Subgroups — C₅×#24988 #11947708

Order 1280.

656 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#472	C₂	1	1	yes	maximal, characteristic
2	C₅×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2081	C₂	1	2	yes	maximal, complemented
4	C₅×#2048	C₂	1	2	yes	maximal, complemented
5	C₅×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1904	C₂	1	2	yes	maximal, complemented
8	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1829	C₂	1	2	yes	maximal, complemented
10	C₅×#1814	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1757	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₅×#518	C₂²	1	2	yes	—
16	C₅×#472	—	2	2	no	—
17	C₅×#472	—	2	2	no	—
18	C₅×#442	—	2	2	no	—
19	C₄×C₅×D₈	—	2	2	no	—
20	C₅×#430	C₂²	1	2	yes	—
21	C₂×C₅×#108	C₂²	1	1	yes	characteristic
22	C₂×C₅×#108	C₂²	1	1	yes	characteristic
23	C₅×#427	C₂²	1	1	yes	characteristic
24	C₅×#421	C₂²	1	2	yes	—
25	C₅×#418	C₂²	1	2	yes	—
26	C₅×#418	C₂²	1	2	yes	—
27	C₅×#413	C₂²	1	1	yes	characteristic
28	C₂×C₅×#100	C₂²	1	2	yes	—
29	C₂×C₅×#100	C₂²	1	2	yes	—
30	C₅×#410	C₂²	1	1	yes	characteristic
31	C₅×#405	C₂²	1	1	yes	characteristic
32	C₅×#405	C₂²	1	1	yes	characteristic
33	C₅×#344	C₂²	1	1	yes	characteristic
34	C₅×#344	C₂²	1	1	yes	characteristic
35	C₅×#344	C₂²	1	2	yes	—
36	C₅×#344	C₂²	1	2	yes	—
37	C₅×#344	C₂²	1	2	yes	—
38	C₅×H(3,ℤ/4)	C₂²	1	2	yes	—
39	#24988	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₅×#41	C₂³	1	1	yes	characteristic
41	C₂²×C₅×D₄	C₂³	1	2	yes	—
42	C₅×AGL(1,ℤ/8)	—	2	4	no	—
43	C₅×AGL(1,ℤ/8)	—	4	2	no	—
44	C₂×C₅×SD₁₆	—	2	2	no	—
45	C₂×C₅×D₈	—	2	2	no	—
46	C₂×C₅×D₈	—	2	1	no	—
47	C₂×C₅×D₈	—	2	1	no	—
48	C₂×C₅×D₈	—	2	1	no	—
49	C₂×C₅×D₈	—	2	1	no	—
50	C₂×C₅×D₈	D₄	1	2	yes	—
51	C₂×C₅×D₈	D₄	1	2	yes	—
52	C₅×#131	—	2	1	no	—
53	C₅×#131	—	2	1	no	—
54	C₅×#131	—	2	1	no	—
55	C₅×#131	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₅×M₁₆	C₂³	1	2	yes	—
60	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₅×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₄×C₅×D₄	—	2	4	no	—
65	C₄×C₅×D₄	—	4	2	no	—
66	C₅×#117	C₂³	1	1	yes	characteristic
67	C₅×#117	C₂³	1	2	yes	—
68	C₅×#117	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₅×#108	—	2	1	no	—
71	C₅×#108	—	2	1	no	—
72	C₅×#108	—	2	1	no	—
73	C₅×#108	—	2	1	no	—
74	C₅×#108	—	4	2	no	—
75	C₅×#107	—	2	1	no	—
76	C₅×#106	—	2	1	no	—
77	C₅×#104	—	4	2	no	—
78	C₅×#102	—	2	4	no	—
79	C₅×#102	—	4	2	no	—
80	C₅×#101	—	2	1	no	—
81	C₅×#100	—	2	4	no	—
82	C₅×#100	—	2	1	no	—
83	C₅×#100	—	4	2	no	—
84	C₅×#99	—	2	2	no	—
85	C₅×#97	—	2	1	no	—
86	C₅×#97	—	2	1	no	—
87	C₄×C₅×C₈	—	2	1	no	—
88	C₄×C₅×C₈	—	2	1	no	—
89	C₂×#472	C₂×C₅	1	1	yes	characteristic
90	#2948	C₂×C₅	1	1	yes	characteristic, complemented
91	#2081	C₂×C₅	1	2	yes	complemented
92	#2048	C₂×C₅	1	2	yes	complemented
93	#1978	C₂×C₅	1	1	yes	characteristic, complemented
94	#1953	C₂×C₅	1	1	yes	characteristic, complemented
95	#1904	C₂×C₅	1	2	yes	complemented
96	#1833	C₂×C₅	1	1	yes	characteristic, complemented
97	#1829	C₂×C₅	1	2	yes	complemented
98	#1814	C₂×C₅	1	1	yes	characteristic, complemented
99	#1757	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	2	2	no	—
101	C₅×#41	—	2	1	no	—
102	C₅×#41	—	2	1	no	—
103	C₅×#41	—	2	1	no	—
104	C₅×#41	—	2	1	no	—
105	C₂×C₅×Q₈	#41	1	1	yes	characteristic
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
113	C₂×C₅×D₄	#41	1	1	yes	characteristic
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	4	4	no	—
116	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₅×SD₁₆	—	4	4	no	—
118	C₅×D₈	—	2	2	no	—
119	C₅×D₈	—	2	2	no	—
