Subgroups — C₅×#19926 #11942646

Order 1280.

626 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3384	C₂	1	2	yes	maximal
2	C₅×#3338	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1692	C₂	1	2	yes	maximal, complemented
6	C₅×#1675	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1644	C₂	1	2	yes	maximal, complemented
9	C₅×#1637	C₂	1	2	yes	maximal, complemented
10	C₅×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×D₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	—	2	1	no	—
13	C₅×#554	C₂²	1	2	yes	—
14	C₅×D₄×Q₈	C₂²	1	2	yes	—
15	C₅×#501	—	2	2	no	—
16	C₅×#500	C₂²	1	1	yes	characteristic
17	C₅×#498	C₂²	1	2	yes	—
18	C₅×#494	C₂²	1	1	yes	characteristic
19	C₅×#487	C₂²	1	2	yes	—
20	C₅×#484	—	2	2	no	—
21	C₅×#478	—	2	2	no	—
22	C₅×#477	C₂²	1	2	yes	—
23	C₅×#476	—	2	2	no	—
24	C₅×#476	C₂²	1	2	yes	—
25	C₅×#474	C₂²	1	2	yes	—
26	C₅×#467	—	2	1	no	—
27	C₅×#467	—	2	1	no	—
28	C₅×#462	C₂²	1	2	yes	—
29	C₅×#451	—	2	2	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×#442	—	2	2	no	—
32	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×#107	—	2	1	no	—
37	C₅×#335	C₂²	1	1	yes	characteristic
38	C₅×#335	C₂²	1	1	yes	characteristic
39	C₅×#333	C₂²	1	2	yes	—
40	C₅×#332	C₂²	1	2	yes	—
41	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×C₈²	C₂²	1	1	yes	characteristic
45	#19926	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	—	2	2	no	—
47	C₂×C₅×Q₁₆	—	2	2	no	—
48	C₂×C₅×Q₁₆	—	2	1	no	—
49	C₂×C₅×Q₁₆	—	2	1	no	—
50	C₂×C₅×Q₁₆	—	4	4	no	—
51	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
52	C₂×C₅×D₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₅×#125	—	2	2	no	—
59	C₅×C₂²⋊Q₈	—	2	2	no	—
60	C₅×C₂²⋊Q₈	—	2	2	no	—
61	C₅×C₂²⋊Q₈	—	4	2	no	—
62	C₅×C₂²⋊Q₈	—	4	2	no	—
63	C₄×C₅×Q₈	C₂³	1	2	yes	—
64	C₄×C₅×D₄	—	2	2	no	—
65	C₄×C₅×D₄	—	2	2	no	—
66	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	—	2	2	no	—
69	C₅×#107	—	2	1	no	—
70	C₅×#107	—	2	1	no	—
71	C₅×#107	—	2	2	no	—
72	C₅×#107	—	2	2	no	—
73	C₅×#107	D₄	1	1	yes	characteristic
74	C₅×#107	D₄	1	1	yes	characteristic
75	C₅×#106	—	2	2	no	—
76	C₅×#106	—	2	2	no	—
77	C₅×#106	—	2	2	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×#103	—	2	2	no	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	4	2	no	—
85	C₅×#103	D₄	1	2	yes	—
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	D₄	1	1	yes	characteristic
89	C₅×#102	D₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	1	no	—
92	C₅×#97	—	2	2	no	—
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	#3384	C₂×C₅	1	2	yes	—
97	#3338	C₂×C₅	1	1	yes	characteristic, complemented
98	D₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
99	#1707	C₂×C₅	1	1	yes	characteristic, complemented
100	#1692	C₂×C₅	1	2	yes	complemented
101	#1675	C₂×C₅	1	1	yes	characteristic, complemented
102	#1669	C₂×C₅	1	1	yes	characteristic, complemented
103	#1644	C₂×C₅	1	2	yes	complemented
104	#1637	C₂×C₅	1	2	yes	complemented
105	#1591	C₂×C₅	1	1	yes	characteristic, complemented
106	C₈×D₈	C₂×C₅	1	1	yes	characteristic
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	4	2	no	—
110	C₂×C₅×Q₈	—	4	4	no	—
111	C₂×C₅×Q₈	—	8	2	no	—
112	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
113	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	4	2	no	—
118	C₂²×C₄×C₅	—	4	2	no	—
119	C₅×Q₁₆	—	2	2	no	—
