Subgroups — C₅×#66108 #13106928

Order 1600.

604 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#4149	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#4144	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#686	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4062	C₂	1	2	yes	maximal, complemented
7	C₅×#4060	C₂	1	2	yes	maximal, complemented
8	C₅×#4057	C₂	1	2	yes	maximal, complemented
9	C₅×D₅×D₈	C₂	1	2	yes	maximal, complemented
10	C₅×#4054	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4053	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅²×#41	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₅×C₂²⋊D₅	—	2	2	no	—
15	C₅×#713	C₂²	1	2	yes	complemented
16	C₅×#711	—	2	1	no	—
17	C₅×#711	C₂²	1	2	yes	complemented
18	C₅×D₄×D₅	—	2	2	no	—
19	C₅×D₄×D₅	—	2	1	no	—
20	C₅×D₄×D₅	C₂²	1	2	yes	complemented
21	C₅×D₄×D₅	C₂²	1	2	yes	complemented
22	C₅×#709	—	2	1	no	—
23	C₅×#709	C₂²	1	1	yes	characteristic
24	C₅×#709	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×D₂₀	—	2	1	no	—
26	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
27	C₅²×SD₁₆	C₂²	1	2	yes	complemented
28	C₅²×D₈	C₂²	1	2	yes	complemented
29	C₅²×M₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₅×#689	C₂²	1	1	yes	characteristic, complemented
31	C₅×#688	C₂²	1	1	yes	characteristic, complemented
32	C₅×#687	C₂²	1	1	yes	characteristic, complemented
33	C₅×#686	C₂²	1	1	yes	characteristic, complemented
34	C₅×#686	C₂²	1	2	yes	complemented
35	C₅×#686	C₂²	1	2	yes	complemented
36	C₂×C₅×#168	C₂²	1	1	yes	characteristic, complemented
37	C₅×D₄₀	C₂²	1	2	yes	complemented
38	C₅×#677	C₂²	1	2	yes	complemented
39	C₅×#676	C₂²	1	2	yes	complemented
40	C₅×C₈×D₅	C₂²	1	2	yes	complemented
41	C₅×#576	—	5	1	no	maximal
42	#66108	C₅	1	1	yes	maximal, characteristic, direct product factor
43	C₂³×C₅²	—	2	1	no	—
44	C₂²×C₅×D₅	—	2	1	no	—
45	C₂²×C₅×D₅	—	2	2	no	—
46	C₂²×C₅×D₅	—	2	2	no	—
47	C₅²×Q₈	C₂³	1	1	yes	characteristic
48	C₅²×D₄	—	2	1	no	—
49	C₅²×D₄	—	2	1	no	—
50	C₅²×D₄	C₂³	1	1	yes	characteristic
51	C₅²×D₄	C₂³	1	2	yes	—
52	C₂×C₄×C₅²	—	2	1	no	—
53	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
54	C₅×C₂²⋊D₅	—	2	1	no	—
55	C₅×C₂²⋊D₅	—	2	2	no	—
56	C₅×C₂²⋊D₅	—	2	2	no	—
57	C₅×C₂²⋊D₅	—	2	2	no	—
58	C₅×C₂²⋊D₅	D₄	1	2	yes	—
59	C₂×C₅×Dic₅	—	2	2	no	—
60	C₅×D₂₀	—	2	2	no	—
61	C₅×D₂₀	—	2	1	no	—
62	C₅×D₂₀	D₄	1	1	yes	characteristic
63	C₅×D₂₀	C₂³	1	2	yes	—
64	C₅×D₂₀	C₂³	1	1	yes	characteristic
65	C₄×C₅×D₅	—	2	1	no	—
66	C₄×C₅×D₅	—	2	2	no	—
67	C₄×C₅×D₅	C₂³	1	2	yes	—
