Subgroups — C₅×#19928 #11942648

Order 1280.

622 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3386	C₂	1	2	yes	maximal
3	C₅×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1694	C₂	1	2	yes	maximal, complemented
6	C₅×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1669	C₂	1	1	yes	maximal, characteristic
8	C₅×#1649	C₂	1	2	yes	maximal
9	C₅×#1648	C₂	1	2	yes	maximal, complemented
10	C₅×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	—	2	1	no	—
13	C₅×#557	C₂²	1	2	yes	—
14	C₅×D₄×Q₈	C₂²	1	2	yes	—
15	C₅×#501	—	2	2	no	—
16	C₅×#500	C₂²	1	2	yes	—
17	C₅×#500	C₂²	1	2	yes	—
18	C₅×#494	—	2	1	no	—
19	C₅×#494	C₂²	1	1	yes	characteristic
20	C₅×#494	C₂²	1	1	yes	characteristic
21	C₅×#478	—	2	2	no	—
22	C₅×#477	—	2	2	no	—
23	C₅×#475	C₂²	1	2	yes	—
24	C₅×#474	C₂²	1	2	yes	—
25	C₅×#467	—	2	1	no	—
26	C₅×#462	—	2	2	no	—
27	C₅×#462	C₂²	1	2	yes	—
28	C₅×#462	C₂²	1	2	yes	—
29	C₅×#451	—	2	2	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
32	C₅×#440	—	2	2	no	—
33	C₄×C₅×Q₁₆	—	2	1	no	—
34	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
36	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	1	yes	characteristic
38	C₅×#334	C₂²	1	1	yes	characteristic
39	C₅×#332	C₂²	1	2	yes	—
40	C₅×#332	C₂²	1	2	yes	—
41	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×C₈²	C₂²	1	1	yes	characteristic
45	#19928	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	2	no	—
49	C₂×C₅×Q₁₆	—	2	1	no	—
50	C₂×C₅×Q₁₆	—	2	1	no	—
51	C₂×C₅×Q₁₆	—	2	1	no	—
52	C₂×C₅×Q₁₆	—	2	1	no	—
53	C₂×C₅×Q₁₆	—	4	4	no	—
54	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
55	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	—	2	2	no	—
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₅×#125	—	2	2	no	—
62	C₅×#125	—	4	2	no	—
63	C₅×C₂²⋊Q₈	—	2	2	no	—
64	C₅×C₂²⋊Q₈	—	4	2	no	—
65	C₄×C₅×Q₈	—	2	2	no	—
66	C₄×C₅×Q₈	—	2	2	no	—
67	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₂³	1	2	yes	—
69	C₄×C₅×D₄	—	2	2	no	—
70	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₅×#107	—	2	2	no	—
72	C₅×#107	—	2	2	no	—
73	C₅×#107	—	2	2	no	—
74	C₅×#107	—	4	2	no	—
75	C₅×#107	D₄	1	1	yes	characteristic
76	C₅×#106	—	2	2	no	—
77	C₅×#106	D₄	1	1	yes	characteristic
78	C₅×C₄⋊C₈	—	2	1	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#103	—	2	2	no	—
86	C₅×#103	D₄	1	1	yes	characteristic
87	C₅×#103	D₄	1	2	yes	—
88	C₅×#102	—	2	2	no	—
89	C₅×#102	D₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×#97	—	2	2	no	—
92	C₄×C₅×C₈	—	2	1	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	#3395	C₂×C₅	1	1	yes	characteristic, complemented
97	#3386	C₂×C₅	1	2	yes	—
98	D₄×Q₁₆	C₂×C₅	1	1	yes	characteristic
99	#1713	C₂×C₅	1	1	yes	characteristic, complemented
100	#1694	C₂×C₅	1	2	yes	complemented
101	#1670	C₂×C₅	1	1	yes	characteristic, complemented
102	#1669	C₂×C₅	1	1	yes	characteristic
103	#1649	C₂×C₅	1	2	yes	—
104	#1648	C₂×C₅	1	2	yes	complemented
105	#1591	C₂×C₅	1	1	yes	characteristic, complemented
106	C₈×SD₁₆	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×Q₈	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	—	4	2	no	—
117	C₅×Q₁₆	—	2	2	no	—
118	C₅×Q₁₆	—	4	4	no	—
119	C₅×Q₁₆	—	4	2	no	—
120	C₅×Q₁₆	—	4	2	no	—
