Subgroups — #13107618

Order 1600.

608 conjugacy classes of subgroups.

The subgroup lattice has 355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#709	C₂	1	1	yes	maximal, characteristic
2	#11717425	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	AGL(1,𝔽₅)×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
5	#11717337	C₂	1	2	yes	maximal, complemented
6	D₅×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	#1042⋊Q₈	C₂	1	2	yes	maximal, complemented
8	#11717323	C₂	1	2	yes	maximal, complemented
9	C₂²×C₅×AGL(1,𝔽₅)	C₂²	1	2	yes	—
10	C₂×D₅×AGL(1,𝔽₅)	C₂²	1	4	yes	—
11	#87900	C₄	1	1	yes	characteristic, complemented
12	C₅×#709	C₄	1	1	yes	characteristic, complemented
13	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
14	D₅×C₂²⋊D₅	C₂²	1	2	yes	—
15	#87879	C₄	1	2	yes	complemented
16	D₅×D₂₀	C₂²	1	1	yes	characteristic
17	C₄×D₅²	C₂²	1	2	yes	—
18	#87874	C₄	1	1	yes	characteristic, complemented
19	#87873	C₄	1	2	yes	complemented
20	#87870	C₄	1	1	yes	characteristic, complemented
21	D₅×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₂²⋊#1042	C₂²	1	2	yes	—
23	C₄⋊#1042	C₂²	1	1	yes	characteristic
24	C₄⋊#1042	C₂²	1	1	yes	characteristic
25	C₄×#1042	C₂²	1	2	yes	—
26	C₅×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
27	C₅×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
28	#87825	C₂²	1	4	yes	—
29	(C₂×AGL(1,𝔽₅))⋊D₅	C₂²	1	4	yes	—
30	Dic₅×AGL(1,𝔽₅)	C₂²	1	4	yes	—
31	#66266	—	5	1	no	maximal
32	#65838	—	5	1	no	maximal
33	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
34	C₂×D₅²	C₂³	1	2	yes	—
35	C₂×#1042	C₂³	1	2	yes	—
36	C₂×#1042	C₂³	1	2	yes	—
37	C₂×C₅×AGL(1,𝔽₅)	—	4	2	no	—
38	C₂×C₅×AGL(1,𝔽₅)	C₂³	1	4	yes	—
39	D₅×AGL(1,𝔽₅)	—	4	4	no	—
40	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂²⋊(C₅⋊D₅)	C₂×C₄	1	2	yes	complemented
42	C₄⋊(C₅⋊D₅)	C₂×C₄	1	1	yes	characteristic, complemented
43	C₄×C₅⋊D₅	C₂×C₄	1	2	yes	complemented
44	#6045	C₂×C₄	1	1	yes	characteristic, complemented
45	C₅×C₂²⋊D₅	C₂×C₄	1	2	yes	complemented
46	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
47	C₅×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
48	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
49	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
50	C₄×C₅×D₅	C₂×C₄	1	2	yes	complemented
51	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
52	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
53	C₅×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
54	#6039	C₂×C₄	1	2	yes	complemented
55	#6038	C₂×C₄	1	2	yes	complemented
56	#6038	C₂×C₄	1	2	yes	complemented
57	#6037	C₂×C₄	1	2	yes	complemented
