Subgroups — C₅×#66109 #13106929

Order 1600.

584 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#4150	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×#687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4061	C₂	1	2	yes	maximal, complemented
7	C₅×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#4058	C₂	1	2	yes	maximal, complemented
9	C₅×#4057	C₂	1	2	yes	maximal, complemented
10	C₅×#4055	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
14	C₂×C₅×C₂²⋊D₅	—	2	2	no	—
15	C₅×Q₈×D₅	C₂²	1	2	yes	complemented
16	C₅×#711	—	2	2	no	—
17	C₅×#711	—	2	1	no	—
18	C₅×#711	C₂²	1	2	yes	—
19	C₅×#711	C₂²	1	2	yes	complemented
20	C₅×D₄×D₅	—	2	1	no	—
21	C₅×D₄×D₅	C₂²	1	2	yes	—
22	C₅×#709	—	2	1	no	—
23	C₅×#709	C₂²	1	1	yes	characteristic
24	C₅×#709	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₁₀	—	2	1	no	—
26	C₂×C₅×Dic₁₀	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	2	yes	complemented
33	C₅×#687	C₂²	1	1	yes	characteristic, complemented
34	C₅×#687	C₂²	1	2	yes	complemented
35	C₅×#686	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#168	C₂²	1	1	yes	characteristic, complemented
37	C₅×Dic₂₀	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×#577	—	5	1	no	maximal
42	#66109	C₅	1	1	yes	maximal, characteristic, direct product factor
43	C₂³×C₅²	—	2	1	no	—
44	C₂²×C₅×D₅	—	2	2	no	—
45	C₅²×Q₈	C₂³	1	1	yes	characteristic
46	C₅²×D₄	—	2	1	no	—
47	C₅²×D₄	—	2	1	no	—
48	C₅²×D₄	C₂³	1	1	yes	characteristic
49	C₅²×D₄	C₂³	1	2	yes	—
50	C₂×C₄×C₅²	—	2	1	no	—
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₅×C₂²⋊D₅	—	2	1	no	—
53	C₅×C₂²⋊D₅	—	2	2	no	—
54	C₅×C₂²⋊D₅	—	2	2	no	—
55	C₅×C₂²⋊D₅	—	2	2	no	—
56	C₅×C₂²⋊D₅	D₄	1	2	yes	—
57	C₂×C₅×Dic₅	—	2	1	no	—
58	C₂×C₅×Dic₅	—	2	2	no	—
59	C₂×C₅×Dic₅	—	2	2	no	—
60	C₅×D₂₀	D₄	1	1	yes	characteristic
61	C₅×D₂₀	C₂³	1	1	yes	characteristic
62	C₄×C₅×D₅	—	2	2	no	—
63	C₄×C₅×D₅	—	2	1	no	—
64	C₄×C₅×D₅	C₂³	1	2	yes	—
65	C₅×Dic₁₀	—	2	1	no	—
66	C₅×Dic₁₀	—	2	2	no	—
67	C₅×Dic₁₀	D₄	1	1	yes	characteristic
68	C₅×Dic₁₀	C₂³	1	2	yes	—
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	C₅×2₋¹⁺⁴	—	5	1	no	—
74	C₅×H(5,𝔽₂)	—	5	1	no	—
75	#4150	C₂×C₅	1	1	yes	characteristic, complemented
76	#4144	C₂×C₅	1	1	yes	characteristic, complemented
77	C₅×#137	—	5	2	no	—
78	C₅×#137	—	5	1	no	—
79	C₅×AGL(1,ℤ/8)	—	2	2	no	—
80	C₅×AGL(1,ℤ/8)	—	5	2	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×SD₁₆	—	5	1	no	—
86	C₂×C₅×SD₁₆	—	5	2	no	—
87	C₅×#131	—	5	1	no	—
88	#4096	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×#687	C₂×C₅	1	1	yes	characteristic, complemented
90	#4061	C₂×C₅	1	2	yes	complemented
91	D₅×SD₁₆	C₂×C₅	1	2	yes	complemented
