Subgroups — C₅×#33612 #11956332

Order 1280.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#509	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, complemented
4	C₅×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2220	C₂	1	2	yes	maximal, complemented
6	C₅×#2218	C₂	1	2	yes	maximal, complemented
7	C₅×#2217	C₂	1	2	yes	maximal, complemented
8	C₅×#2215	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×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₅×#537	—	2	1	no	—
16	C₅×#535	—	2	1	no	—
17	C₅×#509	—	2	4	no	—
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₅×D₁₆	C₂²	1	2	yes	—
20	C₅×#504	—	2	4	no	—
21	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
23	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
25	C₅×#469	—	2	2	no	—
26	C₅×#468	—	2	2	no	—
27	C₅×#467	C₂²	1	2	yes	complemented
28	C₅×#466	C₂²	1	2	yes	—
29	C₅×#466	C₂²	1	2	yes	—
30	C₅×#466	C₂²	1	2	yes	complemented
31	C₅×#427	C₂²	1	1	yes	characteristic
32	C₂×C₅×#107	C₂²	1	1	yes	characteristic
33	C₅×#418	—	2	1	no	—
34	C₅×#417	—	2	1	no	—
35	C₅×#367	C₂²	1	2	yes	complemented
36	C₅×#366	C₂²	1	2	yes	complemented
37	C₅×#358	C₂²	1	1	yes	characteristic, complemented
38	C₅×#358	C₂²	1	1	yes	characteristic, complemented
39	C₅×#357	C₂²	1	2	yes	—
40	C₅×#357	C₂²	1	2	yes	—
41	C₅×#357	C₂²	1	1	yes	characteristic, complemented
42	C₅×#357	C₂²	1	1	yes	characteristic, complemented
43	#33612	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×D₄	—	2	1	no	—
47	C₅×#135	—	2	2	no	—
48	C₅×#135	—	2	2	no	—
49	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	—	2	1	no	—
51	C₂×C₅×D₈	—	2	2	no	—
52	C₂×C₅×D₈	—	2	1	no	—
53	C₂×C₅×D₈	—	2	2	no	—
54	C₂×C₅×D₈	C₂³	1	2	yes	—
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×#127	—	4	1	no	—
63	C₅×#124	—	4	1	no	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×C₂²⋊Q₈	—	4	1	no	—
66	C₅×#121	—	2	2	no	—
67	C₅×#121	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₅×#121	—	4	1	no	—
70	C₅×#121	—	4	2	no	—
71	C₅×#120	—	4	2	no	—
72	C₅×#117	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₅×SD₃₂	—	2	4	no	—
75	C₅×D₁₆	—	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×#102	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×#102	—	2	2	no	—
92	C₂×#509	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, complemented
95	#3058	C₂×C₅	1	1	yes	characteristic, complemented
96	#2220	C₂×C₅	1	2	yes	complemented
97	#2218	C₂×C₅	1	2	yes	complemented
98	#2217	C₂×C₅	1	2	yes	complemented
99	#2215	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×#357	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂⁴×C₅	—	4	1	no	—
104	C₅×#41	—	2	2	no	—
105	C₅×#41	—	2	2	no	—
106	C₅×#41	—	4	2	no	—
107	C₅×#41	—	4	2	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	—	4	2	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂×C₅×D₄	—	4	2	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	D₈	1	2	yes	—
120	C₂×C₅×D₄	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₅	—	4	1	no	—
122	C₂²×C₄×C₅	—	4	1	no	—
123	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₅×Q₁₆	—	2	1	no	—
126	C₅×Q₁₆	—	2	1	no	—
127	C₅×SD₁₆	—	4	2	no	—
128	C₅×D₈	—	2	2	no	—
129	C₅×D₈	—	2	1	no	—
130	C₅×D₈	—	2	2	no	—
131	C₅×D₈	—	2	1	no	—
132	C₅×D₈	—	4	2	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	—	2	4	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
140	C₂×C₅×C₈	#41	1	2	yes	—
141	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	4	1	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×D₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×#131	C₂²×C₅	1	1	yes	characteristic
159	#537	—	2	1	no	—
160	#535	—	2	1	no	—
161	#509	—	2	4	no	—
