Subgroups — C₅×#33856 #11956576

Order 1280.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3416	C₂	1	2	yes	maximal, complemented
2	C₅×#3293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3292	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2223	C₂	1	2	yes	maximal, complemented
6	C₅×#2214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2194	C₂	1	2	yes	maximal, complemented
9	C₅×#2193	C₂	1	2	yes	maximal, complemented
10	C₅×#2178	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#578	—	2	1	no	—
13	C₅×#578	C₂²	1	2	yes	complemented
14	C₅×#576	—	2	1	no	—
15	C₅×#576	C₂²	1	2	yes	—
16	C₅×#510	—	2	2	no	—
17	C₅×#510	C₂²	1	2	yes	—
18	C₅×#509	—	2	2	no	—
19	C₅×#509	C₂²	1	2	yes	complemented
20	C₅×#508	—	2	2	no	—
21	C₅×#508	C₂²	1	1	yes	characteristic
22	C₂×C₅×SD₃₂	—	2	2	no	—
23	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
24	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
25	C₅×#504	C₂²	1	2	yes	complemented
26	C₅×#494	C₂²	1	1	yes	characteristic, complemented
27	C₅×#493	C₂²	1	1	yes	characteristic
28	C₅×#473	—	2	1	no	—
29	C₅×#473	C₂²	1	2	yes	complemented
30	C₅×#472	—	2	1	no	—
31	C₅×#472	C₂²	1	2	yes	—
32	C₅×#456	—	2	2	no	—
33	C₅×#453	—	2	2	no	—
34	C₅×#443	C₂²	1	1	yes	characteristic
35	C₅×#443	C₂²	1	1	yes	characteristic
36	C₅×#443	C₂²	1	1	yes	characteristic, complemented
37	C₅×#368	C₂²	1	1	yes	characteristic, complemented
38	C₅×#364	C₂²	1	1	yes	characteristic, complemented
39	C₅×#362	C₂²	1	2	yes	complemented
40	C₅×#361	C₂²	1	2	yes	complemented
41	C₅×#359	C₂²	1	1	yes	characteristic
42	C₅×#359	C₂²	1	1	yes	characteristic, complemented
43	C₅×#350	C₂²	1	2	yes	complemented
44	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
45	#33856	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₅×2₋¹⁺⁴	—	2	2	no	—
47	C₅×H(5,𝔽₂)	—	2	2	no	—
48	C₅×#137	—	2	2	no	—
49	C₅×#137	—	2	2	no	—
50	C₅×#137	—	4	2	no	—
51	C₅×#137	—	4	2	no	—
52	C₅×AGL(1,ℤ/8)	—	2	2	no	—
53	C₅×AGL(1,ℤ/8)	—	2	2	no	—
54	C₅×AGL(1,ℤ/8)	—	4	2	no	—
55	C₅×AGL(1,ℤ/8)	—	4	2	no	—
56	C₅×#135	—	2	2	no	—
57	C₅×#135	—	2	2	no	—
58	C₅×#135	—	4	1	no	—
59	C₅×#135	—	4	1	no	—
60	C₅×#135	D₄	1	1	yes	characteristic
61	C₅×#135	C₂³	1	1	yes	characteristic
62	C₅×#135	C₂³	1	1	yes	characteristic
63	C₂×C₅×Q₁₆	—	2	2	no	—
64	C₂×C₅×Q₁₆	—	2	1	no	—
65	C₂×C₅×Q₁₆	—	4	1	no	—
66	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
67	C₂×C₅×D₈	—	2	2	no	—
68	C₂×C₅×D₈	—	2	1	no	—
69	C₂×C₅×D₈	—	4	1	no	—
70	C₂×C₅×D₈	C₂³	1	2	yes	—
71	C₅×#131	—	2	1	no	—
72	C₅×#131	—	2	1	no	—
73	C₅×#131	C₂³	1	2	yes	—
74	C₅×C₄⋊Q₈	—	2	1	no	—
75	C₅×#127	—	2	1	no	—
76	C₅×Q₃₂	—	2	2	no	—
77	C₅×Q₃₂	D₄	1	1	yes	characteristic, complemented
78	C₅×SD₃₂	—	2	2	no	—
79	C₅×SD₃₂	—	2	2	no	—
80	C₅×SD₃₂	—	2	2	no	—