120	C₅×D₈	—	2	2	no	—
121	C₅×D₈	—	2	2	no	—
122	C₅×D₈	—	4	4	no	—
123	C₅×M₁₆	—	2	1	no	—
124	C₅×M₁₆	—	2	2	no	—
125	C₅×M₁₆	—	2	1	no	—
126	C₅×M₁₆	—	2	1	no	—
127	C₅×M₁₆	—	2	1	no	—
128	C₅×M₁₆	—	2	2	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	—	2	1	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	—	2	1	no	—
133	C₅×M₁₆	—	4	1	no	—
134	C₅×M₁₆	—	4	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	4	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	#41	1	1	yes	characteristic
145	C₂×C₅×C₈	#41	1	1	yes	characteristic
146	C₂×C₅×C₈	#41	1	1	yes	characteristic
147	C₂×C₅×C₈	#41	1	1	yes	characteristic
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	4	4	no	—
154	C₅×C₂²⋊C₄	#41	1	2	yes	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
159	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×#131	C₂²×C₅	1	1	yes	characteristic
161	#518	C₂²×C₅	1	2	yes	—
162	#472	—	2	2	no	—
163	#472	—	2	2	no	—
164	#442	—	2	2	no	—
165	C₄×D₈	—	2	2	no	—
166	#430	C₂²×C₅	1	2	yes	—
167	C₂×#108	C₂²×C₅	1	1	yes	characteristic
168	C₂×#108	C₂²×C₅	1	1	yes	characteristic
169	#427	C₂²×C₅	1	1	yes	characteristic
170	#421	C₂²×C₅	1	2	yes	—
171	#418	C₂²×C₅	1	2	yes	—
172	#418	C₂²×C₅	1	2	yes	—
173	#413	C₂²×C₅	1	1	yes	characteristic
174	C₂×#100	C₂²×C₅	1	2	yes	—
175	C₂×#100	C₂²×C₅	1	2	yes	—
176	#410	C₂²×C₅	1	1	yes	characteristic
177	#405	C₂²×C₅	1	1	yes	characteristic
178	#405	C₂²×C₅	1	1	yes	characteristic
179	#344	C₂²×C₅	1	2	yes	—
180	#344	C₂²×C₅	1	2	yes	—
181	#344	C₂²×C₅	1	1	yes	characteristic
182	#344	C₂²×C₅	1	1	yes	characteristic
183	#344	C₂²×C₅	1	2	yes	—
184	H(3,ℤ/4)	C₂²×C₅	1	2	yes	—
185	C₂³×C₅	—	2	1	no	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	4	2	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	16	2	no	—
190	C₂³×C₅	C₂×#41	1	1	yes	characteristic
191	C₅×Q₈	—	2	1	no	—
192	C₅×Q₈	—	2	1	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	1	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	2	1	no	—
197	C₅×D₄	—	4	1	no	—
198	C₅×D₄	—	4	1	no	—
199	C₅×D₄	—	4	2	no	—
200	C₅×D₄	—	4	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	16	4	no	—
208	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
214	C₅×C₈	—	4	1	no	—
215	C₅×C₈	—	4	2	no	—
216	C₅×C₈	—	4	1	no	—
217	C₅×C₈	—	4	2	no	—
218	C₅×C₈	—	4	1	no	—
219	C₅×C₈	#123	1	1	yes	characteristic
220	C₅×C₈	#123	1	1	yes	characteristic
221	C₅×C₈	#123	1	1	yes	characteristic
222	C₅×C₈	#123	1	1	yes	characteristic
223	C₂×#41	C₂³×C₅	1	1	yes	characteristic
224	C₂²×D₄	C₂³×C₅	1	2	yes	—
225	AGL(1,ℤ/8)	—	2	4	no	—
226	AGL(1,ℤ/8)	—	4	2	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×D₈	—	2	2	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	C₅×D₄	1	2	yes	—
234	C₂×D₈	C₅×D₄	1	2	yes	—
235	#131	—	2	1	no	—
236	#131	—	2	1	no	—
237	#131	—	2	1	no	—
238	#131	—	2	1	no	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
241	C₂×M₁₆	C₂³×C₅	1	2	yes	—
242	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
243	C₂×M₁₆	C₂³×C₅	1	2	yes	—
244	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	—	4	2	no	—
249	#117	C₂³×C₅	1	2	yes	—
250	#117	C₂³×C₅	1	1	yes	characteristic
251	#117	C₂³×C₅	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	#108	—	2	1	no	—
254	#108	—	2	1	no	—
255	#108	—	2	1	no	—
256	#108	—	2	1	no	—
257	#108	—	4	2	no	—
258	#107	—	2	1	no	—
259	#106	—	2	1	no	—
260	#104	—	4	2	no	—
261	#102	—	2	4	no	—
262	#102	—	4	2	no	—
263	#101	—	2	1	no	—
264	#100	—	2	4	no	—
265	#100	—	2	1	no	—
266	#100	—	4	2	no	—
267	#99	—	2	2	no	—
268	#97	—	2	1	no	—
