Subgroups — C₅×#33613 #11956333

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3061	C₂	1	1	yes	maximal, characteristic
4	C₅×#3059	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2220	C₂	1	2	yes	maximal, complemented
6	C₅×#2219	C₂	1	2	yes	maximal, complemented
7	C₅×#2217	C₂	1	2	yes	maximal, complemented
8	C₅×#2216	C₂	1	2	yes	maximal, complemented
9	C₅×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#358	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₅×#537	—	2	1	no	—
16	C₅×#536	—	2	1	no	—
17	C₅×#510	—	2	4	no	—
18	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
20	C₅×#504	—	2	4	no	—
21	C₂×C₅×M₃₂	C₂²	1	2	yes	—
22	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
25	C₅×#470	—	2	2	no	—
26	C₅×#468	—	2	2	no	—
27	C₅×#467	C₂²	1	2	yes	—
28	C₅×#467	C₂²	1	2	yes	—
29	C₅×#467	C₂²	1	2	yes	—
30	C₅×#466	C₂²	1	2	yes	—
31	C₅×#427	C₂²	1	1	yes	characteristic
32	C₂×C₅×#107	C₂²	1	1	yes	characteristic
33	C₅×#419	—	2	1	no	—
34	C₅×#417	—	2	1	no	—
35	C₅×#367	C₂²	1	2	yes	—
36	C₅×#366	C₂²	1	2	yes	—
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#358	C₂²	1	2	yes	—
39	C₅×#358	C₂²	1	1	yes	characteristic
40	C₅×#358	C₂²	1	1	yes	characteristic
41	C₅×#357	C₂²	1	1	yes	characteristic
42	C₅×#357	C₂²	1	1	yes	characteristic
43	#33613	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	D₄	1	1	yes	characteristic
46	C₂²×C₅×Q₈	—	2	1	no	—
47	C₅×#135	—	2	2	no	—
48	C₅×#135	—	2	2	no	—
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×Q₁₆	—	2	1	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
53	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
56	C₅×#131	—	2	2	no	—
57	C₅×#131	—	2	2	no	—
58	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
59	C₂×C₅×M₁₆	D₄	1	2	yes	—
60	C₂²×C₅×C₈	C₂³	1	2	yes	—
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	—	4	1	no	—
63	C₅×#124	—	4	1	no	—
64	C₅×#123	—	4	2	no	—
65	C₅×C₂²⋊Q₈	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	2	no	—
67	C₅×C₂²⋊Q₈	—	2	2	no	—
68	C₅×C₂²⋊Q₈	—	4	1	no	—
69	C₅×#121	—	2	2	no	—
70	C₅×#121	—	4	1	no	—
71	C₅×#121	—	4	2	no	—
72	C₅×#117	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₅×Q₃₂	—	2	4	no	—
75	C₅×SD₃₂	—	2	4	no	—
76	C₅×M₃₂	—	2	4	no	—
77	C₅×M₃₂	D₄	1	4	yes	complemented
78	C₂×C₅×C₁₆	—	2	2	no	—
79	C₂×C₅×C₁₆	—	2	4	no	—
80	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₁₆	C₂³	1	2	yes	—
83	C₅×#107	—	2	1	no	—
84	C₅×#107	C₂³	1	2	yes	—
85	C₅×#107	C₂³	1	1	yes	characteristic
86	C₅×#107	C₂³	1	1	yes	characteristic
87	C₅×#106	—	2	1	no	—
88	C₅×#103	—	2	2	no	—
89	C₅×#103	—	2	2	no	—
90	C₅×#103	—	2	2	no	—
91	C₅×#102	—	2	2	no	—
92	C₂×#510	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×#504	C₂×C₅	1	1	yes	characteristic, complemented
94	#3061	C₂×C₅	1	1	yes	characteristic
95	#3059	C₂×C₅	1	1	yes	characteristic, complemented
96	#2220	C₂×C₅	1	2	yes	complemented
97	#2219	C₂×C₅	1	2	yes	complemented
98	#2217	C₂×C₅	1	2	yes	complemented
99	#2216	C₂×C₅	1	2	yes	complemented
100	#2159	C₂×C₅	1	1	yes	characteristic, complemented
101	#2138	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#358	C₂×C₅	1	1	yes	characteristic, complemented
103	C₅×#41	—	2	2	no	—
104	C₅×#41	—	2	2	no	—
105	C₅×#41	—	4	2	no	—
106	C₅×#41	—	4	2	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	4	1	no	—
110	C₂×C₅×Q₈	—	4	2	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂×C₅×D₄	—	4	2	no	—
116	C₂×C₅×D₄	D₈	1	2	yes	—
117	C₂×C₅×D₄	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	—	4	1	no	—
120	C₂²×C₄×C₅	—	4	1	no	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₅×Q₁₆	—	2	2	no	—
