Subgroups — C₅×#34316 #11957036

Order 1280.

2548 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
2	C₅×#2374	C₂	1	4	yes	maximal, complemented
3	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	2	yes	maximal, complemented
5	C₅×#2362	C₂	1	2	yes	maximal, complemented
6	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2345	C₂	1	2	yes	maximal, complemented
9	C₅×#2341	C₂	1	2	yes	maximal, complemented
10	C₅×#2335	C₂	1	4	yes	maximal, complemented
11	C₅×#2324	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₅×#2297	C₂	1	2	yes	maximal, complemented
15	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2274	C₂	1	2	yes	maximal, complemented
17	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₅×#41	C₂²	1	2	yes	—
19	C₅×#547	C₄	1	16	yes	complemented
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#123	C₂²	1	4	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₅×#121	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₅×#117	C₂²	1	2	yes	—
32	C₂×C₅×#117	C₂²	1	2	yes	—
33	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₄²×C₅	C₂²	1	2	yes	—
35	C₅×#391	C₂²	1	2	yes	—
36	C₅×#391	C₂²	1	2	yes	—
37	C₅×#390	C₂²	1	1	yes	characteristic
38	C₅×#390	C₂²	1	1	yes	characteristic
39	C₅×#390	C₂²	1	2	yes	—
40	C₅×#390	C₂²	1	4	yes	—
41	C₅×#390	C₂²	1	2	yes	—
42	C₅×#390	C₂²	1	4	yes	—
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	2	yes	—
46	C₅×#389	C₂²	1	2	yes	—
47	C₅×#389	C₂²	1	2	yes	—
48	C₅×#388	C₂²	1	2	yes	—
49	C₅×#388	C₂²	1	2	yes	—
50	C₅×#388	C₂²	1	4	yes	—
51	C₅×#388	C₂²	1	4	yes	—
52	C₅×#388	C₂²	1	4	yes	—
53	C₅×#388	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#387	C₂²	1	4	yes	—
56	C₅×#387	C₂²	1	4	yes	—
57	C₅×#386	C₂²	1	4	yes	—
58	C₅×#386	C₂²	1	4	yes	—
59	C₅×#385	C₂²	1	4	yes	—
60	C₅×#384	C₂²	1	1	yes	characteristic
61	C₅×#380	C₂²	1	2	yes	—
62	C₅×#380	C₂²	1	2	yes	—
63	C₅×#380	C₂²	1	4	yes	—
64	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
68	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
71	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
75	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₄³×C₅	C₂²	1	1	yes	characteristic
84	#34316	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂×C₅×#41	—	4	4	no	—
86	C₂×C₅×#41	—	4	4	no	—
87	C₂×C₅×#41	C₂×C₄	1	16	yes	complemented
88	C₂²×C₅×Q₈	C₂³	1	2	yes	—
89	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂²×C₅×D₄	C₂³	1	4	yes	—
92	C₂³×C₄×C₅	C₂³	1	2	yes	—
93	C₂³×C₄×C₅	C₂³	1	2	yes	—
94	C₂³×C₄×C₅	C₂³	1	2	yes	—
95	C₂³×C₄×C₅	C₂³	1	2	yes	—
96	C₂³×C₄×C₅	C₂³	1	4	yes	—
97	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
98	C₅×#123	C₂×C₄	1	32	yes	complemented
99	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
100	C₅×#121	C₂×C₄	1	16	yes	—
101	C₄×C₅×Q₈	—	4	4	no	—
102	C₄×C₅×Q₈	—	4	4	no	—
103	C₄×C₅×D₄	—	2	4	no	—
104	C₄×C₅×D₄	—	2	4	no	—
105	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
106	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
107	C₅×#117	—	2	8	no	—
108	C₅×#117	—	2	8	no	—
109	C₅×#117	—	4	4	no	—
110	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
111	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₄²×C₅	—	4	4	no	—
