1	no	—
76	C₅×#416	—	3	1	no	—
77	C₅×#416	—	3	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×#67	—	2	1	no	—
82	C₂×C₅×#67	—	2	1	no	—
83	C₂×C₅×#67	—	2	1	no	—
84	C₂²×C₅×Dic₃	—	2	1	no	—
85	C₅×#239	—	2	2	no	—
86	C₅×#239	—	2	2	no	—
87	C₅×#239	—	2	2	no	—
88	C₅×#239	D₄	1	4	yes	complemented
89	C₅×#237	—	2	2	no	—
90	C₅×#237	—	2	2	no	—
91	C₂×C₅×D₁₂	—	2	1	no	—
92	C₂×C₅×D₁₂	—	2	1	no	—
93	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
94	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	—	2	1	no	—
96	C₂×C₄×C₅×D₃	—	2	1	no	—
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	—	2	1	no	—
99	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
102	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
103	C₃×C₅×Q₁₆	—	2	2	no	—
104	C₃×C₅×SD₁₆	—	2	2	no	—
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₄²×C₅	—	2	1	no	—
112	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₅×#216	—	2	2	no	—
114	C₅×#215	—	2	2	no	—
115	C₅×#215	—	2	2	no	—
116	C₅×#213	—	2	2	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×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
122	C₅×C₄⋊Dic₃	—	2	1	no	—
123	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
124	C₅×Dic₃⋊C₄	—	2	1	no	—
125	C₅×Dic₃⋊C₄	—	2	1	no	—
126	C₄×C₅×Dic₃	—	2	1	no	—
127	C₄×C₅×Dic₃	—	2	1	no	—
128	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
129	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
130	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
131	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
133	C₅×D₂₄	—	2	2	no	—
134	C₅×#204	—	2	2	no	—
135	C₅×D₃×C₈	—	2	2	no	—
136	C₅×D₃×C₈	—	2	2	no	—
137	C₂×#919	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#916	C₂×C₅	1	1	yes	characteristic, complemented
139	#5668	C₂×C₅	1	1	yes	characteristic, complemented
140	C₄×#239	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
142	#5182	C₂×C₅	1	1	yes	characteristic, complemented
143	#5163	C₂×C₅	1	1	yes	characteristic, complemented
144	#5057	C₂×C₅	1	1	yes	characteristic, complemented
145	#5028	C₂×C₅	1	1	yes	characteristic, complemented
146	#4844	C₂×C₅	1	1	yes	characteristic, complemented
147	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
148	#4818	C₂×C₅	1	1	yes	characteristic, complemented
149	#4804	C₂×C₅	1	1	yes	characteristic, complemented
150	#4786	C₂×C₅	1	1	yes	characteristic, complemented
151	#4772	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×C₅×#41	—	3	1	no	—
153	C₂×C₅×#41	—	3	1	no	—
154	C₂×C₅×#41	—	3	1	no	—
155	C₅×#135	—	6	4	no	—
156	C₅×#135	—	6	4	no	—
157	C₂×C₅×Q₁₆	—	3	1	no	—
158	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
159	C₂×C₅×SD₁₆	—	3	1	no	—
160	C₂×C₅×SD₁₆	—	3	1	no	—