92	#4058	C₂×C₅	1	2	yes	complemented
93	#4057	C₂×C₅	1	2	yes	complemented
94	#4055	C₂×C₅	1	1	yes	characteristic, complemented
95	#4053	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₅²	—	2	1	no	—
97	C₂²×C₅²	—	2	2	no	—
98	C₂²×C₅²	—	8	1	no	—
99	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
100	C₂×C₅×D₅	—	2	1	no	—
101	C₂×C₅×D₅	—	8	2	no	—
102	C₂×C₅×D₅	C₂×D₄	1	2	yes	—
103	C₄×C₅²	—	2	1	no	—
104	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
105	C₄×C₅²	C₂⁴	1	1	yes	characteristic
106	C₅×Dic₅	—	2	2	no	—
107	C₅×Dic₅	—	2	1	no	—
108	C₅×Dic₅	C₂×D₄	1	2	yes	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	5	1	no	—
111	C₅×#41	—	5	2	no	—
112	C₅×#41	—	5	2	no	—
113	C₅×#41	—	5	1	no	—
114	C₅×#41	—	10	1	no	—
115	C₅×#41	—	10	2	no	—
116	C₅×#41	—	10	1	no	—
117	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
118	C₅×#41	C₂²×C₅	1	1	yes	characteristic, complemented
119	C₂×C₅×Q₈	—	5	2	no	—
120	C₂×C₅×Q₈	—	5	1	no	—
121	C₂×C₅×Q₈	—	10	1	no	—
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	5	2	no	—
124	C₂×C₅×D₄	—	10	1	no	—
125	C₂×C₅×D₄	—	10	2	no	—
126	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₂²⋊D₅	—	2	2	no	—
129	Q₈×D₅	C₂²×C₅	1	2	yes	complemented
130	#711	—	2	2	no	—
131	#711	—	2	1	no	—
132	#711	C₂²×C₅	1	2	yes	—
133	#711	C₂²×C₅	1	2	yes	complemented
134	D₄×D₅	—	2	1	no	—
135	D₄×D₅	C₂²×C₅	1	2	yes	—
136	#709	—	2	1	no	—
137	#709	C₂²×C₅	1	1	yes	characteristic
138	#709	C₂²×C₅	1	1	yes	characteristic
139	C₂×Dic₁₀	—	2	1	no	—
140	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₅×Q₁₆	—	5	1	no	—
142	C₅×Q₁₆	—	5	2	no	—
143	C₅×SD₁₆	—	2	4	no	—
144	C₅×SD₁₆	—	5	1	no	—
145	C₅×SD₁₆	—	5	2	no	—
146	C₅×SD₁₆	—	5	2	no	—
147	C₅×SD₁₆	—	5	1	no	—
148	C₅×SD₁₆	—	5	2	no	—
149	C₅×SD₁₆	C₂×D₅	1	2	yes	complemented
150	C₅×SD₁₆	C₂²×C₅	1	2	yes	complemented
151	C₅×D₈	—	2	4	no	—
152	C₅×D₈	—	5	1	no	—
153	C₅×D₈	C₂×D₅	1	2	yes	complemented
154	C₅×D₈	C₂²×C₅	1	2	yes	complemented
155	C₅×M₁₆	—	2	2	no	—
156	C₅×M₁₆	—	5	2	no	—
157	C₅×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
158	C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₂×C₅×C₈	—	5	1	no	—
160	C₂×C₅×C₈	—	5	2	no	—
161	#689	C₂²×C₅	1	1	yes	characteristic, complemented
162	#688	C₂²×C₅	1	1	yes	characteristic, complemented
163	#687	C₂²×C₅	1	1	yes	characteristic, complemented
164	#687	C₂²×C₅	1	2	yes	complemented
165	#687	C₂²×C₅	1	2	yes	complemented
166	#686	C₂²×C₅	1	1	yes	characteristic, complemented
167	C₂×#168	C₂²×C₅	1	1	yes	characteristic, complemented
168	Dic₂₀	C₂²×C₅	1	2	yes	complemented
169	#677	C₂²×C₅	1	2	yes	complemented
170	#676	C₂²×C₅	1	2	yes	complemented
171	C₈×D₅	C₂²×C₅	1	2	yes	complemented
