Subgroups — C₅×#35318 #11958038

Order 1280.

2106 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2850	C₂	1	1	yes	maximal, characteristic
7	C₅×#2660	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2621	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2620	C₂	1	1	yes	maximal, characteristic
11	C₅×#2556	C₂	1	4	yes	maximal, complemented
12	C₅×#2553	C₂	1	4	yes	maximal, complemented
13	C₅×#2521	C₂	1	4	yes	maximal, complemented
14	C₅×#2519	C₂	1	4	yes	maximal, complemented
15	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#542	—	2	8	no	—
21	C₅×#541	—	2	8	no	—
22	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#126	C₂²	1	2	yes	—
27	C₂×C₅×#126	C₂²	1	2	yes	—
28	C₂×C₅×#126	C₂²	1	2	yes	—
29	C₂×C₅×#125	C₂²	1	2	yes	—
30	C₂×C₅×#125	C₂²	1	2	yes	—
31	C₂×C₅×#125	C₂²	1	1	yes	characteristic
32	C₂×C₅×#124	C₂²	1	2	yes	—
33	C₂×C₅×#124	C₂²	1	1	yes	characteristic
34	C₂×C₅×#124	C₂²	1	1	yes	characteristic
35	C₂×C₅×#124	C₂²	1	1	yes	characteristic
36	C₂×C₅×#123	C₂²	1	2	yes	—
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×#121	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×#117	C₂²	1	1	yes	characteristic
47	C₂×C₅×#117	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
49	C₅×#399	C₂²	1	4	yes	—
50	C₅×#399	C₂²	1	4	yes	—
51	C₅×#398	C₂²	1	4	yes	—
52	C₅×#398	C₂²	1	4	yes	—
53	C₅×#397	C₂²	1	4	yes	—
54	C₅×#396	C₂²	1	4	yes	—
55	C₅×#395	C₂²	1	4	yes	—
56	C₅×#394	C₂²	1	4	yes	—
57	C₅×#391	C₂²	1	4	yes	—
58	C₅×#391	C₂²	1	1	yes	characteristic
59	C₅×#391	C₂²	1	1	yes	characteristic
60	C₅×#391	C₂²	1	1	yes	characteristic
61	C₅×#391	C₂²	1	1	yes	characteristic
62	C₅×#391	C₂²	1	1	yes	characteristic
63	C₅×#391	C₂²	1	1	yes	characteristic
64	C₅×#390	C₂²	1	1	yes	characteristic
65	C₅×#390	C₂²	1	1	yes	characteristic
66	C₅×#389	C₂²	1	4	yes	—
67	C₅×#389	C₂²	1	4	yes	—
68	C₅×#388	C₂²	1	4	yes	—
69	C₅×#388	C₂²	1	4	yes	—
70	C₅×#388	C₂²	1	4	yes	—
71	C₅×#388	C₂²	1	4	yes	—
72	C₅×#388	C₂²	1	4	yes	—
73	C₅×#387	C₂²	1	4	yes	—
74	C₅×#387	C₂²	1	4	yes	—
75	C₅×#386	C₂²	1	4	yes	—
76	C₅×#385	C₂²	1	4	yes	—
77	C₅×#384	C₂²	1	1	yes	characteristic
78	C₅×#384	C₂²	1	1	yes	characteristic
79	C₅×#382	C₂²	1	4	yes	—
80	C₅×#382	C₂²	1	1	yes	characteristic
81	C₅×#382	C₂²	1	1	yes	characteristic
82	C₅×#380	C₂²	1	4	yes	—
83	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
84	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
85	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
86	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
87	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
88	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
89	C₅×#376	C₂²	1	1	yes	characteristic
90	C₅×#376	C₂²	1	1	yes	characteristic
91	C₄³×C₅	C₂²	1	1	yes	characteristic
92	C₄³×C₅	C₂²	1	1	yes	characteristic
93	#35318	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Q₈	C₂³	1	2	yes	—
98	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
