Subgroups — C₅×#33786 #11956506

Order 1280.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2246	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×#2210	C₂	1	2	yes	maximal, complemented
8	C₅×#2206	C₂	1	2	yes	maximal, complemented
9	C₅×#2186	C₂	1	2	yes	maximal, complemented
10	C₅×#2184	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×#540	—	2	1	no	—
16	C₅×#535	—	2	1	no	—
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×D₁₆	C₂²	1	2	yes	—
19	C₂×C₅×D₁₆	C₂²	1	2	yes	—
20	C₂×C₅×D₁₆	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×#493	C₂²	1	1	yes	characteristic
27	C₅×#493	C₂²	1	1	yes	characteristic
28	C₅×#493	C₂²	1	1	yes	characteristic, complemented
29	C₅×#490	—	2	1	no	—
30	C₅×#469	—	2	1	no	—
31	C₅×#466	C₂²	1	2	yes	—
32	C₅×#442	—	2	1	no	—
33	C₄×C₅×D₈	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	#33786	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	C₂³	1	1	yes	characteristic
49	C₂×C₅×SD₁₆	—	2	1	no	—
50	C₂×C₅×SD₁₆	—	2	1	no	—
51	C₂×C₅×SD₁₆	—	2	1	no	—
52	C₂×C₅×D₈	—	2	1	no	—
53	C₂×C₅×D₈	—	2	1	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	4	2	no	—
57	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
58	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
59	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
60	C₂×C₅×D₈	C₂³	1	2	yes	—
61	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₅×#127	—	2	1	no	—
64	C₅×#127	—	2	1	no	—
65	C₅×#127	—	2	1	no	—
66	C₅×#125	—	2	1	no	—
67	C₅×#124	—	2	1	no	—
68	C₅×#124	—	2	1	no	—
69	C₅×#123	—	4	2	no	—
70	C₅×#121	—	2	2	no	—
71	C₅×#121	—	4	2	no	—
72	C₅×#121	—	4	2	no	—
73	C₅×#120	—	4	2	no	—
74	C₄×C₅×D₄	—	2	2	no	—
75	C₅×#117	D₄	1	1	yes	characteristic
76	C₅×SD₃₂	—	4	2	no	—
77	C₅×D₁₆	—	4	2	no	—
78	C₅×D₁₆	—	4	2	no	—
79	C₅×D₁₆	—	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×#102	—	2	2	no	—
85	C₅×#102	—	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	#3176	C₂×C₅	1	1	yes	characteristic, complemented
91	#3155	C₂×C₅	1	1	yes	characteristic, complemented
92	#2250	C₂×C₅	1	1	yes	characteristic, complemented
93	#2246	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	#2210	C₂×C₅	1	2	yes	complemented
97	#2206	C₂×C₅	1	2	yes	complemented
98	#2186	C₂×C₅	1	2	yes	complemented
99	#2184	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	1	no	—
105	C₂×C₅×D₄	—	2	2	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	2	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂×C₅×D₄	—	4	2	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	2	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	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	—	2	2	no	—
128	C₅×D₈	—	2	2	no	—
129	C₅×D₈	—	4	2	no	—
130	C₅×D₈	—	4	2	no	—
131	C₅×D₈	—	4	2	no	—
132	C₅×D₈	—	4	2	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
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	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
139	C₅×C₄⋊C₄	—	2	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	—	4	2	no	—
146	C₅×C₂²⋊C₄	D₈	1	2	yes	—
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	#540	—	2	1	no	—
155	#535	—	2	1	no	—
156	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
157	C₂×D₁₆	C₂²×C₅	1	2	yes	—
158	C₂×D₁₆	C₂²×C₅	1	2	yes	—
159	C₂×D₁₆	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	#493	C₂²×C₅	1	1	yes	characteristic
166	#493	C₂²×C₅	1	1	yes	characteristic
167	#493	C₂²×C₅	1	1	yes	characteristic, complemented
168	#490	—	2	1	no	—
169	#469	—	2	1	no	—
170	#466	C₂²×C₅	1	2	yes	—
171	#442	—	2	1	no	—
172	C₄×D₈	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	2	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	—	8	2	no	—
187	C₂³×C₅	—	16	2	no	—
188	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
189	C₅×Q₈	—	4	1	no	—
190	C₅×Q₈	—	4	1	no	—
191	C₅×D₄	—	4	1	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	4	1	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	1	no	—
197	C₅×D₄	—	4	1	no	—
198	C₅×D₄	—	4	2	no	—
199	C₅×D₄	—	8	2	no	—
200	C₅×D₄	—	8	2	no	—
201	C₅×D₄	—	16	2	no	—
202	C₅×D₄	—	16	2	no	—
203	C₅×D₄	—	16	2	no	—
204	C₅×D₄	—	16	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	8	2	no	—
210	C₂×C₄×C₅	—	16	2	no	—
211	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
212	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
213	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
218	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
219	C₂×#41	—	2	1	no	—
220	C₂²×D₄	—	2	1	no	—
221	AGL(1,ℤ/8)	—	4	4	no	—
222	#135	—	4	2	no	—
