Subgroups — C₅×#66104 #13106924

Order 1600.

578 conjugacy classes of subgroups.

The subgroup lattice has 395 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×#4149	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4064	C₂	1	2	yes	maximal, complemented
7	C₅×#4062	C₂	1	2	yes	maximal, complemented
8	C₅×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₅×#4057	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4047	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅²×#41	C₂²	1	1	yes	characteristic
13	C₅²×#41	C₂²	1	1	yes	characteristic, complemented
14	C₅×#713	C₂²	1	2	yes	—
15	C₅×Q₈×D₅	C₂²	1	2	yes	complemented
16	C₅×#711	—	2	2	no	—
17	C₅×#711	C₂²	1	2	yes	complemented
18	C₅×D₄×D₅	—	2	2	no	—
19	C₅×D₄×D₅	C₂²	1	2	yes	—
20	C₅×#709	—	2	1	no	—
21	C₅×#709	—	2	1	no	—
22	C₅×#709	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₂₀	—	2	1	no	—
24	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₁₀	—	2	1	no	—
26	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
27	C₅²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₅²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₅²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₅²×D₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic, complemented
32	C₅×#689	C₂²	1	2	yes	complemented
33	C₅×#688	C₂²	1	2	yes	complemented
34	C₅×#687	C₂²	1	2	yes	complemented
35	C₅×#686	C₂²	1	2	yes	complemented
36	C₅×#681	C₂²	1	1	yes	characteristic, complemented
37	C₅×#677	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	#66104	C₅	1	1	yes	maximal, characteristic, direct product factor
43	C₂²×C₅×D₅	—	2	1	no	—
44	C₂²×C₅×D₅	—	2	2	no	—
45	C₅²×Q₈	C₂³	1	1	yes	characteristic
46	C₅²×Q₈	C₂³	1	1	yes	characteristic
47	C₅²×D₄	—	2	1	no	—
48	C₅²×D₄	—	2	1	no	—
49	C₅²×D₄	C₂³	1	1	yes	characteristic
50	C₅²×D₄	C₂³	1	1	yes	characteristic
51	C₂×C₄×C₅²	—	2	1	no	—
52	C₂×C₄×C₅²	—	2	1	no	—
53	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
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	C₅×D₂₀	—	2	2	no	—
60	C₅×D₂₀	—	2	1	no	—
61	C₅×D₂₀	D₄	1	1	yes	characteristic
62	C₅×D₂₀	C₂³	1	2	yes	—
63	C₄×C₅×D₅	—	2	2	no	—
64	C₄×C₅×D₅	—	2	2	no	—
65	C₄×C₅×D₅	C₂³	1	2	yes	—
66	C₅×Dic₁₀	—	2	1	no	—
67	C₅×Dic₁₀	—	2	2	no	—
68	C₅×Dic₁₀	D₄	1	1	yes	characteristic
69	C₅×Dic₁₀	C₂³	1	2	yes	—
70	C₅²×C₈	C₂³	1	1	yes	characteristic
71	C₅²×C₈	C₂³	1	1	yes	characteristic
72	C₅×#168	C₂³	1	2	yes	—
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	#4149	C₂×C₅	1	1	yes	characteristic, complemented
77	C₅×#137	—	5	1	no	—
78	C₅×#137	—	5	2	no	—
79	C₅×AGL(1,ℤ/8)	—	5	1	no	—
80	C₅×AGL(1,ℤ/8)	—	5	2	no	—
81	C₅×#135	—	2	2	no	—
82	C₅×#135	—	5	2	no	—
83	C₅×#135	D₅	1	1	yes	characteristic, complemented
84	C₅×#135	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×C₅×SD₁₆	—	5	2	no	—