58	#6036	C₂×C₄	1	2	yes	complemented
59	D₅×Dic₅	C₂×C₄	1	2	yes	complemented
60	D₅×Dic₅	C₂³	1	2	yes	—
61	D₅×#41	—	5	1	no	—
62	C₂×#709	—	5	1	no	—
63	Q₈×AGL(1,𝔽₅)	—	5	2	no	—
64	D₄×AGL(1,𝔽₅)	—	5	4	no	—
65	D₄×AGL(1,𝔽₅)	—	5	2	no	—
66	#4130	—	5	1	no	—
67	#4130	—	5	2	no	—
68	C₂×C₄⋊AGL(1,𝔽₅)	—	5	2	no	—
69	C₂×C₄⋊AGL(1,𝔽₅)	D₅	1	1	yes	characteristic, complemented
70	C₂×C₅×C₄⋊C₄	—	5	1	no	—
71	C₄×C₂²⋊D₅	—	5	4	no	—
72	#4072	—	5	1	no	—
73	#4039	—	5	2	no	—
74	#4038	—	5	2	no	—
75	D₅×C₄⋊C₄	—	5	2	no	—
76	#4033	—	5	2	no	—
77	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₅⋊D₅	C₂²×C₄	1	2	yes	—
79	C₂×C₅×D₅	—	2	1	no	—
80	C₂×C₅×D₅	—	2	1	no	—
81	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₅×D₅	C₂²×C₄	1	2	yes	—
83	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
84	D₅²	—	2	2	no	—
85	D₅²	—	2	2	no	—
86	#1042	—	2	2	no	—
87	#1042	—	2	2	no	—
88	C₅×AGL(1,𝔽₅)	—	2	4	no	—
89	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
90	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
91	#1039	C₂²×C₄	1	2	yes	—
92	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
93	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
94	C₅×Dic₅	C₂²×C₄	1	2	yes	—
95	C₂²×AGL(1,𝔽₅)	—	5	4	no	—
96	C₂²×AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
97	C₅×#41	—	5	1	no	—
98	C₂²×C₄×C₅	—	5	1	no	—
99	C₂²×C₄×C₅	—	5	2	no	—
100	C₂×C₂²⋊D₅	—	5	2	no	—
101	#713	—	5	1	no	—
102	Q₈×D₅	—	5	1	no	—
103	#711	—	5	2	no	—
104	#711	—	5	1	no	—
105	D₄×D₅	—	5	2	no	—
106	D₄×D₅	—	5	1	no	—
107	#709	—	5	1	no	—
108	#709	—	5	1	no	—
109	#709	—	5	2	no	—
110	#709	—	5	1	no	—
111	#709	—	5	2	no	—
112	#709	—	5	2	no	—
113	#709	—	5	1	no	—
114	#709	—	20	1	no	—
115	#709	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
116	C₂×D₂₀	—	5	1	no	—
117	C₂×C₄×D₅	—	5	2	no	—
118	C₂×C₄×D₅	—	5	2	no	—
119	C₂×C₄×D₅	—	5	4	no	—
120	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
121	C₂×Dic₁₀	—	5	1	no	—
122	C₂²⋊AGL(1,𝔽₅)	—	5	2	no	—
123	C₂²⋊AGL(1,𝔽₅)	—	5	4	no	—
124	C₄⋊AGL(1,𝔽₅)	—	5	4	no	—
125	C₄⋊AGL(1,𝔽₅)	—	5	1	no	—
126	C₄⋊AGL(1,𝔽₅)	—	5	1	no	—
127	C₄⋊AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
128	C₄⋊AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
129	C₄×AGL(1,𝔽₅)	—	5	4	no	—
130	C₄×AGL(1,𝔽₅)	—	5	2	no	—
131	C₅×C₄⋊C₄	—	5	2	no	—
132	C₅×C₄⋊C₄	—	5	2	no	—
133	C₂²⋊Dic₅	—	5	2	no	—
134	#685	—	5	4	no	—
135	C₄⋊Dic₅	—	5	1	no	—
136	C₄⋊Dic₅	—	5	1	no	—
137	#683	—	5	4	no	—
138	C₄×Dic₅	—	5	4	no	—
139	C₄×Dic₅	—	5	2	no	—
140	#520	—	25	1	no	Sylow
141	C₂×C₅²	—	2	1	no	—
142	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
143	C₅⋊D₅	—	2	2	no	—
