Subgroups — C₅×#33859 #11956579

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3417	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3415	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3290	C₂	1	2	yes	maximal, complemented
4	C₅×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2222	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2221	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2212	C₂	1	2	yes	maximal, 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	C₂²	1	2	yes	complemented
13	C₅×#577	—	2	2	no	—
14	C₅×#576	C₂²	1	2	yes	—
15	C₅×#510	—	2	2	no	—
16	C₅×#510	C₂²	1	2	yes	complemented
17	C₅×#509	—	2	2	no	—
18	C₅×#509	C₂²	1	2	yes	—
19	C₅×#508	—	2	1	no	—
20	C₅×#508	—	2	1	no	—
21	C₅×#508	C₂²	1	1	yes	characteristic
22	C₂×C₅×Q₃₂	—	2	1	no	—
23	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
25	C₂×C₅×D₁₆	—	2	1	no	—
26	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
27	C₅×#504	C₂²	1	1	yes	characteristic
28	C₅×#504	C₂²	1	1	yes	characteristic, complemented
29	C₅×#495	C₂²	1	2	yes	complemented
30	C₅×#473	C₂²	1	2	yes	—
31	C₅×#472	C₂²	1	2	yes	complemented
32	C₅×#471	—	2	2	no	—
33	C₅×#455	—	2	2	no	—
34	C₅×#454	—	2	2	no	—
35	C₅×#443	C₂²	1	1	yes	characteristic
36	C₅×#443	C₂²	1	2	yes	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	2	yes	complemented
42	C₅×#350	C₂²	1	1	yes	characteristic
43	C₅×#350	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
45	#33859	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	2	no	—
59	C₅×#135	D₄	1	1	yes	characteristic
60	C₅×#135	C₂³	1	2	yes	—
61	C₂×C₅×Q₁₆	—	2	2	no	—
62	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
63	C₂×C₅×SD₁₆	—	2	2	no	—
64	C₂×C₅×SD₁₆	—	4	2	no	—
65	C₂×C₅×D₈	—	2	2	no	—
66	C₂×C₅×D₈	C₂³	1	2	yes	—
67	C₅×#131	—	2	2	no	—
68	C₅×#131	C₂³	1	1	yes	characteristic
69	C₅×#131	C₂³	1	1	yes	characteristic
70	C₅×#124	—	2	2	no	—
71	C₅×Q₃₂	—	2	2	no	—
72	C₅×Q₃₂	—	2	1	no	—
73	C₅×Q₃₂	—	2	1	no	—
74	C₅×Q₃₂	D₄	1	1	yes	characteristic
75	C₅×SD₃₂	—	2	2	no	—
76	C₅×SD₃₂	—	2	2	no	—
77	C₅×SD₃₂	—	4	2	no	—
78	C₅×SD₃₂	D₄	1	2	yes	—
79	C₅×D₁₆	—	2	2	no	—
80	C₅×D₁₆	—	2	1	no	—
81	C₅×D₁₆	—	2	1	no	—
82	C₅×D₁₆	D₄	1	1	yes	characteristic
83	C₅×M₃₂	—	2	1	no	—
84	C₅×M₃₂	—	2	1	no	—
85	C₅×M₃₂	C₂³	1	1	yes	characteristic
86	C₅×M₃₂	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₁₆	—	2	1	no	—
88	C₂×C₅×C₁₆	—	2	1	no	—
89	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
91	C₅×#108	D₄	1	1	yes	characteristic
92	C₅×#108	C₂³	1	2	yes	—
93	C₅×#104	—	2	2	no	—
94	C₅×#104	D₄	1	1	yes	characteristic
95	C₅×#104	D₄	1	1	yes	characteristic
96	C₅×#101	—	2	2	no	—
97	C₅×#100	—	2	2	no	—
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	#3417	C₂×C₅	1	1	yes	characteristic, complemented
100	#3415	C₂×C₅	1	1	yes	characteristic, complemented
101	#3290	C₂×C₅	1	2	yes	complemented
102	#2249	C₂×C₅	1	1	yes	characteristic, complemented
103	#2222	C₂×C₅	1	1	yes	characteristic, complemented
104	#2221	C₂×C₅	1	1	yes	characteristic, complemented
105	#2212	C₂×C₅	1	2	yes	complemented