81	C₅×SD₃₂	—	2	2	no	—
82	C₅×SD₃₂	—	4	2	no	—
83	C₅×SD₃₂	D₄	1	1	yes	characteristic, complemented
84	C₅×SD₃₂	D₄	1	1	yes	characteristic, complemented
85	C₅×D₁₆	—	2	2	no	—
86	C₅×D₁₆	D₄	1	1	yes	characteristic, complemented
87	C₅×M₃₂	—	2	2	no	—
88	C₅×M₃₂	C₂³	1	2	yes	—
89	C₂×C₅×C₁₆	—	2	2	no	—
90	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
92	C₅×#108	D₄	1	1	yes	characteristic
93	C₅×#108	C₂³	1	1	yes	characteristic
94	C₅×#108	C₂³	1	1	yes	characteristic
95	C₅×#104	—	2	1	no	—
96	C₅×#104	—	2	1	no	—
97	C₅×#104	D₄	1	2	yes	—
98	C₅×#101	—	2	2	no	—
99	C₅×#100	—	2	2	no	—
100	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
101	#3416	C₂×C₅	1	2	yes	complemented
102	#3293	C₂×C₅	1	1	yes	characteristic, complemented
103	#3292	C₂×C₅	1	1	yes	characteristic, complemented
104	#2248	C₂×C₅	1	1	yes	characteristic, complemented
105	#2223	C₂×C₅	1	2	yes	complemented
106	#2214	C₂×C₅	1	1	yes	characteristic, complemented
107	#2213	C₂×C₅	1	1	yes	characteristic, complemented
108	#2194	C₂×C₅	1	2	yes	complemented
109	#2193	C₂×C₅	1	2	yes	complemented
110	#2178	C₂×C₅	1	1	yes	characteristic, complemented
111	#2170	C₂×C₅	1	1	yes	characteristic, complemented
112	C₅×#41	—	2	1	no	—
113	C₅×#41	—	2	1	no	—
114	C₅×#41	—	4	2	no	—
115	C₅×#41	—	4	2	no	—
116	C₅×#41	—	4	2	no	—
117	C₅×#41	—	4	2	no	—
118	C₅×#41	—	8	2	no	—
119	C₅×#41	C₂×D₄	1	2	yes	—
120	C₂×C₅×Q₈	—	2	2	no	—
121	C₂×C₅×Q₈	—	4	2	no	—
122	C₂×C₅×Q₈	—	4	2	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂×C₅×D₄	—	4	2	no	—
126	C₂×C₅×D₄	—	8	1	no	—
127	C₂×C₅×D₄	—	8	2	no	—
128	C₅×Q₁₆	—	2	2	no	—
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×Q₁₆	—	4	2	no	—
131	C₅×Q₁₆	—	4	2	no	—
132	C₅×Q₁₆	—	4	1	no	—
133	C₅×Q₁₆	—	4	1	no	—
134	C₅×Q₁₆	D₈	1	1	yes	characteristic
135	C₅×Q₁₆	C₂×D₄	1	1	yes	characteristic
136	C₅×Q₁₆	C₂×D₄	1	1	yes	characteristic
137	C₅×SD₁₆	—	2	1	no	—
138	C₅×SD₁₆	—	2	1	no	—
139	C₅×SD₁₆	—	4	2	no	—
140	C₅×SD₁₆	—	4	2	no	—
141	C₅×SD₁₆	—	4	2	no	—
142	C₅×SD₁₆	—	4	2	no	—
143	C₅×SD₁₆	D₈	1	2	yes	—
144	C₅×D₈	—	2	2	no	—
145	C₅×D₈	—	2	2	no	—
146	C₅×D₈	—	4	2	no	—
147	C₅×D₈	—	4	2	no	—
148	C₅×D₈	—	4	1	no	—
149	C₅×D₈	—	4	1	no	—
150	C₅×D₈	D₈	1	1	yes	characteristic
151	C₅×D₈	C₂×D₄	1	1	yes	characteristic
152	C₅×D₈	C₂×D₄	1	1	yes	characteristic
153	C₅×M₁₆	—	2	2	no	—
154	C₅×M₁₆	—	2	1	no	—
155	C₅×M₁₆	—	2	1	no	—
156	C₅×M₁₆	—	4	1	no	—
157	C₅×M₁₆	—	4	1	no	—
158	C₅×M₁₆	C₂×D₄	1	2	yes	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	4	1	no	—
161	C₂×C₅×C₈	—	4	1	no	—
162	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	8	1	no	—
165	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
166	C₅×C₁₆	—	2	2	no	—
167	C₅×C₁₆	—	2	1	no	—
168	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
