Subgroups — C₅×#36697 #11959417

Order 1280.

1484 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2843	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2839	C₂	1	2	yes	maximal, complemented
3	C₅×#2838	C₂	1	2	yes	maximal, complemented
4	C₅×#2837	C₂	1	2	yes	maximal
5	C₅×#2836	C₂	1	2	yes	maximal, complemented
6	C₅×#2833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2832	C₂	1	1	yes	maximal, characteristic
8	C₅×#2831	C₂	1	2	yes	maximal, complemented
9	C₅×#2823	C₂	1	1	yes	maximal, characteristic
10	C₅×#2821	C₂	1	2	yes	maximal, complemented
11	C₅×#2402	C₂	1	2	yes	maximal, complemented
12	C₅×#2401	C₂	1	2	yes	maximal, complemented
13	C₅×#2399	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2398	C₂	1	1	yes	maximal, characteristic
15	C₅×#2396	C₂	1	2	yes	maximal, complemented
16	C₅×#2396	C₂	1	2	yes	maximal, complemented
17	C₅×#2395	C₂	1	2	yes	maximal
18	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#126	C₂	1	2	yes	maximal, complemented
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#126	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×#117	C₂²	1	2	yes	—
27	C₅×#401	C₂²	1	2	yes	—
28	C₅×#400	C₂²	1	2	yes	—
29	C₅×#400	C₂²	1	2	yes	—
30	C₅×#400	C₂²	1	2	yes	—
31	C₅×#400	C₂²	1	2	yes	—
32	C₅×#400	C₂²	1	2	yes	—
33	C₅×#400	C₂²	1	2	yes	—
34	C₅×#400	C₂²	1	2	yes	—
35	C₅×#400	C₂²	1	2	yes	—
36	C₅×#400	C₂²	1	1	yes	characteristic
37	C₅×#400	C₂²	1	2	yes	—
38	C₅×#400	C₂²	1	2	yes	—
39	C₅×#400	C₂²	1	1	yes	characteristic
40	C₅×#399	C₂²	1	2	yes	—
41	C₅×#399	C₂²	1	2	yes	—
42	C₅×#399	C₂²	1	2	yes	—
43	C₅×#398	C₂²	1	2	yes	—
44	C₅×#398	C₂²	1	2	yes	—
45	C₅×#398	C₂²	1	1	yes	characteristic
46	C₅×#398	C₂²	1	2	yes	—
47	C₅×#398	C₂²	1	2	yes	—
48	C₅×#398	C₂²	1	2	yes	—
49	C₅×#398	C₂²	1	2	yes	—
50	C₅×#398	C₂²	1	1	yes	characteristic
51	C₅×#398	C₂²	1	2	yes	—
52	C₅×#398	C₂²	1	2	yes	—
53	C₅×#398	C₂²	1	2	yes	—
54	C₅×#398	C₂²	1	2	yes	—
55	C₅×#397	C₂²	1	2	yes	—
56	C₅×#397	C₂²	1	2	yes	—
57	C₅×#397	C₂²	1	2	yes	—
58	C₅×#397	C₂²	1	2	yes	—
59	C₅×#397	C₂²	1	2	yes	—
60	C₅×#397	C₂²	1	2	yes	—
61	C₅×#397	C₂²	1	2	yes	—
62	C₅×#396	C₂²	1	2	yes	—
63	C₅×#396	C₂²	1	2	yes	—
64	C₅×#396	C₂²	1	2	yes	—
65	C₅×#396	C₂²	1	2	yes	—
66	C₅×#396	C₂²	1	2	yes	—
67	C₅×#395	C₂²	1	2	yes	—
68	C₅×#395	C₂²	1	2	yes	—
69	C₅×#395	C₂²	1	1	yes	characteristic
70	C₅×#395	C₂²	1	1	yes	characteristic
71	C₅×#395	C₂²	1	2	yes	—
72	C₅×#394	C₂²	1	1	yes	characteristic
73	C₅×#394	C₂²	1	2	yes	—
74	C₅×#394	C₂²	1	2	yes	—
75	C₅×#394	C₂²	1	1	yes	characteristic
76	C₅×#393	C₂²	1	2	yes	—
77	C₅×#393	C₂²	1	2	yes	—
78	C₅×#393	C₂²	1	2	yes	—
79	C₅×#391	C₂²	1	1	yes	characteristic
80	C₅×#391	C₂²	1	1	yes	characteristic
81	C₅×#389	C₂²	1	2	yes	—
82	C₅×#389	C₂²	1	2	yes	—
83	C₅×#388	C₂²	1	2	yes	—
