Subgroups — C₅×#33788 #11956508

Order 1280.

594 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×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3155	C₂	1	1	yes	maximal, characteristic
3	C₅×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2211	C₂	1	2	yes	maximal, complemented
8	C₅×#2207	C₂	1	2	yes	maximal, complemented
9	C₅×#2189	C₂	1	2	yes	maximal, complemented
10	C₅×#2187	C₂	1	2	yes	maximal, complemented
11	C₅×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₅×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₅×#541	—	2	1	no	—
16	C₅×#535	—	2	1	no	—
17	C₂×C₅×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
21	C₅×#499	C₂²	1	1	yes	characteristic, complemented
22	C₅×#496	—	2	1	no	—
23	C₅×#496	—	2	1	no	—
24	C₅×#495	C₂²	1	1	yes	characteristic
25	C₅×#495	C₂²	1	1	yes	characteristic
26	C₅×#494	C₂²	1	1	yes	characteristic, complemented
27	C₅×#493	C₂²	1	1	yes	characteristic
28	C₅×#493	C₂²	1	1	yes	characteristic
29	C₅×#491	—	2	1	no	—
30	C₅×#470	—	2	1	no	—
31	C₅×#467	C₂²	1	2	yes	—
32	C₅×#441	—	2	1	no	—
33	C₄×C₅×Q₁₆	C₂²	1	2	yes	complemented
34	C₅×#405	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₅×#358	C₂²	1	2	yes	complemented
37	C₅×#357	C₂²	1	2	yes	—
38	C₅×#357	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₅×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
43	#33788	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₅×AGL(1,ℤ/8)	—	4	4	no	—
47	C₅×#135	—	4	2	no	—
48	C₂×C₅×Q₁₆	—	2	1	no	—
49	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₅×SD₁₆	—	2	1	no	—
52	C₂×C₅×SD₁₆	—	2	1	no	—
53	C₂×C₅×SD₁₆	—	2	1	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×D₈	—	4	2	no	—
58	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
59	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
60	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
61	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×#127	—	2	1	no	—
65	C₅×#127	—	2	1	no	—
66	C₅×#126	—	4	2	no	—
67	C₅×#125	—	2	1	no	—
68	C₅×#125	—	4	2	no	—
69	C₅×#124	—	2	1	no	—
70	C₅×#124	—	2	1	no	—
71	C₅×C₂²⋊Q₈	—	2	2	no	—
72	C₅×#121	—	4	2	no	—
73	C₅×#120	—	4	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₅×#117	D₄	1	1	yes	characteristic
76	C₅×Q₃₂	—	4	2	no	—
77	C₅×SD₃₂	—	4	2	no	—
78	C₅×SD₃₂	—	4	2	no	—
79	C₅×SD₃₂	—	4	2	no	—
80	C₂×C₅×C₁₆	C₂³	1	2	yes	—
81	C₂×C₅×C₁₆	C₂³	1	2	yes	—
82	C₅×#107	C₂³	1	2	yes	—
83	C₅×#106	—	2	1	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#103	—	2	2	no	—
86	C₅×#97	D₄	1	1	yes	characteristic
87	C₅×#97	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	#3177	C₂×C₅	1	1	yes	characteristic, complemented
91	#3155	C₂×C₅	1	1	yes	characteristic
92	#2251	C₂×C₅	1	1	yes	characteristic, complemented
93	#2248	C₂×C₅	1	1	yes	characteristic, complemented
94	#2244	C₂×C₅	1	1	yes	characteristic, complemented
95	#2242	C₂×C₅	1	1	yes	characteristic, complemented
96	#2211	C₂×C₅	1	2	yes	complemented
97	#2207	C₂×C₅	1	2	yes	complemented
98	#2189	C₂×C₅	1	2	yes	complemented
99	#2187	C₂×C₅	1	2	yes	complemented
100	#2164	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	—	4	1	no	—
102	C₅×#41	—	4	2	no	—
103	C₅×#41	—	4	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	4	2	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	—	4	2	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Q₁₆	—	2	2	no	—
118	C₅×Q₁₆	—	2	2	no	—
119	C₅×Q₁₆	—	2	2	no	—
120	C₅×Q₁₆	—	4	2	no	—
121	C₅×SD₁₆	—	4	2	no	—
122	C₅×SD₁₆	—	4	2	no	—
123	C₅×SD₁₆	—	4	2	no	—
124	C₅×D₈	—	2	2	no	—
125	C₅×D₈	—	2	2	no	—
126	C₅×D₈	—	2	2	no	—
