Subgroups — C₅×#33783 #11956503

Order 1280.

688 conjugacy classes of subgroups.

The subgroup lattice has 382 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	C₂×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2250	C₂	1	2	yes	maximal, complemented
4	C₅×#2244	C₂	1	2	yes	maximal, complemented
5	C₅×#2207	C₂	1	2	yes	maximal, complemented
6	C₅×#2206	C₂	1	2	yes	maximal, complemented
7	C₅×#2187	C₂	1	2	yes	maximal, complemented
8	C₅×#2184	C₂	1	2	yes	maximal, complemented
9	C₅×#2163	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×D₈	—	2	1	no	—
11	C₂²×C₅×D₈	C₂²	1	2	yes	—
12	C₂×C₅×#127	—	2	1	no	—
13	C₅×#529	—	2	1	no	—
14	C₂×C₅×SD₃₂	C₂²	1	4	yes	complemented
15	C₂×C₅×D₁₆	C₂²	1	4	yes	complemented
16	C₅×#499	C₂²	1	1	yes	characteristic, complemented
17	C₅×#495	C₂²	1	1	yes	characteristic, complemented
18	C₅×#493	—	2	1	no	—
19	C₅×#493	—	2	1	no	—
20	C₅×#493	C₂²	1	2	yes	—
21	C₅×#493	C₂²	1	2	yes	—
22	C₅×#488	—	2	1	no	—
23	C₅×#467	C₂²	1	1	yes	characteristic
24	C₅×#466	C₂²	1	1	yes	characteristic
25	C₅×#465	—	2	1	no	—
26	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₅×SD₁₆	—	2	1	no	—
28	C₄×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
31	C₅×#357	C₂²	1	4	yes	complemented
32	C₅×#357	C₂²	1	4	yes	complemented
33	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₅×#346	C₂²	1	2	yes	complemented
35	#33783	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₅×D₄	—	2	2	no	—
37	C₂²×C₅×D₄	—	4	1	no	—
38	C₂²×C₅×D₄	—	4	1	no	—
39	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
40	C₂×C₅×SD₁₆	—	2	1	no	—
41	C₂×C₅×D₈	—	2	2	no	—
42	C₂×C₅×D₈	—	2	2	no	—
43	C₂×C₅×D₈	—	2	2	no	—
44	C₂×C₅×D₈	—	4	4	no	—
45	C₂×C₅×D₈	—	4	4	no	—
46	C₂×C₅×D₈	C₂³	1	4	yes	—
47	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×#127	—	2	2	no	—
51	C₅×#127	—	2	2	no	—
52	C₅×#127	—	4	1	no	—
53	C₅×#127	—	4	1	no	—
54	C₅×#126	—	4	1	no	—
55	C₅×#125	—	2	1	no	—
56	C₅×#124	—	2	1	no	—
57	C₅×#123	—	4	1	no	—
58	C₅×C₂²⋊Q₈	—	2	1	no	—
59	C₅×#121	—	2	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	—	4	1	no	—
63	C₅×#117	—	4	1	no	—
64	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₅×SD₃₂	—	4	4	no	—
66	C₅×D₁₆	—	4	4	no	—
67	C₂×C₅×C₁₆	C₂³	1	4	yes	—
68	C₅×#107	C₂³	1	1	yes	characteristic
69	C₅×#107	C₂³	1	1	yes	characteristic
70	C₅×#106	—	2	1	no	—
71	C₅×#103	—	2	1	no	—
72	C₅×#103	—	2	1	no	—
73	C₅×#102	—	2	1	no	—
74	C₅×#102	—	2	1	no	—
75	C₄×C₅×C₈	D₄	1	1	yes	characteristic
76	C₄×C₅×C₈	D₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	#3168	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×#493	C₂×C₅	1	1	yes	characteristic, complemented
81	#2250	C₂×C₅	1	2	yes	complemented
82	#2244	C₂×C₅	1	2	yes	complemented
83	#2207	C₂×C₅	1	2	yes	complemented
84	#2206	C₂×C₅	1	2	yes	complemented
85	#2187	C₂×C₅	1	2	yes	complemented
86	#2184	C₂×C₅	1	2	yes	complemented
87	#2163	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂⁴×C₅	—	4	2	no	—
89	C₂×C₅×Q₈	—	2	1	no	—
90	C₂×C₅×D₄	—	2	1	no	—
91	C₂×C₅×D₄	—	2	4	no	—
92	C₂×C₅×D₄	—	4	4	no	—
93	C₂×C₅×D₄	—	4	4	no	—
94	C₂×C₅×D₄	—	4	1	no	—
95	C₂×C₅×D₄	—	4	2	no	—
96	C₂×C₅×D₄	—	4	2	no	—
97	C₂×C₅×D₄	—	4	2	no	—
98	C₂×C₅×D₄	—	4	2	no	—
99	C₂×C₅×D₄	—	4	2	no	—
100	C₂×C₅×D₄	—	8	4	no	—
101	C₂×C₅×D₄	—	8	4	no	—
102	C₂²×C₄×C₅	—	4	1	no	—
103	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₅×Q₁₆	—	2	2	no	—
107	C₅×SD₁₆	—	4	2	no	—
108	C₅×D₈	—	2	4	no	—
109	C₅×D₈	—	2	4	no	—
110	C₅×D₈	—	2	2	no	—
111	C₅×D₈	—	4	4	no	—
112	C₅×D₈	—	4	4	no	—
