Subgroups — C₅×#68266 #14289226

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4843	C₂	1	1	yes	maximal, characteristic
4	C₅×#4694	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1627	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	—	2	1	no	—
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#215	—	2	1	no	—
12	C₂×C₅×D₂₄	—	2	1	no	—
13	C₅×#897	—	2	1	no	—
14	C₅×#897	—	2	2	no	—
15	C₅×#874	C₂²	1	1	yes	characteristic
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₅×#869	—	2	1	no	—
19	C₅×#869	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×#821	—	2	2	no	—
23	C₅×#821	—	2	1	no	—
24	C₅×#809	—	2	1	no	—
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#68266	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄×Q₈	—	3	1	no	—
28	C₅×#486	—	3	1	no	—
29	C₅×#460	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
35	C₅×D₃×Q₈	—	4	2	no	—
36	C₅×D₃×Q₈	—	4	2	no	—
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₅×Dic₆	—	2	2	no	—
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₅×#215	—	4	2	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×C₄⋊Dic₃	—	2	2	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
57	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₅×D₂₄	—	4	2	no	—
60	Q₈×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
61	#5027	C₂×C₅	1	1	yes	characteristic, complemented
62	#4843	C₂×C₅	1	1	yes	characteristic
63	#4694	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
65	#4486	C₂×C₅	1	1	yes	characteristic, complemented
66	#4459	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×Q₈	—	6	1	no	—
68	C₂×C₅×SD₁₆	—	6	1	no	—
69	C₂×C₅×D₈	—	6	1	no	—
70	C₅×C₄⋊Q₈	—	3	1	no	—
71	C₅×C₄⋊Q₈	—	6	1	no	—
72	C₅×#127	—	3	1	no	—
73	C₅×C₂²⋊Q₈	—	6	2	no	—
74	C₅×C₂²⋊Q₈	—	6	1	no	—
75	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	3	1	no	—
77	C₄×C₅×D₄	—	6	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	2	no	—
82	C₅×#102	—	6	1	no	—
83	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	#1627	—	3	1	no	Sylow
85	C₂²×C₅×D₃	—	2	1	no	—
86	C₂²×C₅×D₃	—	4	1	no	—
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₃×C₅×Q₈	D₈	1	2	yes	complemented
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	2	no	—
96	C₅×D₁₂	—	2	1	no	—
97	C₅×D₁₂	—	4	2	no	—
98	C₅×D₁₂	—	4	1	no	—
99	C₅×D₁₂	—	4	1	no	—
100	C₅×D₁₂	—	4	1	no	—
101	C₅×D₁₂	—	4	1	no	—
102	C₅×D₁₂	SD₁₆	1	2	yes	complemented
103	C₄×C₅×D₃	—	4	4	no	—
104	C₄×C₅×D₃	—	4	1	no	—
105	C₄×C₅×D₃	—	4	1	no	—
106	C₅×Dic₆	—	4	4	no	—
107	C₅×Dic₆	—	4	1	no	—
108	C₅×Dic₆	—	4	1	no	—
109	C₃×C₅×C₈	—	4	1	no	—
110	C₃×C₅×C₈	—	4	1	no	—
111	C₅×C₃⋊C₈	—	4	1	no	—
112	C₂×D₃×Q₈	—	2	1	no	—
113	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
114	C₂×#215	—	2	1	no	—
115	C₂×D₂₄	—	2	1	no	—
116	#897	—	2	1	no	—
117	#897	—	2	2	no	—
118	#874	C₂²×C₅	1	1	yes	characteristic
119	C₄×D₁₂	—	2	1	no	—
