Subgroups — D₅×#2108 #12251932

Order 1280.

854 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	D₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#2108	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602212	C₂	1	1	yes	maximal, characteristic, complemented
6	#10602192	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600674	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599865	C₂	1	2	yes	maximal, complemented
9	D₅×#346	C₂	1	2	yes	maximal, complemented
10	#10599844	C₂	1	2	yes	maximal, complemented
11	C₄×D₅×C₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
14	D₅×#117	C₄	1	1	yes	characteristic
15	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
17	C₅×#405	C₂²	1	1	yes	characteristic
18	#65411	C₄	1	1	yes	characteristic
19	#65390	C₂²	1	1	yes	characteristic
20	C₂×#3944	C₂²	1	1	yes	characteristic
21	C₂²×#672	C₂²	1	1	yes	characteristic
22	#65286	C₄	1	1	yes	characteristic
23	D₅×M₃₂	C₄	1	8	yes	complemented
24	C₂×#3930	C₂²	1	2	yes	—
25	C₂×D₅×C₁₆	C₄	1	8	yes	complemented
26	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
27	C₂×D₅×C₁₆	C₂²	1	2	yes	—
28	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
29	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
30	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
31	#64997	C₄	1	2	yes	—
32	D₅×#97	C₄	1	2	yes	—
33	#64978	C₂²	1	2	yes	—
34	C₄×C₈×D₅	C₂²	1	2	yes	—
35	C₅×#346	C₂²	1	2	yes	complemented
36	C₄×C₅×C₁₆	C₂²	1	2	yes	complemented
37	#64722	C₂²	1	2	yes	complemented
38	#64722	C₂²	1	2	yes	complemented
39	C₁₆×Dic₅	C₂²	1	2	yes	complemented
40	C₁₆×Dic₅	C₂²	1	2	yes	complemented
41	#64681	C₂²	1	2	yes	complemented
42	C₄×#672	C₂²	1	2	yes	complemented
43	C₂×#2108	—	5	1	no	maximal, Sylow
44	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₅×#117	C₂×C₄	1	1	yes	characteristic
48	#4072	C₂×C₄	1	1	yes	characteristic
49	C₂×#681	C₂×C₄	1	1	yes	characteristic
50	C₂²×#168	C₂×C₄	1	1	yes	characteristic
51	D₅×M₁₆	C₈	1	8	yes	—
52	C₂×#676	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
56	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
57	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
60	#4038	C₈	1	2	yes	—
61	D₅×C₄⋊C₄	C₈	1	2	yes	—
62	D₅×C₂²⋊C₄	C₈	1	2	yes	—
63	#4023	C₈	1	2	yes	—
64	#4018	C₂×C₄	1	2	yes	—
65	C₄²×D₅	C₂×C₄	1	2	yes	—
66	C₅×M₃₂	C₂×C₄	1	4	yes	complemented
67	C₂×C₅×C₁₆	C₂×C₄	1	4	yes	complemented
68	C₂×C₅×C₁₆	C₂³	1	2	yes	—
69	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
71	C₅×#97	C₂×C₄	1	2	yes	—
72	C₄×C₅×C₈	C₂³	1	2	yes	—
73	#3947	C₂×C₄	1	2	yes	—
74	#3947	C₂×C₄	1	2	yes	—
75	C₈×Dic₅	C₂×C₄	1	2	yes	—
76	C₈×Dic₅	C₂³	1	2	yes	—
77	#3944	C₂×C₄	1	4	yes	complemented
78	C₂×#672	C₂×C₄	1	4	yes	complemented
79	C₂×#672	C₂³	1	1	yes	characteristic
80	C₂×#672	C₂³	1	1	yes	characteristic
81	C₂×#672	C₂³	1	2	yes	—
82	#3935	C₂×C₄	1	2	yes	—
83	C₄×#168	C₂×C₄	1	2	yes	—
84	#3930	C₂×C₄	1	8	yes	complemented
85	D₅×C₁₆	C₂×C₄	1	4	yes	—
86	D₅×C₁₆	C₂×C₄	1	4	yes	—
87	D₅×C₁₆	C₂×C₄	1	8	yes	—
88	D₅×C₁₆	C₂×C₄	1	4	yes	complemented
89	D₅×C₁₆	C₂×C₄	1	4	yes	complemented
90	C₂²×M₃₂	—	5	1	no	—
91	C₂³×C₁₆	—	5	1	no	—
92	C₂×#405	—	5	1	no	—