172	#577	—	5	1	no	Sylow
173	C₂×C₅²	—	2	1	no	—
174	C₂×C₅²	—	4	2	no	—
175	C₂×C₅²	—	4	1	no	—
176	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
177	C₅×D₅	—	2	2	no	—
178	C₅×D₅	—	4	1	no	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	1	no	—
181	C₂³×C₅	—	4	2	no	—
182	C₂³×C₅	—	10	2	no	—
183	C₂²×D₅	—	2	2	no	—
184	C₅×Q₈	—	2	2	no	—
185	C₅×Q₈	—	5	1	no	—
186	C₅×Q₈	—	5	2	no	—
187	C₅×Q₈	—	5	1	no	—
188	C₅×Q₈	—	10	2	no	—
189	C₅×Q₈	—	10	1	no	—
190	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
191	C₅×Q₈	C₂³×C₅	1	1	yes	characteristic
192	C₅×D₄	—	2	1	no	—
193	C₅×D₄	—	2	1	no	—
194	C₅×D₄	—	2	1	no	—
195	C₅×D₄	—	2	1	no	—
196	C₅×D₄	—	2	2	no	—
197	C₅×D₄	—	2	4	no	—
198	C₅×D₄	—	4	2	no	—
199	C₅×D₄	—	4	2	no	—
200	C₅×D₄	—	5	2	no	—
201	C₅×D₄	—	5	1	no	—
202	C₅×D₄	—	5	1	no	—
203	C₅×D₄	—	10	2	no	—
204	C₅×D₄	—	10	2	no	—
205	C₅×D₄	—	10	2	no	—
206	C₅×D₄	—	10	1	no	—
207	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
208	C₅×D₄	C₂²×D₅	1	2	yes	—
209	C₅×D₄	C₂³×C₅	1	1	yes	characteristic
210	C₅×D₄	C₂³×C₅	1	2	yes	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	5	2	no	—
216	C₂×C₄×C₅	—	10	2	no	—
217	C₂×C₄×C₅	—	10	2	no	—
218	C₂×C₄×C₅	—	10	2	no	—
219	C₂×C₄×C₅	—	10	1	no	—
220	C₂×C₄×C₅	—	10	1	no	—
221	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
223	C₂²⋊D₅	—	2	1	no	—
224	C₂²⋊D₅	—	2	2	no	—
225	C₂²⋊D₅	—	2	2	no	—
226	C₂²⋊D₅	—	2	2	no	—
227	C₂²⋊D₅	C₅×D₄	1	2	yes	—
228	C₂×Dic₅	—	2	1	no	—
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	2	2	no	—
231	D₂₀	C₅×D₄	1	1	yes	characteristic
232	D₂₀	C₂³×C₅	1	1	yes	characteristic
233	C₄×D₅	—	2	2	no	—
234	C₄×D₅	—	2	1	no	—
235	C₄×D₅	C₂³×C₅	1	2	yes	—
236	Dic₁₀	—	2	1	no	—
237	Dic₁₀	—	2	2	no	—
238	Dic₁₀	C₅×D₄	1	1	yes	characteristic
239	Dic₁₀	C₂³×C₅	1	2	yes	—
240	Dic₁₀	C₂³×C₅	1	1	yes	characteristic
241	C₅×C₈	—	2	4	no	—
242	C₅×C₈	—	5	1	no	—
243	C₅×C₈	—	5	1	no	—
244	C₅×C₈	C₂²×D₅	1	2	yes	—
245	C₅×C₈	C₂³×C₅	1	2	yes	—
246	#168	C₂³×C₅	1	1	yes	characteristic
247	#168	C₂³×C₅	1	1	yes	characteristic
248	2₋¹⁺⁴	—	5	1	no	—
249	H(5,𝔽₂)	—	5	1	no	—
250	#137	—	5	2	no	—
251	#137	—	5	1	no	—
252	AGL(1,ℤ/8)	—	5	2	no	—
253	AGL(1,ℤ/8)	C₅×D₅	1	1	yes	characteristic, complemented
254	#135	—	5	1	no	—
255	#135	—	5	2	no	—
256	C₂×SD₁₆	—	5	1	no	—
257	C₂×SD₁₆	—	5	2	no	—
258	#131	—	5	1	no	—
259	C₅²	#577	1	1	yes	characteristic, complemented, Sylow
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	5	2	no	—
268	C₂²×C₅	—	8	1	no	—
269	C₂²×C₅	—	8	1	no	—
270	C₂²×C₅	—	8	4	no	—
271	C₂²×C₅	—	10	1	no	—
272	C₂²×C₅	—	40	2	no	—
273	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
274	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×D₅	—	2	1	no	—