99	C₂²×C₅×D₄	C₂³	1	2	yes	—
100	C₂³×C₄×C₅	C₂³	1	2	yes	—
101	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅	C₂³	1	2	yes	—
103	C₅×C₄⋊Q₈	—	2	4	no	—
104	C₅×C₄⋊Q₈	—	2	4	no	—
105	C₅×C₄⋊Q₈	—	2	4	no	—
106	C₅×C₄⋊Q₈	—	2	4	no	—
107	C₅×#126	—	2	8	no	—
108	C₅×#126	—	2	8	no	—
109	C₅×#126	—	2	8	no	—
110	C₅×#125	—	2	8	no	—
111	C₅×#125	—	2	8	no	—
112	C₅×#125	—	2	4	no	—
113	C₅×#124	—	2	8	no	—
114	C₅×#124	—	2	4	no	—
115	C₅×#124	—	2	4	no	—
116	C₅×#124	—	2	4	no	—
117	C₅×#123	—	2	8	no	—
118	C₅×C₂²⋊Q₈	—	2	4	no	—
119	C₅×C₂²⋊Q₈	—	2	4	no	—
120	C₅×C₂²⋊Q₈	—	2	4	no	—
121	C₅×C₂²⋊Q₈	—	2	8	no	—
122	C₅×#121	—	2	4	no	—
123	C₄×C₅×Q₈	—	2	4	no	—
124	C₄×C₅×Q₈	—	2	4	no	—
125	C₄×C₅×Q₈	—	2	4	no	—
126	C₄×C₅×D₄	—	2	4	no	—
127	C₅×#117	—	2	4	no	—
128	C₅×#117	D₄	1	8	yes	—
129	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₅	—	2	4	no	—
166	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₅	C₂³	1	2	yes	—
169	C₂×C₄²×C₅	C₂³	1	2	yes	—
170	C₂×C₄²×C₅	C₂³	1	2	yes	—
171	C₂×C₄²×C₅	C₂³	1	2	yes	—
172	C₂×C₄²×C₅	C₂³	1	2	yes	—
173	C₂×C₄²×C₅	C₂³	1	2	yes	—
174	C₂×C₄²×C₅	C₂³	1	2	yes	—
175	C₂×C₄²×C₅	C₂³	1	2	yes	—
176	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
180	C₅×#95	C₂³	1	2	yes	—
181	C₅×#95	C₂³	1	2	yes	—
182	C₅×#95	C₂³	1	2	yes	—
183	C₅×#95	C₂³	1	2	yes	—
184	C₅×#95	C₂³	1	4	yes	—
185	C₅×#95	C₂³	1	4	yes	—
186	C₅×#95	C₂³	1	4	yes	—
187	C₅×#95	C₂³	1	4	yes	—
188	C₅×#95	C₂³	1	4	yes	—
189	C₅×#95	C₂³	1	4	yes	—
190	C₅×#95	C₂³	1	4	yes	—
191	C₅×#95	C₂³	1	4	yes	—
192	C₂×#542	C₂×C₅	1	1	yes	characteristic
193	C₂×#541	C₂×C₅	1	1	yes	characteristic, complemented
194	#2862	C₂×C₅	1	1	yes	characteristic, complemented
195	#2861	C₂×C₅	1	1	yes	characteristic, complemented
196	#2857	C₂×C₅	1	1	yes	characteristic, complemented
197	#2850	C₂×C₅	1	1	yes	characteristic
198	#2660	C₂×C₅	1	1	yes	characteristic, complemented
199	#2658	C₂×C₅	1	1	yes	characteristic, complemented
200	#2621	C₂×C₅	1	1	yes	characteristic, complemented
201	#2620	C₂×C₅	1	1	yes	characteristic
202	#2556	C₂×C₅	1	4	yes	complemented
203	#2553	C₂×C₅	1	4	yes	complemented
204	#2521	C₂×C₅	1	4	yes	complemented
205	#2519	C₂×C₅	1	4	yes	complemented
206	#2327	C₂×C₅	1	1	yes	characteristic, complemented
207	#2326	C₂×C₅	1	1	yes	characteristic, complemented
208	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
209	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
210	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
211	C₂⁴×C₅	C₂⁴	1	2	yes	—
212	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
213	C₂×C₅×Q₈	—	2	2	no	—
214	C₂×C₅×Q₈	—	2	2	no	—
215	C₂×C₅×Q₈	—	2	2	no	—
216	C₂×C₅×Q₈	—	2	4	no	—
217	C₂×C₅×Q₈	—	2	2	no	—
218	C₂×C₅×Q₈	—	2	2	no	—
219	C₂×C₅×Q₈	—	2	2	no	—
220	C₂×C₅×Q₈	—	2	2	no	—
221	C₂×C₅×Q₈	—	2	2	no	—
222	C₂×C₅×Q₈	—	2	2	no	—
223	C₂×C₅×Q₈	—	4	4	no	—
224	C₂×C₅×D₄	—	2	4	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	2	2	no	—
227	C₂×C₅×D₄	—	2	2	no	—