68	C₅×Dic₁₀	D₄	1	1	yes	characteristic
69	C₅×Dic₁₀	C₂³	1	1	yes	characteristic
70	C₅²×C₈	C₂³	1	2	yes	—
71	C₅×#168	C₂³	1	1	yes	characteristic
72	C₅×#168	C₂³	1	1	yes	characteristic
73	C₅×H(5,𝔽₂)	—	5	1	no	—
74	C₅×H(5,𝔽₂)	—	5	1	no	—
75	#4149	C₂×C₅	1	1	yes	characteristic, complemented
76	#4144	C₂×C₅	1	1	yes	characteristic, complemented
77	C₅×AGL(1,ℤ/8)	—	2	2	no	—
78	C₅×AGL(1,ℤ/8)	—	5	2	no	—
79	C₅×AGL(1,ℤ/8)	—	5	2	no	—
80	C₅×AGL(1,ℤ/8)	—	5	1	no	—
81	C₅×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
82	C₅×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
83	C₅×#135	—	5	1	no	—
84	C₅×#135	—	5	2	no	—
85	C₂×C₅×D₈	—	5	1	no	—
86	C₂×C₅×D₈	—	5	2	no	—
87	C₅×#131	—	5	1	no	—
88	#4096	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#686	C₂×C₅	1	1	yes	characteristic, complemented
90	#4062	C₂×C₅	1	2	yes	complemented
91	#4060	C₂×C₅	1	2	yes	complemented
92	#4057	C₂×C₅	1	2	yes	complemented
93	D₅×D₈	C₂×C₅	1	2	yes	complemented
94	#4054	C₂×C₅	1	1	yes	characteristic, complemented
95	#4053	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₅²	—	2	2	no	—
97	C₂²×C₅²	—	2	1	no	—
98	C₂²×C₅²	—	8	1	no	—
99	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
100	C₂×C₅×D₅	—	2	2	no	—
101	C₂×C₅×D₅	—	2	1	no	—
102	C₂×C₅×D₅	—	8	1	no	—
103	C₂×C₅×D₅	—	8	2	no	—
104	C₂×C₅×D₅	—	8	2	no	—
105	C₂×C₅×D₅	C₂×D₄	1	2	yes	—
106	C₄×C₅²	—	2	1	no	—
107	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
108	C₄×C₅²	C₂⁴	1	1	yes	characteristic
109	C₅×Dic₅	—	2	1	no	—
110	C₅×Dic₅	C₂×D₄	1	2	yes	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	5	1	no	—
113	C₅×#41	—	5	2	no	—
114	C₅×#41	—	5	2	no	—
115	C₅×#41	—	5	1	no	—
116	C₅×#41	—	10	1	no	—
117	C₅×#41	—	10	1	no	—
118	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
119	C₅×#41	C₂²×C₅	1	1	yes	characteristic, complemented
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	5	2	no	—
122	C₂×C₅×D₄	—	5	2	no	—
123	C₂×C₅×D₄	—	5	1	no	—
124	C₂×C₅×D₄	—	10	1	no	—
125	C₂×C₅×D₄	—	10	2	no	—
126	C₂×C₅×D₄	—	10	1	no	—
127	C₂×C₅×D₄	—	10	2	no	—
128	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
129	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₂×C₂²⋊D₅	—	2	2	no	—
131	#713	C₂²×C₅	1	2	yes	complemented
132	#711	—	2	1	no	—
133	#711	C₂²×C₅	1	2	yes	complemented
134	D₄×D₅	—	2	2	no	—
135	D₄×D₅	—	2	1	no	—
136	D₄×D₅	C₂²×C₅	1	2	yes	complemented
137	D₄×D₅	C₂²×C₅	1	2	yes	complemented
138	#709	—	2	1	no	—
139	#709	C₂²×C₅	1	1	yes	characteristic
140	#709	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₂×D₂₀	—	2	1	no	—