86	C₂×C₅×SD₁₆	—	5	1	no	—
87	C₅×#131	—	5	1	no	—
88	#4097	C₂×C₅	1	1	yes	characteristic, complemented
89	#4095	C₂×C₅	1	1	yes	characteristic, complemented
90	#4064	C₂×C₅	1	2	yes	complemented
91	#4062	C₂×C₅	1	2	yes	complemented
92	D₅×SD₁₆	C₂×C₅	1	2	yes	complemented
93	#4057	C₂×C₅	1	2	yes	complemented
94	C₂×#677	C₂×C₅	1	1	yes	characteristic, complemented
95	#4047	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₅²	—	2	1	no	—
97	C₂²×C₅²	—	2	1	no	—
98	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
99	C₂×C₅×D₅	—	2	2	no	—
100	C₂×C₅×D₅	—	8	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	—	2	1	no	—
105	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
106	C₄×C₅²	C₂⁴	1	1	yes	characteristic
107	C₅×Dic₅	—	2	2	no	—
108	C₅×Dic₅	C₂×D₄	1	2	yes	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	5	1	no	—
112	C₅×#41	—	5	2	no	—
113	C₅×#41	—	5	2	no	—
114	C₅×#41	—	10	1	no	—
115	C₅×#41	—	10	1	no	—
116	C₅×#41	—	10	2	no	—
117	C₅×#41	C₂×D₅	1	1	yes	characteristic
118	C₅×#41	C₂×D₅	1	1	yes	characteristic, complemented
119	C₅×#41	C₂²×C₅	1	1	yes	characteristic
120	C₅×#41	C₂²×C₅	1	1	yes	characteristic, complemented
121	C₂×C₅×Q₈	—	5	2	no	—
122	C₂×C₅×Q₈	—	5	1	no	—
123	C₂×C₅×Q₈	—	10	1	no	—
124	C₂×C₅×D₄	—	5	2	no	—
125	C₂×C₅×D₄	—	5	1	no	—
126	C₂×C₅×D₄	—	10	1	no	—
127	C₂×C₅×D₄	—	10	2	no	—
128	#713	C₂²×C₅	1	2	yes	—
129	Q₈×D₅	C₂²×C₅	1	2	yes	complemented
130	#711	—	2	2	no	—
131	#711	C₂²×C₅	1	2	yes	complemented
132	D₄×D₅	—	2	2	no	—
133	D₄×D₅	C₂²×C₅	1	2	yes	—
134	#709	—	2	1	no	—
135	#709	—	2	1	no	—
136	#709	C₂²×C₅	1	1	yes	characteristic
137	C₂×D₂₀	—	2	1	no	—
138	C₂×D₂₀	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	—	2	2	no	—
142	C₅×Q₁₆	—	5	2	no	—
143	C₅×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
144	C₅×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₅×SD₁₆	—	2	2	no	—
146	C₅×SD₁₆	—	2	2	no	—
147	C₅×SD₁₆	—	5	2	no	—
148	C₅×SD₁₆	—	5	2	no	—
149	C₅×SD₁₆	—	5	2	no	—
150	C₅×SD₁₆	—	5	2	no	—
151	C₅×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
152	C₅×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
153	C₅×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
154	C₅×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₅×D₈	—	2	2	no	—
156	C₅×D₈	—	5	2	no	—
157	C₅×D₈	C₂×D₅	1	1	yes	characteristic, complemented
158	C₅×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₅×M₁₆	—	5	1	no	—
160	C₅×M₁₆	—	5	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	5	2	no	—
163	C₂×C₅×C₈	C₂×D₅	1	1	yes	characteristic, complemented
164	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
165	#689	C₂²×C₅	1	2	yes	complemented
166	#688	C₂²×C₅	1	2	yes	complemented
167	#687	C₂²×C₅	1	2	yes	complemented
168	#686	C₂²×C₅	1	2	yes	complemented
169	#681	C₂²×C₅	1	1	yes	characteristic, complemented