228	C₂×C₅×D₄	—	4	4	no	—
229	C₂²×C₄×C₅	—	2	2	no	—
230	C₂²×C₄×C₅	—	2	2	no	—
231	C₂²×C₄×C₅	—	2	4	no	—
232	C₂²×C₄×C₅	—	2	4	no	—
233	C₂²×C₄×C₅	—	2	4	no	—
234	C₂²×C₄×C₅	—	4	2	no	—
235	C₂²×C₄×C₅	—	4	4	no	—
236	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
254	C₅×C₄⋊C₄	—	2	2	no	—
255	C₅×C₄⋊C₄	—	2	2	no	—
256	C₅×C₄⋊C₄	—	2	4	no	—
257	C₅×C₄⋊C₄	—	2	2	no	—
258	C₅×C₄⋊C₄	—	2	2	no	—
259	C₅×C₄⋊C₄	—	2	4	no	—
260	C₅×C₄⋊C₄	—	2	4	no	—
261	C₅×C₄⋊C₄	—	2	4	no	—
262	C₅×C₄⋊C₄	—	2	4	no	—
263	C₅×C₄⋊C₄	—	2	4	no	—
264	C₅×C₄⋊C₄	—	2	4	no	—
265	C₅×C₄⋊C₄	—	2	4	no	—
266	C₅×C₄⋊C₄	—	2	4	no	—
267	C₅×C₄⋊C₄	—	2	4	no	—
268	C₅×C₄⋊C₄	—	2	4	no	—
269	C₅×C₄⋊C₄	—	2	4	no	—
270	C₅×C₄⋊C₄	—	2	8	no	—
271	C₅×C₄⋊C₄	—	2	8	no	—
272	C₅×C₄⋊C₄	—	4	4	no	—
273	C₅×C₄⋊C₄	—	4	4	no	—
274	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
275	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
276	C₅×C₂²⋊C₄	—	2	4	no	—
277	C₅×C₂²⋊C₄	—	2	4	no	—
278	C₅×C₂²⋊C₄	—	2	4	no	—
279	C₅×C₂²⋊C₄	—	2	4	no	—
280	C₅×C₂²⋊C₄	—	2	4	no	—
281	C₅×C₂²⋊C₄	—	2	4	no	—
282	C₅×C₂²⋊C₄	—	2	4	no	—
283	C₅×C₂²⋊C₄	—	2	4	no	—
284	C₅×C₂²⋊C₄	—	2	8	no	—
285	C₅×C₂²⋊C₄	—	2	8	no	—
286	C₅×C₂²⋊C₄	—	2	8	no	—
287	C₅×C₂²⋊C₄	—	4	4	no	—
288	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
289	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
290	C₄²×C₅	—	2	4	no	—
291	C₄²×C₅	—	2	4	no	—
292	C₄²×C₅	—	2	4	no	—
293	C₄²×C₅	—	2	4	no	—
294	C₄²×C₅	—	2	2	no	—
295	C₄²×C₅	—	2	2	no	—
296	C₄²×C₅	—	2	4	no	—
297	C₄²×C₅	—	2	4	no	—
298	C₄²×C₅	—	4	2	no	—
299	C₄²×C₅	—	4	2	no	—
300	C₄²×C₅	C₂×D₄	1	4	yes	—
301	C₄²×C₅	C₂×D₄	1	4	yes	—
302	C₄²×C₅	#41	1	4	yes	—
303	C₄²×C₅	#41	1	4	yes	—
304	#542	—	2	8	no	—
305	#541	—	2	8	no	—
306	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
307	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
310	C₂×#126	C₂²×C₅	1	2	yes	—
311	C₂×#126	C₂²×C₅	1	2	yes	—
312	C₂×#126	C₂²×C₅	1	2	yes	—
313	C₂×#125	C₂²×C₅	1	1	yes	characteristic
314	C₂×#125	C₂²×C₅	1	2	yes	—
315	C₂×#125	C₂²×C₅	1	2	yes	—
316	C₂×#124	C₂²×C₅	1	1	yes	characteristic
317	C₂×#124	C₂²×C₅	1	1	yes	characteristic
318	C₂×#124	C₂²×C₅	1	1	yes	characteristic
319	C₂×#124	C₂²×C₅	1	2	yes	—
320	C₂×#123	C₂²×C₅	1	2	yes	—
321	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
322	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
323	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
325	C₂×#121	C₂²×C₅	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
329	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
330	C₂×#117	C₂²×C₅	1	1	yes	characteristic
331	C₂×#117	C₂²×C₅	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
333	#399	C₂²×C₅	1	4	yes	—
334	#399	C₂²×C₅	1	4	yes	—
335	#398	C₂²×C₅	1	4	yes	—
336	#398	C₂²×C₅	1	4	yes	—
337	#397	C₂²×C₅	1	4	yes	—
338	#396	C₂²×C₅	1	4	yes	—
339	#395	C₂²×C₅	1	4	yes	—
340	#394	C₂²×C₅	1	4	yes	—
341	#391	C₂²×C₅	1	1	yes	characteristic
342	#391	C₂²×C₅	1	1	yes	characteristic