84	C₅×#388	C₂²	1	2	yes	—
85	C₅×#388	C₂²	1	2	yes	—
86	C₅×#387	C₂²	1	2	yes	—
87	C₅×#387	C₂²	1	2	yes	—
88	C₅×#387	C₂²	1	2	yes	—
89	C₅×#384	C₂²	1	1	yes	characteristic
90	C₅×#383	C₂²	1	2	yes	—
91	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₅×#376	C₂²	1	1	yes	characteristic
105	C₅×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₅	C₂²	1	1	yes	characteristic
107	#36697	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅	C₂³	1	2	yes	—
113	C₅×C₄⋊Q₈	—	2	4	no	—
114	C₅×#126	—	2	8	no	—
115	C₄×C₅×Q₈	—	4	2	no	—
116	C₄×C₅×Q₈	—	4	2	no	—
117	C₄×C₅×Q₈	—	4	2	no	—
118	C₄×C₅×D₄	—	4	2	no	—
119	C₅×#117	—	4	4	no	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₅×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
157	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₄²×C₅	C₂³	1	2	yes	—
160	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅	C₂³	1	2	yes	—
162	C₂×C₄²×C₅	C₂³	1	2	yes	—
163	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₅	C₂³	1	2	yes	—
166	C₂×C₄²×C₅	C₂³	1	2	yes	—
167	C₂×C₄²×C₅	C₂³	1	2	yes	—
168	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
170	C₅×#95	C₂³	1	2	yes	—
171	C₅×#95	C₂³	1	1	yes	characteristic
172	C₅×#95	C₂³	1	1	yes	characteristic
173	C₅×#95	C₂³	1	1	yes	characteristic
174	C₅×#95	C₂³	1	2	yes	—
175	C₅×#95	C₂³	1	1	yes	characteristic
176	C₅×#95	C₂³	1	2	yes	—
177	C₅×#95	C₂³	1	2	yes	—
178	C₅×#95	C₂³	1	2	yes	—
179	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
185	C₅×#95	C₂³	1	2	yes	—
186	C₅×#95	C₂³	1	2	yes	—
187	C₅×#95	C₂³	1	2	yes	—
188	C₅×#95	C₂³	1	2	yes	—
189	C₅×#95	C₂³	1	2	yes	—
190	C₅×#95	C₂³	1	2	yes	—
191	C₅×#95	C₂³	1	2	yes	—
192	C₅×#95	C₂³	1	2	yes	—
193	C₅×#95	C₂³	1	2	yes	—
194	C₅×#95	C₂³	1	2	yes	—
195	C₅×#95	C₂³	1	2	yes	—
196	C₅×#95	C₂³	1	2	yes	—
197	C₅×#95	C₂³	1	2	yes	—
198	C₅×#95	C₂³	1	2	yes	—
199	C₅×#95	C₂³	1	2	yes	—
200	C₅×#95	C₂³	1	2	yes	—
201	C₅×#95	C₂³	1	2	yes	—
202	#2843	C₂×C₅	1	1	yes	characteristic, complemented
203	#2839	C₂×C₅	1	2	yes	complemented
204	#2838	C₂×C₅	1	2	yes	complemented
205	#2837	C₂×C₅	1	2	yes	—
206	#2836	C₂×C₅	1	2	yes	complemented
207	#2833	C₂×C₅	1	1	yes	characteristic, complemented
208	#2832	C₂×C₅	1	1	yes	characteristic
209	#2831	C₂×C₅	1	2	yes	complemented
210	#2823	C₂×C₅	1	1	yes	characteristic
211	#2821	C₂×C₅	1	2	yes	complemented
212	#2402	C₂×C₅	1	2	yes	complemented
213	#2401	C₂×C₅	1	2	yes	complemented
214	#2399	C₂×C₅	1	1	yes	characteristic, complemented
215	#2398	C₂×C₅	1	1	yes	characteristic
216	#2396	C₂×C₅	1	2	yes	complemented
217	#2396	C₂×C₅	1	2	yes	complemented
218	#2395	C₂×C₅	1	2	yes	—
219	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
220	C₄×#126	C₂×C₅	1	2	yes	complemented
221	C₂⁴×C₅	C₂⁴	1	2	yes	—
222	C₂×C₅×Q₈	—	2	2	no	—