141	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂³	1	4	yes	—
146	C₂×C₄²×C₅	C₂³	1	2	yes	—
147	C₂×C₄²×C₅	C₂³	1	2	yes	—
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₅	C₂³	1	2	yes	—
150	C₂×C₄²×C₅	C₂³	1	2	yes	—
151	C₂×C₄²×C₅	C₂³	1	4	yes	—
152	C₂×C₄²×C₅	C₂³	1	4	yes	—
153	C₂×C₄²×C₅	C₂³	1	4	yes	—
154	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
156	C₅×#95	C₂³	1	2	yes	—
157	C₅×#95	C₂³	1	2	yes	—
158	C₅×#95	C₂³	1	2	yes	—
159	C₅×#95	C₂³	1	4	yes	—
160	C₅×#95	C₂³	1	2	yes	—
161	C₅×#95	C₂³	1	4	yes	—
162	C₅×#95	C₂³	1	4	yes	—
163	C₅×#95	C₂³	1	4	yes	—
164	C₅×#95	C₂³	1	4	yes	—
165	C₅×#95	C₂³	1	2	yes	—
166	C₅×#95	C₂³	1	4	yes	—
167	C₅×#95	C₂³	1	2	yes	—
168	C₂×#547	C₂×C₅	1	1	yes	characteristic
169	#2374	C₂×C₅	1	4	yes	complemented
170	#2365	C₂×C₅	1	1	yes	characteristic, complemented
171	#2363	C₂×C₅	1	2	yes	complemented
172	#2362	C₂×C₅	1	2	yes	complemented
173	#2354	C₂×C₅	1	1	yes	characteristic, complemented
174	#2354	C₂×C₅	1	1	yes	characteristic, complemented
175	#2345	C₂×C₅	1	2	yes	complemented
176	#2341	C₂×C₅	1	2	yes	complemented
177	#2335	C₂×C₅	1	4	yes	complemented
178	#2324	C₂×C₅	1	2	yes	complemented
179	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
181	#2297	C₂×C₅	1	2	yes	complemented
182	#2293	C₂×C₅	1	1	yes	characteristic, complemented
183	#2274	C₂×C₅	1	2	yes	complemented
184	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
185	C₂⁴×C₅	C₂⁴	1	2	yes	—
186	C₂⁴×C₅	C₂⁴	1	2	yes	—
187	C₅×#41	—	4	32	no	—
188	C₂×C₅×Q₈	—	2	4	no	—
189	C₂×C₅×Q₈	—	2	4	no	—
190	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
191	C₂×C₅×D₄	—	2	2	no	—
192	C₂×C₅×D₄	—	2	2	no	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	4	4	no	—
196	C₂×C₅×D₄	—	4	4	no	—
197	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
198	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
199	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
200	C₂²×C₄×C₅	—	2	4	no	—
201	C₂²×C₄×C₅	—	2	4	no	—
202	C₂²×C₄×C₅	—	2	4	no	—
203	C₂²×C₄×C₅	—	2	4	no	—
204	C₂²×C₄×C₅	—	2	4	no	—
205	C₂²×C₄×C₅	—	2	4	no	—
206	C₂²×C₄×C₅	—	2	4	no	—
207	C₂²×C₄×C₅	—	4	2	no	—
208	C₂²×C₄×C₅	—	4	2	no	—
209	C₂²×C₄×C₅	—	4	2	no	—
210	C₂²×C₄×C₅	—	4	4	no	—
211	C₂²×C₄×C₅	—	4	4	no	—
212	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
213	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
214	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
215	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	4	no	—
232	C₅×C₄⋊C₄	—	2	4	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	2	no	—
235	C₅×C₄⋊C₄	—	2	4	no	—
236	C₅×C₄⋊C₄	—	2	2	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	—	4	4	no	—
239	C₅×C₄⋊C₄	—	4	4	no	—
240	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
241	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
242	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
243	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
244	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
245	C₅×C₄⋊C₄	#41	1	4	yes	complemented
246	C₅×C₂²⋊C₄	—	2	8	no	—
247	C₅×C₂²⋊C₄	—	2	4	no	—
248	C₅×C₂²⋊C₄	—	2	4	no	—