343	#391	C₂²×C₅	1	1	yes	characteristic
344	#391	C₂²×C₅	1	1	yes	characteristic
345	#391	C₂²×C₅	1	1	yes	characteristic
346	#391	C₂²×C₅	1	1	yes	characteristic
347	#391	C₂²×C₅	1	4	yes	—
348	#390	C₂²×C₅	1	1	yes	characteristic
349	#390	C₂²×C₅	1	1	yes	characteristic
350	#389	C₂²×C₅	1	4	yes	—
351	#389	C₂²×C₅	1	4	yes	—
352	#388	C₂²×C₅	1	4	yes	—
353	#388	C₂²×C₅	1	4	yes	—
354	#388	C₂²×C₅	1	4	yes	—
355	#388	C₂²×C₅	1	4	yes	—
356	#388	C₂²×C₅	1	4	yes	—
357	#387	C₂²×C₅	1	4	yes	—
358	#387	C₂²×C₅	1	4	yes	—
359	#386	C₂²×C₅	1	4	yes	—
360	#385	C₂²×C₅	1	4	yes	—
361	#384	C₂²×C₅	1	1	yes	characteristic
362	#384	C₂²×C₅	1	1	yes	characteristic
363	#382	C₂²×C₅	1	1	yes	characteristic
364	#382	C₂²×C₅	1	4	yes	—
365	#382	C₂²×C₅	1	1	yes	characteristic
366	#380	C₂²×C₅	1	4	yes	—
367	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
368	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
373	#376	C₂²×C₅	1	1	yes	characteristic
374	#376	C₂²×C₅	1	1	yes	characteristic
375	C₄³	C₂²×C₅	1	1	yes	characteristic
376	C₄³	C₂²×C₅	1	1	yes	characteristic
377	C₂³×C₅	—	2	1	no	—
378	C₂³×C₅	—	2	1	no	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	—	2	2	no	—
382	C₂³×C₅	—	2	2	no	—
383	C₂³×C₅	—	2	2	no	—
384	C₂³×C₅	—	2	4	no	—
385	C₂³×C₅	—	2	4	no	—
386	C₂³×C₅	C₂²×D₄	1	2	yes	—
387	C₂³×C₅	C₂⁵	1	1	yes	characteristic
388	C₅×Q₈	—	4	4	no	—
389	C₅×Q₈	—	4	4	no	—
390	C₅×Q₈	—	4	4	no	—
391	C₅×Q₈	—	8	4	no	—
392	C₅×D₄	—	4	4	no	—
393	C₅×D₄	—	8	4	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	2	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	2	no	—
398	C₂×C₄×C₅	—	2	2	no	—
399	C₂×C₄×C₅	—	2	2	no	—
400	C₂×C₄×C₅	—	2	2	no	—
401	C₂×C₄×C₅	—	2	2	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	—	2	2	no	—
404	C₂×C₄×C₅	—	2	2	no	—
405	C₂×C₄×C₅	—	2	2	no	—
406	C₂×C₄×C₅	—	2	8	no	—
407	C₂×C₄×C₅	—	2	2	no	—
408	C₂×C₄×C₅	—	2	2	no	—
409	C₂×C₄×C₅	—	2	2	no	—
410	C₂×C₄×C₅	—	2	2	no	—
411	C₂×C₄×C₅	—	2	2	no	—
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	—	2	2	no	—
414	C₂×C₄×C₅	—	2	2	no	—
415	C₂×C₄×C₅	—	2	2	no	—
416	C₂×C₄×C₅	—	2	2	no	—
417	C₂×C₄×C₅	—	2	2	no	—
418	C₂×C₄×C₅	—	2	2	no	—
419	C₂×C₄×C₅	—	2	2	no	—
420	C₂×C₄×C₅	—	2	2	no	—
421	C₂×C₄×C₅	—	2	2	no	—
422	C₂×C₄×C₅	—	2	4	no	—
423	C₂×C₄×C₅	—	2	2	no	—
424	C₂×C₄×C₅	—	2	4	no	—
425	C₂×C₄×C₅	—	2	4	no	—
426	C₂×C₄×C₅	—	2	4	no	—
427	C₂×C₄×C₅	—	4	8	no	—
428	C₂×C₄×C₅	—	8	4	no	—
429	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₅	C₂×#41	1	4	yes	—
436	C₂×C₄×C₅	C₂×#41	1	4	yes	—
437	C₂×C₄×C₅	C₂×#41	1	2	yes	—
438	C₂×C₄×C₅	C₂×#41	1	2	yes	—
439	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
440	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
441	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₅	1	2	yes	—
444	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₅	1	2	yes	—
446	C₂³×C₄	C₂³×C₅	1	2	yes	—
447	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₅	1	2	yes	—
449	C₄⋊Q₈	—	2	4	no	—