120	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
121	#869	—	2	1	no	—
122	#869	C₂²×C₅	1	1	yes	characteristic
123	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
125	#821	—	2	2	no	—
126	#821	—	2	1	no	—
127	#809	—	2	1	no	—
128	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₅×Q₈	—	6	2	no	—
130	C₂×C₅×Q₈	—	6	1	no	—
131	C₂×C₅×Q₈	—	12	2	no	—
132	C₂×C₅×Q₈	—	12	2	no	—
133	C₂×C₅×Q₈	D₁₂	1	1	yes	characteristic
134	C₂×C₅×D₄	—	3	1	no	—
135	C₂×C₅×D₄	—	6	1	no	—
136	C₂×C₅×D₄	—	6	1	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₅×SD₁₆	—	12	2	no	—
141	C₅×D₈	—	12	2	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	3	1	no	—
147	C₅×C₄⋊C₄	—	3	2	no	—
148	C₅×C₄⋊C₄	—	6	2	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	—	6	2	no	—
152	C₅×C₂²⋊C₄	—	6	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
155	D₄×Q₈	—	3	1	no	—
156	#486	—	3	1	no	—
157	#460	—	3	1	no	—
158	#459	—	3	1	no	—
159	#332	—	3	1	no	—
160	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
161	D₄⋊C₈	—	3	1	no	—
162	C₂²×C₃×C₅	#120	1	1	yes	characteristic
163	C₂×C₅×D₃	—	2	2	no	—
164	C₂×C₅×D₃	—	4	1	no	—
165	C₂×C₅×D₃	—	4	1	no	—
166	C₂×C₅×D₃	—	8	1	no	—
167	C₂×C₅×D₃	—	8	1	no	—
168	C₂×C₅×D₃	—	8	1	no	—
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	4	1	no	—
172	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
174	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₃×C₄×C₅	#137	1	1	yes	characteristic
176	C₅×Dic₃	—	4	1	no	—
177	C₅×Dic₃	—	4	2	no	—
178	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
179	D₃×Q₈	—	4	2	no	—
180	D₃×Q₈	—	4	2	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	—	2	1	no	—
183	C₂×D₁₂	—	2	1	no	—
184	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
185	C₂×C₄×D₃	—	2	2	no	—
186	C₂×C₄×D₃	—	2	1	no	—
187	C₂×Dic₆	—	2	2	no	—
188	C₂×Dic₆	—	2	1	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
195	#215	—	4	2	no	—
196	(C₂×D₃)⋊C₄	—	2	2	no	—
197	(C₂×D₃)⋊C₄	—	2	1	no	—
198	C₄⋊Dic₃	—	2	2	no	—
199	C₄⋊Dic₃	—	2	1	no	—
200	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
201	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
202	C₂×C₃⋊C₈	—	2	1	no	—
203	D₂₄	—	4	2	no	—
204	C₂³×C₅	—	6	1	no	—
205	C₂³×C₅	—	12	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	12	4	no	—
208	C₅×Q₈	—	12	1	no	—
209	C₅×Q₈	—	12	1	no	—
210	C₅×Q₈	D₂₄	1	2	yes	complemented
211	C₅×D₄	—	3	2	no	—
212	C₅×D₄	—	6	1	no	—
213	C₅×D₄	—	12	2	no	—
214	C₅×D₄	—	12	1	no	—
215	C₅×D₄	—	12	1	no	—
216	C₅×D₄	—	12	1	no	—
217	C₅×D₄	—	12	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	6	2	no	—
221	C₂×C₄×C₅	—	6	1	no	—
222	C₂×C₄×C₅	—	12	4	no	—
223	C₂×C₄×C₅	—	12	1	no	—
224	C₂×C₄×C₅	—	12	1	no	—
225	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
226	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
228	C₅×C₈	—	4	1	no	—
229	C₅×C₈	—	4	1	no	—
230	C₅×C₈	—	12	1	no	—
231	C₂²×Q₈	—	6	1	no	—