106	#2194	C₂×C₅	1	2	yes	complemented
107	#2193	C₂×C₅	1	2	yes	complemented
108	#2178	C₂×C₅	1	1	yes	characteristic, complemented
109	#2170	C₂×C₅	1	1	yes	characteristic, complemented
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	4	2	no	—
112	C₅×#41	—	4	2	no	—
113	C₅×#41	—	4	2	no	—
114	C₅×#41	—	4	2	no	—
115	C₅×#41	—	8	2	no	—
116	C₅×#41	C₂×D₄	1	1	yes	characteristic
117	C₅×#41	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	4	2	no	—
120	C₂×C₅×Q₈	—	4	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	—	4	2	no	—
124	C₂×C₅×D₄	—	8	2	no	—
125	C₅×Q₁₆	—	2	2	no	—
126	C₅×Q₁₆	—	2	2	no	—
127	C₅×Q₁₆	—	4	2	no	—
128	C₅×Q₁₆	—	4	2	no	—
129	C₅×Q₁₆	D₈	1	1	yes	characteristic
130	C₅×Q₁₆	C₂×D₄	1	2	yes	—
131	C₅×SD₁₆	—	2	2	no	—
132	C₅×SD₁₆	—	4	2	no	—
133	C₅×SD₁₆	—	4	2	no	—
134	C₅×SD₁₆	—	4	2	no	—
135	C₅×SD₁₆	—	4	2	no	—
136	C₅×SD₁₆	—	4	2	no	—
137	C₅×SD₁₆	—	4	2	no	—
138	C₅×SD₁₆	D₈	1	1	yes	characteristic
139	C₅×SD₁₆	D₈	1	1	yes	characteristic
140	C₅×D₈	—	2	2	no	—
141	C₅×D₈	—	2	2	no	—
142	C₅×D₈	—	4	2	no	—
143	C₅×D₈	—	4	2	no	—
144	C₅×D₈	D₈	1	1	yes	characteristic
145	C₅×D₈	C₂×D₄	1	2	yes	—
146	C₅×M₁₆	—	2	1	no	—
147	C₅×M₁₆	—	2	1	no	—
148	C₅×M₁₆	—	2	2	no	—
149	C₅×M₁₆	—	4	2	no	—
150	C₅×M₁₆	C₂×D₄	1	1	yes	characteristic
151	C₅×M₁₆	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	4	2	no	—
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	8	2	no	—
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₅×C₁₆	—	2	1	no	—
160	C₅×C₁₆	—	2	1	no	—
161	C₅×C₁₆	—	2	1	no	—
162	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
163	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
164	#578	C₂²×C₅	1	2	yes	complemented
165	#577	—	2	2	no	—
166	#576	C₂²×C₅	1	2	yes	—
167	#510	—	2	2	no	—
168	#510	C₂²×C₅	1	2	yes	complemented
169	#509	—	2	2	no	—
170	#509	C₂²×C₅	1	2	yes	—
171	#508	—	2	1	no	—
172	#508	—	2	1	no	—
173	#508	C₂²×C₅	1	1	yes	characteristic
174	C₂×Q₃₂	—	2	1	no	—
175	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
177	C₂×D₁₆	—	2	1	no	—
178	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
179	#504	C₂²×C₅	1	1	yes	characteristic
180	#504	C₂²×C₅	1	1	yes	characteristic, complemented
181	#495	C₂²×C₅	1	2	yes	complemented
182	#473	C₂²×C₅	1	2	yes	—
183	#472	C₂²×C₅	1	2	yes	complemented
184	#471	—	2	2	no	—
185	#455	—	2	2	no	—
186	#454	—	2	2	no	—
187	#443	C₂²×C₅	1	1	yes	characteristic
188	#443	C₂²×C₅	1	2	yes	complemented
189	#368	C₂²×C₅	1	1	yes	characteristic, complemented
190	#364	C₂²×C₅	1	1	yes	characteristic, complemented
191	#362	C₂²×C₅	1	2	yes	complemented
192	#361	C₂²×C₅	1	2	yes	complemented
193	#359	C₂²×C₅	1	2	yes	complemented
194	#350	C₂²×C₅	1	1	yes	characteristic
195	#350	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂³×C₅	—	4	2	no	—
198	C₂³×C₅	—	8	2	no	—
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	8	2	no	—
203	C₅×Q₈	C₂×D₈	1	1	yes	characteristic
204	C₅×Q₈	C₂×D₈	1	1	yes	characteristic
205	C₅×D₄	—	2	1	no	—
206	C₅×D₄	—	2	1	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	2	no	—
211	C₅×D₄	—	8	2	no	—