142	C₂×D₂₀	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₅×Q₁₆	—	5	1	no	—
144	C₅×SD₁₆	—	2	4	no	—
145	C₅×SD₁₆	—	5	1	no	—
146	C₅×SD₁₆	—	5	1	no	—
147	C₅×SD₁₆	—	5	2	no	—
148	C₅×SD₁₆	C₂×D₅	1	2	yes	complemented
149	C₅×SD₁₆	C₂²×C₅	1	2	yes	complemented
150	C₅×D₈	—	2	4	no	—
151	C₅×D₈	—	5	2	no	—
152	C₅×D₈	—	5	1	no	—
153	C₅×D₈	—	5	2	no	—
154	C₅×D₈	—	5	2	no	—
155	C₅×D₈	C₂×D₅	1	2	yes	complemented
156	C₅×D₈	C₂²×C₅	1	2	yes	complemented
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	—	5	2	no	—
159	C₅×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
160	C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
161	C₂×C₅×C₈	—	5	1	no	—
162	C₂×C₅×C₈	—	5	2	no	—
163	#689	C₂²×C₅	1	1	yes	characteristic, complemented
164	#688	C₂²×C₅	1	1	yes	characteristic, complemented
165	#687	C₂²×C₅	1	1	yes	characteristic, complemented
166	#686	C₂²×C₅	1	1	yes	characteristic, complemented
167	#686	C₂²×C₅	1	2	yes	complemented
168	#686	C₂²×C₅	1	2	yes	complemented
169	C₂×#168	C₂²×C₅	1	1	yes	characteristic, complemented
170	D₄₀	C₂²×C₅	1	2	yes	complemented
171	#677	C₂²×C₅	1	2	yes	complemented
172	#676	C₂²×C₅	1	2	yes	complemented
173	C₈×D₅	C₂²×C₅	1	2	yes	complemented
174	#576	—	5	1	no	Sylow
175	C₂×C₅²	—	2	1	no	—
176	C₂×C₅²	—	4	1	no	—
177	C₂×C₅²	—	4	2	no	—
178	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
179	C₅×D₅	—	2	2	no	—
180	C₅×D₅	—	4	2	no	—
181	C₅×D₅	—	4	1	no	—
182	C₂³×C₅	—	2	1	no	—
183	C₂³×C₅	—	2	1	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	—	10	2	no	—
186	C₂³×C₅	—	10	2	no	—
187	C₂³×C₅	—	10	1	no	—
188	C₂²×D₅	—	2	1	no	—
189	C₂²×D₅	—	2	2	no	—
190	C₂²×D₅	—	2	2	no	—
191	C₅×Q₈	—	2	2	no	—
192	C₅×Q₈	—	5	1	no	—
193	C₅×Q₈	—	5	1	no	—
194	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
195	C₅×Q₈	C₂³×C₅	1	1	yes	characteristic
196	C₅×D₄	—	2	1	no	—
197	C₅×D₄	—	2	1	no	—
198	C₅×D₄	—	2	1	no	—
199	C₅×D₄	—	2	1	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	—	2	4	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	5	2	no	—
205	C₅×D₄	—	5	1	no	—
206	C₅×D₄	—	5	2	no	—
207	C₅×D₄	—	5	1	no	—
208	C₅×D₄	—	10	2	no	—
209	C₅×D₄	—	10	2	no	—
210	C₅×D₄	—	10	2	no	—
211	C₅×D₄	—	10	2	no	—
212	C₅×D₄	—	10	1	no	—
213	C₅×D₄	—	10	1	no	—
214	C₅×D₄	C₂²×D₅	1	2	yes	—
215	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
216	C₅×D₄	C₂³×C₅	1	2	yes	—
217	C₅×D₄	C₂³×C₅	1	1	yes	characteristic
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	5	2	no	—
223	C₂×C₄×C₅	—	10	2	no	—
224	C₂×C₄×C₅	—	10	2	no	—
225	C₂×C₄×C₅	—	10	1	no	—
226	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