161	C₂×C₅×SD₁₆	—	3	1	no	—
162	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
163	C₂×C₅×D₈	—	3	1	no	—
164	C₂×C₅×D₈	—	3	1	no	—
165	C₂²×C₅×C₈	—	3	1	no	—
166	C₂²×C₅×C₈	—	3	1	no	—
167	C₅×C₄⋊Q₈	—	3	1	no	—
168	C₅×#127	—	3	1	no	—
169	C₅×#124	—	3	1	no	—
170	C₅×#124	C₂×D₃	1	1	yes	characteristic
171	C₅×#121	—	6	1	no	—
172	C₅×#121	—	6	1	no	—
173	C₄×C₅×Q₈	—	3	1	no	—
174	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
175	C₄×C₅×D₄	—	3	1	no	—
176	C₄×C₅×D₄	—	3	1	no	—
177	C₄×C₅×D₄	—	6	1	no	—
178	C₄×C₅×D₄	—	6	1	no	—
179	C₄×C₅×D₄	—	6	1	no	—
180	C₄×C₅×D₄	—	6	1	no	—
181	C₅×#117	—	3	1	no	—
182	C₅×#117	—	6	1	no	—
183	C₂×C₄²×C₅	—	3	1	no	—
184	C₂×C₄²×C₅	—	6	1	no	—
185	C₅×C₄⋊C₈	—	3	1	no	—
186	C₅×C₄⋊C₈	—	3	1	no	—
187	C₅×C₄⋊C₈	—	3	1	no	—
188	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
189	C₅×#103	—	3	1	no	—
190	C₅×#103	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	C₂×D₃	1	1	yes	characteristic
193	C₅×#102	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	C₂×D₃	1	1	yes	characteristic
197	#3035	—	3	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	1	no	—
200	C₂²×C₅×D₃	—	2	1	no	—
201	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
202	C₃×C₅×Q₈	—	2	1	no	—
203	C₃×C₅×Q₈	—	2	1	no	—
204	C₃×C₅×Q₈	—	2	1	no	—
205	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
216	C₅×#67	—	4	2	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	4	2	no	—
220	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
221	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
222	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
223	C₅×D₁₂	—	2	4	no	—
224	C₅×D₁₂	—	2	1	no	—
225	C₅×D₁₂	—	2	1	no	—
226	C₅×D₁₂	—	2	1	no	—
227	C₅×D₁₂	—	4	2	no	—
228	C₅×D₁₂	C₂×D₄	1	2	yes	—
229	C₄×C₅×D₃	—	2	4	no	—
230	C₄×C₅×D₃	—	2	2	no	—
231	C₄×C₅×D₃	—	4	1	no	—
232	C₄×C₅×D₃	—	4	2	no	—
233	C₄×C₅×D₃	—	4	2	no	—
234	C₄×C₅×D₃	—	4	2	no	—
235	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
236	C₄×C₅×D₃	#41	1	2	yes	—
237	C₅×Dic₆	—	2	1	no	—
238	C₅×Dic₆	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₃×C₅×C₈	—	2	1	no	—
241	C₅×C₃⋊C₈	—	2	1	no	—
242	C₅×C₃⋊C₈	—	2	1	no	—
243	C₂×#239	C₂²×C₅	1	1	yes	characteristic
244	C₂×#239	C₂²×C₅	1	1	yes	characteristic
245	C₂×#237	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
248	C₃×#124	C₂²×C₅	1	1	yes	characteristic
249	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
250	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
251	#944	C₂²×C₅	1	1	yes	characteristic
252	C₂×#216	C₂²×C₅	1	1	yes	characteristic
253	C₂×#215	C₂²×C₅	1	1	yes	characteristic
254	C₂×#215	C₂²×C₅	1	1	yes	characteristic
255	#940	C₂²×C₅	1	1	yes	characteristic
256	C₂×#213	C₂²×C₅	1	1	yes	characteristic
