Subgroups — C₅×#19887 #11942607

Order 1280.

690 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3334	C₂	1	1	yes	maximal, characteristic
3	C₅×#3276	C₂	1	2	yes	maximal, complemented
4	C₅×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1689	C₂	1	2	yes	maximal, complemented
6	C₅×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1649	C₂	1	2	yes	maximal, complemented
9	C₅×#1647	C₂	1	2	yes	maximal, complemented
10	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	2	2	no	—
13	C₅×D₄×Q₈	C₂²	1	2	yes	—
14	C₅×#547	C₂²	1	2	yes	—
15	C₅×#500	—	2	1	no	—
16	C₅×#500	C₂²	1	1	yes	characteristic
17	C₅×#500	C₂²	1	1	yes	characteristic
18	C₅×#500	C₂²	1	2	yes	—
19	C₅×#494	C₂²	1	2	yes	—
20	C₅×#480	—	2	2	no	—
21	C₅×#474	—	2	2	no	—
22	C₅×#474	C₂²	1	2	yes	—
23	C₅×#474	C₂²	1	2	yes	—
24	C₅×#470	—	2	2	no	—
25	C₅×#466	—	2	1	no	—
26	C₅×#462	C₂²	1	2	yes	—
27	C₅×#461	C₂²	1	2	yes	—
28	C₅×#452	—	2	2	no	—
29	C₅×#451	—	2	2	no	—
30	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₈	—	2	1	no	—
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₅×#436	C₂²	1	2	yes	—
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×#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×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	2	yes	—
44	C₅×C₈²	C₂²	1	1	yes	characteristic
45	#19887	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	2	no	—
47	C₂²×C₅×Q₈	—	2	2	no	—
48	C₅×#137	—	4	8	no	—
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
54	C₂×C₅×D₈	D₄	1	1	yes	characteristic
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₅×#123	—	4	2	no	—
61	C₅×C₂²⋊Q₈	—	2	2	no	—
62	C₅×C₂²⋊Q₈	—	2	2	no	—
63	C₅×C₂²⋊Q₈	—	4	2	no	—
64	C₅×#121	—	2	2	no	—
65	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×D₄	—	2	2	no	—
67	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₄×C₅×D₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	—	2	2	no	—
70	C₅×#107	—	2	1	no	—
71	C₅×#107	—	2	1	no	—
72	C₅×#107	—	2	1	no	—
73	C₅×#107	—	2	1	no	—
74	C₅×#107	—	2	2	no	—
75	C₅×#107	—	2	2	no	—
76	C₅×#107	—	4	2	no	—
77	C₅×#107	D₄	1	1	yes	characteristic
78	C₅×#106	D₄	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	2	1	no	—
80	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#103	D₄	1	1	yes	characteristic
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	D₄	1	2	yes	—
89	C₅×#102	D₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	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	Q₈×D₈	C₂×C₅	1	1	yes	characteristic, complemented
97	#3334	C₂×C₅	1	1	yes	characteristic
98	#3276	C₂×C₅	1	2	yes	complemented
99	#1713	C₂×C₅	1	1	yes	characteristic, complemented
100	#1689	C₂×C₅	1	2	yes	complemented
101	#1674	C₂×C₅	1	1	yes	characteristic, complemented
102	#1673	C₂×C₅	1	1	yes	characteristic, complemented
103	#1649	C₂×C₅	1	2	yes	complemented
104	#1647	C₂×C₅	1	2	yes	complemented
105	#1589	C₂×C₅	1	1	yes	characteristic, complemented
106	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
107	C₅×#41	—	4	4	no	—
108	C₅×#41	—	8	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×Q₈	—	4	4	no	—
113	C₂×C₅×Q₈	—	8	2	no	—
114	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₅×D₄	—	4	2	no	—
116	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
117	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	4	2	no	—