120	C₅×Q₁₆	—	4	4	no	—
121	C₅×Q₁₆	—	4	2	no	—
122	C₅×Q₁₆	—	8	1	no	—
123	C₅×D₈	Q₁₆	1	4	yes	complemented
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	4	2	no	—
129	C₂×C₅×C₈	—	4	2	no	—
130	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
143	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
144	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₅×C₂²⋊C₄	—	2	1	no	—
146	C₅×C₂²⋊C₄	—	2	1	no	—
147	C₅×C₂²⋊C₄	—	4	2	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	C₂⁴	1	1	yes	characteristic
151	C₂²×Q₁₆	—	2	1	no	—
152	#554	C₂²×C₅	1	2	yes	—
153	D₄×Q₈	C₂²×C₅	1	2	yes	—
154	#501	—	2	2	no	—
155	#500	C₂²×C₅	1	1	yes	characteristic
156	#498	C₂²×C₅	1	2	yes	—
157	#494	C₂²×C₅	1	1	yes	characteristic
158	#487	C₂²×C₅	1	2	yes	—
159	#484	—	2	2	no	—
160	#478	—	2	2	no	—
161	#477	C₂²×C₅	1	2	yes	—
162	#476	—	2	2	no	—
163	#476	C₂²×C₅	1	2	yes	—
164	#474	C₂²×C₅	1	2	yes	—
165	#467	—	2	1	no	—
166	#467	—	2	1	no	—
167	#462	C₂²×C₅	1	2	yes	—
168	#451	—	2	2	no	—
169	#446	C₂²×C₅	1	2	yes	—
170	#442	—	2	2	no	—
171	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
173	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
174	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
175	C₂×#107	—	2	1	no	—
176	#335	C₂²×C₅	1	1	yes	characteristic
177	#335	C₂²×C₅	1	1	yes	characteristic
178	#333	C₂²×C₅	1	2	yes	—
179	#332	C₂²×C₅	1	2	yes	—
180	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
181	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
183	C₈²	C₂²×C₅	1	1	yes	characteristic
184	C₂³×C₅	—	2	1	no	—
185	C₂³×C₅	—	2	1	no	—
186	C₅×Q₈	—	2	2	no	—
187	C₅×Q₈	—	2	2	no	—
188	C₅×Q₈	—	4	2	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	—	8	2	no	—
191	C₅×Q₈	—	8	4	no	—
192	C₅×D₄	—	2	1	no	—
193	C₅×D₄	—	2	1	no	—
194	C₅×D₄	C₂×Q₁₆	1	2	yes	—
195	C₅×D₄	C₂×Q₁₆	1	2	yes	complemented
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	8	4	no	—
207	C₂×C₄×C₅	—	16	2	no	—
208	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
211	C₅×C₈	—	2	1	no	—
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	—	4	1	no	—
214	C₅×C₈	—	4	1	no	—
215	C₅×C₈	—	4	1	no	—
216	C₅×C₈	—	4	2	no	—
217	C₅×C₈	C₂×Q₁₆	1	2	yes	complemented
218	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
219	C₂²×Q₈	—	2	2	no	—
220	C₂×Q₁₆	—	2	2	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₂×Q₁₆	—	2	1	no	—
223	C₂×Q₁₆	—	4	4	no	—
224	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
225	C₂×D₈	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
230	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
231	#125	—	2	2	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	C₂²⋊Q₈	—	2	2	no	—
234	C₂²⋊Q₈	—	4	2	no	—
235	C₂²⋊Q₈	—	4	2	no	—
236	C₄×Q₈	C₂³×C₅	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
240	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₄	—	2	2	no	—
242	#107	—	2	1	no	—
243	#107	—	2	1	no	—
244	#107	—	2	2	no	—
245	#107	—	2	2	no	—
246	#107	C₅×D₄	1	1	yes	characteristic
247	#107	C₅×D₄	1	1	yes	characteristic
248	#106	—	2	2	no	—
249	#106	—	2	2	no	—
250	#106	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
253	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
254	C₄⋊C₈	C₂³×C₅	1	2	yes	—
255	#103	—	2	2	no	—
256	#103	—	2	2	no	—
257	#103	—	4	2	no	—
258	#103	C₅×D₄	1	2	yes	—
259	#102	—	2	2	no	—
260	#102	—	2	2	no	—
