Subgroups — C₅×#33785 #11956505

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2250	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2244	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2211	C₂	1	2	yes	maximal, complemented
8	C₅×#2210	C₂	1	2	yes	maximal, complemented
9	C₅×#2189	C₂	1	2	yes	maximal, complemented
10	C₅×#2186	C₂	1	2	yes	maximal, complemented
11	C₅×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	—	2	1	no	—
13	C₂×C₅×#135	C₂²	1	2	yes	—
14	C₅×#532	—	2	1	no	—
15	C₅×#529	—	2	1	no	—
16	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₅×D₁₆	C₂²	1	2	yes	—
20	C₅×#499	C₂²	1	1	yes	characteristic
21	C₅×#495	—	2	1	no	—
22	C₅×#495	C₂²	1	2	yes	—
23	C₅×#495	C₂²	1	1	yes	characteristic
24	C₅×#494	C₂²	1	1	yes	characteristic
25	C₅×#493	C₂²	1	1	yes	characteristic
26	C₅×#492	—	2	1	no	—
27	C₅×#488	—	2	1	no	—
28	C₅×#467	C₂²	1	1	yes	characteristic
29	C₅×#466	C₂²	1	1	yes	characteristic
30	C₅×#465	—	2	1	no	—
31	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₅×#358	C₂²	1	2	yes	—
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#357	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	2	yes	—
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₅×#346	C₂²	1	1	yes	characteristic
42	C₅×#346	C₂²	1	1	yes	characteristic
43	#33785	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	2	no	—
45	C₅×#135	—	4	2	no	—
46	C₅×#135	—	4	2	no	—
47	C₅×#135	—	4	4	no	—
48	C₂×C₅×Q₁₆	—	2	1	no	—
49	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₅×SD₁₆	—	2	1	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×#127	—	2	1	no	—
61	C₅×#126	—	4	1	no	—
62	C₅×#125	—	2	1	no	—
63	C₅×#124	—	2	1	no	—
64	C₅×#124	—	2	2	no	—
65	C₅×#123	—	4	1	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₅×#121	—	2	1	no	—
68	C₅×#121	—	4	1	no	—
69	C₅×#121	—	4	1	no	—
70	C₄×C₅×Q₈	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	4	1	no	—
73	C₄×C₅×D₄	—	4	1	no	—
74	C₄×C₅×D₄	—	4	1	no	—
75	C₅×#117	—	4	1	no	—
76	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₅×Q₃₂	—	4	2	no	—
78	C₅×SD₃₂	—	4	2	no	—
79	C₅×SD₃₂	—	4	2	no	—
80	C₅×D₁₆	—	4	2	no	—
81	C₂×C₅×C₁₆	C₂³	1	2	yes	—
82	C₂×C₅×C₁₆	C₂³	1	2	yes	—
83	C₅×#107	C₂³	1	1	yes	characteristic
84	C₅×#107	C₂³	1	1	yes	characteristic
85	C₅×#106	—	2	1	no	—
86	C₅×#103	—	2	1	no	—
87	C₅×#103	—	2	1	no	—
88	C₅×#102	—	2	1	no	—
89	C₅×#102	—	2	1	no	—
90	C₄×C₅×C₈	D₄	1	1	yes	characteristic
91	C₄×C₅×C₈	D₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	#3168	C₂×C₅	1	1	yes	characteristic, complemented
95	#3147	C₂×C₅	1	1	yes	characteristic, complemented
96	#2251	C₂×C₅	1	1	yes	characteristic, complemented
97	#2250	C₂×C₅	1	1	yes	characteristic, complemented
98	#2245	C₂×C₅	1	1	yes	characteristic, complemented
99	#2244	C₂×C₅	1	1	yes	characteristic, complemented
100	#2211	C₂×C₅	1	2	yes	complemented
101	#2210	C₂×C₅	1	2	yes	complemented
102	#2189	C₂×C₅	1	2	yes	complemented
103	#2186	C₂×C₅	1	2	yes	complemented
104	#2163	C₂×C₅	1	1	yes	characteristic, complemented
105	C₅×#41	—	4	4	no	—
106	C₅×#41	—	4	4	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×D₄	—	2	1	no	—
110	C₂×C₅×D₄	—	2	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	1	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	2	no	—
121	C₅×Q₁₆	—	2	2	no	—
122	C₅×Q₁₆	—	2	2	no	—
123	C₅×Q₁₆	—	4	2	no	—
124	C₅×SD₁₆	—	4	4	no	—