276	C₂×D₅	—	8	2	no	—
277	C₂×D₅	C₂×C₅×D₄	1	2	yes	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	5	2	no	—
284	C₄×C₅	—	10	1	no	—
285	C₄×C₅	—	10	2	no	—
286	C₄×C₅	D₄×D₅	1	1	yes	characteristic
287	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
288	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
289	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
290	Dic₅	—	2	2	no	—
291	Dic₅	—	2	1	no	—
292	Dic₅	C₂×C₅×D₄	1	2	yes	—
293	#41	—	5	1	no	—
294	#41	—	5	2	no	—
295	#41	—	5	2	no	—
296	#41	—	5	1	no	—
297	#41	—	10	1	no	—
298	#41	—	10	2	no	—
299	#41	—	10	1	no	—
300	#41	C₂×C₅×D₅	1	1	yes	characteristic, complemented
301	C₂×Q₈	—	5	2	no	—
302	C₂×Q₈	—	5	1	no	—
303	C₂×Q₈	—	10	1	no	—
304	C₂×D₄	—	5	2	no	—
305	C₂×D₄	—	10	1	no	—
306	C₂×D₄	—	10	2	no	—
307	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
308	Q₁₆	—	5	1	no	—
309	Q₁₆	—	5	2	no	—
310	SD₁₆	—	5	1	no	—
311	SD₁₆	—	5	2	no	—
312	SD₁₆	—	5	2	no	—
313	SD₁₆	—	5	1	no	—
314	SD₁₆	—	5	2	no	—
315	SD₁₆	C₂×C₅×D₅	1	2	yes	complemented
316	D₈	—	5	1	no	—
317	D₈	C₂×C₅×D₅	1	2	yes	complemented
318	M₁₆	—	5	2	no	—
319	M₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
320	C₂×C₈	—	5	1	no	—
321	C₂×C₈	—	5	2	no	—
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	4	2	no	—
326	C₂×C₅	—	4	1	no	—
327	C₂×C₅	—	4	2	no	—
328	C₂×C₅	—	4	2	no	—
329	C₂×C₅	—	4	1	no	—
330	C₂×C₅	—	8	2	no	—
331	C₂×C₅	—	8	4	no	—
332	C₂×C₅	—	10	2	no	—
333	C₂×C₅	—	20	1	no	—
334	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
335	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
336	D₅	—	2	2	no	—
337	D₅	—	4	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	10	2	no	—
340	Q₈	—	5	1	no	—
341	Q₈	—	5	2	no	—
342	Q₈	—	5	1	no	—
343	Q₈	—	10	2	no	—
344	Q₈	—	10	1	no	—
345	Q₈	C₂²×C₅×D₅	1	1	yes	characteristic
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	5	2	no	—
349	D₄	—	5	1	no	—
350	D₄	—	5	1	no	—
351	D₄	—	10	2	no	—
352	D₄	—	10	2	no	—
353	D₄	—	10	2	no	—
354	D₄	—	10	1	no	—
355	D₄	C₂²×C₅×D₅	1	1	yes	characteristic
356	D₄	C₂²×C₅×D₅	1	2	yes	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	5	2	no	—
359	C₂×C₄	—	10	2	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	—	10	2	no	—
362	C₂×C₄	—	10	1	no	—
363	C₂×C₄	—	10	1	no	—
364	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
365	C₈	—	5	1	no	—
366	C₈	—	5	1	no	—
367	C₈	C₂²×C₅×D₅	1	2	yes	—
368	C₅	—	2	2	no	—
369	C₅	#66109	1	1	yes	characteristic, direct product factor
370	C₅	C₅×#577	1	1	yes	characteristic, complemented
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	5	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	10	1	no	—
376	C₂²	—	40	2	no	—