257	#919	—	2	4	no	—
258	#916	—	2	4	no	—
259	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×#204	C₂²×C₅	1	1	yes	characteristic
261	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
263	#893	—	2	1	no	—
264	#893	C₂²×C₅	1	1	yes	characteristic
265	#892	—	2	1	no	—
266	#892	C₂²×C₅	1	1	yes	characteristic
267	#884	—	2	1	no	—
268	#884	—	2	1	no	—
269	#67⋊C₄	—	2	1	no	—
270	#67⋊C₄	—	2	1	no	—
271	#875	C₂²×C₅	1	1	yes	characteristic
272	C₄×D₁₂	—	2	1	no	—
273	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
274	C₄²×D₃	—	2	1	no	—
275	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
276	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	C₃×#103	C₂²×C₅	1	1	yes	characteristic
278	C₃×#102	C₂²×C₅	1	1	yes	characteristic
279	#835	C₂²×C₅	1	1	yes	characteristic
280	#832	C₂²×C₅	1	1	yes	characteristic
281	#821	C₂²×C₅	1	1	yes	characteristic
282	#816	C₂²×C₅	1	1	yes	characteristic
283	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
284	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
285	#810	C₂²×C₅	1	1	yes	characteristic
286	#809	C₂²×C₅	1	1	yes	characteristic
287	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
288	C₅×#41	—	3	4	no	—
289	C₅×#41	—	6	2	no	—
290	C₅×#41	—	6	2	no	—
291	C₅×#41	—	6	2	no	—
292	C₅×#41	—	6	2	no	—
293	C₅×#41	—	6	2	no	—
294	C₂×C₅×Q₈	—	3	1	no	—
295	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
296	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂×C₅×D₄	—	3	1	no	—
299	C₂×C₅×D₄	—	6	1	no	—
300	C₂×C₅×D₄	—	6	1	no	—
301	C₂×C₅×D₄	—	6	1	no	—
302	C₂×C₅×D₄	—	6	1	no	—
303	C₂×C₅×D₄	—	6	1	no	—
304	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	6	1	no	—
309	C₂²×C₄×C₅	—	6	1	no	—
310	C₂²×C₄×C₅	—	6	1	no	—
311	C₂²×C₄×C₅	—	6	1	no	—
312	C₂²×C₄×C₅	—	6	1	no	—
313	C₅×Q₁₆	—	2	2	no	—
314	C₅×Q₁₆	—	6	2	no	—
315	C₅×SD₁₆	—	2	2	no	—
316	C₅×SD₁₆	—	6	2	no	—
317	C₅×SD₁₆	—	6	2	no	—
318	C₅×SD₁₆	—	6	2	no	—
319	C₅×D₈	—	6	2	no	—
320	C₅×D₈	—	6	2	no	—
321	C₂×C₅×C₈	—	3	1	no	—
322	C₂×C₅×C₈	—	3	1	no	—
323	C₂×C₅×C₈	—	6	2	no	—
324	C₂×C₅×C₈	—	6	2	no	—
325	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
326	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
327	C₅×C₄⋊C₄	—	2	1	no	—
328	C₅×C₄⋊C₄	—	3	1	no	—
329	C₅×C₄⋊C₄	—	6	1	no	—
330	C₅×C₄⋊C₄	—	6	1	no	—
331	C₅×C₄⋊C₄	—	6	1	no	—
332	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
333	C₅×C₂²⋊C₄	—	2	1	no	—
334	C₅×C₂²⋊C₄	—	2	1	no	—
335	C₅×C₂²⋊C₄	—	6	1	no	—
336	C₅×C₂²⋊C₄	—	6	1	no	—
337	C₅×C₂²⋊C₄	—	6	1	no	—
338	C₅×C₂²⋊C₄	—	6	1	no	—
339	C₅×C₂²⋊C₄	—	6	1	no	—
340	C₄²×C₅	—	2	1	no	—
341	C₄²×C₅	—	3	1	no	—
342	C₄²×C₅	—	3	1	no	—
343	C₄²×C₅	—	3	1	no	—
344	C₄²×C₅	—	6	1	no	—
345	C₄²×C₅	—	6	1	no	—
346	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