450	C₄⋊Q₈	—	2	4	no	—
451	C₄⋊Q₈	—	2	4	no	—
452	C₄⋊Q₈	—	2	4	no	—
453	#126	—	2	8	no	—
454	#126	—	2	8	no	—
455	#126	—	2	8	no	—
456	#125	—	2	8	no	—
457	#125	—	2	8	no	—
458	#125	—	2	4	no	—
459	#124	—	2	8	no	—
460	#124	—	2	4	no	—
461	#124	—	2	4	no	—
462	#124	—	2	4	no	—
463	#123	—	2	8	no	—
464	C₂²⋊Q₈	—	2	4	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	4	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	#121	—	2	4	no	—
469	C₄×Q₈	—	2	4	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×Q₈	—	2	4	no	—
472	C₄×D₄	—	2	4	no	—
473	#117	—	2	4	no	—
474	#117	C₅×D₄	1	8	yes	—
475	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
511	C₂×C₄²	—	2	4	no	—
512	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₅	1	2	yes	—
514	C₂×C₄²	C₂³×C₅	1	2	yes	—
515	C₂×C₄²	C₂³×C₅	1	2	yes	—
516	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₅	1	2	yes	—
518	C₂×C₄²	C₂³×C₅	1	2	yes	—
519	C₂×C₄²	C₂³×C₅	1	2	yes	—
520	C₂×C₄²	C₂³×C₅	1	2	yes	—
521	C₂×C₄²	C₂³×C₅	1	2	yes	—
522	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
526	#95	C₂³×C₅	1	2	yes	—
527	#95	C₂³×C₅	1	2	yes	—
528	#95	C₂³×C₅	1	2	yes	—
529	#95	C₂³×C₅	1	2	yes	—
530	#95	C₂³×C₅	1	4	yes	—
531	#95	C₂³×C₅	1	4	yes	—
532	#95	C₂³×C₅	1	4	yes	—
533	#95	C₂³×C₅	1	4	yes	—
534	#95	C₂³×C₅	1	4	yes	—
535	#95	C₂³×C₅	1	4	yes	—
536	#95	C₂³×C₅	1	4	yes	—
537	#95	C₂³×C₅	1	4	yes	—
538	C₂²×C₅	—	2	2	no	—
539	C₂²×C₅	—	2	2	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	4	2	no	—
542	C₂²×C₅	—	4	2	no	—
543	C₂²×C₅	—	4	2	no	—
544	C₂²×C₅	—	4	4	no	—
545	C₂²×C₅	—	4	4	no	—
546	C₂²×C₅	—	4	2	no	—
547	C₂²×C₅	—	4	2	no	—
548	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
549	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
550	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
551	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
552	C₂²×C₅	#585	1	2	yes	—
553	C₄×C₅	—	2	2	no	—
554	C₄×C₅	—	2	4	no	—
555	C₄×C₅	—	2	4	no	—
556	C₄×C₅	—	2	4	no	—
557	C₄×C₅	—	2	2	no	—
558	C₄×C₅	—	2	2	no	—
559	C₄×C₅	—	2	2	no	—
560	C₄×C₅	—	2	2	no	—
561	C₄×C₅	—	4	2	no	—
562	C₄×C₅	—	4	2	no	—
563	C₄×C₅	—	4	2	no	—
564	C₄×C₅	—	4	2	no	—
565	C₄×C₅	—	4	2	no	—
566	C₄×C₅	—	4	2	no	—
567	C₄×C₅	—	4	2	no	—
568	C₄×C₅	—	4	2	no	—
569	C₄×C₅	#532	1	4	yes	—
570	C₂⁴	C₂⁴×C₅	1	2	yes	—
571	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	4	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	8	no	—
630	C₄⋊C₄	—	2	8	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
634	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
648	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	4	2	no	—
658	C₄²	—	4	2	no	—
659	C₄²	C₂×C₅×D₄	1	4	yes	—
660	C₄²	C₂×C₅×D₄	1	4	yes	—
661	C₄²	C₅×#41	1	4	yes	—
662	C₄²	C₅×#41	1	4	yes	—
663	C₂×C₅	—	4	2	no	—
664	C₂×C₅	—	8	2	no	—
665	C₂×C₅	C₂×#532	1	1	yes	characteristic
666	C₂×C₅	#3461	1	2	yes	—
667	C₂×C₅	#3495	1	2	yes	—
668	C₂×C₅	#3499	1	1	yes	characteristic
669	C₂×C₅	#3500	1	1	yes	characteristic