170	#677	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	#577	—	5	1	no	Sylow
175	C₂×C₅²	—	2	1	no	—
176	C₂×C₅²	—	4	1	no	—
177	C₂×C₅²	—	4	1	no	—
178	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
179	C₅×D₅	—	2	2	no	—
180	C₅×D₅	—	4	2	no	—
181	C₂³×C₅	—	10	2	no	—
182	C₂³×C₅	—	10	1	no	—
183	C₂²×D₅	—	2	1	no	—
184	C₂²×D₅	—	2	2	no	—
185	C₅×Q₈	—	2	2	no	—
186	C₅×Q₈	—	2	2	no	—
187	C₅×Q₈	—	5	1	no	—
188	C₅×Q₈	—	5	2	no	—
189	C₅×Q₈	—	10	2	no	—
190	C₅×Q₈	—	10	1	no	—
191	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
192	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
193	C₅×Q₈	C₂³×C₅	1	1	yes	characteristic
194	C₅×Q₈	C₂³×C₅	1	1	yes	characteristic
195	C₅×D₄	—	2	1	no	—
196	C₅×D₄	—	2	1	no	—
197	C₅×D₄	—	2	1	no	—
198	C₅×D₄	—	2	1	no	—
199	C₅×D₄	—	2	2	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	5	2	no	—
204	C₅×D₄	—	5	1	no	—
205	C₅×D₄	—	5	2	no	—
206	C₅×D₄	—	10	2	no	—
207	C₅×D₄	—	10	2	no	—
208	C₅×D₄	—	10	2	no	—
209	C₅×D₄	—	10	1	no	—
210	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
211	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
212	C₅×D₄	C₂³×C₅	1	1	yes	characteristic
213	C₅×D₄	C₂³×C₅	1	1	yes	characteristic
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	5	2	no	—
222	C₂×C₄×C₅	—	10	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	2	no	—
229	C₂²⋊D₅	—	2	2	no	—
230	C₂²⋊D₅	C₅×D₄	1	2	yes	—
231	C₂×Dic₅	—	2	1	no	—
232	C₂×Dic₅	—	2	2	no	—
233	D₂₀	—	2	2	no	—
234	D₂₀	—	2	1	no	—
235	D₂₀	C₅×D₄	1	1	yes	characteristic
236	D₂₀	C₂³×C₅	1	2	yes	—
237	C₄×D₅	—	2	2	no	—
238	C₄×D₅	—	2	2	no	—
239	C₄×D₅	C₂³×C₅	1	2	yes	—
240	Dic₁₀	—	2	1	no	—
241	Dic₁₀	—	2	2	no	—
242	Dic₁₀	C₅×D₄	1	1	yes	characteristic
243	Dic₁₀	C₂³×C₅	1	2	yes	—
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	5	2	no	—
247	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
248	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
249	C₅×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₅×C₈	C₂³×C₅	1	1	yes	characteristic
251	#168	C₂³×C₅	1	2	yes	—
252	2₋¹⁺⁴	—	5	1	no	—
253	H(5,𝔽₂)	—	5	1	no	—
254	#137	—	5	1	no	—
255	#137	—	5	2	no	—
256	AGL(1,ℤ/8)	—	5	1	no	—
257	AGL(1,ℤ/8)	—	5	2	no	—
258	#135	—	5	2	no	—
259	#135	C₅×D₅	1	1	yes	characteristic, complemented
260	C₂×SD₁₆	—	5	2	no	—
261	C₂×SD₁₆	—	5	1	no	—
262	#131	—	5	1	no	—
263	C₅²	#577	1	1	yes	characteristic, complemented, Sylow
264	C₂²×C₅	—	2	1	no	—
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	2	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	5	2	no	—
272	C₂²×C₅	—	10	2	no	—
273	C₂²×C₅	—	40	1	no	—
274	C₂²×C₅	—	40	2	no	—
275	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
276	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂×D₅	—	2	2	no	—
278	C₂×D₅	—	8	2	no	—
279	C₂×D₅	—	8	1	no	—