347	C₂×#135	—	3	1	no	—
348	C₂×#135	—	3	1	no	—
349	#532	—	3	1	no	—
350	C₄×#41	—	3	1	no	—
351	#464	—	3	1	no	—
352	#464	C₅×D₃	1	1	yes	characteristic, complemented
353	#463	—	3	1	no	—
354	#463	—	3	1	no	—
355	#462	—	3	1	no	—
356	#461	—	3	1	no	—
357	#460	—	3	1	no	—
358	#459	—	3	1	no	—
359	C₂×C₄⋊C₈	—	3	1	no	—
360	#416	—	3	1	no	—
361	#416	—	3	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	—	4	1	no	—
365	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₅×D₃	—	2	1	no	—
367	C₂×C₅×D₃	—	2	1	no	—
368	C₂×C₅×D₃	—	2	2	no	—
369	C₂×C₅×D₃	—	4	1	no	—
370	C₂×C₅×D₃	—	4	1	no	—
371	C₂×C₅×D₃	—	4	1	no	—
372	C₂×C₅×D₃	—	4	1	no	—
373	C₂×C₅×D₃	—	4	1	no	—
374	C₂×C₅×D₃	#121	1	2	yes	—
375	C₃×C₄×C₅	—	2	2	no	—
376	C₃×C₄×C₅	—	2	1	no	—
377	C₃×C₄×C₅	—	2	1	no	—
378	C₃×C₄×C₅	—	4	1	no	—
379	C₃×C₄×C₅	—	4	1	no	—
380	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
381	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
382	C₅×Dic₃	—	2	1	no	—
383	C₅×Dic₃	—	4	1	no	—
384	C₅×Dic₃	—	4	1	no	—
385	C₅×Dic₃	#121	1	2	yes	—
386	C₅×Dic₃	#135	1	2	yes	complemented
387	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×#67	—	2	1	no	—
391	C₂×#67	—	2	1	no	—
392	C₂×#67	—	2	1	no	—
393	C₂²×Dic₃	—	2	1	no	—
394	#239	—	2	2	no	—
395	#239	—	2	2	no	—
396	#239	—	2	2	no	—
397	#239	C₅×D₄	1	4	yes	complemented
398	#237	—	2	2	no	—
399	#237	—	2	2	no	—
400	C₂×D₁₂	—	2	1	no	—
401	C₂×D₁₂	—	2	1	no	—
402	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
403	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄×D₃	—	2	1	no	—
405	C₂×C₄×D₃	—	2	1	no	—
406	C₂×C₄×D₃	—	2	1	no	—
407	C₂×C₄×D₃	—	2	1	no	—
408	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
409	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
410	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
411	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
412	C₃×Q₁₆	—	2	2	no	—
413	C₃×SD₁₆	—	2	2	no	—
414	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₃×C₄⋊C₄	—	2	1	no	—
417	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₄²	—	2	1	no	—
421	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
422	#216	—	2	2	no	—
423	#215	—	2	2	no	—
424	#215	—	2	2	no	—
425	#213	—	2	2	no	—
426	(C₂×D₃)⋊C₄	—	2	1	no	—
427	(C₂×D₃)⋊C₄	—	2	1	no	—
428	(C₂×D₃)⋊C₄	—	2	1	no	—
429	(C₂×D₃)⋊C₄	—	2	1	no	—
430	(C₂×D₃)⋊C₄	—	2	1	no	—
431	C₄⋊Dic₃	—	2	1	no	—
432	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
433	Dic₃⋊C₄	—	2	1	no	—
434	Dic₃⋊C₄	—	2	1	no	—
435	C₄×Dic₃	—	2	1	no	—
436	C₄×Dic₃	—	2	1	no	—
437	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
438	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
439	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