162	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
163	C₂×D₁₆	C₂²×C₅	1	2	yes	—
164	#504	—	2	4	no	—
165	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
166	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
167	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
169	#469	—	2	2	no	—
170	#468	—	2	2	no	—
171	#467	C₂²×C₅	1	2	yes	complemented
172	#466	C₂²×C₅	1	2	yes	—
173	#466	C₂²×C₅	1	2	yes	—
174	#466	C₂²×C₅	1	2	yes	complemented
175	#427	C₂²×C₅	1	1	yes	characteristic
176	C₂×#107	C₂²×C₅	1	1	yes	characteristic
177	#418	—	2	1	no	—
178	#417	—	2	1	no	—
179	#367	C₂²×C₅	1	2	yes	complemented
180	#366	C₂²×C₅	1	2	yes	complemented
181	#358	C₂²×C₅	1	1	yes	characteristic, complemented
182	#358	C₂²×C₅	1	1	yes	characteristic, complemented
183	#357	C₂²×C₅	1	2	yes	—
184	#357	C₂²×C₅	1	2	yes	—
185	#357	C₂²×C₅	1	1	yes	characteristic, complemented
186	#357	C₂²×C₅	1	1	yes	characteristic, complemented
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	8	2	no	—
190	C₂³×C₅	—	16	1	no	—
191	C₂³×C₅	—	16	1	no	—
192	C₂³×C₅	C₂×D₈	1	2	yes	—
193	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
194	C₅×Q₈	—	2	2	no	—
195	C₅×Q₈	—	4	1	no	—
196	C₅×Q₈	—	4	1	no	—
197	C₅×D₄	—	2	4	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	4	2	no	—
200	C₅×D₄	—	4	1	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	1	no	—
203	C₅×D₄	—	8	2	no	—
204	C₅×D₄	—	8	2	no	—
205	C₅×D₄	—	16	2	no	—
206	C₅×D₄	—	16	2	no	—
207	C₅×D₄	—	16	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	8	2	no	—
215	C₂×C₄×C₅	—	16	1	no	—
216	C₂×C₄×C₅	#121	1	2	yes	—
217	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
219	C₂×C₄×C₅	#135	1	2	yes	—
220	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	#121	1	2	yes	—
223	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
224	C₅×C₈	C₂×#41	1	1	yes	characteristic
225	C₂×#41	—	2	1	no	—
226	C₂×#41	C₅×D₄	1	1	yes	characteristic
227	C₂²×D₄	—	2	1	no	—
228	#135	—	2	2	no	—
229	#135	—	2	2	no	—
230	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
231	C₂×SD₁₆	—	2	1	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	2	2	no	—
235	C₂×D₈	C₂³×C₅	1	2	yes	—
236	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
237	#131	—	2	2	no	—
238	#131	—	2	2	no	—
239	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
240	C₂×M₁₆	C₅×D₄	1	2	yes	—
241	C₂²×C₈	C₂³×C₅	1	2	yes	—
242	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
243	#127	—	4	1	no	—
244	#124	—	4	1	no	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	4	1	no	—
247	#121	—	2	2	no	—
248	#121	—	2	2	no	—
249	#121	—	2	2	no	—
250	#121	—	4	1	no	—
251	#121	—	4	2	no	—
252	#120	—	4	2	no	—
253	#117	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	SD₃₂	—	2	4	no	—
256	D₁₆	—	2	4	no	—
257	M₃₂	—	2	4	no	—
258	M₃₂	C₅×D₄	1	4	yes	complemented
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	2	4	no	—
261	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₁₆	C₂³×C₅	1	2	yes	—
264	#107	—	2	1	no	—
265	#107	C₂³×C₅	1	2	yes	—
266	#107	C₂³×C₅	1	1	yes	characteristic
267	#107	C₂³×C₅	1	1	yes	characteristic
268	#106	—	2	1	no	—
269	#103	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	—	8	2	no	—
280	C₂²×C₅	—	8	2	no	—
281	C₂²×C₅	—	8	1	no	—
282	C₂²×C₅	—	8	1	no	—
283	C₂²×C₅	—	8	2	no	—
284	C₂²×C₅	—	16	4	no	—
285	C₂²×C₅	#466	1	2	yes	—
286	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	8	2	no	—
289	C₄×C₅	—	8	1	no	—
290	C₄×C₅	—	8	1	no	—
291	C₄×C₅	—	8	1	no	—
292	C₄×C₅	#466	1	2	yes	—
293	C₄×C₅	C₂×#121	1	1	yes	characteristic
294	C₄×C₅	C₂×#135	1	1	yes	characteristic
295	C₂⁴	—	4	1	no	—
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	4	2	no	—