113	C₅×D₈	—	4	4	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
120	C₅×C₄⋊C₄	—	2	1	no	—
121	C₅×C₄⋊C₄	—	2	1	no	—
122	C₅×C₄⋊C₄	—	4	1	no	—
123	C₅×C₄⋊C₄	—	4	1	no	—
124	C₅×C₄⋊C₄	—	4	1	no	—
125	C₅×C₄⋊C₄	—	4	1	no	—
126	C₅×C₂²⋊C₄	—	4	1	no	—
127	C₅×C₂²⋊C₄	—	4	1	no	—
128	C₅×C₂²⋊C₄	—	4	1	no	—
129	C₅×C₂²⋊C₄	—	4	1	no	—
130	C₅×C₂²⋊C₄	—	4	1	no	—
131	C₄²×C₅	—	4	1	no	—
132	C₄²×C₅	D₈	1	1	yes	characteristic
133	C₄²×C₅	D₈	1	1	yes	characteristic
134	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
136	C₅×C₁₆	—	2	4	no	—
137	C₂²×D₈	—	2	1	no	—
138	C₂²×D₈	C₂²×C₅	1	2	yes	—
139	C₂×#127	—	2	1	no	—
140	#529	—	2	1	no	—
141	C₂×SD₃₂	C₂²×C₅	1	4	yes	complemented
142	C₂×D₁₆	C₂²×C₅	1	4	yes	complemented
143	#499	C₂²×C₅	1	1	yes	characteristic, complemented
144	#495	C₂²×C₅	1	1	yes	characteristic, complemented
145	#493	—	2	1	no	—
146	#493	—	2	1	no	—
147	#493	C₂²×C₅	1	2	yes	—
148	#493	C₂²×C₅	1	2	yes	—
149	#488	—	2	1	no	—
150	#467	C₂²×C₅	1	1	yes	characteristic
151	#466	C₂²×C₅	1	1	yes	characteristic
152	#465	—	2	1	no	—
153	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
154	C₄×SD₁₆	—	2	1	no	—
155	C₄×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
156	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
158	#357	C₂²×C₅	1	4	yes	complemented
159	#357	C₂²×C₅	1	4	yes	complemented
160	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
161	#346	C₂²×C₅	1	2	yes	complemented
162	C₂³×C₅	—	4	1	no	—
163	C₂³×C₅	—	4	4	no	—
164	C₂³×C₅	—	8	4	no	—
165	C₂³×C₅	—	8	4	no	—
166	C₂³×C₅	—	8	4	no	—
167	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
168	C₅×Q₈	—	4	1	no	—
169	C₅×Q₈	—	4	1	no	—
170	C₅×D₄	—	4	4	no	—
171	C₅×D₄	—	4	1	no	—
172	C₅×D₄	—	4	4	no	—
173	C₅×D₄	—	4	1	no	—
174	C₅×D₄	—	8	4	no	—
175	C₅×D₄	—	8	4	no	—
176	C₅×D₄	—	8	4	no	—
177	C₅×D₄	—	8	4	no	—
178	C₅×D₄	—	8	2	no	—
179	C₅×D₄	—	8	4	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	4	1	no	—
185	C₂×C₄×C₅	—	4	1	no	—
186	C₂×C₄×C₅	—	4	1	no	—
187	C₂×C₄×C₅	—	8	2	no	—
188	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₅×C₈	—	2	1	no	—
195	C₅×C₈	—	2	1	no	—
196	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
197	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
198	C₂²×D₄	—	2	2	no	—
199	C₂²×D₄	—	4	1	no	—
200	C₂²×D₄	—	4	1	no	—
201	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
202	C₂×SD₁₆	—	2	1	no	—
203	C₂×D₈	—	2	2	no	—
204	C₂×D₈	—	2	2	no	—
205	C₂×D₈	—	2	2	no	—
206	C₂×D₈	—	4	4	no	—
207	C₂×D₈	—	4	4	no	—
208	C₂×D₈	C₂³×C₅	1	4	yes	—
209	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
210	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
212	#127	—	2	2	no	—
213	#127	—	2	2	no	—
214	#127	—	4	1	no	—
215	#127	—	4	1	no	—
216	#126	—	4	1	no	—
217	#125	—	2	1	no	—
218	#124	—	2	1	no	—
219	#123	—	4	1	no	—
220	C₂²⋊Q₈	—	2	1	no	—
221	#121	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	4	1	no	—
225	#117	—	4	1	no	—
226	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
227	SD₃₂	—	4	4	no	—
228	D₁₆	—	4	4	no	—
229	C₂×C₁₆	C₂³×C₅	1	4	yes	—
230	#107	C₂³×C₅	1	1	yes	characteristic
231	#107	C₂³×C₅	1	1	yes	characteristic
232	#106	—	2	1	no	—
233	#103	—	2	1	no	—
234	#103	—	2	1	no	—
235	#102	—	2	1	no	—
236	#102	—	2	1	no	—
237	C₄×C₈	C₅×D₄	1	1	yes	characteristic
238	C₄×C₈	C₅×D₄	1	1	yes	characteristic
239	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
240	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	8	1	no	—
244	C₂²×C₅	—	8	4	no	—
245	C₂²×C₅	—	8	4	no	—
246	C₂²×C₅	—	8	1	no	—
247	C₂²×C₅	—	8	4	no	—