127	C₅×D₈	—	4	2	no	—
128	C₅×D₈	—	4	2	no	—
129	C₅×D₈	—	4	2	no	—
130	C₅×M₁₆	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	D₈	1	2	yes	—
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	D₈	1	2	yes	—
146	C₄²×C₅	—	4	2	no	—
147	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₅×C₁₆	—	2	2	no	—
150	C₅×C₁₆	—	2	2	no	—
151	C₂×AGL(1,ℤ/8)	—	2	1	no	—
152	C₂×#135	C₂²×C₅	1	1	yes	characteristic
153	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
154	#541	—	2	1	no	—
155	#535	—	2	1	no	—
156	C₂×Q₃₂	C₂²×C₅	1	2	yes	complemented
157	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
158	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
159	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
160	#499	C₂²×C₅	1	1	yes	characteristic, complemented
161	#496	—	2	1	no	—
162	#496	—	2	1	no	—
163	#495	C₂²×C₅	1	1	yes	characteristic
164	#495	C₂²×C₅	1	1	yes	characteristic
165	#494	C₂²×C₅	1	1	yes	characteristic, complemented
166	#493	C₂²×C₅	1	1	yes	characteristic
167	#493	C₂²×C₅	1	1	yes	characteristic
168	#491	—	2	1	no	—
169	#470	—	2	1	no	—
170	#467	C₂²×C₅	1	2	yes	—
171	#441	—	2	1	no	—
172	C₄×Q₁₆	C₂²×C₅	1	2	yes	complemented
173	#405	C₂²×C₅	1	1	yes	characteristic
174	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
175	#358	C₂²×C₅	1	2	yes	complemented
176	#357	C₂²×C₅	1	2	yes	—
177	#357	C₂²×C₅	1	2	yes	—
178	#357	C₂²×C₅	1	2	yes	complemented
179	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
180	#346	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	8	2	no	—
186	C₂³×C₅	—	16	2	no	—
187	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
188	C₅×Q₈	—	4	1	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	—	4	1	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	4	1	no	—
194	C₅×D₄	—	4	1	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	1	no	—
197	C₅×D₄	—	4	1	no	—
198	C₅×D₄	—	8	2	no	—
199	C₅×D₄	—	8	2	no	—
200	C₅×D₄	—	16	2	no	—
201	C₅×D₄	—	16	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	8	2	no	—
208	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
209	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
210	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
215	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
216	C₂×#41	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	AGL(1,ℤ/8)	—	4	4	no	—
219	#135	—	4	2	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
222	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
223	C₂×SD₁₆	—	2	1	no	—
224	C₂×SD₁₆	—	2	1	no	—
225	C₂×SD₁₆	—	2	1	no	—
226	C₂×D₈	—	2	1	no	—
227	C₂×D₈	—	2	1	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	4	2	no	—
230	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
231	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
232	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
233	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	1	no	—
236	#127	—	2	1	no	—
237	#127	—	2	1	no	—
238	#126	—	4	2	no	—
239	#125	—	2	1	no	—
240	#125	—	4	2	no	—
241	#124	—	2	1	no	—
242	#124	—	2	1	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	#121	—	4	2	no	—
245	#120	—	4	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	#117	C₅×D₄	1	1	yes	characteristic
248	Q₃₂	—	4	2	no	—
249	SD₃₂	—	4	2	no	—
250	SD₃₂	—	4	2	no	—
251	SD₃₂	—	4	2	no	—
252	C₂×C₁₆	C₂³×C₅	1	2	yes	—
253	C₂×C₁₆	C₂³×C₅	1	2	yes	—
254	#107	C₂³×C₅	1	2	yes	—
255	#106	—	2	1	no	—
256	#103	—	2	2	no	—
257	#103	—	2	2	no	—
258	#97	C₅×D₄	1	1	yes	characteristic
259	#97	C₅×D₄	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	1	no	—