121	C₂²×C₄×C₅	—	4	2	no	—
122	C₅×Q₁₆	—	4	4	no	—
123	C₅×Q₁₆	—	4	4	no	—
124	C₅×Q₁₆	—	8	2	no	—
125	C₅×SD₁₆	—	4	4	no	—
126	C₅×SD₁₆	D₈	1	4	yes	complemented
127	C₅×D₈	—	2	2	no	—
128	C₅×M₁₆	—	4	4	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	4	2	no	—
134	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	4	2	no	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₅×C₂²⋊C₄	—	2	2	no	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	4	2	no	—
151	C₅×C₂²⋊C₄	—	4	2	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×#137	—	2	2	no	—
155	D₄×Q₈	C₂²×C₅	1	2	yes	—
156	#547	C₂²×C₅	1	2	yes	—
157	#500	—	2	1	no	—
158	#500	C₂²×C₅	1	1	yes	characteristic
159	#500	C₂²×C₅	1	1	yes	characteristic
160	#500	C₂²×C₅	1	2	yes	—
161	#494	C₂²×C₅	1	2	yes	—
162	#480	—	2	2	no	—
163	#474	—	2	2	no	—
164	#474	C₂²×C₅	1	2	yes	—
165	#474	C₂²×C₅	1	2	yes	—
166	#470	—	2	2	no	—
167	#466	—	2	1	no	—
168	#462	C₂²×C₅	1	2	yes	—
169	#461	C₂²×C₅	1	2	yes	—
170	#452	—	2	2	no	—
171	#451	—	2	2	no	—
172	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
173	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
174	C₄×D₈	—	2	1	no	—
175	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
176	#436	C₂²×C₅	1	2	yes	—
177	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×#107	—	2	1	no	—
179	#335	C₂²×C₅	1	1	yes	characteristic
180	#334	C₂²×C₅	1	1	yes	characteristic
181	#332	C₂²×C₅	1	2	yes	—
182	#332	C₂²×C₅	1	2	yes	—
183	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
184	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
185	D₄⋊C₈	C₂²×C₅	1	2	yes	—
186	C₈²	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₅	—	2	1	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₅×Q₈	—	2	1	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×D₈	1	2	yes	—
196	C₅×D₄	—	2	2	no	—
197	C₅×D₄	—	2	1	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	8	4	no	—
200	C₅×D₄	C₂×D₈	1	2	yes	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	8	4	no	—
212	C₂×C₄×C₅	—	8	4	no	—
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	—	2	1	no	—
218	C₅×C₈	—	2	1	no	—
219	C₅×C₈	—	4	2	no	—
220	C₅×C₈	—	4	1	no	—
221	C₅×C₈	—	4	1	no	—
222	C₅×C₈	C₂×D₈	1	2	yes	—
223	C₅×C₈	#137	1	2	yes	complemented
224	C₂×#41	—	2	2	no	—
225	C₂²×Q₈	—	2	2	no	—
226	#137	—	4	8	no	—
227	C₂×Q₁₆	—	2	2	no	—
228	C₂×Q₁₆	—	2	2	no	—
229	C₂×Q₁₆	—	2	2	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
232	C₂×D₈	C₅×D₄	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
237	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
238	#123	—	4	2	no	—
239	C₂²⋊Q₈	—	2	2	no	—
240	C₂²⋊Q₈	—	2	2	no	—
241	C₂²⋊Q₈	—	4	2	no	—
242	#121	—	2	2	no	—
243	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
246	C₄×D₄	C₂³×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	#107	—	2	1	no	—
249	#107	—	2	1	no	—
250	#107	—	2	1	no	—
251	#107	—	2	1	no	—
252	#107	—	2	2	no	—
253	#107	—	2	2	no	—
254	#107	—	4	2	no	—
255	#107	C₅×D₄	1	1	yes	characteristic
256	#106	C₅×D₄	1	1	yes	characteristic
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
259	C₄⋊C₈	C₂³×C₅	1	2	yes	—
260	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
261	#103	—	2	2	no	—
262	#103	—	2	2	no	—
263	#103	C₅×D₄	1	1	yes	characteristic
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	#102	C₅×D₄	1	2	yes	—