121	C₅×Q₁₆	—	8	1	no	—
122	C₅×Q₁₆	—	8	1	no	—
123	C₅×Q₁₆	—	8	2	no	—
124	C₅×SD₁₆	Q₁₆	1	4	yes	complemented
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	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	1	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	—	2	2	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	—	4	2	no	—
143	C₅×C₄⋊C₄	—	4	2	no	—
144	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	—	2	1	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	4	2	no	—
152	C₄²×C₅	C₂⁴	1	1	yes	characteristic
153	C₂²×Q₁₆	—	2	1	no	—
154	#557	C₂²×C₅	1	2	yes	—
155	D₄×Q₈	C₂²×C₅	1	2	yes	—
156	#501	—	2	2	no	—
157	#500	C₂²×C₅	1	2	yes	—
158	#500	C₂²×C₅	1	2	yes	—
159	#494	—	2	1	no	—
160	#494	C₂²×C₅	1	1	yes	characteristic
161	#494	C₂²×C₅	1	1	yes	characteristic
162	#478	—	2	2	no	—
163	#477	—	2	2	no	—
164	#475	C₂²×C₅	1	2	yes	—
165	#474	C₂²×C₅	1	2	yes	—
166	#467	—	2	1	no	—
167	#462	—	2	2	no	—
168	#462	C₂²×C₅	1	2	yes	—
169	#462	C₂²×C₅	1	2	yes	—
170	#451	—	2	2	no	—
171	#446	C₂²×C₅	1	2	yes	—
172	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
173	#440	—	2	2	no	—
174	C₄×Q₁₆	—	2	1	no	—
175	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
176	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
177	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
178	#335	C₂²×C₅	1	1	yes	characteristic
179	#334	C₂²×C₅	1	1	yes	characteristic
180	#332	C₂²×C₅	1	2	yes	—
181	#332	C₂²×C₅	1	2	yes	—
182	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
183	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
184	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
185	C₈²	C₂²×C₅	1	1	yes	characteristic
186	C₂³×C₅	—	2	1	no	—
187	C₅×Q₈	—	2	1	no	—
188	C₅×Q₈	—	2	2	no	—
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×Q₈	—	4	2	no	—
194	C₅×Q₈	—	8	4	no	—
195	C₅×Q₈	C₂×Q₁₆	1	2	yes	complemented
196	C₅×D₄	—	2	1	no	—
197	C₅×D₄	C₂×Q₁₆	1	2	yes	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	8	4	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	2	no	—
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	—	2	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	2	no	—
222	C₂×Q₁₆	—	2	1	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×Q₁₆	—	2	1	no	—
226	C₂×Q₁₆	—	4	4	no	—
227	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
228	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
229	C₂²×C₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
233	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
234	#125	—	2	2	no	—
235	#125	—	4	2	no	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	—	4	2	no	—
238	C₄×Q₈	—	2	2	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₄×Q₈	C₂³×C₅	1	2	yes	—
241	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
244	#107	—	2	2	no	—
245	#107	—	2	2	no	—
246	#107	—	2	2	no	—
247	#107	—	4	2	no	—
248	#107	C₅×D₄	1	1	yes	characteristic
249	#106	—	2	2	no	—
250	#106	C₅×D₄	1	1	yes	characteristic
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
254	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
255	C₄⋊C₈	C₂³×C₅	1	2	yes	—
256	#103	—	2	2	no	—
257	#103	—	2	2	no	—
258	#103	—	2	2	no	—