249	C₅×C₂²⋊C₄	—	2	4	no	—
250	C₅×C₂²⋊C₄	—	2	4	no	—
251	C₅×C₂²⋊C₄	—	2	4	no	—
252	C₅×C₂²⋊C₄	—	4	2	no	—
253	C₅×C₂²⋊C₄	—	4	4	no	—
254	C₅×C₂²⋊C₄	—	4	4	no	—
255	C₅×C₂²⋊C₄	—	4	4	no	—
256	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
257	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
258	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
259	C₄²×C₅	—	2	8	no	—
260	C₄²×C₅	—	2	4	no	—
261	C₄²×C₅	—	2	2	no	—
262	C₄²×C₅	—	2	2	no	—
263	C₄²×C₅	—	2	4	no	—
264	C₄²×C₅	—	2	2	no	—
265	C₄²×C₅	—	2	2	no	—
266	C₄²×C₅	—	4	2	no	—
267	C₄²×C₅	—	4	2	no	—
268	C₄²×C₅	—	4	1	no	—
269	C₄²×C₅	—	4	4	no	—
270	C₄²×C₅	—	4	4	no	—
271	C₄²×C₅	—	4	4	no	—
272	C₄²×C₅	C₂²×C₄	1	4	yes	—
273	C₄²×C₅	#41	1	4	yes	complemented
274	C₂²×#41	C₂²×C₅	1	2	yes	—
275	#547	C₄×C₅	1	16	yes	complemented
276	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
277	C₂×#123	C₂²×C₅	1	4	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
279	C₂×#121	C₂²×C₅	1	2	yes	—
280	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
281	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
282	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×#117	C₂²×C₅	1	2	yes	—
287	C₂×#117	C₂²×C₅	1	2	yes	—
288	C₂×#117	C₂²×C₅	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
290	C₂²×C₄²	C₂²×C₅	1	2	yes	—
291	#391	C₂²×C₅	1	2	yes	—
292	#391	C₂²×C₅	1	2	yes	—
293	#390	C₂²×C₅	1	4	yes	—
294	#390	C₂²×C₅	1	2	yes	—
295	#390	C₂²×C₅	1	4	yes	—
296	#390	C₂²×C₅	1	1	yes	characteristic
297	#390	C₂²×C₅	1	2	yes	—
298	#390	C₂²×C₅	1	1	yes	characteristic
299	#389	C₂²×C₅	1	2	yes	—
300	#389	C₂²×C₅	1	2	yes	—
301	#389	C₂²×C₅	1	2	yes	—
302	#389	C₂²×C₅	1	1	yes	characteristic
303	#389	C₂²×C₅	1	1	yes	characteristic
304	#388	C₂²×C₅	1	4	yes	—
305	#388	C₂²×C₅	1	2	yes	—
306	#388	C₂²×C₅	1	4	yes	—
307	#388	C₂²×C₅	1	4	yes	—
308	#388	C₂²×C₅	1	4	yes	—
309	#388	C₂²×C₅	1	2	yes	—
310	#387	C₂²×C₅	1	4	yes	—
311	#387	C₂²×C₅	1	4	yes	—
312	#387	C₂²×C₅	1	4	yes	—
313	#386	C₂²×C₅	1	4	yes	—
314	#386	C₂²×C₅	1	4	yes	—
315	#385	C₂²×C₅	1	4	yes	—
316	#384	C₂²×C₅	1	1	yes	characteristic
317	#380	C₂²×C₅	1	2	yes	—
318	#380	C₂²×C₅	1	4	yes	—
319	#380	C₂²×C₅	1	2	yes	—
320	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
321	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
322	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
323	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
324	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
325	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
329	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
331	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
332	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
334	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
336	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
338	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
339	C₄³	C₂²×C₅	1	1	yes	characteristic
340	C₂³×C₅	—	2	2	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	2	2	no	—
346	C₂³×C₅	—	2	2	no	—
347	C₂³×C₅	—	2	2	no	—
348	C₂³×C₅	—	2	2	no	—
349	C₂³×C₅	—	2	2	no	—
350	C₂³×C₅	—	2	2	no	—
351	C₂³×C₅	—	2	2	no	—
352	C₂³×C₅	C₂³×C₄	1	4	yes	—