228	C₂²⋊D₅	—	2	1	no	—
229	C₂²⋊D₅	—	2	2	no	—
230	C₂²⋊D₅	—	2	2	no	—
231	C₂²⋊D₅	—	2	2	no	—
232	C₂²⋊D₅	C₅×D₄	1	2	yes	—
233	C₂×Dic₅	—	2	2	no	—
234	D₂₀	—	2	2	no	—
235	D₂₀	—	2	1	no	—
236	D₂₀	C₅×D₄	1	1	yes	characteristic
237	D₂₀	C₂³×C₅	1	2	yes	—
238	D₂₀	C₂³×C₅	1	1	yes	characteristic
239	C₄×D₅	—	2	1	no	—
240	C₄×D₅	—	2	2	no	—
241	C₄×D₅	C₂³×C₅	1	2	yes	—
242	Dic₁₀	C₅×D₄	1	1	yes	characteristic
243	Dic₁₀	C₂³×C₅	1	1	yes	characteristic
244	C₅×C₈	—	2	4	no	—
245	C₅×C₈	—	5	1	no	—
246	C₅×C₈	—	5	1	no	—
247	C₅×C₈	C₂²×D₅	1	2	yes	—
248	C₅×C₈	C₂³×C₅	1	2	yes	—
249	#168	C₂³×C₅	1	1	yes	characteristic
250	#168	C₂³×C₅	1	1	yes	characteristic
251	H(5,𝔽₂)	—	5	1	no	—
252	H(5,𝔽₂)	—	5	1	no	—
253	AGL(1,ℤ/8)	—	5	2	no	—
254	AGL(1,ℤ/8)	—	5	2	no	—
255	AGL(1,ℤ/8)	—	5	1	no	—
256	AGL(1,ℤ/8)	C₅×D₅	1	1	yes	characteristic, complemented
257	#135	—	5	1	no	—
258	#135	—	5	2	no	—
259	C₂×D₈	—	5	1	no	—
260	C₂×D₈	—	5	2	no	—
261	#131	—	5	1	no	—
262	C₅²	#576	1	1	yes	characteristic, complemented, Sylow
263	C₂²×C₅	—	2	1	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	4	no	—
270	C₂²×C₅	—	5	2	no	—
271	C₂²×C₅	—	8	1	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	—	8	4	no	—
274	C₂²×C₅	—	10	2	no	—
275	C₂²×C₅	—	10	1	no	—
276	C₂²×C₅	—	40	1	no	—
277	C₂²×C₅	—	40	2	no	—
278	C₂²×C₅	—	40	2	no	—
279	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
280	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂×D₅	—	2	2	no	—
282	C₂×D₅	—	2	1	no	—
283	C₂×D₅	—	8	2	no	—
284	C₂×D₅	—	8	2	no	—
285	C₂×D₅	—	8	1	no	—
286	C₂×D₅	C₂×C₅×D₄	1	2	yes	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	4	2	no	—
292	C₄×C₅	—	5	2	no	—
293	C₄×C₅	—	10	1	no	—
294	C₄×C₅	D₄×D₅	1	1	yes	characteristic
295	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
296	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
297	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
298	Dic₅	—	2	1	no	—
299	Dic₅	C₂×C₅×D₄	1	2	yes	—
300	#41	—	5	1	no	—
301	#41	—	5	2	no	—
302	#41	—	5	2	no	—
303	#41	—	5	1	no	—
304	#41	—	10	1	no	—
305	#41	—	10	1	no	—
306	#41	C₂×C₅×D₅	1	1	yes	characteristic, complemented
307	C₂×D₄	—	5	2	no	—
308	C₂×D₄	—	5	2	no	—
309	C₂×D₄	—	5	1	no	—
310	C₂×D₄	—	10	1	no	—
311	C₂×D₄	—	10	2	no	—
312	C₂×D₄	—	10	1	no	—
313	C₂×D₄	—	10	2	no	—
314	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
315	Q₁₆	—	5	1	no	—
316	SD₁₆	—	5	1	no	—
317	SD₁₆	—	5	1	no	—
318	SD₁₆	—	5	2	no	—
319	SD₁₆	C₂×C₅×D₅	1	2	yes	complemented
320	D₈	—	5	2	no	—
321	D₈	—	5	1	no	—
322	D₈	—	5	2	no	—
323	D₈	—	5	2	no	—