124	C₅×Q₁₆	—	2	1	no	—
125	C₅×Q₁₆	—	2	2	no	—
126	C₅×Q₁₆	—	2	1	no	—
127	C₅×Q₁₆	—	4	2	no	—
128	C₅×SD₁₆	—	4	2	no	—
129	C₅×D₈	—	2	1	no	—
130	C₅×D₈	—	2	1	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	—	2	4	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₅×C₈	#41	1	2	yes	—
139	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	4	1	no	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₂²⋊C₄	—	4	1	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₅×C₂²⋊C₄	—	4	2	no	—
150	C₅×C₂²⋊C₄	—	4	2	no	—
151	C₅×C₂²⋊C₄	—	4	2	no	—
152	C₄²×C₅	—	4	1	no	—
153	C₅×C₁₆	—	2	1	no	—
154	C₅×C₁₆	—	2	1	no	—
155	C₅×C₁₆	C₂×D₄	1	4	yes	—
156	C₂×#135	C₂²×C₅	1	1	yes	characteristic
157	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
158	C₂×#131	C₂²×C₅	1	1	yes	characteristic
159	#537	—	2	1	no	—
160	#536	—	2	1	no	—
161	#510	—	2	4	no	—
162	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
163	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
164	#504	—	2	4	no	—
165	C₂×M₃₂	C₂²×C₅	1	2	yes	—
166	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
169	#470	—	2	2	no	—
170	#468	—	2	2	no	—
171	#467	C₂²×C₅	1	2	yes	—
172	#467	C₂²×C₅	1	2	yes	—
173	#467	C₂²×C₅	1	2	yes	—
174	#466	C₂²×C₅	1	2	yes	—
175	#427	C₂²×C₅	1	1	yes	characteristic
176	C₂×#107	C₂²×C₅	1	1	yes	characteristic
177	#419	—	2	1	no	—
178	#417	—	2	1	no	—
179	#367	C₂²×C₅	1	2	yes	—
180	#366	C₂²×C₅	1	2	yes	—
181	#358	C₂²×C₅	1	2	yes	—
182	#358	C₂²×C₅	1	2	yes	—
183	#358	C₂²×C₅	1	1	yes	characteristic
184	#358	C₂²×C₅	1	1	yes	characteristic
185	#357	C₂²×C₅	1	1	yes	characteristic
186	#357	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	C₂×D₈	1	2	yes	—
189	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
190	C₅×Q₈	—	2	2	no	—
191	C₅×Q₈	—	4	1	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×Q₈	—	4	2	no	—
194	C₅×Q₈	—	4	1	no	—
195	C₅×Q₈	—	8	2	no	—
196	C₅×D₄	—	2	4	no	—
197	C₅×D₄	—	2	2	no	—
198	C₅×D₄	—	4	1	no	—
199	C₅×D₄	—	4	1	no	—
200	C₅×D₄	—	8	2	no	—
201	C₅×D₄	—	16	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	8	2	no	—
210	C₂×C₄×C₅	—	8	2	no	—
211	C₂×C₄×C₅	—	16	1	no	—
212	C₂×C₄×C₅	#121	1	2	yes	—
213	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
214	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
215	C₂×C₄×C₅	#135	1	2	yes	—
216	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	#121	1	2	yes	—
219	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
220	C₅×C₈	C₂×#41	1	1	yes	characteristic
221	C₂×#41	—	2	1	no	—
222	C₂×#41	C₅×D₄	1	1	yes	characteristic
223	C₂²×Q₈	—	2	1	no	—
224	#135	—	2	2	no	—
225	#135	—	2	2	no	—
226	C₂×Q₁₆	—	2	2	no	—
227	C₂×Q₁₆	—	2	1	no	—
228	C₂×Q₁₆	—	2	2	no	—
229	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
230	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
231	C₂×SD₁₆	—	2	1	no	—
232	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
233	#131	—	2	2	no	—
234	#131	—	2	2	no	—
235	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
236	C₂×M₁₆	C₅×D₄	1	2	yes	—
237	C₂²×C₈	C₂³×C₅	1	2	yes	—
238	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
239	C₄⋊Q₈	—	4	1	no	—
240	#124	—	4	1	no	—
241	#123	—	4	2	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	4	1	no	—
246	#121	—	2	2	no	—
247	#121	—	4	1	no	—
248	#121	—	4	2	no	—
249	#117	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	Q₃₂	—	2	4	no	—
252	SD₃₂	—	2	4	no	—
253	M₃₂	—	2	4	no	—
254	M₃₂	C₅×D₄	1	4	yes	complemented
255	C₂×C₁₆	—	2	2	no	—
256	C₂×C₁₆	—	2	4	no	—
257	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₁₆	C₂³×C₅	1	2	yes	—