377	C₂²	C₅×D₄×D₅	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	5	2	no	—
380	C₄	—	10	1	no	—
381	C₄	—	10	2	no	—
382	C₄	C₅×D₄×D₅	1	1	yes	characteristic
383	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
384	C₂	—	2	1	no	—
385	C₂	—	4	2	no	—
386	C₂	—	4	1	no	—
387	C₂	—	10	2	no	—
388	C₂	—	20	1	no	—
389	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×#577
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×#4150	C₂	semidirect
2. C₅×#4144	C₂	semidirect
3. C₅²×AGL(1,ℤ/8)	C₂	semidirect
4. C₅×#4096	C₂	semidirect
5. C₂×C₅×#687	C₂	semidirect
6. C₅×#4061	C₂	semidirect
7. C₅×D₅×SD₁₆	C₂	semidirect
8. C₅×#4058	C₂	semidirect
9. C₅×#4057	C₂	semidirect
10. C₅×#4055	C₂	semidirect
11. C₅×#4053	C₂	semidirect
12. C₅²×#41	C₂²	semidirect
15. C₅×Q₈×D₅	C₂²	semidirect
19. C₅×#711	C₂²	semidirect
26. C₂×C₅×Dic₁₀	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×#687	C₂²	semidirect
34. C₅×#687	C₂²	semidirect
35. C₅×#686	C₂²	semidirect
36. C₂×C₅×#168	C₂²	semidirect
37. C₅×Dic₂₀	C₂²	semidirect
38. C₅×#677	C₂²	semidirect
39. C₅×#676	C₂²	semidirect
40. C₅×C₈×D₅	C₂²	semidirect
42. #66109	C₅	direct (N × H)
75. #4150	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×#687	C₂×C₅	semidirect
90. #4061	C₂×C₅	semidirect
91. D₅×SD₁₆	C₂×C₅	semidirect
92. #4058	C₂×C₅	semidirect
93. #4057	C₂×C₅	semidirect
94. #4055	C₂×C₅	semidirect
95. #4053	C₂×C₅	semidirect
117. C₅×#41	C₂×D₅	semidirect
118. C₅×#41	C₂²×C₅	semidirect
129. Q₈×D₅	C₂²×C₅	semidirect
133. #711	C₂²×C₅	semidirect
140. C₂×Dic₁₀	C₂²×C₅	semidirect
149. C₅×SD₁₆	C₂×D₅	semidirect
150. C₅×SD₁₆	C₂²×C₅	semidirect
153. C₅×D₈	C₂×D₅	semidirect
154. C₅×D₈	C₂²×C₅	semidirect
157. C₅×M₁₆	C₂×D₅	semidirect
158. C₅×M₁₆	C₂²×C₅	semidirect
161. #689	C₂²×C₅	semidirect
162. #688	C₂²×C₅	semidirect
163. #687	C₂²×C₅	semidirect
164. #687	C₂²×C₅	semidirect
165. #687	C₂²×C₅	semidirect
166. #686	C₂²×C₅	semidirect
167. C₂×#168	C₂²×C₅	semidirect
168. Dic₂₀	C₂²×C₅	semidirect
169. #677	C₂²×C₅	semidirect
170. #676	C₂²×C₅	semidirect
171. C₈×D₅	C₂²×C₅	semidirect
253. AGL(1,ℤ/8)	C₅×D₅	semidirect
259. C₅²	#577	semidirect
300. #41	C₂×C₅×D₅	semidirect
315. SD₁₆	C₂×C₅×D₅	semidirect
317. D₈	C₂×C₅×D₅	semidirect
319. M₁₆	C₂×C₅×D₅	semidirect
369. C₅	#66109	direct (N × H)
370. C₅	C₅×#577	semidirect

Maximal subgroups

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

subgroup	index
C₅×#4150	2
C₅×#4144	2
C₅²×AGL(1,ℤ/8)	2
C₅×#4096	2
C₂×C₅×#687	2
C₅×#4061	2
C₅×D₅×SD₁₆	2
C₅×#4058	2
C₅×#4057	2
C₅×#4055	2
C₅×#4053	2
C₅×#577	5
#66109	5

Subgroups — C5×#66109 #13106929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66109 #13106929