324	D₈	C₂×C₅×D₅	1	2	yes	complemented
325	M₁₆	—	5	2	no	—
326	M₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
327	C₂×C₈	—	5	1	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	2	1	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	4	2	no	—
333	C₂×C₅	—	4	2	no	—
334	C₂×C₅	—	4	1	no	—
335	C₂×C₅	—	4	1	no	—
336	C₂×C₅	—	4	2	no	—
337	C₂×C₅	—	8	2	no	—
338	C₂×C₅	—	8	4	no	—
339	C₂×C₅	—	10	2	no	—
340	C₂×C₅	—	20	2	no	—
341	C₂×C₅	—	20	1	no	—
342	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
343	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
344	D₅	—	2	2	no	—
345	D₅	—	4	2	no	—
346	D₅	—	4	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	10	2	no	—
349	C₂³	—	10	2	no	—
350	C₂³	—	10	1	no	—
351	Q₈	—	5	1	no	—
352	Q₈	—	5	1	no	—
353	Q₈	C₂²×C₅×D₅	1	1	yes	characteristic
354	D₄	—	2	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	5	2	no	—
357	D₄	—	5	1	no	—
358	D₄	—	5	2	no	—
359	D₄	—	5	1	no	—
360	D₄	—	10	2	no	—
361	D₄	—	10	2	no	—
362	D₄	—	10	2	no	—
363	D₄	—	10	2	no	—
364	D₄	—	10	1	no	—
365	D₄	—	10	1	no	—
366	D₄	C₂²×C₅×D₅	1	2	yes	—
367	D₄	C₂²×C₅×D₅	1	1	yes	characteristic
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	5	2	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	10	2	no	—
372	C₂×C₄	—	10	1	no	—
373	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
374	C₈	—	5	1	no	—
375	C₈	—	5	1	no	—
376	C₈	C₂²×C₅×D₅	1	2	yes	—
377	C₅	—	2	2	no	—
378	C₅	#66108	1	1	yes	characteristic, direct product factor
379	C₅	C₅×#576	1	1	yes	characteristic, complemented
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	5	2	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	10	2	no	—
385	C₂²	—	10	1	no	—
386	C₂²	—	40	1	no	—
387	C₂²	—	40	2	no	—
388	C₂²	—	40	2	no	—
389	C₂²	C₅×D₄×D₅	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	5	2	no	—
392	C₄	—	10	1	no	—
393	C₄	C₅×D₄×D₅	1	1	yes	characteristic
394	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
395	C₂	—	2	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	4	1	no	—
398	C₂	—	10	2	no	—
399	C₂	—	20	2	no	—
400	C₂	—	20	1	no	—
401	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₅
Fitting	C₅²×AGL(1,ℤ/8)	C₂
socle	C₂×C₅²	C₂²×D₄
hypercenter	C₅×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₅×#576
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₅×#4149	C₂	semidirect
2. C₅×#4144	C₂	semidirect
3. C₅²×AGL(1,ℤ/8)	C₂	semidirect
4. C₅×#4096	C₂	semidirect
5. C₂×C₅×#686	C₂	semidirect
6. C₅×#4062	C₂	semidirect
7. C₅×#4060	C₂	semidirect