93	#2108	—	5	1	no	—
94	#2108	—	5	1	no	—
95	#2108	—	5	1	no	—
96	#2108	—	5	2	no	—
97	#2108	—	5	2	no	—
98	#2108	D₅	1	1	yes	characteristic, direct product factor
99	C₂×#346	—	5	2	no	—
100	C₂×C₄×C₁₆	—	5	2	no	—
101	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₅	C₄²	1	4	yes	—
105	C₂×C₄×D₅	C₂×C₈	1	4	yes	—
106	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
108	C₂×C₄×D₅	C₂×C₈	1	4	yes	—
109	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
111	C₅×M₁₆	C₂×C₈	1	4	yes	—
112	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
115	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
116	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
117	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
118	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
119	C₄²×C₅	C₂²×C₄	1	2	yes	—
120	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
121	#685	C₂×C₈	1	4	yes	—
122	C₄⋊Dic₅	C₂×C₈	1	2	yes	—
123	#683	C₂×C₈	1	4	yes	—
124	C₄×Dic₅	C₂×C₈	1	4	yes	—
125	C₄×Dic₅	C₂²×C₄	1	2	yes	—
126	#681	C₂×C₈	1	4	yes	—
127	C₂×#168	C₄²	1	4	yes	—
128	C₂×#168	C₂²×C₄	1	1	yes	characteristic
129	C₂×#168	C₂²×C₄	1	1	yes	characteristic
130	C₂×#168	C₂²×C₄	1	2	yes	—
131	#676	C₂×C₈	1	8	yes	—
132	C₈×D₅	C₄²	1	4	yes	—
133	C₈×D₅	C₄²	1	4	yes	—
134	C₈×D₅	C₂×C₈	1	8	yes	—
135	C₈×D₅	C₂²×C₄	1	2	yes	—
136	C₈×D₅	C₂²×C₄	1	2	yes	—
137	C₈×D₅	C₂²×C₄	1	2	yes	—
138	C₈×D₅	C₂²×C₄	1	2	yes	—
139	C₅×C₁₆	C₂²×C₄	1	2	yes	—
140	C₅×C₁₆	C₂²×C₄	1	2	yes	—
141	C₅×C₁₆	C₂²×C₄	1	4	yes	—
142	#672	C₂²×C₄	1	2	yes	—
143	#672	C₂²×C₄	1	2	yes	—
144	#672	C₂²×C₄	1	4	yes	—
145	C₂²×M₁₆	—	5	1	no	—
146	C₂³×C₈	—	5	1	no	—
147	C₂×#117	—	5	1	no	—
148	C₂×M₃₂	—	5	1	no	—
149	C₂×M₃₂	—	5	8	no	—
150	C₂×M₃₂	—	5	2	no	—
151	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
152	C₂²×C₁₆	—	5	1	no	—
153	C₂²×C₁₆	—	5	8	no	—
154	C₂²×C₁₆	—	5	2	no	—
155	C₂²×C₁₆	—	5	1	no	—
156	C₂²×C₁₆	—	5	1	no	—
157	C₂²×C₁₆	—	5	1	no	—
158	C₂²×C₁₆	—	5	1	no	—
159	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
160	#405	—	5	1	no	—
161	#405	—	5	1	no	—
162	#405	—	5	1	no	—
163	#405	—	5	2	no	—
164	#405	—	5	2	no	—
165	#405	C₂×D₅	1	1	yes	characteristic
166	C₂×#97	—	5	2	no	—
167	C₂×C₄×C₈	—	5	2	no	—
168	#346	—	5	2	no	—
169	#346	—	5	2	no	—
170	#346	—	5	2	no	—
171	#346	C₂×D₅	1	2	yes	complemented
172	C₄×C₁₆	—	5	2	no	—
173	C₄×C₁₆	—	5	2	no	—
174	C₄×C₁₆	—	5	2	no	—
175	C₄×C₁₆	C₂×D₅	1	2	yes	complemented
176	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
177	C₂²×D₅	—	2	4	no	—
178	C₂²×D₅	C₄×C₈	1	4	yes	—
179	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
180	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
182	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
183	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
184	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×Dic₅	C₄×C₈	1	4	yes	—
187	C₂×Dic₅	C₂²×C₈	1	4	yes	—
188	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
190	C₄×D₅	—	2	8	no	—
191	C₄×D₅	C₄×C₈	1	4	yes	—
192	C₄×D₅	C₄×C₈	1	4	yes	—
193	C₄×D₅	C₂×C₄²	1	2	yes	—
194	C₄×D₅	C₂×C₄²	1	2	yes	—
195	C₄×D₅	C₂²×C₈	1	2	yes	—
196	C₄×D₅	C₂²×C₈	1	2	yes	—
197	C₅×C₈	C₂×C₄²	1	2	yes	—
198	C₅×C₈	C₂²×C₈	1	4	yes	—