442	D₂₄	—	2	2	no	—
443	#204	—	2	2	no	—
444	D₃×C₈	—	2	2	no	—
445	D₃×C₈	—	2	2	no	—
446	C₂³×C₅	—	2	1	no	—
447	C₂³×C₅	—	3	1	no	—
448	C₂³×C₅	—	6	1	no	—
449	C₂³×C₅	—	6	1	no	—
450	C₅×Q₈	—	2	1	no	—
451	C₅×Q₈	—	2	1	no	—
452	C₅×Q₈	—	2	1	no	—
453	C₅×Q₈	—	6	1	no	—
454	C₅×Q₈	—	6	1	no	—
455	C₅×Q₈	D₃×D₄	1	2	yes	—
456	C₅×D₄	—	2	1	no	—
457	C₅×D₄	—	2	1	no	—
458	C₅×D₄	—	3	2	no	—
459	C₅×D₄	—	6	4	no	—
460	C₅×D₄	—	6	1	no	—
461	C₅×D₄	—	6	1	no	—
462	C₅×D₄	—	6	1	no	—
463	C₅×D₄	—	12	2	no	—
464	C₅×D₄	—	12	2	no	—
465	C₅×D₄	—	12	2	no	—
466	C₅×D₄	—	12	2	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	—	3	1	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	2	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	3	1	no	—
475	C₂×C₄×C₅	—	6	2	no	—
476	C₂×C₄×C₅	—	6	4	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	12	1	no	—
480	C₂×C₄×C₅	—	12	2	no	—
481	C₂×C₄×C₅	—	12	2	no	—
482	C₂×C₄×C₅	—	12	2	no	—
483	C₂×C₄×C₅	—	12	2	no	—
484	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
485	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
486	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
487	C₅×C₈	—	2	1	no	—
488	C₅×C₈	—	2	1	no	—
489	C₅×C₈	—	6	1	no	—
490	C₅×C₈	—	6	1	no	—
491	C₂×#41	—	3	1	no	—
492	C₂×#41	—	3	1	no	—
493	C₂×#41	—	3	1	no	—
494	#135	—	6	4	no	—
495	#135	—	6	4	no	—
496	C₂×Q₁₆	—	3	1	no	—
497	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
498	C₂×SD₁₆	—	3	1	no	—
499	C₂×SD₁₆	—	3	1	no	—
500	C₂×SD₁₆	—	3	1	no	—
501	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
502	C₂×D₈	—	3	1	no	—
503	C₂×D₈	—	3	1	no	—
504	C₂²×C₈	—	3	1	no	—
505	C₂²×C₈	—	3	1	no	—
506	C₄⋊Q₈	—	3	1	no	—
507	#127	—	3	1	no	—
508	#124	—	3	1	no	—
509	#124	C₂×C₅×D₃	1	1	yes	characteristic
510	#121	—	6	1	no	—
511	#121	—	6	1	no	—
512	C₄×Q₈	—	3	1	no	—
513	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	6	1	no	—
517	C₄×D₄	—	6	1	no	—
518	C₄×D₄	—	6	1	no	—
519	C₄×D₄	—	6	1	no	—
520	#117	—	3	1	no	—
521	#117	—	6	1	no	—
522	C₂×C₄²	—	3	1	no	—
523	C₂×C₄²	—	6	1	no	—
524	C₄⋊C₈	—	3	1	no	—
525	C₄⋊C₈	—	3	1	no	—
526	C₄⋊C₈	—	3	1	no	—
527	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
528	#103	—	3	1	no	—
529	#103	—	3	1	no	—
530	#103	—	3	1	no	—
531	#103	C₂×C₅×D₃	1	1	yes	characteristic
532	#102	—	3	1	no	—
533	#102	—	3	1	no	—
534	#102	—	3	1	no	—
535	#102	C₂×C₅×D₃	1	1	yes	characteristic
536	C₂×C₃×C₅	—	8	1	no	—
537	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
538	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
539	C₂×C₃×C₅	#575	1	1	yes	characteristic
540	C₅×D₃	—	2	2	no	—
541	C₅×D₃	—	4	2	no	—
542	C₅×D₃	—	8	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂²×D₃	—	2	1	no	—
545	C₂²×D₃	—	2	1	no	—