259	#103	C₅×D₄	1	1	yes	characteristic
260	#103	C₅×D₄	1	2	yes	—
261	#102	—	2	2	no	—
262	#102	C₅×D₄	1	1	yes	characteristic
263	C₂²⋊C₈	—	2	1	no	—
264	#97	—	2	2	no	—
265	C₄×C₈	—	2	1	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	—	4	1	no	—
271	C₂²×C₅	—	4	1	no	—
272	C₂²×C₅	D₄²	1	1	yes	characteristic
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	4	1	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	1	no	—
279	C₄×C₅	—	8	2	no	—
280	C₄×C₅	—	8	2	no	—
281	C₄×C₅	C₂²×Q₁₆	1	1	yes	characteristic
282	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₄×C₅	#576	1	1	yes	characteristic
284	C₄×C₅	#578	1	1	yes	characteristic
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
291	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	4	4	no	—
297	Q₁₆	—	4	2	no	—
298	Q₁₆	—	4	2	no	—
299	Q₁₆	—	8	1	no	—
300	Q₁₆	—	8	1	no	—
301	Q₁₆	—	8	2	no	—
302	SD₁₆	C₅×Q₁₆	1	4	yes	complemented
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
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	—	4	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	2	yes	—
324	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂⁴×C₅	1	1	yes	characteristic
331	C₂×C₅	—	4	2	no	—
332	C₂×C₅	#3274	1	1	yes	characteristic
333	C₂×C₅	D₄×Q₁₆	1	1	yes	characteristic
334	C₂×C₅	#3293	1	1	yes	characteristic
335	C₂³	—	2	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	2	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	8	4	no	—
344	Q₈	C₂×C₅×Q₁₆	1	2	yes	complemented
345	D₄	—	2	1	no	—
346	D₄	C₂×C₅×Q₁₆	1	2	yes	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	4	1	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	C₂×C₅×Q₁₆	1	2	yes	complemented
367	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
368	C₅	#19928	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	2	2	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	C₅×D₄²	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	2	no	—
381	C₄	C₂²×C₅×Q₁₆	1	1	yes	characteristic
382	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₄	C₅×#576	1	1	yes	characteristic
384	C₄	C₅×#578	1	1	yes	characteristic
385	C₂	—	4	2	no	—
386	C₂	C₅×#3274	1	1	yes	characteristic
387	C₂	C₅×D₄×Q₁₆	1	1	yes	characteristic
388	C₂	C₅×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×D₄	C₂×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
1. C₅×#3395	C₂	semidirect
4. C₅×#1713	C₂	semidirect
5. C₅×#1694	C₂	semidirect
6. C₅×#1670	C₂	semidirect
9. C₅×#1648	C₂	semidirect
10. C₅×#1591	C₂	semidirect
45. #19928	C₅	direct (N × H)
96. #3395	C₂×C₅	semidirect
99. #1713	C₂×C₅	semidirect
100. #1694	C₂×C₅	semidirect
101. #1670	C₂×C₅	semidirect
104. #1648	C₂×C₅	semidirect
105. #1591	C₂×C₅	semidirect
124. C₅×SD₁₆	Q₁₆	semidirect
195. C₅×Q₈	C₂×Q₁₆	semidirect
217. C₅×C₈	C₂×Q₁₆	semidirect
302. SD₁₆	C₅×Q₁₆	semidirect
344. Q₈	C₂×C₅×Q₁₆	semidirect
366. C₈	C₂×C₅×Q₁₆	semidirect
368. C₅	#19928	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×#3395	2
C₅×#3386	2
C₅×D₄×Q₁₆	2
C₅×#1713	2
C₅×#1694	2
C₅×#1670	2
C₅×#1669	2
C₅×#1649	2
C₅×#1648	2
C₅×#1591	2
C₅×C₈×SD₁₆	2
#19928	5

Subgroups — C5×#19928 #11942648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19928 #11942648