267	#102	C₅×D₄	1	1	yes	characteristic
268	C₂²⋊C₈	—	2	1	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	4	2	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	D₄²	1	1	yes	characteristic
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	4	2	no	—
285	C₄×C₅	—	4	1	no	—
286	C₄×C₅	—	8	2	no	—
287	C₄×C₅	—	8	2	no	—
288	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
289	C₄×C₅	C₂×#137	1	1	yes	characteristic
290	C₄×C₅	#576	1	1	yes	characteristic
291	C₄×C₅	#578	1	1	yes	characteristic
292	#41	—	4	4	no	—
293	#41	—	8	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	—	8	2	no	—
299	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
302	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	Q₁₆	—	4	4	no	—
308	Q₁₆	—	4	4	no	—
309	Q₁₆	—	8	2	no	—
310	SD₁₆	—	4	4	no	—
311	SD₁₆	C₅×D₈	1	4	yes	complemented
312	D₈	—	2	2	no	—
313	M₁₆	—	4	4	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
332	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	C₂⁴×C₅	1	1	yes	characteristic
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	—	8	2	no	—
341	C₂×C₅	#3276	1	1	yes	characteristic
342	C₂×C₅	D₄×D₈	1	1	yes	characteristic
343	C₂×C₅	#3293	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	2	2	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	8	4	no	—
352	Q₈	C₂×C₅×D₈	1	2	yes	—
353	D₄	—	2	2	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	2	no	—
356	D₄	—	8	4	no	—
357	D₄	C₂×C₅×D₈	1	2	yes	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
372	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
373	C₈	—	2	2	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	C₂×C₅×D₈	1	2	yes	—
380	C₈	C₅×#137	1	2	yes	complemented
381	C₅	#19887	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	2	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	C₅×D₄²	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
397	C₄	C₂×C₅×#137	1	1	yes	characteristic
398	C₄	C₅×#576	1	1	yes	characteristic
399	C₄	C₅×#578	1	1	yes	characteristic
400	C₂	—	4	2	no	—
401	C₂	—	8	2	no	—
402	C₂	C₅×#3276	1	1	yes	characteristic
403	C₂	C₅×D₄×D₈	1	1	yes	characteristic
404	C₂	C₅×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3334	C₂
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×Q₈×D₈	C₂	semidirect
3. C₅×#3276	C₂	semidirect
4. C₅×#1713	C₂	semidirect
5. C₅×#1689	C₂	semidirect
6. C₅×#1674	C₂	semidirect
7. C₅×#1673	C₂	semidirect
8. C₅×#1649	C₂	semidirect
9. C₅×#1647	C₂	semidirect
10. C₅×#1589	C₂	semidirect
11. C₅×C₈×SD₁₆	C₂	semidirect
45. #19887	C₅	direct (N × H)
96. Q₈×D₈	C₂×C₅	semidirect
98. #3276	C₂×C₅	semidirect
99. #1713	C₂×C₅	semidirect
100. #1689	C₂×C₅	semidirect
101. #1674	C₂×C₅	semidirect
102. #1673	C₂×C₅	semidirect
103. #1649	C₂×C₅	semidirect
104. #1647	C₂×C₅	semidirect
105. #1589	C₂×C₅	semidirect
106. C₈×SD₁₆	C₂×C₅	semidirect
126. C₅×SD₁₆	D₈	semidirect
223. C₅×C₈	#137	semidirect
311. SD₁₆	C₅×D₈	semidirect
380. C₈	C₅×#137	semidirect
381. C₅	#19887	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×Q₈×D₈	2
C₅×#3334	2
C₅×#3276	2
C₅×#1713	2
C₅×#1689	2
C₅×#1674	2
C₅×#1673	2
C₅×#1649	2
C₅×#1647	2
C₅×#1589	2
C₅×C₈×SD₁₆	2
#19887	5

Subgroups — C5×#19887 #11942607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19887 #11942607