299	#41	—	4	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	C₅×D₈	1	2	yes	—
312	C₂×D₄	C₅×D₈	1	1	yes	characteristic
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	Q₁₆	—	2	1	no	—
318	Q₁₆	—	2	1	no	—
319	SD₁₆	—	4	2	no	—
320	D₈	—	2	1	no	—
321	D₈	—	2	2	no	—
322	D₈	—	2	2	no	—
323	D₈	—	2	1	no	—
324	D₈	—	4	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
330	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₈	C₅×#41	1	2	yes	—
333	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₄²	—	4	1	no	—
345	C₁₆	—	2	1	no	—
346	C₁₆	—	2	1	no	—
347	C₁₆	C₂×C₅×D₄	1	4	yes	—
348	C₂×C₅	—	2	2	no	—
349	C₂×C₅	—	4	2	no	—
350	C₂×C₅	—	16	1	no	—
351	C₂×C₅	—	16	2	no	—
352	C₂×C₅	C₂×#466	1	1	yes	characteristic
353	C₂×C₅	#3415	1	1	yes	characteristic
354	C₂×C₅	#3416	1	1	yes	characteristic
355	C₂³	—	4	1	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	2	no	—
358	C₂³	—	16	1	no	—
359	C₂³	—	16	1	no	—
360	C₂³	C₂×C₅×D₈	1	2	yes	—
361	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	1	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	8	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	16	2	no	—
374	D₄	—	16	2	no	—
375	D₄	—	16	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	16	1	no	—
384	C₂×C₄	C₅×#121	1	2	yes	—
385	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
386	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
387	C₂×C₄	C₅×#135	1	2	yes	—
388	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	C₅×#121	1	2	yes	—
391	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₈	C₂×C₅×#41	1	1	yes	characteristic
393	C₅	#33612	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	16	4	no	—
406	C₂²	C₅×#466	1	2	yes	—
407	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₅×#466	1	2	yes	—
414	C₄	C₂×C₅×#121	1	1	yes	characteristic
415	C₄	C₂×C₅×#135	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	16	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₅×#466	1	1	yes	characteristic
421	C₂	C₅×#3415	1	1	yes	characteristic
422	C₂	C₅×#3416	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×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×#509	C₂	semidirect
2. C₂×C₅×#504	C₂	semidirect
3. C₅×#3061	C₂	semidirect
4. C₅×#3058	C₂	semidirect
5. C₅×#2220	C₂	semidirect
6. C₅×#2218	C₂	semidirect
7. C₅×#2217	C₂	semidirect
8. C₅×#2215	C₂	semidirect
9. C₅×#2159	C₂	semidirect
10. C₅×#2138	C₂	semidirect
11. C₂×C₅×#357	C₂	semidirect
22. C₂×C₅×M₃₂	C₂²	semidirect
24. C₂²×C₅×C₁₆	C₂²	semidirect
27. C₅×#467	C₂²	semidirect
30. C₅×#466	C₂²	semidirect
35. C₅×#367	C₂²	semidirect
36. C₅×#366	C₂²	semidirect
37. C₅×#358	C₂²	semidirect
38. C₅×#358	C₂²	semidirect
41. C₅×#357	C₂²	semidirect
42. C₅×#357	C₂²	semidirect
43. #33612	C₅	direct (N × H)
77. C₅×M₃₂	D₄	semidirect
92. C₂×#509	C₂×C₅	semidirect
93. C₂×#504	C₂×C₅	semidirect
94. #3061	C₂×C₅	semidirect
95. #3058	C₂×C₅	semidirect
96. #2220	C₂×C₅	semidirect
97. #2218	C₂×C₅	semidirect
98. #2217	C₂×C₅	semidirect
99. #2215	C₂×C₅	semidirect
100. #2159	C₂×C₅	semidirect
101. #2138	C₂×C₅	semidirect
102. C₂×#357	C₂×C₅	semidirect
166. C₂×M₃₂	C₂²×C₅	semidirect
168. C₂²×C₁₆	C₂²×C₅	semidirect
171. #467	C₂²×C₅	semidirect
174. #466	C₂²×C₅	semidirect
179. #367	C₂²×C₅	semidirect
180. #366	C₂²×C₅	semidirect
181. #358	C₂²×C₅	semidirect
182. #358	C₂²×C₅	semidirect
185. #357	C₂²×C₅	semidirect
186. #357	C₂²×C₅	semidirect
258. M₃₂	C₅×D₄	semidirect
393. C₅	#33612	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×#509	2
C₂×C₅×#504	2
C₅×#3061	2
C₅×#3058	2
C₅×#2220	2
C₅×#2218	2
C₅×#2217	2
C₅×#2215	2
C₅×#2159	2
C₅×#2138	2
C₂×C₅×#357	2
#33612	5

Subgroups — C5×#33612 #11956332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33612 #11956332