280	C₂×D₅	C₂×C₅×D₄	1	2	yes	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	5	2	no	—
290	C₄×C₅	—	10	2	no	—
291	C₄×C₅	D₄×D₅	1	1	yes	characteristic
292	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
293	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
294	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
295	Dic₅	—	2	2	no	—
296	Dic₅	C₂×C₅×D₄	1	2	yes	—
297	#41	—	5	1	no	—
298	#41	—	5	2	no	—
299	#41	—	5	2	no	—
300	#41	—	10	1	no	—
301	#41	—	10	1	no	—
302	#41	—	10	2	no	—
303	#41	C₂×C₅×D₅	1	1	yes	characteristic
304	#41	C₂×C₅×D₅	1	1	yes	characteristic, complemented
305	C₂×Q₈	—	5	2	no	—
306	C₂×Q₈	—	5	1	no	—
307	C₂×Q₈	—	10	1	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	Q₁₆	—	5	2	no	—
313	Q₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
314	SD₁₆	—	5	2	no	—
315	SD₁₆	—	5	2	no	—
316	SD₁₆	—	5	2	no	—
317	SD₁₆	—	5	2	no	—
318	SD₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
319	SD₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
320	D₈	—	5	2	no	—
321	D₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
322	M₁₆	—	5	1	no	—
323	M₁₆	—	5	2	no	—
324	C₂×C₈	—	5	2	no	—
325	C₂×C₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
326	C₂×C₅	—	2	1	no	—
327	C₂×C₅	—	2	1	no	—
328	C₂×C₅	—	2	2	no	—
329	C₂×C₅	—	4	2	no	—
330	C₂×C₅	—	4	1	no	—
331	C₂×C₅	—	4	1	no	—
332	C₂×C₅	—	4	1	no	—
333	C₂×C₅	—	4	1	no	—
334	C₂×C₅	—	8	2	no	—
335	C₂×C₅	—	8	2	no	—
336	C₂×C₅	—	10	2	no	—
337	C₂×C₅	—	20	2	no	—
338	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
339	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
340	D₅	—	2	2	no	—
341	D₅	—	4	2	no	—
342	C₂³	—	10	2	no	—
343	C₂³	—	10	1	no	—
344	Q₈	—	5	1	no	—
345	Q₈	—	5	2	no	—
346	Q₈	—	10	2	no	—
347	Q₈	—	10	1	no	—
348	Q₈	C₂²×C₅×D₅	1	1	yes	characteristic
349	Q₈	C₂²×C₅×D₅	1	1	yes	characteristic
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	5	2	no	—
353	D₄	—	5	1	no	—
354	D₄	—	5	2	no	—
355	D₄	—	10	2	no	—
356	D₄	—	10	2	no	—
357	D₄	—	10	2	no	—
358	D₄	—	10	1	no	—
359	D₄	C₂²×C₅×D₅	1	1	yes	characteristic
360	D₄	C₂²×C₅×D₅	1	1	yes	characteristic
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	5	2	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	10	2	no	—
366	C₂×C₄	—	10	2	no	—
367	C₂×C₄	—	10	1	no	—
368	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
369	C₈	—	5	2	no	—
370	C₈	C₂²×C₅×D₅	1	1	yes	characteristic
371	C₈	C₂²×C₅×D₅	1	1	yes	characteristic
372	C₅	—	2	2	no	—
373	C₅	#66104	1	1	yes	characteristic, direct product factor
374	C₅	C₅×#577	1	1	yes	characteristic, complemented
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	5	2	no	—
378	C₂²	—	10	2	no	—
379	C₂²	—	40	1	no	—
380	C₂²	—	40	2	no	—
381	C₂²	C₅×D₄×D₅	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	5	2	no	—
385	C₄	—	10	2	no	—
386	C₄	C₅×D₄×D₅	1	1	yes	characteristic