199	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
200	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
201	#168	C₂×C₄²	1	2	yes	—
202	#168	C₂×C₄²	1	2	yes	—
203	#168	C₂²×C₈	1	4	yes	—
204	C₂³×C₄	—	5	1	no	—
205	C₂×M₁₆	—	5	1	no	—
206	C₂×M₁₆	—	5	8	no	—
207	C₂×M₁₆	—	5	2	no	—
208	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
209	C₂²×C₈	—	5	1	no	—
210	C₂²×C₈	—	5	1	no	—
211	C₂²×C₈	—	5	1	no	—
212	C₂²×C₈	—	5	4	no	—
213	C₂²×C₈	—	5	4	no	—
214	C₂²×C₈	—	5	2	no	—
215	C₂²×C₈	—	5	1	no	—
216	C₂²×C₈	—	5	1	no	—
217	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
218	#117	—	5	1	no	—
219	#117	—	5	2	no	—
220	#117	—	5	2	no	—
221	#117	—	5	2	no	—
222	#117	C₄×D₅	1	1	yes	characteristic
223	C₂×C₄⋊C₄	—	5	2	no	—
224	C₂×C₂²⋊C₄	—	5	2	no	—
225	C₂×C₄²	—	5	2	no	—
226	M₃₂	—	5	4	no	—
227	M₃₂	—	5	8	no	—
228	M₃₂	C₄×D₅	1	4	yes	complemented
229	C₂×C₁₆	—	5	4	no	—
230	C₂×C₁₆	—	5	1	no	—
231	C₂×C₁₆	—	5	2	no	—
232	C₂×C₁₆	—	5	1	no	—
233	C₂×C₁₆	—	5	4	no	—
234	C₂×C₁₆	—	5	4	no	—
235	C₂×C₁₆	—	5	8	no	—
236	C₂×C₁₆	—	5	4	no	—
237	C₂×C₁₆	—	5	4	no	—
238	C₂×C₁₆	C₄×D₅	1	4	yes	complemented
239	C₂×C₁₆	C₂²×D₅	1	2	yes	—
240	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
241	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
242	#97	—	5	2	no	—
243	#97	—	5	2	no	—
244	#97	—	5	2	no	—
245	#97	C₄×D₅	1	2	yes	—
246	C₄×C₈	—	5	2	no	—
247	C₄×C₈	—	5	2	no	—
248	C₄×C₈	—	5	2	no	—
249	C₄×C₈	C₂²×D₅	1	2	yes	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	C₂×C₄×C₈	1	2	yes	—
252	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
253	C₂×D₅	—	2	2	no	—
254	C₂×D₅	—	2	8	no	—
255	C₂×D₅	C₂×C₄×C₈	1	2	yes	—
256	C₂×D₅	C₂×C₄×C₈	1	2	yes	—
257	C₂×D₅	#504	1	4	yes	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	C₂×C₄×C₈	1	2	yes	—
260	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
261	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
262	Dic₅	—	2	4	no	—
263	Dic₅	C₂×C₄×C₈	1	2	yes	—
264	Dic₅	C₂×C₄×C₈	1	2	yes	—
265	C₂⁴	—	5	1	no	—
266	C₂²×C₄	—	5	1	no	—
267	C₂²×C₄	—	5	1	no	—
268	C₂²×C₄	—	5	1	no	—
269	C₂²×C₄	—	5	4	no	—
270	C₂²×C₄	—	5	1	no	—
271	C₂²×C₄	—	5	1	no	—
272	C₂²×C₄	—	5	4	no	—
273	C₂²×C₄	—	5	4	no	—
274	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
275	M₁₆	—	5	4	no	—
276	M₁₆	—	5	8	no	—
277	M₁₆	C₈×D₅	1	4	yes	—
278	C₂×C₈	—	5	1	no	—
279	C₂×C₈	—	5	2	no	—
280	C₂×C₈	—	5	1	no	—
281	C₂×C₈	—	5	4	no	—
282	C₂×C₈	—	5	2	no	—
283	C₂×C₈	—	5	2	no	—
284	C₂×C₈	—	5	2	no	—
285	C₂×C₈	—	5	2	no	—
286	C₂×C₈	—	5	4	no	—
287	C₂×C₈	—	5	4	no	—
288	C₂×C₈	—	5	8	no	—
289	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
290	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
291	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
292	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
293	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
294	C₄⋊C₄	—	5	4	no	—
295	C₄⋊C₄	—	5	2	no	—
296	C₄⋊C₄	C₈×D₅	1	2	yes	—
297	C₂²⋊C₄	—	5	2	no	—
298	C₂²⋊C₄	—	5	4	no	—
299	C₂²⋊C₄	C₈×D₅	1	2	yes	—
300	C₄²	—	5	2	no	—
301	C₄²	—	5	4	no	—
302	C₄²	C₂×C₄×D₅	1	2	yes	—
303	C₁₆	—	5	2	no	—
304	C₁₆	—	5	2	no	—
305	C₁₆	—	5	4	no	—
306	C₁₆	C₂×C₄×D₅	1	2	yes	—