125	C₅×SD₁₆	—	4	4	no	—
126	C₅×SD₁₆	—	4	2	no	—
127	C₅×D₈	—	2	2	no	—
128	C₅×D₈	—	2	2	no	—
129	C₅×D₈	—	2	2	no	—
130	C₅×D₈	—	4	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₄⋊C₄	—	4	1	no	—
142	C₅×C₄⋊C₄	—	4	1	no	—
143	C₅×C₄⋊C₄	—	4	1	no	—
144	C₅×C₄⋊C₄	—	4	1	no	—
145	C₅×C₂²⋊C₄	—	4	1	no	—
146	C₅×C₂²⋊C₄	—	4	1	no	—
147	C₅×C₂²⋊C₄	—	4	1	no	—
148	C₅×C₂²⋊C₄	—	4	1	no	—
149	C₅×C₂²⋊C₄	—	4	2	no	—
150	C₅×C₂²⋊C₄	—	4	2	no	—
151	C₅×C₂²⋊C₄	—	4	1	no	—
152	C₄²×C₅	—	4	1	no	—
153	C₄²×C₅	D₈	1	1	yes	characteristic
154	C₄²×C₅	D₈	1	1	yes	characteristic
155	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₅×C₁₆	—	2	2	no	—
158	C₅×C₁₆	—	2	2	no	—
159	C₂×#135	—	2	1	no	—
160	C₂×#135	C₂²×C₅	1	2	yes	—
161	#532	—	2	1	no	—
162	#529	—	2	1	no	—
163	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
164	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
165	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
166	C₂×D₁₆	C₂²×C₅	1	2	yes	—
167	#499	C₂²×C₅	1	1	yes	characteristic
168	#495	—	2	1	no	—
169	#495	C₂²×C₅	1	2	yes	—
170	#495	C₂²×C₅	1	1	yes	characteristic
171	#494	C₂²×C₅	1	1	yes	characteristic
172	#493	C₂²×C₅	1	1	yes	characteristic
173	#492	—	2	1	no	—
174	#488	—	2	1	no	—
175	#467	C₂²×C₅	1	1	yes	characteristic
176	#466	C₂²×C₅	1	1	yes	characteristic
177	#465	—	2	1	no	—
178	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
179	C₄×SD₁₆	—	2	1	no	—
180	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
182	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
183	#358	C₂²×C₅	1	2	yes	—
184	#358	C₂²×C₅	1	2	yes	—
185	#357	C₂²×C₅	1	2	yes	—
186	#357	C₂²×C₅	1	2	yes	—
187	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
188	#346	C₂²×C₅	1	1	yes	characteristic
189	#346	C₂²×C₅	1	1	yes	characteristic
190	C₂³×C₅	—	4	1	no	—
191	C₂³×C₅	—	4	2	no	—
192	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
193	C₅×Q₈	—	4	2	no	—
194	C₅×Q₈	—	4	1	no	—
195	C₅×Q₈	—	4	2	no	—
196	C₅×Q₈	—	4	1	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	1	no	—
199	C₅×D₄	—	4	2	no	—
200	C₅×D₄	—	4	1	no	—
201	C₅×D₄	—	8	2	no	—
202	C₅×D₄	—	8	2	no	—
203	C₅×D₄	—	8	2	no	—
204	C₅×D₄	—	8	4	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	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	8	2	no	—
214	C₂×C₄×C₅	—	8	4	no	—
215	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₅×C₈	—	2	1	no	—
222	C₅×C₈	—	2	1	no	—
223	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
224	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
225	C₂×#41	—	2	2	no	—
226	#135	—	4	2	no	—
227	#135	—	4	2	no	—
228	#135	—	4	4	no	—
229	C₂×Q₁₆	—	2	1	no	—
230	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
231	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	1	no	—
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	C₂³×C₅	1	2	yes	—
237	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
238	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	1	no	—
241	#127	—	2	1	no	—
242	#126	—	4	1	no	—
243	#125	—	2	1	no	—
244	#124	—	2	1	no	—
245	#124	—	2	2	no	—
246	#123	—	4	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	#121	—	2	1	no	—
249	#121	—	4	1	no	—
250	#121	—	4	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	4	1	no	—
254	C₄×D₄	—	4	1	no	—
255	C₄×D₄	—	4	1	no	—
256	#117	—	4	1	no	—
257	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