212	C₅×D₄	—	8	2	no	—
213	C₅×D₄	—	8	2	no	—
214	C₅×D₄	C₂×D₈	1	1	yes	characteristic
215	C₅×D₄	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	8	2	no	—
222	C₂×C₄×C₅	—	8	2	no	—
223	C₂×C₄×C₅	—	8	2	no	—
224	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	—	2	1	no	—
227	C₅×C₈	—	4	2	no	—
228	C₅×C₈	C₂×D₈	1	1	yes	characteristic
229	C₅×C₈	C₂×D₈	1	1	yes	characteristic
230	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
231	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
232	2₋¹⁺⁴	—	2	2	no	—
233	H(5,𝔽₂)	—	2	2	no	—
234	#137	—	2	2	no	—
235	#137	—	2	2	no	—
236	#137	—	4	2	no	—
237	#137	—	4	2	no	—
238	AGL(1,ℤ/8)	—	2	2	no	—
239	AGL(1,ℤ/8)	—	2	2	no	—
240	AGL(1,ℤ/8)	—	4	2	no	—
241	AGL(1,ℤ/8)	—	4	2	no	—
242	#135	—	2	2	no	—
243	#135	—	2	2	no	—
244	#135	—	4	2	no	—
245	#135	C₅×D₄	1	1	yes	characteristic
246	#135	C₂³×C₅	1	2	yes	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	C₂³×C₅	1	2	yes	—
253	#131	—	2	2	no	—
254	#131	C₂³×C₅	1	1	yes	characteristic
255	#131	C₂³×C₅	1	1	yes	characteristic
256	#124	—	2	2	no	—
257	Q₃₂	—	2	2	no	—
258	Q₃₂	—	2	1	no	—
259	Q₃₂	—	2	1	no	—
260	Q₃₂	C₅×D₄	1	1	yes	characteristic
261	SD₃₂	—	2	2	no	—
262	SD₃₂	—	2	2	no	—
263	SD₃₂	—	4	2	no	—
264	SD₃₂	C₅×D₄	1	2	yes	—
265	D₁₆	—	2	2	no	—
266	D₁₆	—	2	1	no	—
267	D₁₆	—	2	1	no	—
268	D₁₆	C₅×D₄	1	1	yes	characteristic
269	M₃₂	—	2	1	no	—
270	M₃₂	—	2	1	no	—
271	M₃₂	C₂³×C₅	1	1	yes	characteristic
272	M₃₂	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₁₆	—	2	1	no	—
274	C₂×C₁₆	—	2	1	no	—
275	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
277	#108	C₅×D₄	1	1	yes	characteristic
278	#108	C₂³×C₅	1	2	yes	—
279	#104	—	2	2	no	—
280	#104	C₅×D₄	1	1	yes	characteristic
281	#104	C₅×D₄	1	1	yes	characteristic
282	#101	—	2	2	no	—
283	#100	—	2	2	no	—
284	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	—	8	2	no	—
289	C₂²×C₅	—	16	2	no	—
290	C₂²×C₅	—	32	2	no	—
291	C₂²×C₅	#576	1	1	yes	characteristic
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	1	no	—
294	C₄×C₅	—	4	1	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	—	8	2	no	—
297	C₄×C₅	D₄²	1	1	yes	characteristic
298	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
299	#41	—	2	2	no	—
300	#41	—	4	2	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	#41	—	4	2	no	—
304	#41	—	8	2	no	—
305	#41	C₂×C₅×D₄	1	1	yes	characteristic
306	#41	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	2	no	—
314	Q₁₆	—	2	2	no	—
315	Q₁₆	—	2	2	no	—
316	Q₁₆	—	4	2	no	—
317	Q₁₆	—	4	2	no	—
318	Q₁₆	C₅×D₈	1	1	yes	characteristic
319	Q₁₆	C₂×C₅×D₄	1	2	yes	—
320	SD₁₆	—	2	2	no	—
321	SD₁₆	—	4	2	no	—
322	SD₁₆	—	4	2	no	—
323	SD₁₆	—	4	2	no	—
324	SD₁₆	—	4	2	no	—
325	SD₁₆	—	4	2	no	—
326	SD₁₆	—	4	2	no	—
327	SD₁₆	C₅×D₈	1	1	yes	characteristic
328	SD₁₆	C₅×D₈	1	1	yes	characteristic
329	D₈	—	2	2	no	—
330	D₈	—	2	2	no	—
331	D₈	—	4	2	no	—
332	D₈	—	4	2	no	—
333	D₈	C₅×D₈	1	1	yes	characteristic
334	D₈	C₂×C₅×D₄	1	2	yes	—
335	M₁₆	—	2	1	no	—
336	M₁₆	—	2	1	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	C₂×C₅×D₄	1	1	yes	characteristic