223	C₂×C₅×Q₈	—	2	2	no	—
224	C₂×C₅×Q₈	—	4	1	no	—
225	C₂×C₅×Q₈	—	4	1	no	—
226	C₂×C₅×Q₈	—	4	1	no	—
227	C₂×C₅×Q₈	—	4	1	no	—
228	C₂×C₅×Q₈	—	4	1	no	—
229	C₂×C₅×Q₈	—	4	2	no	—
230	C₂×C₅×D₄	—	4	1	no	—
231	C₂×C₅×D₄	—	4	2	no	—
232	C₂²×C₄×C₅	—	2	4	no	—
233	C₂²×C₄×C₅	—	2	4	no	—
234	C₂²×C₄×C₅	—	2	4	no	—
235	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
253	C₅×C₄⋊C₄	—	2	4	no	—
254	C₅×C₄⋊C₄	—	2	4	no	—
255	C₅×C₄⋊C₄	—	2	4	no	—
256	C₅×C₄⋊C₄	—	2	4	no	—
257	C₅×C₄⋊C₄	—	2	4	no	—
258	C₅×C₄⋊C₄	—	4	2	no	—
259	C₅×C₄⋊C₄	—	4	2	no	—
260	C₅×C₄⋊C₄	—	4	2	no	—
261	C₅×C₄⋊C₄	—	4	2	no	—
262	C₅×C₄⋊C₄	—	4	2	no	—
263	C₅×C₄⋊C₄	—	4	2	no	—
264	C₅×C₄⋊C₄	—	4	2	no	—
265	C₅×C₄⋊C₄	—	4	2	no	—
266	C₅×C₄⋊C₄	—	4	2	no	—
267	C₅×C₄⋊C₄	—	4	2	no	—
268	C₅×C₄⋊C₄	—	4	2	no	—
269	C₅×C₄⋊C₄	—	4	2	no	—
270	C₅×C₄⋊C₄	—	4	2	no	—
271	C₅×C₄⋊C₄	—	4	1	no	—
272	C₅×C₄⋊C₄	—	4	1	no	—
273	C₅×C₄⋊C₄	—	4	1	no	—
274	C₅×C₄⋊C₄	—	4	1	no	—
275	C₅×C₄⋊C₄	—	4	1	no	—
276	C₅×C₄⋊C₄	—	4	2	no	—
277	C₅×C₄⋊C₄	—	4	2	no	—
278	C₅×C₄⋊C₄	—	4	1	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	—	4	2	no	—
283	C₅×C₂²⋊C₄	—	4	2	no	—
284	C₅×C₂²⋊C₄	—	4	2	no	—
285	C₅×C₂²⋊C₄	—	4	2	no	—
286	C₅×C₂²⋊C₄	—	4	2	no	—
287	C₅×C₂²⋊C₄	—	4	2	no	—
288	C₅×C₂²⋊C₄	—	4	2	no	—
289	C₅×C₂²⋊C₄	—	4	2	no	—
290	C₅×C₂²⋊C₄	—	4	2	no	—
291	C₅×C₂²⋊C₄	—	4	2	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	2	no	—
297	C₄²×C₅	—	2	4	no	—
298	C₄²×C₅	—	2	4	no	—
299	C₄²×C₅	—	2	4	no	—
300	C₄²×C₅	—	4	2	no	—
301	C₄²×C₅	—	4	1	no	—
302	C₄²×C₅	#41	1	4	yes	—
303	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
304	C₂×#126	C₂²×C₅	1	2	yes	—
305	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
306	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
309	C₂×#117	C₂²×C₅	1	2	yes	—
310	#401	C₂²×C₅	1	2	yes	—
311	#400	C₂²×C₅	1	2	yes	—
312	#400	C₂²×C₅	1	2	yes	—
313	#400	C₂²×C₅	1	2	yes	—
314	#400	C₂²×C₅	1	2	yes	—
315	#400	C₂²×C₅	1	2	yes	—
316	#400	C₂²×C₅	1	2	yes	—
317	#400	C₂²×C₅	1	2	yes	—
318	#400	C₂²×C₅	1	2	yes	—
319	#400	C₂²×C₅	1	1	yes	characteristic
320	#400	C₂²×C₅	1	2	yes	—
321	#400	C₂²×C₅	1	2	yes	—
322	#400	C₂²×C₅	1	1	yes	characteristic
323	#399	C₂²×C₅	1	2	yes	—
324	#399	C₂²×C₅	1	2	yes	—
325	#399	C₂²×C₅	1	2	yes	—
326	#398	C₂²×C₅	1	2	yes	—
327	#398	C₂²×C₅	1	2	yes	—
328	#398	C₂²×C₅	1	1	yes	characteristic
329	#398	C₂²×C₅	1	2	yes	—
330	#398	C₂²×C₅	1	2	yes	—
331	#398	C₂²×C₅	1	2	yes	—
332	#398	C₂²×C₅	1	2	yes	—
333	#398	C₂²×C₅	1	1	yes	characteristic
334	#398	C₂²×C₅	1	2	yes	—
335	#398	C₂²×C₅	1	2	yes	—
336	#398	C₂²×C₅	1	2	yes	—
337	#398	C₂²×C₅	1	2	yes	—
338	#397	C₂²×C₅	1	2	yes	—
339	#397	C₂²×C₅	1	2	yes	—
340	#397	C₂²×C₅	1	2	yes	—
341	#397	C₂²×C₅	1	2	yes	—
342	#397	C₂²×C₅	1	2	yes	—
343	#397	C₂²×C₅	1	2	yes	—
344	#397	C₂²×C₅	1	2	yes	—