261	#102	C₅×D₄	1	1	yes	characteristic
262	#102	C₅×D₄	1	1	yes	characteristic
263	C₂²⋊C₈	—	2	1	no	—
264	C₂²⋊C₈	—	2	1	no	—
265	#97	—	2	2	no	—
266	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	4	1	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	4	1	no	—
275	C₂²×C₅	D₄²	1	1	yes	characteristic
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	4	1	no	—
278	C₄×C₅	—	4	1	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	8	2	no	—
282	C₄×C₅	—	8	2	no	—
283	C₄×C₅	C₂²×Q₁₆	1	1	yes	characteristic
284	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₅	#577	1	1	yes	characteristic
286	C₄×C₅	#578	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	8	2	no	—
292	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
293	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	4	4	no	—
301	Q₁₆	—	4	2	no	—
302	Q₁₆	—	8	1	no	—
303	D₈	C₅×Q₁₆	1	4	yes	complemented
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	C₂⁴×C₅	1	1	yes	characteristic
331	C₂×C₅	—	4	2	no	—
332	C₂×C₅	—	4	2	no	—
333	C₂×C₅	#3272	1	1	yes	characteristic
334	C₂×C₅	D₄×Q₁₆	1	1	yes	characteristic
335	C₂×C₅	#3290	1	1	yes	characteristic
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	Q₈	—	2	2	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	8	2	no	—
343	Q₈	—	8	4	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	1	no	—
346	D₄	C₂×C₅×Q₁₆	1	2	yes	—
347	D₄	C₂×C₅×Q₁₆	1	2	yes	complemented
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	—	16	2	no	—
360	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
362	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	1	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	2	no	—
369	C₈	C₂×C₅×Q₁₆	1	2	yes	complemented
370	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
371	C₅	#19926	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	C₅×D₄²	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂²×C₅×Q₁₆	1	1	yes	characteristic
387	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₄	C₅×#577	1	1	yes	characteristic
389	C₄	C₅×#578	1	1	yes	characteristic
390	C₂	—	4	2	no	—
391	C₂	—	4	2	no	—
392	C₂	C₅×#3272	1	1	yes	characteristic
393	C₂	C₅×D₄×Q₁₆	1	1	yes	characteristic
394	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×D₈	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3338	C₂	semidirect
3. C₅×D₄×Q₁₆	C₂	semidirect
4. C₅×#1707	C₂	semidirect
5. C₅×#1692	C₂	semidirect
6. C₅×#1675	C₂	semidirect
7. C₅×#1669	C₂	semidirect
8. C₅×#1644	C₂	semidirect
9. C₅×#1637	C₂	semidirect
10. C₅×#1591	C₂	semidirect
45. #19926	C₅	direct (N × H)
97. #3338	C₂×C₅	semidirect
98. D₄×Q₁₆	C₂×C₅	semidirect
99. #1707	C₂×C₅	semidirect
100. #1692	C₂×C₅	semidirect
101. #1675	C₂×C₅	semidirect
102. #1669	C₂×C₅	semidirect
103. #1644	C₂×C₅	semidirect
104. #1637	C₂×C₅	semidirect
105. #1591	C₂×C₅	semidirect
123. C₅×D₈	Q₁₆	semidirect
195. C₅×D₄	C₂×Q₁₆	semidirect
217. C₅×C₈	C₂×Q₁₆	semidirect
303. D₈	C₅×Q₁₆	semidirect
347. D₄	C₂×C₅×Q₁₆	semidirect
369. C₈	C₂×C₅×Q₁₆	semidirect
371. C₅	#19926	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×#3384	2
C₅×#3338	2
C₅×D₄×Q₁₆	2
C₅×#1707	2
C₅×#1692	2
C₅×#1675	2
C₅×#1669	2
C₅×#1644	2
C₅×#1637	2
C₅×#1591	2
C₅×C₈×D₈	2
#19926	5

Subgroups — C5×#19926 #11942646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19926 #11942646