223	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
224	C₂×SD₁₆	—	2	1	no	—
225	C₂×SD₁₆	—	2	1	no	—
226	C₂×SD₁₆	—	2	1	no	—
227	C₂×D₈	—	2	1	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	4	2	no	—
232	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
233	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
234	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
235	C₂×D₈	C₂³×C₅	1	2	yes	—
236	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
238	#127	—	2	1	no	—
239	#127	—	2	1	no	—
240	#127	—	2	1	no	—
241	#125	—	2	1	no	—
242	#124	—	2	1	no	—
243	#124	—	2	1	no	—
244	#123	—	4	2	no	—
245	#121	—	2	2	no	—
246	#121	—	4	2	no	—
247	#121	—	4	2	no	—
248	#120	—	4	2	no	—
249	C₄×D₄	—	2	2	no	—
250	#117	C₅×D₄	1	1	yes	characteristic
251	SD₃₂	—	4	2	no	—
252	D₁₆	—	4	2	no	—
253	D₁₆	—	4	2	no	—
254	D₁₆	—	4	2	no	—
255	C₂×C₁₆	C₂³×C₅	1	2	yes	—
256	C₂×C₁₆	C₂³×C₅	1	2	yes	—
257	#107	C₂³×C₅	1	2	yes	—
258	#106	—	2	1	no	—
259	#102	—	2	2	no	—
260	#102	—	2	2	no	—
261	#97	C₅×D₄	1	1	yes	characteristic
262	#97	C₅×D₄	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	8	2	no	—
268	C₂²×C₅	—	8	2	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	—	8	1	no	—
274	C₂²×C₅	—	8	1	no	—
275	C₂²×C₅	—	8	2	no	—
276	C₂²×C₅	—	16	4	no	—
277	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	8	2	no	—
282	C₄×C₅	—	8	1	no	—
283	C₄×C₅	#535	1	1	yes	characteristic
284	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂⁴	—	4	1	no	—
286	#41	—	4	2	no	—
287	#41	—	4	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	Q₁₆	—	2	2	no	—
305	SD₁₆	—	4	2	no	—
306	SD₁₆	—	4	2	no	—
307	SD₁₆	—	4	2	no	—
308	D₈	—	2	2	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	4	2	no	—
314	D₈	—	4	2	no	—
315	D₈	—	4	2	no	—
316	D₈	—	4	2	no	—
317	M₁₆	—	2	2	no	—
318	C₂×C₈	—	2	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	C₂⁴×C₅	1	1	yes	characteristic
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	C₅×D₈	1	2	yes	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	C₅×D₈	1	2	yes	—
331	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
332	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₂×C₅	—	4	1	no	—
336	C₂×C₅	—	16	2	no	—
337	C₂×C₅	—	16	1	no	—
338	C₂×C₅	—	16	1	no	—
339	C₂×C₅	—	16	1	no	—
340	C₂×C₅	#3205	1	1	yes	characteristic
341	C₂×C₅	#3415	1	2	yes	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	16	2	no	—
348	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	2	no	—
362	D₄	—	16	2	no	—
363	D₄	—	16	2	no	—
364	D₄	—	16	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	—	16	2	no	—
371	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
372	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
373	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
378	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
379	C₅	#33786	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	16	4	no	—
392	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₅×#535	1	1	yes	characteristic
399	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	—	16	1	no	—
403	C₂	—	16	2	no	—
404	C₂	—	16	1	no	—
405	C₂	C₅×#3205	1	1	yes	characteristic
406	C₂	C₅×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
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×#3176	C₂	semidirect
2. C₅×#3155	C₂	semidirect
3. C₅×#2250	C₂	semidirect
4. C₅×#2246	C₂	semidirect
5. C₅×#2244	C₂	semidirect
6. C₅×#2242	C₂	semidirect
7. C₅×#2210	C₂	semidirect
8. C₅×#2206	C₂	semidirect
9. C₅×#2186	C₂	semidirect
10. C₅×#2184	C₂	semidirect
11. C₅×#2164	C₂	semidirect
17. C₂×C₅×SD₃₂	C₂²	semidirect
20. C₂×C₅×D₁₆	C₂²	semidirect
21. C₅×#499	C₂²	semidirect
28. C₅×#493	C₂²	semidirect
33. C₄×C₅×D₈	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. #33786	C₅	direct (N × H)
90. #3176	C₂×C₅	semidirect
91. #3155	C₂×C₅	semidirect
92. #2250	C₂×C₅	semidirect
93. #2246	C₂×C₅	semidirect
94. #2244	C₂×C₅	semidirect
95. #2242	C₂×C₅	semidirect
96. #2210	C₂×C₅	semidirect
97. #2206	C₂×C₅	semidirect
98. #2186	C₂×C₅	semidirect
99. #2184	C₂×C₅	semidirect
100. #2164	C₂×C₅	semidirect
156. C₂×SD₃₂	C₂²×C₅	semidirect
159. C₂×D₁₆	C₂²×C₅	semidirect
160. #499	C₂²×C₅	semidirect
167. #493	C₂²×C₅	semidirect
172. C₄×D₈	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
379. C₅	#33786	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×#3176	2
C₅×#3155	2
C₅×#2250	2
C₅×#2246	2
C₅×#2244	2
C₅×#2242	2
C₅×#2210	2
C₅×#2206	2
C₅×#2186	2
C₅×#2184	2
C₅×#2164	2
#33786	5

Subgroups — C5×#33786 #11956506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33786 #11956506