345	#396	C₂²×C₅	1	2	yes	—
346	#396	C₂²×C₅	1	2	yes	—
347	#396	C₂²×C₅	1	2	yes	—
348	#396	C₂²×C₅	1	2	yes	—
349	#396	C₂²×C₅	1	2	yes	—
350	#395	C₂²×C₅	1	2	yes	—
351	#395	C₂²×C₅	1	2	yes	—
352	#395	C₂²×C₅	1	1	yes	characteristic
353	#395	C₂²×C₅	1	1	yes	characteristic
354	#395	C₂²×C₅	1	2	yes	—
355	#394	C₂²×C₅	1	1	yes	characteristic
356	#394	C₂²×C₅	1	2	yes	—
357	#394	C₂²×C₅	1	2	yes	—
358	#394	C₂²×C₅	1	1	yes	characteristic
359	#393	C₂²×C₅	1	2	yes	—
360	#393	C₂²×C₅	1	2	yes	—
361	#393	C₂²×C₅	1	2	yes	—
362	#391	C₂²×C₅	1	1	yes	characteristic
363	#391	C₂²×C₅	1	1	yes	characteristic
364	#389	C₂²×C₅	1	2	yes	—
365	#389	C₂²×C₅	1	2	yes	—
366	#388	C₂²×C₅	1	2	yes	—
367	#388	C₂²×C₅	1	2	yes	—
368	#388	C₂²×C₅	1	2	yes	—
369	#387	C₂²×C₅	1	2	yes	—
370	#387	C₂²×C₅	1	2	yes	—
371	#387	C₂²×C₅	1	2	yes	—
372	#384	C₂²×C₅	1	1	yes	characteristic
373	#383	C₂²×C₅	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
380	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
381	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
383	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
384	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
385	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
386	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
387	#376	C₂²×C₅	1	1	yes	characteristic
388	#376	C₂²×C₅	1	1	yes	characteristic
389	C₄³	C₂²×C₅	1	1	yes	characteristic
390	C₂³×C₅	—	2	2	no	—
391	C₂³×C₅	—	2	2	no	—
392	C₂³×C₅	—	2	2	no	—
393	C₂³×C₅	—	2	2	no	—
394	C₂³×C₅	—	2	2	no	—
395	C₂³×C₅	—	2	2	no	—
396	C₂³×C₅	—	2	2	no	—
397	C₂³×C₅	C₂⁵	1	1	yes	characteristic
398	C₅×Q₈	—	4	4	no	—
399	C₅×Q₈	—	4	4	no	—
400	C₅×Q₈	—	4	4	no	—
401	C₅×D₄	—	4	4	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	2	no	—
404	C₂×C₄×C₅	—	2	2	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	2	no	—
407	C₂×C₄×C₅	—	2	2	no	—
408	C₂×C₄×C₅	—	2	2	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	2	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	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	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	2	no	—
422	C₂×C₄×C₅	—	2	2	no	—
423	C₂×C₄×C₅	—	2	2	no	—
424	C₂×C₄×C₅	—	2	2	no	—
425	C₂×C₄×C₅	—	2	2	no	—
426	C₂×C₄×C₅	—	2	2	no	—
427	C₂×C₄×C₅	—	2	2	no	—
428	C₂×C₄×C₅	—	2	2	no	—
429	C₂×C₄×C₅	—	2	2	no	—
430	C₂×C₄×C₅	—	2	2	no	—
431	C₂×C₄×C₅	—	2	2	no	—
432	C₂×C₄×C₅	—	2	2	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	2	no	—
435	C₂×C₄×C₅	—	2	2	no	—
436	C₂×C₄×C₅	—	2	2	no	—
437	C₂×C₄×C₅	—	2	2	no	—
438	C₂×C₄×C₅	—	2	2	no	—
439	C₂×C₄×C₅	—	2	2	no	—
440	C₂×C₄×C₅	—	2	2	no	—
441	C₂×C₄×C₅	—	2	2	no	—
442	C₂×C₄×C₅	—	2	2	no	—
443	C₂×C₄×C₅	—	2	2	no	—
444	C₂×C₄×C₅	—	2	2	no	—
445	C₂×C₄×C₅	—	2	2	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	2	no	—