8. C₅×#4057	C₂	semidirect
9. C₅×D₅×D₈	C₂	semidirect
10. C₅×#4054	C₂	semidirect
11. C₅×#4053	C₂	semidirect
12. C₅²×#41	C₂²	semidirect
13. C₂×C₅²×D₄	C₂²	semidirect
15. C₅×#713	C₂²	semidirect
17. C₅×#711	C₂²	semidirect
20. C₅×D₄×D₅	C₂²	semidirect
21. C₅×D₄×D₅	C₂²	semidirect
24. C₅×#709	C₂²	semidirect
26. C₂×C₅×D₂₀	C₂²	semidirect
27. C₅²×SD₁₆	C₂²	semidirect
28. C₅²×D₈	C₂²	semidirect
29. C₅²×M₁₆	C₂²	semidirect
30. C₅×#689	C₂²	semidirect
31. C₅×#688	C₂²	semidirect
32. C₅×#687	C₂²	semidirect
33. C₅×#686	C₂²	semidirect
34. C₅×#686	C₂²	semidirect
35. C₅×#686	C₂²	semidirect
36. C₂×C₅×#168	C₂²	semidirect
37. C₅×D₄₀	C₂²	semidirect
38. C₅×#677	C₂²	semidirect
39. C₅×#676	C₂²	semidirect
40. C₅×C₈×D₅	C₂²	semidirect
42. #66108	C₅	direct (N × H)
75. #4149	C₂×C₅	semidirect
76. #4144	C₂×C₅	semidirect
81. C₅×AGL(1,ℤ/8)	D₅	semidirect
82. C₅×AGL(1,ℤ/8)	C₂×C₅	semidirect
88. #4096	C₂×C₅	semidirect
89. C₂×#686	C₂×C₅	semidirect
90. #4062	C₂×C₅	semidirect
91. #4060	C₂×C₅	semidirect
92. #4057	C₂×C₅	semidirect
93. D₅×D₈	C₂×C₅	semidirect
94. #4054	C₂×C₅	semidirect
95. #4053	C₂×C₅	semidirect
118. C₅×#41	C₂×D₅	semidirect
119. C₅×#41	C₂²×C₅	semidirect
128. C₂×C₅×D₄	C₂×D₅	semidirect
129. C₂×C₅×D₄	C₂²×C₅	semidirect
131. #713	C₂²×C₅	semidirect
133. #711	C₂²×C₅	semidirect
136. D₄×D₅	C₂²×C₅	semidirect
137. D₄×D₅	C₂²×C₅	semidirect
140. #709	C₂²×C₅	semidirect
142. C₂×D₂₀	C₂²×C₅	semidirect
148. C₅×SD₁₆	C₂×D₅	semidirect
149. C₅×SD₁₆	C₂²×C₅	semidirect
155. C₅×D₈	C₂×D₅	semidirect
156. C₅×D₈	C₂²×C₅	semidirect
159. C₅×M₁₆	C₂×D₅	semidirect
160. C₅×M₁₆	C₂²×C₅	semidirect
163. #689	C₂²×C₅	semidirect
164. #688	C₂²×C₅	semidirect
165. #687	C₂²×C₅	semidirect
166. #686	C₂²×C₅	semidirect
167. #686	C₂²×C₅	semidirect
168. #686	C₂²×C₅	semidirect
169. C₂×#168	C₂²×C₅	semidirect
170. D₄₀	C₂²×C₅	semidirect
171. #677	C₂²×C₅	semidirect
172. #676	C₂²×C₅	semidirect
173. C₈×D₅	C₂²×C₅	semidirect
256. AGL(1,ℤ/8)	C₅×D₅	semidirect
262. C₅²	#576	semidirect
306. #41	C₂×C₅×D₅	semidirect
314. C₂×D₄	C₂×C₅×D₅	semidirect
319. SD₁₆	C₂×C₅×D₅	semidirect
324. D₈	C₂×C₅×D₅	semidirect
326. M₁₆	C₂×C₅×D₅	semidirect
378. C₅	#66108	direct (N × H)
379. C₅	C₅×#576	semidirect

Maximal subgroups

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

subgroup	index
C₅×#4149	2
C₅×#4144	2
C₅²×AGL(1,ℤ/8)	2
C₅×#4096	2
C₂×C₅×#686	2
C₅×#4062	2
C₅×#4060	2
C₅×#4057	2
C₅×D₅×D₈	2
C₅×#4054	2
C₅×#4053	2
C₅×#576	5
#66108	5

Subgroups — C5×#66108 #13106928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66108 #13106928