144	C₅×D₅	—	2	2	no	—
145	C₅×D₅	—	2	1	no	—
146	C₅×D₅	H(5,𝔽₂)	1	1	yes	characteristic
147	C₅×D₅	2₋¹⁺⁴	1	1	yes	characteristic
148	C₂³×C₅	—	5	1	no	—
149	C₂²×D₅	—	5	2	no	—
150	C₂²×D₅	—	5	2	no	—
151	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
152	C₂×AGL(1,𝔽₅)	—	4	2	no	—
153	C₂×AGL(1,𝔽₅)	—	5	2	no	—
154	C₂×AGL(1,𝔽₅)	—	5	2	no	—
155	C₂×AGL(1,𝔽₅)	—	20	4	no	—
156	C₂×AGL(1,𝔽₅)	C₂²×D₅	1	4	yes	—
157	C₅×Q₈	—	5	1	no	—
158	C₅×D₄	—	5	2	no	—
159	C₅×D₄	—	5	1	no	—
160	C₂×C₄×C₅	—	4	1	no	—
161	C₂×C₄×C₅	—	5	1	no	—
162	C₂×C₄×C₅	—	5	2	no	—
163	C₂×C₄×C₅	—	5	1	no	—
164	C₂×C₄×C₅	—	5	1	no	—
165	C₂×C₄×C₅	—	5	1	no	—
166	C₂×C₄×C₅	—	5	1	no	—
167	C₂×C₄×C₅	—	5	4	no	—
168	C₂×C₄×C₅	—	20	2	no	—
169	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic, complemented
170	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
171	C₂²⋊D₅	—	5	2	no	—
172	C₂²⋊D₅	—	5	2	no	—
173	C₂²⋊D₅	—	5	2	no	—
174	C₂²⋊D₅	—	5	2	no	—
175	C₂²⋊D₅	—	5	2	no	—
176	C₂²⋊D₅	—	5	2	no	—
177	C₂²⋊D₅	—	20	2	no	—
178	C₂²⋊D₅	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
179	C₂×Dic₅	—	5	2	no	—
180	C₂×Dic₅	—	5	2	no	—
181	C₂×Dic₅	—	5	2	no	—
182	C₂×Dic₅	—	5	2	no	—
183	C₂×Dic₅	C₄×D₅	1	1	yes	characteristic, complemented
184	D₂₀	—	5	2	no	—
185	D₂₀	—	5	2	no	—
186	D₂₀	—	5	1	no	—
187	D₂₀	—	5	1	no	—
188	D₂₀	—	20	1	no	—
189	D₂₀	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
190	C₄×D₅	—	5	2	no	—
191	C₄×D₅	—	5	2	no	—
192	C₄×D₅	—	5	2	no	—
193	C₄×D₅	—	5	2	no	—
194	C₄×D₅	—	5	2	no	—
195	C₄×D₅	—	5	2	no	—
196	C₄×D₅	—	20	2	no	—
197	C₄×D₅	—	20	4	no	—
198	C₄×D₅	C₄×D₅	1	1	yes	characteristic, complemented
199	C₄×D₅	C₄×D₅	1	1	yes	characteristic, complemented
200	C₄×D₅	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
201	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
202	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
203	Dic₁₀	—	5	1	no	—
204	Dic₁₀	—	5	1	no	—
205	Dic₁₀	—	5	2	no	—
206	Dic₁₀	—	5	2	no	—
207	Dic₁₀	—	20	1	no	—
208	Dic₁₀	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
209	C₂×#41	—	25	1	no	—
210	C₄×Q₈	—	25	2	no	—
211	C₄×D₄	—	25	2	no	—
212	C₄×D₄	—	25	4	no	—
213	#117	—	25	2	no	—
214	#117	—	25	1	no	—
215	C₂×C₄⋊C₄	—	5	1	no	—
216	C₂×C₄⋊C₄	—	25	2	no	—
217	C₅²	#520	1	1	yes	characteristic, complemented, Sylow
218	C₂²×C₅	—	4	1	no	—
219	C₂²×C₅	—	5	1	no	—
220	C₂²×C₅	—	5	2	no	—
221	C₂²×C₅	—	5	1	no	—
222	C₂²×C₅	—	10	1	no	—
223	C₂²×C₅	—	10	1	no	—
224	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
225	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
226	C₂×D₅	—	2	1	no	—
227	C₂×D₅	—	2	1	no	—
228	C₂×D₅	—	5	2	no	—
229	C₂×D₅	—	5	2	no	—