353	C₂³×C₅	C₂³×C₄	1	4	yes	—
354	C₂³×C₅	C₂⁵	1	1	yes	characteristic
355	C₅×Q₈	—	2	16	no	—
356	C₅×D₄	—	2	8	no	—
357	C₅×D₄	—	2	8	no	—
358	C₅×D₄	—	4	16	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	4	no	—
369	C₂×C₄×C₅	—	2	4	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	2	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	16	no	—
376	C₂×C₄×C₅	—	2	16	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	4	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	4	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	2	no	—
390	C₂×C₄×C₅	—	2	4	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	4	16	no	—
393	C₂×C₄×C₅	—	4	8	no	—
394	C₂×C₄×C₅	—	4	8	no	—
395	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
396	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
397	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
398	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
399	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
400	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
401	C₂×C₄×C₅	C₂×#41	1	4	yes	—
402	C₂×C₄×C₅	C₂×#41	1	2	yes	—
403	C₂×C₄×C₅	C₂×#41	1	2	yes	—
404	C₂×C₄×C₅	C₂×#41	1	2	yes	—
405	C₂×C₄×C₅	C₂×#41	1	2	yes	—
406	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
409	C₂×#41	—	4	4	no	—
410	C₂×#41	—	4	4	no	—
411	C₂×#41	C₂×C₄×C₅	1	16	yes	complemented
412	C₂²×Q₈	C₂³×C₅	1	2	yes	—
413	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
415	C₂²×D₄	C₂³×C₅	1	4	yes	—
416	C₂³×C₄	C₂³×C₅	1	2	yes	—
417	C₂³×C₄	C₂³×C₅	1	2	yes	—
418	C₂³×C₄	C₂³×C₅	1	2	yes	—
419	C₂³×C₄	C₂³×C₅	1	2	yes	—
420	C₂³×C₄	C₂³×C₅	1	4	yes	—
421	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
422	#123	C₂×C₄×C₅	1	32	yes	complemented
423	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
424	#121	C₂×C₄×C₅	1	16	yes	—
425	C₄×Q₈	—	4	4	no	—
426	C₄×Q₈	—	4	4	no	—
427	C₄×D₄	—	2	4	no	—
428	C₄×D₄	—	2	4	no	—
429	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
430	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
431	#117	—	2	8	no	—
432	#117	—	2	8	no	—
433	#117	—	4	4	no	—
434	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
435	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
464	C₂×C₄²	—	4	4	no	—
465	C₂×C₄²	C₂³×C₅	1	4	yes	—
466	C₂×C₄²	C₂³×C₅	1	2	yes	—
467	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₅	1	2	yes	—
470	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₅	1	4	yes	—
473	C₂×C₄²	C₂³×C₅	1	4	yes	—
474	C₂×C₄²	C₂³×C₅	1	4	yes	—
475	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₅	1	2	yes	—
477	C₂×C₄²	C₂³×C₅	1	2	yes	—
478	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
480	#95	C₂³×C₅	1	2	yes	—
481	#95	C₂³×C₅	1	2	yes	—
482	#95	C₂³×C₅	1	2	yes	—
483	#95	C₂³×C₅	1	4	yes	—
484	#95	C₂³×C₅	1	2	yes	—
485	#95	C₂³×C₅	1	4	yes	—
486	#95	C₂³×C₅	1	4	yes	—
487	#95	C₂³×C₅	1	4	yes	—
488	#95	C₂³×C₅	1	4	yes	—
489	#95	C₂³×C₅	1	2	yes	—
490	#95	C₂³×C₅	1	4	yes	—
491	#95	C₂³×C₅	1	2	yes	—
492	C₂²×C₅	—	2	4	no	—
493	C₂²×C₅	—	2	4	no	—
494	C₂²×C₅	—	2	4	no	—
495	C₂²×C₅	—	2	4	no	—
496	C₂²×C₅	—	2	4	no	—
497	C₂²×C₅	—	2	4	no	—
498	C₂²×C₅	—	4	2	no	—
499	C₂²×C₅	—	4	2	no	—
500	C₂²×C₅	—	4	2	no	—