232	C₂×SD₁₆	—	6	1	no	—
233	C₂×D₈	—	6	1	no	—
234	C₄⋊Q₈	—	3	1	no	—
235	C₄⋊Q₈	—	6	1	no	—
236	#127	—	3	1	no	—
237	C₂²⋊Q₈	—	6	2	no	—
238	C₂²⋊Q₈	—	6	1	no	—
239	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
240	C₄×D₄	—	3	1	no	—
241	C₄×D₄	—	6	1	no	—
242	C₄⋊C₈	—	3	1	no	—
243	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
244	#102	—	6	1	no	—
245	#102	—	6	2	no	—
246	#102	—	6	1	no	—
247	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
248	C₂×C₃×C₅	#447	1	1	yes	characteristic
249	C₂×C₃×C₅	#448	1	1	yes	characteristic
250	C₂×C₃×C₅	#454	1	1	yes	characteristic
251	C₅×D₃	—	4	2	no	—
252	C₅×D₃	—	16	1	no	—
253	C₂²×D₃	—	2	1	no	—
254	C₂²×D₃	—	4	1	no	—
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	C₅×D₈	1	2	yes	complemented
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂×Dic₃	—	2	1	no	—
263	C₂×Dic₃	—	2	2	no	—
264	D₁₂	—	2	1	no	—
265	D₁₂	—	4	2	no	—
266	D₁₂	—	4	1	no	—
267	D₁₂	—	4	1	no	—
268	D₁₂	—	4	1	no	—
269	D₁₂	—	4	1	no	—
270	D₁₂	C₅×SD₁₆	1	2	yes	complemented
271	C₄×D₃	—	4	4	no	—
272	C₄×D₃	—	4	1	no	—
273	C₄×D₃	—	4	1	no	—
274	Dic₆	—	4	4	no	—
275	Dic₆	—	4	1	no	—
276	Dic₆	—	4	1	no	—
277	C₃×C₈	—	4	1	no	—
278	C₃×C₈	—	4	1	no	—
279	C₃⋊C₈	—	4	1	no	—
280	C₂²×C₅	—	6	2	no	—
281	C₂²×C₅	—	12	1	no	—
282	C₂²×C₅	—	12	1	no	—
283	C₂²×C₅	—	24	1	no	—
284	C₂²×C₅	—	24	1	no	—
285	C₂²×C₅	—	24	1	no	—
286	C₂²×C₅	#882	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	4	1	no	—
290	C₄×C₅	—	12	2	no	—
291	C₄×C₅	—	12	1	no	—
292	C₄×C₅	C₂×D₂₄	1	1	yes	characteristic
293	C₄×C₅	#908	1	1	yes	characteristic
294	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
295	C₄×C₅	#918	1	1	yes	characteristic
296	C₂×Q₈	—	6	2	no	—
297	C₂×Q₈	—	6	1	no	—
298	C₂×Q₈	—	12	2	no	—
299	C₂×Q₈	—	12	2	no	—
300	C₂×Q₈	C₅×D₁₂	1	1	yes	characteristic
301	C₂×D₄	—	3	1	no	—
302	C₂×D₄	—	6	1	no	—
303	C₂×D₄	—	6	1	no	—
304	C₂×D₄	—	6	1	no	—
305	C₂²×C₄	—	6	2	no	—
306	C₂²×C₄	—	6	1	no	—
307	SD₁₆	—	12	2	no	—
308	D₈	—	12	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	6	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	3	1	no	—
314	C₄⋊C₄	—	3	2	no	—
315	C₄⋊C₄	—	6	2	no	—
316	C₄⋊C₄	—	6	1	no	—
317	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
318	C₂²⋊C₄	—	6	2	no	—
319	C₂²⋊C₄	—	6	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
322	C₃×C₅	#1627	1	1	yes	characteristic, complemented, Hall
323	C₂²×C₃	C₅×#120	1	1	yes	characteristic
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	4	1	no	—
326	C₂×D₃	—	4	1	no	—
327	C₂×D₃	—	8	1	no	—
328	C₂×D₃	—	8	1	no	—
329	C₂×D₃	—	8	1	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	4	1	no	—
333	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
334	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
335	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₃×C₄	C₅×#137	1	1	yes	characteristic
337	Dic₃	—	4	1	no	—
338	Dic₃	—	4	2	no	—