230	C₂×D₅	—	10	2	no	—
231	C₂×D₅	—	10	2	no	—
232	C₂×D₅	—	10	2	no	—
233	C₂×D₅	—	10	2	no	—
234	C₂×D₅	—	20	2	no	—
235	C₂×D₅	C₂×C₄×D₅	1	1	yes	characteristic
236	C₂×D₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
237	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
238	AGL(1,𝔽₅)	—	2	4	no	—
239	AGL(1,𝔽₅)	—	10	2	no	—
240	AGL(1,𝔽₅)	—	10	2	no	—
241	C₄×C₅	—	4	1	no	—
242	C₄×C₅	—	4	1	no	—
243	C₄×C₅	—	5	2	no	—
244	C₄×C₅	—	5	1	no	—
245	C₄×C₅	—	5	1	no	—
246	C₄×C₅	—	10	4	no	—
247	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
248	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
249	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
251	Dic₅	—	5	2	no	—
252	Dic₅	—	5	2	no	—
253	Dic₅	—	10	2	no	—
254	Dic₅	—	10	2	no	—
255	Dic₅	—	20	2	no	—
256	Dic₅	C₂×C₄×D₅	1	1	yes	characteristic
257	Dic₅	C₂×C₄×D₅	1	1	yes	characteristic
258	Dic₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
259	#41	—	5	1	no	—
260	#41	—	25	2	no	—
261	#41	—	25	2	no	—
262	#41	—	25	1	no	—
263	#41	—	25	1	no	—
264	#41	—	25	1	no	—
265	C₂×Q₈	—	25	1	no	—
266	C₂×D₄	—	25	1	no	—
267	C₂×D₄	—	25	2	no	—
268	C₂²×C₄	—	5	1	no	—
269	C₂²×C₄	—	5	2	no	—
270	C₂²×C₄	—	25	2	no	—
271	C₂²×C₄	—	25	4	no	—
272	C₄⋊C₄	—	5	2	no	—
273	C₄⋊C₄	—	5	2	no	—
274	C₄⋊C₄	—	25	1	no	—
275	C₄⋊C₄	—	25	4	no	—
276	C₄⋊C₄	—	25	1	no	—
277	C₂²⋊C₄	—	25	4	no	—
278	C₂²⋊C₄	—	25	2	no	—
279	C₄²	—	25	2	no	—
280	C₄²	—	25	4	no	—
281	C₂×C₅	—	2	1	no	—
282	C₂×C₅	—	2	1	no	—
283	C₂×C₅	—	4	1	no	—
284	C₂×C₅	—	5	1	no	—
285	C₂×C₅	—	5	1	no	—
286	C₂×C₅	—	8	1	no	—
287	C₂×C₅	—	10	2	no	—
288	C₂×C₅	—	10	1	no	—
289	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
290	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
291	D₅	—	2	1	no	—
292	D₅	—	2	2	no	—
293	D₅	—	10	2	no	—
294	D₅	—	10	2	no	—
295	D₅	—	40	2	no	—
296	D₅	#4144	1	1	yes	characteristic
297	D₅	#4147	1	1	yes	characteristic
298	C₂³	—	5	1	no	—
299	C₂³	—	25	2	no	—
300	Q₈	—	5	1	no	—
301	Q₈	—	25	2	no	—
302	Q₈	—	25	1	no	—
303	D₄	—	5	2	no	—
304	D₄	—	5	1	no	—
305	D₄	—	25	2	no	—
306	D₄	—	25	2	no	—
307	D₄	—	25	2	no	—
308	D₄	—	25	2	no	—
309	D₄	—	25	1	no	—
310	C₂×C₄	—	5	1	no	—
311	C₂×C₄	—	5	1	no	—
312	C₂×C₄	—	5	1	no	—
313	C₂×C₄	—	5	1	no	—
314	C₂×C₄	—	5	1	no	—
315	C₂×C₄	—	5	2	no	—
316	C₂×C₄	—	5	4	no	—
317	C₂×C₄	—	20	2	no	—
318	C₂×C₄	—	25	2	no	—
319	C₂×C₄	—	25	2	no	—
320	C₂×C₄	—	25	2	no	—
321	C₂×C₄	—	25	2	no	—
322	C₂×C₄	—	25	2	no	—
323	C₂×C₄	—	25	2	no	—
324	C₂×C₄	—	100	4	no	—
325	C₂×C₄	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
326	C₅	—	4	1	no	—
327	C₅	#65838	1	1	yes	characteristic, complemented