387	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
388	C₂	—	2	1	no	—
389	C₂	—	4	1	no	—
390	C₂	—	4	1	no	—
391	C₂	—	10	2	no	—
392	C₂	—	20	2	no	—
393	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×#135	C₂
socle	C₂×C₅²	C₂²×D₄
hypercenter	C₅×#135	D₅
hypocenter	C₅	C₅×#577
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₅×#4150	C₂	semidirect
2. C₅×#4149	C₂	semidirect
3. C₅²×#135	C₂	semidirect
4. C₅×#4097	C₂	semidirect
5. C₅×#4095	C₂	semidirect
6. C₅×#4064	C₂	semidirect
7. C₅×#4062	C₂	semidirect
8. C₅×D₅×SD₁₆	C₂	semidirect
9. C₅×#4057	C₂	semidirect
10. C₂×C₅×#677	C₂	semidirect
11. C₅×#4047	C₂	semidirect
13. C₅²×#41	C₂²	semidirect
15. C₅×Q₈×D₅	C₂²	semidirect
17. C₅×#711	C₂²	semidirect
26. C₂×C₅×Dic₁₀	C₂²	semidirect
27. C₅²×Q₁₆	C₂²	semidirect
28. C₅²×SD₁₆	C₂²	semidirect
29. C₅²×SD₁₆	C₂²	semidirect
30. C₅²×D₈	C₂²	semidirect
31. C₂×C₅²×C₈	C₂²	semidirect
32. C₅×#689	C₂²	semidirect
33. C₅×#688	C₂²	semidirect
34. C₅×#687	C₂²	semidirect
35. C₅×#686	C₂²	semidirect
36. C₅×#681	C₂²	semidirect
37. C₅×#677	C₂²	semidirect
38. C₅×#677	C₂²	semidirect
39. C₅×#676	C₂²	semidirect
40. C₅×C₈×D₅	C₂²	semidirect
42. #66104	C₅	direct (N × H)
75. #4150	C₂×C₅	semidirect
76. #4149	C₂×C₅	semidirect
83. C₅×#135	D₅	semidirect
84. C₅×#135	C₂×C₅	semidirect
88. #4097	C₂×C₅	semidirect
89. #4095	C₂×C₅	semidirect
90. #4064	C₂×C₅	semidirect
91. #4062	C₂×C₅	semidirect
92. D₅×SD₁₆	C₂×C₅	semidirect
93. #4057	C₂×C₅	semidirect
94. C₂×#677	C₂×C₅	semidirect
95. #4047	C₂×C₅	semidirect
118. C₅×#41	C₂×D₅	semidirect
120. C₅×#41	C₂²×C₅	semidirect
129. Q₈×D₅	C₂²×C₅	semidirect
131. #711	C₂²×C₅	semidirect
140. C₂×Dic₁₀	C₂²×C₅	semidirect
143. C₅×Q₁₆	C₂×D₅	semidirect
144. C₅×Q₁₆	C₂²×C₅	semidirect
151. C₅×SD₁₆	C₂×D₅	semidirect
152. C₅×SD₁₆	C₂×D₅	semidirect
153. C₅×SD₁₆	C₂²×C₅	semidirect
154. C₅×SD₁₆	C₂²×C₅	semidirect
157. C₅×D₈	C₂×D₅	semidirect
158. C₅×D₈	C₂²×C₅	semidirect
163. C₂×C₅×C₈	C₂×D₅	semidirect
164. C₂×C₅×C₈	C₂²×C₅	semidirect
165. #689	C₂²×C₅	semidirect
166. #688	C₂²×C₅	semidirect
167. #687	C₂²×C₅	semidirect
168. #686	C₂²×C₅	semidirect
169. #681	C₂²×C₅	semidirect
170. #677	C₂²×C₅	semidirect
171. #677	C₂²×C₅	semidirect
172. #676	C₂²×C₅	semidirect
173. C₈×D₅	C₂²×C₅	semidirect
259. #135	C₅×D₅	semidirect
263. C₅²	#577	semidirect
304. #41	C₂×C₅×D₅	semidirect
313. Q₁₆	C₂×C₅×D₅	semidirect
318. SD₁₆	C₂×C₅×D₅	semidirect
319. SD₁₆	C₂×C₅×D₅	semidirect
321. D₈	C₂×C₅×D₅	semidirect
325. C₂×C₈	C₂×C₅×D₅	semidirect
373. C₅	#66104	direct (N × H)
374. 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×#4149	2
C₅²×#135	2
C₅×#4097	2
C₅×#4095	2
C₅×#4064	2
C₅×#4062	2
C₅×D₅×SD₁₆	2
C₅×#4057	2
C₂×C₅×#677	2
C₅×#4047	2
C₅×#577	5
#66104	5

Subgroups — C5×#66104 #13106924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66104 #13106924