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	4	no	—
679	C₂³	C₂²×C₅×D₄	1	2	yes	—
680	C₂³	C₂⁵×C₅	1	1	yes	characteristic
681	Q₈	—	4	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	4	4	no	—
684	Q₈	—	8	4	no	—
685	D₄	—	4	4	no	—
686	D₄	—	8	4	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
723	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
724	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
725	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
726	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
727	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
728	C₂×C₄	C₂×C₅×#41	1	4	yes	—
729	C₂×C₄	C₂×C₅×#41	1	4	yes	—
730	C₂×C₄	C₂×C₅×#41	1	2	yes	—
731	C₂×C₄	C₂×C₅×#41	1	2	yes	—
732	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
733	C₅	#35318	1	1	yes	characteristic, direct product factor, Sylow
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
745	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
746	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
747	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
748	C₂²	C₅×#585	1	2	yes	—
749	C₄	—	2	2	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	4	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	C₅×#532	1	4	yes	—
766	C₂	—	4	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₂×C₅×#532	1	1	yes	characteristic
769	C₂	C₅×#3461	1	2	yes	—
770	C₂	C₅×#3495	1	2	yes	—
771	C₂	C₅×#3499	1	1	yes	characteristic
772	C₂	C₅×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#541	C₂	semidirect
3. C₅×#2862	C₂	semidirect
4. C₅×#2861	C₂	semidirect
5. C₅×#2857	C₂	semidirect
7. C₅×#2660	C₂	semidirect
8. C₅×#2658	C₂	semidirect
9. C₅×#2621	C₂	semidirect
11. C₅×#2556	C₂	semidirect
12. C₅×#2553	C₂	semidirect
13. C₅×#2521	C₂	semidirect
14. C₅×#2519	C₂	semidirect
15. C₅×#2327	C₂	semidirect
16. C₅×#2326	C₂	semidirect
17. C₄×C₅×C₄⋊Q₈	C₂	semidirect
18. C₄×C₅×#124	C₂	semidirect
19. C₄×C₅×#117	C₂	semidirect
93. #35318	C₅	direct (N × H)
193. C₂×#541	C₂×C₅	semidirect
194. #2862	C₂×C₅	semidirect
195. #2861	C₂×C₅	semidirect
196. #2857	C₂×C₅	semidirect
198. #2660	C₂×C₅	semidirect
199. #2658	C₂×C₅	semidirect
200. #2621	C₂×C₅	semidirect
202. #2556	C₂×C₅	semidirect
203. #2553	C₂×C₅	semidirect
204. #2521	C₂×C₅	semidirect
205. #2519	C₂×C₅	semidirect
206. #2327	C₂×C₅	semidirect
207. #2326	C₂×C₅	semidirect
208. C₄×C₄⋊Q₈	C₂×C₅	semidirect
209. C₄×#124	C₂×C₅	semidirect
210. C₄×#117	C₂×C₅	semidirect
733. C₅	#35318	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#542	2
C₂×C₅×#541	2
C₅×#2862	2
C₅×#2861	2
C₅×#2857	2
C₅×#2850	2
C₅×#2660	2
C₅×#2658	2
C₅×#2621	2
C₅×#2620	2
C₅×#2556	2
C₅×#2553	2
C₅×#2521	2
C₅×#2519	2
C₅×#2327	2
C₅×#2326	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#124	2
C₄×C₅×#117	2
#35318	5

Subgroups — C5×#35318 #11958038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35318 #11958038