448	C₂×C₄×C₅	—	4	8	no	—
449	C₂×C₄×C₅	C₂×#41	1	4	yes	—
450	C₂×C₄×C₅	C₂×#41	1	2	yes	—
451	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
452	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
453	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₅	1	2	yes	—
458	C₄⋊Q₈	—	2	4	no	—
459	#126	—	2	8	no	—
460	C₄×Q₈	—	4	2	no	—
461	C₄×Q₈	—	4	2	no	—
462	C₄×Q₈	—	4	2	no	—
463	C₄×D₄	—	4	2	no	—
464	#117	—	4	4	no	—
465	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
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×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
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×C₄²	C₂³×C₅	1	2	yes	—
505	C₂×C₄²	C₂³×C₅	1	2	yes	—
506	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₅	1	2	yes	—
510	C₂×C₄²	C₂³×C₅	1	2	yes	—
511	C₂×C₄²	C₂³×C₅	1	2	yes	—
512	C₂×C₄²	C₂³×C₅	1	2	yes	—
513	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
515	#95	C₂³×C₅	1	2	yes	—
516	#95	C₂³×C₅	1	1	yes	characteristic
517	#95	C₂³×C₅	1	1	yes	characteristic
518	#95	C₂³×C₅	1	1	yes	characteristic
519	#95	C₂³×C₅	1	2	yes	—
520	#95	C₂³×C₅	1	1	yes	characteristic
521	#95	C₂³×C₅	1	2	yes	—
522	#95	C₂³×C₅	1	2	yes	—
523	#95	C₂³×C₅	1	2	yes	—
524	#95	C₂³×C₅	1	2	yes	—
525	#95	C₂³×C₅	1	2	yes	—
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	2	yes	—
531	#95	C₂³×C₅	1	2	yes	—
532	#95	C₂³×C₅	1	2	yes	—
533	#95	C₂³×C₅	1	2	yes	—
534	#95	C₂³×C₅	1	2	yes	—
535	#95	C₂³×C₅	1	2	yes	—
536	#95	C₂³×C₅	1	2	yes	—
537	#95	C₂³×C₅	1	2	yes	—
538	#95	C₂³×C₅	1	2	yes	—
539	#95	C₂³×C₅	1	2	yes	—
540	#95	C₂³×C₅	1	2	yes	—
541	#95	C₂³×C₅	1	2	yes	—
542	#95	C₂³×C₅	1	2	yes	—
543	#95	C₂³×C₅	1	2	yes	—
544	#95	C₂³×C₅	1	2	yes	—
545	#95	C₂³×C₅	1	2	yes	—
546	#95	C₂³×C₅	1	2	yes	—
547	C₂²×C₅	—	4	2	no	—
548	C₂²×C₅	—	4	2	no	—
549	C₂²×C₅	—	4	2	no	—
550	C₂²×C₅	—	4	2	no	—
551	C₂²×C₅	—	4	2	no	—
552	C₂²×C₅	—	4	2	no	—
553	C₂²×C₅	—	4	2	no	—
554	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
555	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
557	C₂²×C₅	#585	1	1	yes	characteristic
558	C₂²×C₅	#585	1	2	yes	—
559	C₄×C₅	—	2	2	no	—
560	C₄×C₅	—	2	4	no	—
561	C₄×C₅	—	4	2	no	—
562	C₄×C₅	—	4	1	no	—
563	C₄×C₅	—	4	2	no	—
564	C₄×C₅	—	4	1	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	—	4	1	no	—
570	C₄×C₅	—	4	1	no	—
571	C₄×C₅	—	4	2	no	—
572	C₄×C₅	—	4	1	no	—
573	C₄×C₅	—	4	2	no	—
574	C₄×C₅	—	4	2	no	—
575	C₄×C₅	—	4	2	no	—
576	C₄×C₅	#563	1	4	yes	—
577	C₂⁴	C₂⁴×C₅	1	2	yes	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	4	1	no	—
581	C₂×Q₈	—	4	1	no	—
582	C₂×Q₈	—	4	1	no	—
583	C₂×Q₈	—	4	1	no	—
584	C₂×Q₈	—	4	1	no	—
585	C₂×Q₈	—	4	2	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	1	no	—
617	C₄⋊C₄	—	4	1	no	—
618	C₄⋊C₄	—	4	1	no	—