169	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
170	#578	—	2	1	no	—
171	#578	C₂²×C₅	1	2	yes	complemented
172	#576	—	2	1	no	—
173	#576	C₂²×C₅	1	2	yes	—
174	#510	—	2	2	no	—
175	#510	C₂²×C₅	1	2	yes	—
176	#509	—	2	2	no	—
177	#509	C₂²×C₅	1	2	yes	complemented
178	#508	—	2	2	no	—
179	#508	C₂²×C₅	1	1	yes	characteristic
180	C₂×SD₃₂	—	2	2	no	—
181	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
182	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
183	#504	C₂²×C₅	1	2	yes	complemented
184	#494	C₂²×C₅	1	1	yes	characteristic, complemented
185	#493	C₂²×C₅	1	1	yes	characteristic
186	#473	—	2	1	no	—
187	#473	C₂²×C₅	1	2	yes	complemented
188	#472	—	2	1	no	—
189	#472	C₂²×C₅	1	2	yes	—
190	#456	—	2	2	no	—
191	#453	—	2	2	no	—
192	#443	C₂²×C₅	1	1	yes	characteristic
193	#443	C₂²×C₅	1	1	yes	characteristic
194	#443	C₂²×C₅	1	1	yes	characteristic, complemented
195	#368	C₂²×C₅	1	1	yes	characteristic, complemented
196	#364	C₂²×C₅	1	1	yes	characteristic, complemented
197	#362	C₂²×C₅	1	2	yes	complemented
198	#361	C₂²×C₅	1	2	yes	complemented
199	#359	C₂²×C₅	1	1	yes	characteristic
200	#359	C₂²×C₅	1	1	yes	characteristic, complemented
201	#350	C₂²×C₅	1	2	yes	complemented
202	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	—	8	2	no	—
205	C₅×Q₈	—	2	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	8	2	no	—
210	C₅×Q₈	C₂×D₈	1	2	yes	—
211	C₅×D₄	—	2	2	no	—
212	C₅×D₄	—	2	1	no	—
213	C₅×D₄	—	2	1	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	4	1	no	—
216	C₅×D₄	—	4	2	no	—
217	C₅×D₄	—	4	2	no	—
218	C₅×D₄	—	8	2	no	—
219	C₅×D₄	—	8	2	no	—
220	C₅×D₄	—	8	2	no	—
221	C₅×D₄	—	16	2	no	—
222	C₅×D₄	C₂×D₈	1	2	yes	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	8	2	no	—
229	C₂×C₄×C₅	—	8	2	no	—
230	C₂×C₄×C₅	—	8	2	no	—
231	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₅×C₈	—	2	2	no	—
233	C₅×C₈	—	4	1	no	—
234	C₅×C₈	—	4	1	no	—
235	C₅×C₈	C₂×D₈	1	1	yes	characteristic
236	C₅×C₈	C₂×D₈	1	1	yes	characteristic
237	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
238	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
239	2₋¹⁺⁴	—	2	2	no	—
240	H(5,𝔽₂)	—	2	2	no	—
241	#137	—	2	2	no	—
242	#137	—	2	2	no	—
243	#137	—	4	2	no	—
244	#137	—	4	2	no	—
245	AGL(1,ℤ/8)	—	2	2	no	—
246	AGL(1,ℤ/8)	—	2	2	no	—
247	AGL(1,ℤ/8)	—	4	2	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	#135	—	2	2	no	—
250	#135	—	2	2	no	—
251	#135	—	4	1	no	—
252	#135	—	4	1	no	—
253	#135	C₅×D₄	1	1	yes	characteristic
254	#135	C₂³×C₅	1	1	yes	characteristic
255	#135	C₂³×C₅	1	1	yes	characteristic
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	—	4	1	no	—
259	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	4	1	no	—
263	C₂×D₈	C₂³×C₅	1	2	yes	—
264	#131	—	2	1	no	—