339	C₂×C₅	—	12	2	no	—
340	C₂×C₅	—	48	1	no	—
341	C₂×C₅	#4732	1	1	yes	characteristic
342	C₂×C₅	#4806	1	1	yes	characteristic
343	C₂×C₅	#4827	1	1	yes	characteristic
344	C₂³	—	6	1	no	—
345	C₂³	—	12	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	12	4	no	—
348	Q₈	—	12	1	no	—
349	Q₈	—	12	1	no	—
350	Q₈	C₅×D₂₄	1	2	yes	complemented
351	D₄	—	3	2	no	—
352	D₄	—	6	1	no	—
353	D₄	—	12	2	no	—
354	D₄	—	12	1	no	—
355	D₄	—	12	1	no	—
356	D₄	—	12	1	no	—
357	D₄	—	12	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	6	1	no	—
362	C₂×C₄	—	12	4	no	—
363	C₂×C₄	—	12	1	no	—
364	C₂×C₄	—	12	1	no	—
365	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
366	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
367	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	12	1	no	—
371	C₂×C₃	C₅×#447	1	1	yes	characteristic
372	C₂×C₃	C₅×#448	1	1	yes	characteristic
373	C₂×C₃	C₅×#454	1	1	yes	characteristic
374	D₃	—	4	2	no	—
375	D₃	—	16	1	no	—
376	C₅	#68266	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	6	2	no	—
378	C₂²	—	12	1	no	—
379	C₂²	—	12	1	no	—
380	C₂²	—	24	1	no	—
381	C₂²	—	24	1	no	—
382	C₂²	—	24	1	no	—
383	C₂²	C₅×#882	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	1	no	—
387	C₄	—	12	2	no	—
388	C₄	—	12	1	no	—
389	C₄	C₂×C₅×D₂₄	1	1	yes	characteristic
390	C₄	C₅×#908	1	1	yes	characteristic
391	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
392	C₄	C₅×#918	1	1	yes	characteristic
393	C₃	C₅×#1627	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	12	2	no	—
395	C₂	—	48	1	no	—
396	C₂	C₅×#4732	1	1	yes	characteristic
397	C₂	C₅×#4806	1	1	yes	characteristic
398	C₂	C₅×#4827	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#882
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#4843	C₂
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1627
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₅×Q₈×D₁₂	C₂	semidirect
2. C₅×#5027	C₂	semidirect
4. C₅×#4694	C₂	semidirect
5. C₃×C₅×Q₈⋊C₈	C₂	semidirect
6. C₅×#4486	C₂	semidirect
7. C₅×#4459	C₂	semidirect
26. #68266	C₅	direct (N × H)
32. C₅×Q₈⋊C₈	D₃	semidirect
60. Q₈×D₁₂	C₂×C₅	semidirect
61. #5027	C₂×C₅	semidirect
63. #4694	C₂×C₅	semidirect
64. C₃×Q₈⋊C₈	C₂×C₅	semidirect
65. #4486	C₂×C₅	semidirect
66. #4459	C₂×C₅	semidirect
88. C₃×C₅×Q₈	D₈	semidirect
102. C₅×D₁₂	SD₁₆	semidirect
160. Q₈⋊C₈	C₅×D₃	semidirect
210. C₅×Q₈	D₂₄	semidirect
256. C₃×Q₈	C₅×D₈	semidirect
270. D₁₂	C₅×SD₁₆	semidirect
322. C₃×C₅	#1627	semidirect
350. Q₈	C₅×D₂₄	semidirect
376. C₅	#68266	direct (N × H)
393. C₃	C₅×#1627	semidirect

Maximal subgroups

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

subgroup	index
C₅×Q₈×D₁₂	2
C₅×#5027	2
C₅×#4843	2
C₅×#4694	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4486	2
C₅×#4459	2
C₅×#1627	3
#68266	5

Subgroups — C5×#68266 #14289226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68266 #14289226