619	C₄⋊C₄	—	4	1	no	—
620	C₄⋊C₄	—	4	1	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	1	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	4	1	no	—
658	C₄²	C₅×#41	1	4	yes	—
659	C₂×C₅	—	8	2	no	—
660	C₂×C₅	#3460	1	1	yes	characteristic
661	C₂×C₅	#3461	1	2	yes	—
662	C₂×C₅	C₂×#563	1	1	yes	characteristic
663	C₂×C₅	#3529	1	1	yes	characteristic
664	C₂×C₅	#3531	1	2	yes	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	C₂⁵×C₅	1	1	yes	characteristic
673	Q₈	—	4	4	no	—
674	Q₈	—	4	4	no	—
675	Q₈	—	4	4	no	—
676	D₄	—	4	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	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	1	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	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	C₂×C₅×#41	1	4	yes	—
725	C₂×C₄	C₂×C₅×#41	1	2	yes	—
726	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
727	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
728	C₅	#36697	1	1	yes	characteristic, direct product factor, Sylow
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
737	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
739	C₂²	C₅×#585	1	1	yes	characteristic
740	C₂²	C₅×#585	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	C₅×#563	1	4	yes	—
759	C₂	—	8	2	no	—
760	C₂	C₅×#3460	1	1	yes	characteristic
761	C₂	C₅×#3461	1	2	yes	—
762	C₂	C₂×C₅×#563	1	1	yes	characteristic
763	C₂	C₅×#3529	1	1	yes	characteristic
764	C₂	C₅×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2843	C₂	semidirect
2. C₅×#2839	C₂	semidirect
3. C₅×#2838	C₂	semidirect
5. C₅×#2836	C₂	semidirect
6. C₅×#2833	C₂	semidirect
8. C₅×#2831	C₂	semidirect
10. C₅×#2821	C₂	semidirect
11. C₅×#2402	C₂	semidirect
12. C₅×#2401	C₂	semidirect
13. C₅×#2399	C₂	semidirect
15. C₅×#2396	C₂	semidirect
16. C₅×#2396	C₂	semidirect
18. C₄×C₅×C₄⋊Q₈	C₂	semidirect
19. C₄×C₅×#126	C₂	semidirect
107. #36697	C₅	direct (N × H)
202. #2843	C₂×C₅	semidirect
203. #2839	C₂×C₅	semidirect
204. #2838	C₂×C₅	semidirect
206. #2836	C₂×C₅	semidirect
207. #2833	C₂×C₅	semidirect
209. #2831	C₂×C₅	semidirect
211. #2821	C₂×C₅	semidirect
212. #2402	C₂×C₅	semidirect
213. #2401	C₂×C₅	semidirect
214. #2399	C₂×C₅	semidirect
216. #2396	C₂×C₅	semidirect
217. #2396	C₂×C₅	semidirect
219. C₄×C₄⋊Q₈	C₂×C₅	semidirect
220. C₄×#126	C₂×C₅	semidirect
728. C₅	#36697	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2843	2
C₅×#2839	2
C₅×#2838	2
C₅×#2837	2
C₅×#2836	2
C₅×#2833	2
C₅×#2832	2
C₅×#2831	2
C₅×#2823	2
C₅×#2821	2
C₅×#2402	2
C₅×#2401	2
C₅×#2399	2
C₅×#2398	2
C₅×#2396	2
C₅×#2395	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#126	2
#36697	5

Subgroups — C5×#36697 #11959417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#36697 #11959417