340	M₁₆	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
346	C₂²⋊C₄	—	8	2	no	—
347	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
348	C₁₆	—	2	1	no	—
349	C₁₆	—	2	1	no	—
350	C₁₆	—	2	1	no	—
351	C₁₆	C₂×C₅×D₄	1	1	yes	characteristic
352	C₁₆	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	—	4	1	no	—
355	C₂×C₅	—	4	1	no	—
356	C₂×C₅	—	8	2	no	—
357	C₂×C₅	—	16	2	no	—
358	C₂×C₅	D₄×D₈	1	1	yes	characteristic
359	C₂³	—	4	2	no	—
360	C₂³	—	8	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	8	2	no	—
365	Q₈	C₂×C₅×D₈	1	1	yes	characteristic
366	Q₈	C₂×C₅×D₈	1	1	yes	characteristic
367	D₄	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	D₄	C₂×C₅×D₈	1	1	yes	characteristic
377	D₄	C₂×C₅×D₈	1	1	yes	characteristic
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	—	4	2	no	—
390	C₈	C₂×C₅×D₈	1	1	yes	characteristic
391	C₈	C₂×C₅×D₈	1	1	yes	characteristic
392	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
394	C₅	#33859	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	—	32	2	no	—
401	C₂²	C₅×#576	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₅×D₄²	1	1	yes	characteristic
408	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	4	1	no	—
411	C₂	—	4	1	no	—
412	C₂	—	8	2	no	—
413	C₂	—	16	2	no	—
414	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×#3417	C₂	semidirect
2. C₅×#3415	C₂	semidirect
3. C₅×#3290	C₂	semidirect
4. C₅×#2249	C₂	semidirect
5. C₅×#2222	C₂	semidirect
6. C₅×#2221	C₂	semidirect
7. C₅×#2212	C₂	semidirect
8. C₅×#2194	C₂	semidirect
9. C₅×#2193	C₂	semidirect
10. C₅×#2178	C₂	semidirect
11. C₅×#2170	C₂	semidirect
12. C₅×#578	C₂²	semidirect
16. C₅×#510	C₂²	semidirect
23. C₂×C₅×Q₃₂	C₂²	semidirect
24. C₂×C₅×SD₃₂	C₂²	semidirect
28. C₅×#504	C₂²	semidirect
29. C₅×#495	C₂²	semidirect
31. C₅×#472	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
41. C₅×#359	C₂²	semidirect
43. C₅×#350	C₂²	semidirect
44. C₄×C₅×C₁₆	C₂²	semidirect
45. #33859	C₅	direct (N × H)
99. #3417	C₂×C₅	semidirect
100. #3415	C₂×C₅	semidirect
101. #3290	C₂×C₅	semidirect
102. #2249	C₂×C₅	semidirect
103. #2222	C₂×C₅	semidirect
104. #2221	C₂×C₅	semidirect
105. #2212	C₂×C₅	semidirect
106. #2194	C₂×C₅	semidirect
107. #2193	C₂×C₅	semidirect
108. #2178	C₂×C₅	semidirect
109. #2170	C₂×C₅	semidirect
164. #578	C₂²×C₅	semidirect
168. #510	C₂²×C₅	semidirect
175. C₂×Q₃₂	C₂²×C₅	semidirect
176. C₂×SD₃₂	C₂²×C₅	semidirect
180. #504	C₂²×C₅	semidirect
181. #495	C₂²×C₅	semidirect
183. #472	C₂²×C₅	semidirect
188. #443	C₂²×C₅	semidirect
189. #368	C₂²×C₅	semidirect
190. #364	C₂²×C₅	semidirect
191. #362	C₂²×C₅	semidirect
192. #361	C₂²×C₅	semidirect
193. #359	C₂²×C₅	semidirect
195. #350	C₂²×C₅	semidirect
196. C₄×C₁₆	C₂²×C₅	semidirect
394. C₅	#33859	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×#3417	2
C₅×#3415	2
C₅×#3290	2
C₅×#2249	2
C₅×#2222	2
C₅×#2221	2
C₅×#2212	2
C₅×#2194	2
C₅×#2193	2
C₅×#2178	2
C₅×#2170	2
#33859	5

Subgroups — C5×#33859 #11956579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33859 #11956579