248	C₂²×C₅	—	8	1	no	—
249	C₂²×C₅	—	16	8	no	—
250	C₂²×C₅	#509	1	2	yes	—
251	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	8	1	no	—
257	C₄×C₅	—	8	1	no	—
258	C₄×C₅	—	8	1	no	—
259	C₄×C₅	#509	1	2	yes	—
260	C₄×C₅	#535	1	1	yes	characteristic
261	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂⁴	—	4	2	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	8	4	no	—
275	C₂×D₄	—	8	4	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
278	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	Q₁₆	—	2	2	no	—
281	SD₁₆	—	4	2	no	—
282	D₈	—	2	2	no	—
283	D₈	—	2	4	no	—
284	D₈	—	2	4	no	—
285	D₈	—	4	4	no	—
286	D₈	—	4	4	no	—
287	D₈	—	4	4	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₂²⋊C₄	—	4	1	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	C₅×D₈	1	1	yes	characteristic
307	C₄²	C₅×D₈	1	1	yes	characteristic
308	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
309	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
310	C₁₆	—	2	4	no	—
311	C₂×C₅	—	2	2	no	—
312	C₂×C₅	—	16	1	no	—
313	C₂×C₅	—	16	4	no	—
314	C₂×C₅	#3205	1	1	yes	characteristic
315	C₂×C₅	C₂×#509	1	1	yes	characteristic
316	C₂×C₅	C₂×#509	1	1	yes	characteristic
317	C₂³	—	4	1	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	4	no	—
322	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
323	Q₈	—	4	1	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	1	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	1	no	—
329	D₄	—	8	4	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
352	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
353	C₅	#33783	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	1	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	16	8	no	—
363	C₂²	C₅×#509	1	2	yes	—
364	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	C₅×#509	1	2	yes	—
373	C₄	C₅×#535	1	1	yes	characteristic
374	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₂	—	2	2	no	—
376	C₂	—	16	4	no	—
377	C₂	—	16	1	no	—
378	C₂	C₅×#3205	1	1	yes	characteristic
379	C₂	C₂×C₅×#509	1	1	yes	characteristic
380	C₂	C₂×C₅×#509	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. C₂×C₅×#493	C₂	semidirect
3. C₅×#2250	C₂	semidirect
4. C₅×#2244	C₂	semidirect
5. C₅×#2207	C₂	semidirect
6. C₅×#2206	C₂	semidirect
7. C₅×#2187	C₂	semidirect
8. C₅×#2184	C₂	semidirect
9. C₅×#2163	C₂	semidirect
14. C₂×C₅×SD₃₂	C₂²	semidirect
15. C₂×C₅×D₁₆	C₂²	semidirect
16. C₅×#499	C₂²	semidirect
17. C₅×#495	C₂²	semidirect
26. C₄×C₅×Q₁₆	C₂²	semidirect
28. C₄×C₅×D₈	C₂²	semidirect
30. C₅×C₄⋊C₁₆	C₂²	semidirect
31. C₅×#357	C₂²	semidirect
32. C₅×#357	C₂²	semidirect
34. C₅×#346	C₂²	semidirect
35. #33783	C₅	direct (N × H)
79. #3168	C₂×C₅	semidirect
80. C₂×#493	C₂×C₅	semidirect
81. #2250	C₂×C₅	semidirect
82. #2244	C₂×C₅	semidirect
83. #2207	C₂×C₅	semidirect
84. #2206	C₂×C₅	semidirect
85. #2187	C₂×C₅	semidirect
86. #2184	C₂×C₅	semidirect
87. #2163	C₂×C₅	semidirect
141. C₂×SD₃₂	C₂²×C₅	semidirect
142. C₂×D₁₆	C₂²×C₅	semidirect
143. #499	C₂²×C₅	semidirect
144. #495	C₂²×C₅	semidirect
153. C₄×Q₁₆	C₂²×C₅	semidirect
155. C₄×D₈	C₂²×C₅	semidirect
157. C₄⋊C₁₆	C₂²×C₅	semidirect
158. #357	C₂²×C₅	semidirect
159. #357	C₂²×C₅	semidirect
161. #346	C₂²×C₅	semidirect
353. C₅	#33783	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
C₂×C₅×#493	2
C₅×#2250	2
C₅×#2244	2
C₅×#2207	2
C₅×#2206	2
C₅×#2187	2
C₅×#2184	2
C₅×#2163	2
#33783	5

Subgroups — C5×#33783 #11956503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33783 #11956503