258	Q₃₂	—	4	2	no	—
259	SD₃₂	—	4	2	no	—
260	SD₃₂	—	4	2	no	—
261	D₁₆	—	4	2	no	—
262	C₂×C₁₆	C₂³×C₅	1	2	yes	—
263	C₂×C₁₆	C₂³×C₅	1	2	yes	—
264	#107	C₂³×C₅	1	1	yes	characteristic
265	#107	C₂³×C₅	1	1	yes	characteristic
266	#106	—	2	1	no	—
267	#103	—	2	1	no	—
268	#103	—	2	1	no	—
269	#102	—	2	1	no	—
270	#102	—	2	1	no	—
271	C₄×C₈	C₅×D₄	1	1	yes	characteristic
272	C₄×C₈	C₅×D₄	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	—	8	2	no	—
280	C₂²×C₅	—	8	2	no	—
281	C₂²×C₅	—	8	1	no	—
282	C₂²×C₅	—	8	2	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	8	1	no	—
291	C₄×C₅	—	8	1	no	—
292	C₄×C₅	—	8	2	no	—
293	C₄×C₅	—	8	1	no	—
294	C₄×C₅	#535	1	1	yes	characteristic
295	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	#41	—	4	4	no	—
297	#41	—	4	4	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
309	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	4	2	no	—
315	SD₁₆	—	4	4	no	—
316	SD₁₆	—	4	4	no	—
317	SD₁₆	—	4	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₅×D₈	1	1	yes	characteristic
345	C₄²	C₅×D₈	1	1	yes	characteristic
346	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
347	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	2	no	—
350	C₂×C₅	—	4	1	no	—
351	C₂×C₅	—	16	1	no	—
352	C₂×C₅	—	16	2	no	—
353	C₂×C₅	#3205	1	1	yes	characteristic
354	C₂×C₅	#3414	1	1	yes	characteristic
355	C₂×C₅	#3414	1	1	yes	characteristic
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
359	Q₈	—	4	2	no	—
360	Q₈	—	4	1	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	1	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	1	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	4	no	—
370	D₄	—	8	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
383	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
385	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
390	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
391	C₅	#33785	1	1	yes	characteristic, direct product factor, Sylow
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	C₅×#535	1	1	yes	characteristic
412	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₂	—	4	1	no	—
414	C₂	—	16	1	no	—
415	C₂	—	16	2	no	—
416	C₂	C₅×#3205	1	1	yes	characteristic
417	C₂	C₅×#3414	1	1	yes	characteristic
418	C₂	C₅×#3414	1	1	yes	characteristic

	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 ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3168	C₂	semidirect
2. C₅×#3147	C₂	semidirect
3. C₅×#2251	C₂	semidirect
4. C₅×#2250	C₂	semidirect
5. C₅×#2245	C₂	semidirect
6. C₅×#2244	C₂	semidirect
7. C₅×#2211	C₂	semidirect
8. C₅×#2210	C₂	semidirect
9. C₅×#2189	C₂	semidirect
10. C₅×#2186	C₂	semidirect
11. C₅×#2163	C₂	semidirect
43. #33785	C₅	direct (N × H)
94. #3168	C₂×C₅	semidirect
95. #3147	C₂×C₅	semidirect
96. #2251	C₂×C₅	semidirect
97. #2250	C₂×C₅	semidirect
98. #2245	C₂×C₅	semidirect
99. #2244	C₂×C₅	semidirect
100. #2211	C₂×C₅	semidirect
101. #2210	C₂×C₅	semidirect
102. #2189	C₂×C₅	semidirect
103. #2186	C₂×C₅	semidirect
104. #2163	C₂×C₅	semidirect
391. C₅	#33785	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×#3168	2
C₅×#3147	2
C₅×#2251	2
C₅×#2250	2
C₅×#2245	2
C₅×#2244	2
C₅×#2211	2
C₅×#2210	2
C₅×#2189	2
C₅×#2186	2
C₅×#2163	2
#33785	5

Subgroups — C5×#33785 #11956505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33785 #11956505