307	C₁₆	C₂×C₄×D₅	1	2	yes	—
308	C₁₆	C₂×C₄×D₅	1	4	yes	—
309	C₂×C₅	—	2	2	no	—
310	C₂×C₅	C₂²×C₄×C₈	1	1	yes	characteristic
311	C₂×C₅	C₂×#504	1	2	yes	—
312	D₅	—	2	2	no	—
313	D₅	#2108	1	4	yes	direct product factor
314	C₂³	—	5	1	no	—
315	C₂³	—	5	1	no	—
316	C₂³	—	5	4	no	—
317	C₂³	—	10	4	no	—
318	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
319	C₂×C₄	—	5	1	no	—
320	C₂×C₄	—	5	1	no	—
321	C₂×C₄	—	5	4	no	—
322	C₂×C₄	—	5	2	no	—
323	C₂×C₄	—	5	2	no	—
324	C₂×C₄	—	5	2	no	—
325	C₂×C₄	—	5	2	no	—
326	C₂×C₄	—	5	4	no	—
327	C₂×C₄	—	5	4	no	—
328	C₂×C₄	—	5	4	no	—
329	C₂×C₄	—	10	8	no	—
330	C₂×C₄	C₄²×D₅	1	2	yes	—
331	C₂×C₄	C₂×C₈×D₅	1	4	yes	—
332	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
333	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
335	C₈	—	5	2	no	—
336	C₈	—	5	2	no	—
337	C₈	—	5	4	no	—
338	C₈	C₄²×D₅	1	2	yes	—
339	C₈	C₂×C₈×D₅	1	4	yes	—
340	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
341	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
342	C₅	C₂×#2108	1	1	yes	characteristic, complemented, Sylow
343	C₂²	—	2	2	no	—
344	C₂²	—	5	2	no	—
345	C₂²	—	5	4	no	—
346	C₂²	—	5	2	no	—
347	C₂²	—	10	8	no	—
348	C₂²	—	10	2	no	—
349	C₂²	C₄×C₈×D₅	1	2	yes	—
350	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	5	2	no	—
353	C₄	—	5	2	no	—
354	C₄	—	10	4	no	—
355	C₄	C₄×C₈×D₅	1	2	yes	—
356	C₄	C₂×C₄²×D₅	1	1	yes	characteristic
357	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	5	4	no	—
360	C₂	—	10	2	no	—
361	C₂	C₂×C₄×C₈×D₅	1	1	yes	characteristic
362	C₂	D₅×#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₅
commutator	C₂×C₅	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₅
Fitting	C₅×#2108	C₂
socle	C₂²×C₅	C₂³×C₈
prime radical	C₂³×D₅	C₂×C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2108	D₅
hypocenter	C₅	C₂×#2108
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₆ ◁ #2108

Complements

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

N	H ≅ G/N	type
4. C₅×#2108	C₂	semidirect
5. #10602212	C₂	semidirect
6. #10602192	C₂	semidirect
7. #10600674	C₂	semidirect
8. #10599865	C₂	semidirect
9. D₅×#346	C₂	semidirect
10. #10599844	C₂	semidirect
11. C₄×D₅×C₁₆	C₂	semidirect
23. D₅×M₃₂	C₄	semidirect
25. C₂×D₅×C₁₆	C₄	semidirect
35. C₅×#346	C₂²	semidirect
36. C₄×C₅×C₁₆	C₂²	semidirect
37. #64722	C₂²	semidirect
38. #64722	C₂²	semidirect
39. C₁₆×Dic₅	C₂²	semidirect
40. C₁₆×Dic₅	C₂²	semidirect
41. #64681	C₂²	semidirect
42. C₄×#672	C₂²	semidirect
66. C₅×M₃₂	C₂×C₄	semidirect
67. C₂×C₅×C₁₆	C₂×C₄	semidirect
77. #3944	C₂×C₄	semidirect
78. C₂×#672	C₂×C₄	semidirect
84. #3930	C₂×C₄	semidirect
88. D₅×C₁₆	C₂×C₄	semidirect
89. D₅×C₁₆	C₂×C₄	semidirect
98. #2108	D₅	direct (N × H)
171. #346	C₂×D₅	semidirect
175. C₄×C₁₆	C₂×D₅	semidirect
228. M₃₂	C₄×D₅	semidirect
238. C₂×C₁₆	C₄×D₅	semidirect
313. D₅	#2108	direct (N × H)
342. C₅	C₂×#2108	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×M₃₂	2
C₂²×D₅×C₁₆	2
D₅×#405	2
C₅×#2108	2
#10602212	2
#10602192	2
#10600674	2
#10599865	2
D₅×#346	2
#10599844	2
C₄×D₅×C₁₆	2
C₂×#2108	5

Subgroups — D5×#2108 #12251932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#2108 #12251932