501	C₂²×C₅	—	4	2	no	—
502	C₂²×C₅	—	4	2	no	—
503	C₂²×C₅	—	4	2	no	—
504	C₂²×C₅	—	4	2	no	—
505	C₂²×C₅	—	4	2	no	—
506	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
507	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
509	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
512	C₂²×C₅	#585	1	1	yes	characteristic
513	C₄×C₅	—	2	4	no	—
514	C₄×C₅	—	2	4	no	—
515	C₄×C₅	—	2	8	no	—
516	C₄×C₅	—	2	2	no	—
517	C₄×C₅	—	2	2	no	—
518	C₄×C₅	—	2	2	no	—
519	C₄×C₅	—	2	2	no	—
520	C₄×C₅	—	2	4	no	—
521	C₄×C₅	—	4	2	no	—
522	C₄×C₅	—	4	2	no	—
523	C₄×C₅	—	4	2	no	—
524	C₄×C₅	—	4	1	no	—
525	C₄×C₅	—	4	4	no	—
526	C₄×C₅	C₄×#41	1	4	yes	—
527	C₄×C₅	#518	1	4	yes	—
528	C₂⁴	C₂⁴×C₅	1	2	yes	—
529	C₂⁴	C₂⁴×C₅	1	2	yes	—
530	#41	—	4	32	no	—
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
541	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
542	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
556	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
557	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
558	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
584	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
585	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
586	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
587	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
588	C₄⋊C₄	C₅×#41	1	4	yes	complemented
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
600	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
601	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
602	C₄²	—	2	8	no	—
603	C₄²	—	2	4	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	4	2	no	—
610	C₄²	—	4	2	no	—
611	C₄²	—	4	4	no	—
612	C₄²	—	4	4	no	—
613	C₄²	—	4	4	no	—
614	C₄²	—	4	1	no	—
615	C₄²	C₂²×C₄×C₅	1	4	yes	—
616	C₄²	C₅×#41	1	4	yes	complemented
617	C₂×C₅	—	4	4	no	—
618	C₂×C₅	—	4	4	no	—
619	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
620	C₂×C₅	C₂×#518	1	1	yes	characteristic
621	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
622	C₂×C₅	#3506	1	1	yes	characteristic
623	C₂×C₅	#3511	1	1	yes	characteristic
624	C₂×C₅	#3517	1	1	yes	characteristic
625	C₂×C₅	#3520	1	1	yes	characteristic
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	C₂³×C₄×C₅	1	4	yes	—
639	C₂³	C₂³×C₄×C₅	1	4	yes	—
640	C₂³	C₂⁵×C₅	1	1	yes	characteristic
641	Q₈	—	2	16	no	—
642	D₄	—	2	8	no	—
643	D₄	—	2	8	no	—
644	D₄	—	4	16	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	16	no	—
662	C₂×C₄	—	2	16	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	4	16	no	—
679	C₂×C₄	—	4	8	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
682	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
683	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
684	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
685	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
686	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
687	C₂×C₄	C₂×C₅×#41	1	4	yes	—
688	C₂×C₄	C₂×C₅×#41	1	2	yes	—
689	C₂×C₄	C₂×C₅×#41	1	2	yes	—
690	C₂×C₄	C₂×C₅×#41	1	2	yes	—
691	C₂×C₄	C₂×C₅×#41	1	2	yes	—
692	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