260	#107	—	2	1	no	—
261	#107	C₂³×C₅	1	1	yes	characteristic
262	#107	C₂³×C₅	1	1	yes	characteristic
263	#107	C₂³×C₅	1	2	yes	—
264	#106	—	2	1	no	—
265	#103	—	2	2	no	—
266	#103	—	2	2	no	—
267	#103	—	2	2	no	—
268	#102	—	2	2	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	8	1	no	—
275	C₂²×C₅	—	8	1	no	—
276	C₂²×C₅	—	8	1	no	—
277	C₂²×C₅	#466	1	2	yes	—
278	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	8	1	no	—
281	C₄×C₅	—	8	2	no	—
282	C₄×C₅	—	8	1	no	—
283	C₄×C₅	—	8	1	no	—
284	C₄×C₅	—	8	2	no	—
285	C₄×C₅	#466	1	2	yes	—
286	C₄×C₅	C₂×#121	1	1	yes	characteristic
287	C₄×C₅	C₂×#135	1	1	yes	characteristic
288	#41	—	2	2	no	—
289	#41	—	2	2	no	—
290	#41	—	4	2	no	—
291	#41	—	4	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	C₅×D₈	1	2	yes	—
302	C₂×D₄	C₅×D₈	1	1	yes	characteristic
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	Q₁₆	—	2	2	no	—
309	Q₁₆	—	2	1	no	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	1	no	—
312	Q₁₆	—	4	2	no	—
313	SD₁₆	—	4	2	no	—
314	D₈	—	2	1	no	—
315	D₈	—	2	1	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	4	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₈	C₅×#41	1	2	yes	—
324	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	4	1	no	—
338	C₁₆	—	2	1	no	—
339	C₁₆	—	2	1	no	—
340	C₁₆	C₂×C₅×D₄	1	4	yes	—
341	C₂×C₅	—	2	2	no	—
342	C₂×C₅	—	4	2	no	—
343	C₂×C₅	—	16	1	no	—
344	C₂×C₅	C₂×#466	1	1	yes	characteristic
345	C₂×C₅	#3416	1	1	yes	characteristic
346	C₂×C₅	#3417	1	1	yes	characteristic
347	C₂³	—	4	1	no	—
348	C₂³	C₂×C₅×D₈	1	2	yes	—
349	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	4	1	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	8	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	16	1	no	—
372	C₂×C₄	C₅×#121	1	2	yes	—
373	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
374	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
375	C₂×C₄	C₅×#135	1	2	yes	—
376	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	C₅×#121	1	2	yes	—
379	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
380	C₈	C₂×C₅×#41	1	1	yes	characteristic
381	C₅	#33613	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	C₅×#466	1	2	yes	—
391	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	1	no	—
397	C₄	—	8	1	no	—
398	C₄	C₅×#466	1	2	yes	—
399	C₄	C₂×C₅×#121	1	1	yes	characteristic
400	C₄	C₂×C₅×#135	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	4	2	no	—
403	C₂	—	16	1	no	—
404	C₂	C₂×C₅×#466	1	1	yes	characteristic
405	C₂	C₅×#3416	1	1	yes	characteristic
406	C₂	C₅×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3061	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#510	C₂	semidirect
2. C₂×C₅×#504	C₂	semidirect
4. C₅×#3059	C₂	semidirect
5. C₅×#2220	C₂	semidirect
6. C₅×#2219	C₂	semidirect
7. C₅×#2217	C₂	semidirect
8. C₅×#2216	C₂	semidirect
9. C₅×#2159	C₂	semidirect
10. C₅×#2138	C₂	semidirect
11. C₂×C₅×#358	C₂	semidirect
43. #33613	C₅	direct (N × H)
77. C₅×M₃₂	D₄	semidirect
92. C₂×#510	C₂×C₅	semidirect
93. C₂×#504	C₂×C₅	semidirect
95. #3059	C₂×C₅	semidirect
96. #2220	C₂×C₅	semidirect
97. #2219	C₂×C₅	semidirect
98. #2217	C₂×C₅	semidirect
99. #2216	C₂×C₅	semidirect
100. #2159	C₂×C₅	semidirect
101. #2138	C₂×C₅	semidirect
102. C₂×#358	C₂×C₅	semidirect
254. M₃₂	C₅×D₄	semidirect
381. C₅	#33613	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×#510	2
C₂×C₅×#504	2
C₅×#3061	2
C₅×#3059	2
C₅×#2220	2
C₅×#2219	2
C₅×#2217	2
C₅×#2216	2
C₅×#2159	2
C₅×#2138	2
C₂×C₅×#358	2
#33613	5

Subgroups — C5×#33613 #11956333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33613 #11956333