265	#131	—	2	1	no	—
266	#131	C₂³×C₅	1	2	yes	—
267	C₄⋊Q₈	—	2	1	no	—
268	#127	—	2	1	no	—
269	Q₃₂	—	2	2	no	—
270	Q₃₂	C₅×D₄	1	1	yes	characteristic, complemented
271	SD₃₂	—	2	2	no	—
272	SD₃₂	—	2	2	no	—
273	SD₃₂	—	2	2	no	—
274	SD₃₂	—	2	2	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	C₅×D₄	1	1	yes	characteristic, complemented
277	SD₃₂	C₅×D₄	1	1	yes	characteristic, complemented
278	D₁₆	—	2	2	no	—
279	D₁₆	C₅×D₄	1	1	yes	characteristic, complemented
280	M₃₂	—	2	2	no	—
281	M₃₂	C₂³×C₅	1	2	yes	—
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
285	#108	C₅×D₄	1	1	yes	characteristic
286	#108	C₂³×C₅	1	1	yes	characteristic
287	#108	C₂³×C₅	1	1	yes	characteristic
288	#104	—	2	1	no	—
289	#104	—	2	1	no	—
290	#104	C₅×D₄	1	2	yes	—
291	#101	—	2	2	no	—
292	#100	—	2	2	no	—
293	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	4	1	no	—
296	C₂²×C₅	—	4	1	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	—	16	2	no	—
299	C₂²×C₅	—	32	2	no	—
300	C₂²×C₅	#576	1	1	yes	characteristic
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	4	1	no	—
304	C₄×C₅	—	4	1	no	—
305	C₄×C₅	—	8	2	no	—
306	C₄×C₅	D₄²	1	1	yes	characteristic
307	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
308	#41	—	2	1	no	—
309	#41	—	2	1	no	—
310	#41	—	4	2	no	—
311	#41	—	4	2	no	—
312	#41	—	4	2	no	—
313	#41	—	4	2	no	—
314	#41	—	8	2	no	—
315	#41	C₂×C₅×D₄	1	2	yes	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	8	1	no	—
323	C₂×D₄	—	8	2	no	—
324	Q₁₆	—	2	2	no	—
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	4	2	no	—
327	Q₁₆	—	4	2	no	—
328	Q₁₆	—	4	1	no	—
329	Q₁₆	—	4	1	no	—
330	Q₁₆	C₅×D₈	1	1	yes	characteristic
331	Q₁₆	C₂×C₅×D₄	1	1	yes	characteristic
332	Q₁₆	C₂×C₅×D₄	1	1	yes	characteristic
333	SD₁₆	—	2	1	no	—
334	SD₁₆	—	2	1	no	—
335	SD₁₆	—	4	2	no	—
336	SD₁₆	—	4	2	no	—
337	SD₁₆	—	4	2	no	—
338	SD₁₆	—	4	2	no	—
339	SD₁₆	C₅×D₈	1	2	yes	—
340	D₈	—	2	2	no	—
341	D₈	—	2	2	no	—
342	D₈	—	4	2	no	—
343	D₈	—	4	2	no	—
344	D₈	—	4	1	no	—
345	D₈	—	4	1	no	—
346	D₈	C₅×D₈	1	1	yes	characteristic
347	D₈	C₂×C₅×D₄	1	1	yes	characteristic
348	D₈	C₂×C₅×D₄	1	1	yes	characteristic
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	C₂×C₅×D₄	1	2	yes	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
360	C₄⋊C₄	—	8	1	no	—
361	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
362	C₁₆	—	2	2	no	—
363	C₁₆	—	2	1	no	—
364	C₁₆	C₂×C₅×D₄	1	1	yes	characteristic
365	C₁₆	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×C₅	—	2	1	no	—
367	C₂×C₅	—	4	2	no	—
368	C₂×C₅	—	8	1	no	—
369	C₂×C₅	—	8	1	no	—
370	C₂×C₅	—	16	2	no	—
371	C₂×C₅	D₄×D₈	1	1	yes	characteristic
372	C₂³	—	4	2	no	—
373	C₂³	—	8	2	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	8	2	no	—