546	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
547	C₃×Q₈	—	2	1	no	—
548	C₃×Q₈	—	2	1	no	—
549	C₃×Q₈	—	2	1	no	—
550	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
551	C₃×D₄	—	2	1	no	—
552	C₃×D₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
557	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
558	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
559	#67	—	4	2	no	—
560	#67	—	4	2	no	—
561	#67	—	4	2	no	—
562	C₂×Dic₃	—	2	1	no	—
563	C₂×Dic₃	—	2	1	no	—
564	C₂×Dic₃	—	4	2	no	—
565	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
566	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
567	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
568	D₁₂	—	2	4	no	—
569	D₁₂	—	2	1	no	—
570	D₁₂	—	2	1	no	—
571	D₁₂	—	2	1	no	—
572	D₁₂	—	4	2	no	—
573	D₁₂	C₂×C₅×D₄	1	2	yes	—
574	C₄×D₃	—	2	4	no	—
575	C₄×D₃	—	2	2	no	—
576	C₄×D₃	—	4	1	no	—
577	C₄×D₃	—	4	2	no	—
578	C₄×D₃	—	4	2	no	—
579	C₄×D₃	—	4	2	no	—
580	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
581	C₄×D₃	C₅×#41	1	2	yes	—
582	Dic₆	—	2	1	no	—
583	Dic₆	—	2	1	no	—
584	C₃×C₈	—	2	1	no	—
585	C₃×C₈	—	2	1	no	—
586	C₃⋊C₈	—	2	1	no	—
587	C₃⋊C₈	—	2	1	no	—
588	C₂²×C₅	—	3	2	no	—
589	C₂²×C₅	—	4	1	no	—
590	C₂²×C₅	—	4	1	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	6	1	no	—
593	C₂²×C₅	—	6	1	no	—
594	C₂²×C₅	—	6	2	no	—
595	C₂²×C₅	—	12	1	no	—
596	C₂²×C₅	—	12	1	no	—
597	C₂²×C₅	—	12	1	no	—
598	C₂²×C₅	—	12	1	no	—
599	C₂²×C₅	—	12	1	no	—
600	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
601	C₄×C₅	—	2	1	no	—
602	C₄×C₅	—	2	1	no	—
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	3	2	no	—
605	C₄×C₅	—	3	2	no	—
606	C₄×C₅	—	4	1	no	—
607	C₄×C₅	—	4	1	no	—
608	C₄×C₅	—	6	1	no	—
609	C₄×C₅	—	12	1	no	—
610	C₄×C₅	—	12	1	no	—
611	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
612	C₄×C₅	D₃×#41	1	1	yes	characteristic
613	#41	—	3	4	no	—
614	#41	—	6	2	no	—
615	#41	—	6	2	no	—
616	#41	—	6	2	no	—
617	#41	—	6	2	no	—
618	#41	—	6	2	no	—
619	C₂×Q₈	—	3	1	no	—
620	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
621	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₂×D₄	—	3	1	no	—
623	C₂×D₄	—	3	1	no	—
624	C₂×D₄	—	6	1	no	—
625	C₂×D₄	—	6	1	no	—
626	C₂×D₄	—	6	1	no	—
627	C₂×D₄	—	6	1	no	—
628	C₂×D₄	—	6	1	no	—
629	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
630	C₂²×C₄	—	3	1	no	—
631	C₂²×C₄	—	3	1	no	—
632	C₂²×C₄	—	3	1	no	—
633	C₂²×C₄	—	6	1	no	—
634	C₂²×C₄	—	6	1	no	—
635	C₂²×C₄	—	6	1	no	—
636	C₂²×C₄	—	6	1	no	—
637	C₂²×C₄	—	6	1	no	—
638	Q₁₆	—	2	2	no	—
639	Q₁₆	—	6	2	no	—
640	SD₁₆	—	2	2	no	—
641	SD₁₆	—	6	2	no	—
642	SD₁₆	—	6	2	no	—
643	SD₁₆	—	6	2	no	—
644	D₈	—	6	2	no	—
645	D₈	—	6	2	no	—
646	C₂×C₈	—	3	1	no	—
647	C₂×C₈	—	3	1	no	—