328	C₅	#66266	1	1	yes	characteristic, complemented
329	C₂²	—	5	1	no	—
330	C₂²	—	5	1	no	—
331	C₂²	—	5	2	no	—
332	C₂²	—	10	1	no	—
333	C₂²	—	10	1	no	—
334	C₂²	—	25	2	no	—
335	C₂²	—	50	2	no	—
336	C₂²	—	50	2	no	—
337	C₂²	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
338	C₄	—	5	1	no	—
339	C₄	—	5	1	no	—
340	C₄	—	5	2	no	—
341	C₄	—	10	4	no	—
342	C₄	—	25	2	no	—
343	C₄	—	50	2	no	—
344	C₄	—	50	2	no	—
345	C₄	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
346	C₄	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
347	C₂	—	2	1	no	—
348	C₂	—	5	1	no	—
349	C₂	—	5	1	no	—
350	C₂	—	10	1	no	—
351	C₂	—	10	2	no	—
352	C₂	—	50	2	no	—
353	C₂	C₂²×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×D₅×AGL(1,𝔽₅)
commutator, socle	C₂×C₅²	C₂³×C₄
Fitting	C₂×C₄×C₅²	C₂×C₄
prime radical	D₅×#709	C₂
cosocle	C₂×C₅×D₅	C₂⁴
hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
hypocenter	C₅²	#520
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #11717425	C₂	semidirect
3. C₂×C₅×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
4. AGL(1,𝔽₅)×C₂²⋊D₅	C₂	semidirect
5. #11717337	C₂	semidirect
6. D₅×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
7. #1042⋊Q₈	C₂	semidirect
8. #11717323	C₂	semidirect
11. #87900	C₄	semidirect
12. C₅×#709	C₄	semidirect
15. #87879	C₄	semidirect
18. #87874	C₄	semidirect
19. #87873	C₄	semidirect
20. #87870	C₄	semidirect
40. C₂×C₄×C₅²	C₂×C₄	semidirect
41. C₂²⋊(C₅⋊D₅)	C₂×C₄	semidirect
42. C₄⋊(C₅⋊D₅)	C₂×C₄	semidirect
43. C₄×C₅⋊D₅	C₂×C₄	semidirect
44. #6045	C₂×C₄	semidirect
45. C₅×C₂²⋊D₅	C₂×C₄	semidirect
46. C₂×C₅×Dic₅	C₂×C₄	semidirect
47. C₅×D₂₀	C₂×C₄	semidirect
48. C₄×C₅×D₅	C₂×C₄	semidirect
49. C₄×C₅×D₅	C₂×C₄	semidirect
50. C₄×C₅×D₅	C₂×C₄	semidirect
53. C₅×Dic₁₀	C₂×C₄	semidirect
54. #6039	C₂×C₄	semidirect
55. #6038	C₂×C₄	semidirect
56. #6038	C₂×C₄	semidirect
57. #6037	C₂×C₄	semidirect
58. #6036	C₂×C₄	semidirect
59. D₅×Dic₅	C₂×C₄	semidirect
69. C₂×C₄⋊AGL(1,𝔽₅)	D₅	semidirect
115. #709	AGL(1,𝔽₅)	semidirect
169. C₂×C₄×C₅	C₄×D₅	semidirect
170. C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
178. C₂²⋊D₅	C₂×AGL(1,𝔽₅)	semidirect
183. C₂×Dic₅	C₄×D₅	semidirect
189. D₂₀	C₂×AGL(1,𝔽₅)	semidirect
198. C₄×D₅	C₄×D₅	semidirect
199. C₄×D₅	C₄×D₅	semidirect
200. C₄×D₅	C₂×AGL(1,𝔽₅)	semidirect
208. Dic₁₀	C₂×AGL(1,𝔽₅)	semidirect
217. C₅²	#520	semidirect
325. C₂×C₄	D₅×AGL(1,𝔽₅)	semidirect
327. C₅	#65838	semidirect
328. C₅	#66266	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₅×#709	2
#11717425	2
C₂×C₅×C₄⋊AGL(1,𝔽₅)	2
AGL(1,𝔽₅)×C₂²⋊D₅	2
#11717337	2
D₅×C₄⋊AGL(1,𝔽₅)	2
#1042⋊Q₈	2
#11717323	2
#66266	5
#65838	5