693	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
694	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
695	C₅	#34316	1	1	yes	characteristic, direct product factor, Sylow
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
711	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
712	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
713	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
716	C₂²	C₅×#585	1	1	yes	characteristic
717	C₄	—	2	4	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	8	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	4	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	4	no	—
730	C₄	C₄×C₅×#41	1	4	yes	—
731	C₄	C₅×#518	1	4	yes	—
732	C₂	—	4	4	no	—
733	C₂	—	4	4	no	—
734	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
735	C₂	C₂×C₅×#518	1	1	yes	characteristic
736	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
737	C₂	C₅×#3506	1	1	yes	characteristic
738	C₂	C₅×#3511	1	1	yes	characteristic
739	C₂	C₅×#3517	1	1	yes	characteristic
740	C₂	C₅×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2374	C₂	semidirect
3. C₅×#2365	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2362	C₂	semidirect
6. C₅×#2354	C₂	semidirect
7. C₅×#2354	C₂	semidirect
8. C₅×#2345	C₂	semidirect
9. C₅×#2341	C₂	semidirect
10. C₅×#2335	C₂	semidirect
11. C₅×#2324	C₂	semidirect
12. C₄×C₅×C₄⋊Q₈	C₂	semidirect
13. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
14. C₅×#2297	C₂	semidirect
15. C₅×#2293	C₂	semidirect
16. C₅×#2274	C₂	semidirect
17. C₄²×C₅×D₄	C₂	semidirect
19. C₅×#547	C₄	semidirect
84. #34316	C₅	direct (N × H)
87. C₂×C₅×#41	C₂×C₄	semidirect
97. C₅×C₄⋊Q₈	C₂×C₄	semidirect
98. C₅×#123	C₂×C₄	semidirect
99. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
106. C₄×C₅×D₄	C₂×C₄	semidirect
110. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
169. #2374	C₂×C₅	semidirect
170. #2365	C₂×C₅	semidirect
171. #2363	C₂×C₅	semidirect
172. #2362	C₂×C₅	semidirect
173. #2354	C₂×C₅	semidirect
174. #2354	C₂×C₅	semidirect
175. #2345	C₂×C₅	semidirect
176. #2341	C₂×C₅	semidirect
177. #2335	C₂×C₅	semidirect
178. #2324	C₂×C₅	semidirect
179. C₄×C₄⋊Q₈	C₂×C₅	semidirect
180. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
181. #2297	C₂×C₅	semidirect
182. #2293	C₂×C₅	semidirect
183. #2274	C₂×C₅	semidirect
184. C₄²×D₄	C₂×C₅	semidirect
245. C₅×C₄⋊C₄	#41	semidirect
273. C₄²×C₅	#41	semidirect
275. #547	C₄×C₅	semidirect
411. C₂×#41	C₂×C₄×C₅	semidirect
421. C₄⋊Q₈	C₂×C₄×C₅	semidirect
422. #123	C₂×C₄×C₅	semidirect
423. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
430. C₄×D₄	C₂×C₄×C₅	semidirect
434. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
588. C₄⋊C₄	C₅×#41	semidirect
616. C₄²	C₅×#41	semidirect
695. C₅	#34316	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×#547	2
C₅×#2374	2
C₅×#2365	2
C₅×#2363	2
C₅×#2362	2
C₅×#2354	2
C₅×#2345	2
C₅×#2341	2
C₅×#2335	2
C₅×#2324	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2297	2
C₅×#2293	2
C₅×#2274	2
C₄²×C₅×D₄	2
#34316	5

Subgroups — C5×#34316 #11957036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34316 #11957036