648	C₂×C₈	—	6	2	no	—
649	C₂×C₈	—	6	2	no	—
650	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
651	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	3	1	no	—
654	C₄⋊C₄	—	6	1	no	—
655	C₄⋊C₄	—	6	1	no	—
656	C₄⋊C₄	—	6	1	no	—
657	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	6	1	no	—
661	C₂²⋊C₄	—	6	1	no	—
662	C₂²⋊C₄	—	6	1	no	—
663	C₂²⋊C₄	—	6	1	no	—
664	C₂²⋊C₄	—	6	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	3	1	no	—
667	C₄²	—	3	1	no	—
668	C₄²	—	3	1	no	—
669	C₄²	—	6	1	no	—
670	C₄²	—	6	1	no	—
671	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
672	C₃×C₅	#3035	1	1	yes	characteristic, complemented, Hall
673	C₂²×C₃	—	4	1	no	—
674	C₂²×C₃	—	4	1	no	—
675	C₂²×C₃	—	4	1	no	—
676	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
677	C₂×D₃	—	2	1	no	—
678	C₂×D₃	—	2	1	no	—
679	C₂×D₃	—	2	2	no	—
680	C₂×D₃	—	4	1	no	—
681	C₂×D₃	—	4	1	no	—
682	C₂×D₃	—	4	1	no	—
683	C₂×D₃	—	4	1	no	—
684	C₂×D₃	—	4	1	no	—
685	C₂×D₃	C₅×#121	1	2	yes	—
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	2	1	no	—
688	C₃×C₄	—	2	1	no	—
689	C₃×C₄	—	4	1	no	—
690	C₃×C₄	—	4	1	no	—
691	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
692	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
693	Dic₃	—	2	1	no	—
694	Dic₃	—	4	1	no	—
695	Dic₃	—	4	1	no	—
696	Dic₃	C₅×#121	1	2	yes	—
697	Dic₃	C₅×#135	1	2	yes	complemented
698	C₂×C₅	—	6	2	no	—
699	C₂×C₅	—	8	1	no	—
700	C₂×C₅	—	12	2	no	—
701	C₂×C₅	—	24	1	no	—
702	C₂×C₅	D₃×#121	1	1	yes	characteristic
703	C₂×C₅	D₃×#135	1	1	yes	characteristic
704	C₂×C₅	#5777	1	1	yes	characteristic
705	C₂³	—	2	1	no	—
706	C₂³	—	3	1	no	—
707	C₂³	—	6	1	no	—
708	C₂³	—	6	1	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	2	1	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	6	1	no	—
713	Q₈	—	6	1	no	—
714	Q₈	C₅×D₃×D₄	1	2	yes	—
715	D₄	—	2	1	no	—
716	D₄	—	2	1	no	—
717	D₄	—	3	2	no	—
718	D₄	—	6	4	no	—
719	D₄	—	6	1	no	—
720	D₄	—	6	1	no	—
721	D₄	—	6	1	no	—
722	D₄	—	12	2	no	—
723	D₄	—	12	2	no	—
724	D₄	—	12	2	no	—
725	D₄	—	12	2	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	3	1	no	—
730	C₂×C₄	—	3	1	no	—
731	C₂×C₄	—	3	2	no	—
732	C₂×C₄	—	3	2	no	—
733	C₂×C₄	—	3	1	no	—
734	C₂×C₄	—	6	2	no	—
735	C₂×C₄	—	6	4	no	—
736	C₂×C₄	—	6	1	no	—
737	C₂×C₄	—	6	1	no	—
738	C₂×C₄	—	12	1	no	—
739	C₂×C₄	—	12	2	no	—
740	C₂×C₄	—	12	2	no	—
741	C₂×C₄	—	12	2	no	—
742	C₂×C₄	—	12	2	no	—
743	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
744	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
745	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	6	1	no	—
749	C₈	—	6	1	no	—
750	C₂×C₃	—	8	1	no	—
751	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
752	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