264	C₂²×C₅	—	8	2	no	—
265	C₂²×C₅	—	8	2	no	—
266	C₂²×C₅	—	8	2	no	—
267	C₂²×C₅	—	8	1	no	—
268	C₂²×C₅	—	8	1	no	—
269	C₂²×C₅	—	8	1	no	—
270	C₂²×C₅	—	16	4	no	—
271	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	8	2	no	—
276	C₄×C₅	—	8	1	no	—
277	C₄×C₅	—	8	2	no	—
278	C₄×C₅	#535	1	1	yes	characteristic
279	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₂⁴	—	4	1	no	—
281	#41	—	4	2	no	—
282	#41	—	4	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	4	2	no	—
300	SD₁₆	—	4	2	no	—
301	SD₁₆	—	4	2	no	—
302	SD₁₆	—	4	2	no	—
303	D₈	—	2	2	no	—
304	D₈	—	2	2	no	—
305	D₈	—	2	2	no	—
306	D₈	—	4	2	no	—
307	D₈	—	4	2	no	—
308	D₈	—	4	2	no	—
309	M₁₆	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
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	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	C₅×D₈	1	2	yes	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	C₅×D₈	1	2	yes	—
325	C₄²	—	4	2	no	—
326	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
327	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
328	C₁₆	—	2	2	no	—
329	C₁₆	—	2	2	no	—
330	C₂×C₅	—	4	1	no	—
331	C₂×C₅	—	16	1	no	—
332	C₂×C₅	—	16	1	no	—
333	C₂×C₅	—	16	1	no	—
334	C₂×C₅	#3205	1	1	yes	characteristic
335	C₂×C₅	#3416	1	2	yes	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	8	2	no	—
340	C₂³	—	16	2	no	—
341	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
342	Q₈	—	4	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	16	2	no	—
355	D₄	—	16	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
363	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
364	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
369	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
370	C₅	#33788	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	2	no	—
387	C₄	C₅×#535	1	1	yes	characteristic
388	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂	—	4	1	no	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	—	16	1	no	—
393	C₂	C₅×#3205	1	1	yes	characteristic
394	C₂	C₅×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3177	C₂	semidirect
3. C₅×#2251	C₂	semidirect
4. C₅×#2248	C₂	semidirect
5. C₅×#2244	C₂	semidirect
6. C₅×#2242	C₂	semidirect
7. C₅×#2211	C₂	semidirect
8. C₅×#2207	C₂	semidirect
9. C₅×#2189	C₂	semidirect
10. C₅×#2187	C₂	semidirect
11. C₅×#2164	C₂	semidirect
17. C₂×C₅×Q₃₂	C₂²	semidirect
20. C₂×C₅×SD₃₂	C₂²	semidirect
21. C₅×#499	C₂²	semidirect
26. C₅×#494	C₂²	semidirect
33. C₄×C₅×Q₁₆	C₂²	semidirect
35. C₅×C₄⋊C₁₆	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
41. C₅×#346	C₂²	semidirect
42. C₄×C₅×C₁₆	C₂²	semidirect
43. #33788	C₅	direct (N × H)
90. #3177	C₂×C₅	semidirect
92. #2251	C₂×C₅	semidirect
93. #2248	C₂×C₅	semidirect
94. #2244	C₂×C₅	semidirect
95. #2242	C₂×C₅	semidirect
96. #2211	C₂×C₅	semidirect
97. #2207	C₂×C₅	semidirect
98. #2189	C₂×C₅	semidirect
99. #2187	C₂×C₅	semidirect
100. #2164	C₂×C₅	semidirect
156. C₂×Q₃₂	C₂²×C₅	semidirect
159. C₂×SD₃₂	C₂²×C₅	semidirect
160. #499	C₂²×C₅	semidirect
165. #494	C₂²×C₅	semidirect
172. C₄×Q₁₆	C₂²×C₅	semidirect
174. C₄⋊C₁₆	C₂²×C₅	semidirect
175. #358	C₂²×C₅	semidirect
178. #357	C₂²×C₅	semidirect
180. #346	C₂²×C₅	semidirect
181. C₄×C₁₆	C₂²×C₅	semidirect
370. C₅	#33788	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×#3177	2
C₅×#3155	2
C₅×#2251	2
C₅×#2248	2
C₅×#2244	2
C₅×#2242	2
C₅×#2211	2
C₅×#2207	2
C₅×#2189	2
C₅×#2187	2
C₅×#2164	2
#33788	5

Subgroups — C5×#33788 #11956508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33788 #11956508