269	#97	—	2	1	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	4	4	no	—
275	C₂²×C₅	—	8	4	no	—
276	C₂²×C₅	—	8	1	no	—
277	C₂²×C₅	—	16	2	no	—
278	C₂²×C₅	—	16	2	no	—
279	C₂²×C₅	#529	1	1	yes	characteristic
280	C₂²×C₅	#546	1	1	yes	characteristic
281	C₂²×C₅	#555	1	1	yes	characteristic
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	8	1	no	—
285	C₄×C₅	—	8	2	no	—
286	C₄×C₅	C₂×#123	1	1	yes	characteristic
287	C₄×C₅	#540	1	1	yes	characteristic
288	C₄×C₅	#546	1	1	yes	characteristic
289	C₄×C₅	#553	1	1	yes	characteristic
290	C₂⁴	—	2	2	no	—
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	#41	—	2	1	no	—
295	C₂×Q₈	C₅×#41	1	1	yes	characteristic
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
303	C₂×D₄	C₅×#41	1	1	yes	characteristic
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
307	SD₁₆	—	4	4	no	—
308	D₈	—	2	2	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	4	no	—
313	M₁₆	—	2	1	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×C₈	C₅×#41	1	1	yes	characteristic
335	C₂×C₈	C₅×#41	1	1	yes	characteristic
336	C₂×C₈	C₅×#41	1	1	yes	characteristic
337	C₂×C₈	C₅×#41	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	C₅×#41	1	2	yes	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₂×C₅	—	2	1	no	—
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	—	2	1	no	—
351	C₂×C₅	—	8	1	no	—
352	C₂×C₅	—	8	4	no	—
353	C₂×C₅	#2420	1	1	yes	characteristic
354	C₂³	—	2	1	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	16	2	no	—
359	C₂³	C₂×C₅×#41	1	1	yes	characteristic
360	Q₈	—	2	1	no	—
361	Q₈	—	2	1	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	16	4	no	—
377	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
381	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	1	no	—
387	C₈	—	4	1	no	—
388	C₈	C₅×#123	1	1	yes	characteristic
389	C₈	C₅×#123	1	1	yes	characteristic
390	C₈	C₅×#123	1	1	yes	characteristic
391	C₈	C₅×#123	1	1	yes	characteristic
392	C₅	#24988	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	4	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	16	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	C₅×#529	1	1	yes	characteristic
401	C₂²	C₅×#546	1	1	yes	characteristic
402	C₂²	C₅×#555	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	—	4	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	1	no	—
407	C₄	C₂×C₅×#123	1	1	yes	characteristic
408	C₄	C₅×#540	1	1	yes	characteristic
409	C₄	C₅×#546	1	1	yes	characteristic
410	C₄	C₅×#553	1	1	yes	characteristic
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	8	4	no	—
415	C₂	—	8	1	no	—
416	C₂	C₅×#2420	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#472	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2948	C₂	semidirect
3. C₅×#2081	C₂	semidirect
4. C₅×#2048	C₂	semidirect
5. C₅×#1978	C₂	semidirect
6. C₅×#1953	C₂	semidirect
7. C₅×#1904	C₂	semidirect
8. C₅×#1833	C₂	semidirect
9. C₅×#1829	C₂	semidirect
10. C₅×#1814	C₂	semidirect
11. C₅×#1757	C₂	semidirect
39. #24988	C₅	direct (N × H)
90. #2948	C₂×C₅	semidirect
91. #2081	C₂×C₅	semidirect
92. #2048	C₂×C₅	semidirect
93. #1978	C₂×C₅	semidirect
94. #1953	C₂×C₅	semidirect
95. #1904	C₂×C₅	semidirect
96. #1833	C₂×C₅	semidirect
97. #1829	C₂×C₅	semidirect
98. #1814	C₂×C₅	semidirect
99. #1757	C₂×C₅	semidirect
392. C₅	#24988	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#472	2
C₅×#2948	2
C₅×#2081	2
C₅×#2048	2
C₅×#1978	2
C₅×#1953	2
C₅×#1904	2
C₅×#1833	2
C₅×#1829	2
C₅×#1814	2
C₅×#1757	2
#24988	5

Subgroups — C5×#24988 #11947708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24988 #11947708