753	C₂×C₃	C₅×#575	1	1	yes	characteristic
754	D₃	—	2	2	no	—
755	D₃	—	4	2	no	—
756	D₃	—	8	1	no	—
757	C₅	#80597	1	1	yes	characteristic, direct product factor, Sylow
758	C₂²	—	3	2	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	6	1	no	—
763	C₂²	—	6	1	no	—
764	C₂²	—	6	2	no	—
765	C₂²	—	12	1	no	—
766	C₂²	—	12	1	no	—
767	C₂²	—	12	1	no	—
768	C₂²	—	12	1	no	—
769	C₂²	—	12	1	no	—
770	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	2	no	—
774	C₄	—	3	2	no	—
775	C₄	—	3	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	6	1	no	—
779	C₄	—	12	1	no	—
780	C₄	—	12	1	no	—
781	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
782	C₄	C₅×D₃×#41	1	1	yes	characteristic
783	C₃	C₅×#3035	1	1	yes	characteristic, complemented, Sylow
784	C₂	—	6	2	no	—
785	C₂	—	8	1	no	—
786	C₂	—	12	2	no	—
787	C₂	—	24	1	no	—
788	C₂	C₅×D₃×#121	1	1	yes	characteristic
789	C₂	C₅×D₃×#135	1	1	yes	characteristic
790	C₂	C₅×#5777	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×#464	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#464	D₃
hypocenter	C₃	C₅×#3035
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#464

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#919	C₂	semidirect
2. C₂×C₅×#916	C₂	semidirect
3. C₅×#5668	C₂	semidirect
4. C₄×C₅×#239	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₅×#5182	C₂	semidirect
7. C₅×#5163	C₂	semidirect
8. C₅×#5057	C₂	semidirect
9. C₅×#5028	C₂	semidirect
10. C₅×#4844	C₂	semidirect
11. C₅×D₃×C₄⋊C₈	C₂	semidirect
12. C₅×#4818	C₂	semidirect
13. C₅×#4804	C₂	semidirect
14. C₅×#4786	C₂	semidirect
15. C₅×#4772	C₂	semidirect
62. #80597	C₅	direct (N × H)
68. C₅×#464	D₃	semidirect
88. C₅×#239	D₄	semidirect
137. C₂×#919	C₂×C₅	semidirect
138. C₂×#916	C₂×C₅	semidirect
139. #5668	C₂×C₅	semidirect
140. C₄×#239	C₂×C₅	semidirect
141. C₃×#464	C₂×C₅	semidirect
142. #5182	C₂×C₅	semidirect
143. #5163	C₂×C₅	semidirect
144. #5057	C₂×C₅	semidirect
145. #5028	C₂×C₅	semidirect
146. #4844	C₂×C₅	semidirect
147. D₃×C₄⋊C₈	C₂×C₅	semidirect
148. #4818	C₂×C₅	semidirect
149. #4804	C₂×C₅	semidirect
150. #4786	C₂×C₅	semidirect
151. #4772	C₂×C₅	semidirect
352. #464	C₅×D₃	semidirect
386. C₅×Dic₃	#135	semidirect
397. #239	C₅×D₄	semidirect
672. C₃×C₅	#3035	semidirect
697. Dic₃	C₅×#135	semidirect
757. C₅	#80597	direct (N × H)
783. C₃	C₅×#3035	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#919	2
C₂×C₅×#916	2
C₅×#5668	2
C₄×C₅×#239	2
C₃×C₅×#464	2
C₅×#5182	2
C₅×#5163	2
C₅×#5057	2
C₅×#5028	2
C₅×#4844	2
C₅×D₃×C₄⋊C₈	2
C₅×#4818	2
C₅×#4804	2
C₅×#4786	2
C₅×#4772	2
C₅×#3035	3
#80597	5

Subgroups — C5×#80597 #14426223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80597 #14426223