379	Q₈	C₂×C₅×D₈	1	2	yes	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	16	2	no	—
391	D₄	C₂×C₅×D₈	1	2	yes	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	C₂×C₅×D₈	1	1	yes	characteristic
405	C₈	C₂×C₅×D₈	1	1	yes	characteristic
406	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
407	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
408	C₅	#33856	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	32	2	no	—
415	C₂²	C₅×#576	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	2	no	—
421	C₄	C₅×D₄²	1	1	yes	characteristic
422	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	8	1	no	—
427	C₂	—	16	2	no	—
428	C₂	C₅×D₄×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3416	C₂	semidirect
2. C₅×#3293	C₂	semidirect
3. C₅×#3292	C₂	semidirect
4. C₅×#2248	C₂	semidirect
5. C₅×#2223	C₂	semidirect
6. C₅×#2214	C₂	semidirect
7. C₅×#2213	C₂	semidirect
8. C₅×#2194	C₂	semidirect
9. C₅×#2193	C₂	semidirect
10. C₅×#2178	C₂	semidirect
11. C₅×#2170	C₂	semidirect
13. C₅×#578	C₂²	semidirect
19. C₅×#509	C₂²	semidirect
23. C₂×C₅×SD₃₂	C₂²	semidirect
24. C₂×C₅×SD₃₂	C₂²	semidirect
25. C₅×#504	C₂²	semidirect
26. C₅×#494	C₂²	semidirect
29. C₅×#473	C₂²	semidirect
36. C₅×#443	C₂²	semidirect
37. C₅×#368	C₂²	semidirect
38. C₅×#364	C₂²	semidirect
39. C₅×#362	C₂²	semidirect
40. C₅×#361	C₂²	semidirect
42. C₅×#359	C₂²	semidirect
43. C₅×#350	C₂²	semidirect
44. C₄×C₅×C₁₆	C₂²	semidirect
45. #33856	C₅	direct (N × H)
77. C₅×Q₃₂	D₄	semidirect
83. C₅×SD₃₂	D₄	semidirect
84. C₅×SD₃₂	D₄	semidirect
86. C₅×D₁₆	D₄	semidirect
101. #3416	C₂×C₅	semidirect
102. #3293	C₂×C₅	semidirect
103. #3292	C₂×C₅	semidirect
104. #2248	C₂×C₅	semidirect
105. #2223	C₂×C₅	semidirect
106. #2214	C₂×C₅	semidirect
107. #2213	C₂×C₅	semidirect
108. #2194	C₂×C₅	semidirect
109. #2193	C₂×C₅	semidirect
110. #2178	C₂×C₅	semidirect
111. #2170	C₂×C₅	semidirect
171. #578	C₂²×C₅	semidirect
177. #509	C₂²×C₅	semidirect
181. C₂×SD₃₂	C₂²×C₅	semidirect
182. C₂×SD₃₂	C₂²×C₅	semidirect
183. #504	C₂²×C₅	semidirect
184. #494	C₂²×C₅	semidirect
187. #473	C₂²×C₅	semidirect
194. #443	C₂²×C₅	semidirect
195. #368	C₂²×C₅	semidirect
196. #364	C₂²×C₅	semidirect
197. #362	C₂²×C₅	semidirect
198. #361	C₂²×C₅	semidirect
200. #359	C₂²×C₅	semidirect
201. #350	C₂²×C₅	semidirect
202. C₄×C₁₆	C₂²×C₅	semidirect
270. Q₃₂	C₅×D₄	semidirect
276. SD₃₂	C₅×D₄	semidirect
277. SD₃₂	C₅×D₄	semidirect
279. D₁₆	C₅×D₄	semidirect
408. C₅	#33856	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×#3416	2
C₅×#3293	2
C₅×#3292	2
C₅×#2248	2
C₅×#2223	2
C₅×#2214	2
C₅×#2213	2
C₅×#2194	2
C₅×#2193	2
C₅×#2178	2
C₅×#2170	2
#33856	5

Subgroups — C5×#33856 #11956576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33856 #11956576