Subgroups — C₅×#5590 #11755975

Order 960.

856 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#67	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#939	C₂	1	2	yes	maximal, complemented
6	C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#884	C₂	1	2	yes	maximal, complemented
8	C₅×#882	C₂	1	2	yes	maximal, complemented
9	C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×D₄²	—	3	1	no	maximal, Hall
11	C₂⁴×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
12	C₂³×C₅×D₃	C₂²	1	2	yes	complemented
13	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₅×#67	—	2	8	no	—
17	C₂×C₅×#67	C₂²	1	2	yes	—
18	C₂×C₅×#67	C₂²	1	2	yes	complemented
19	C₂×C₅×#67	C₂²	1	2	yes	complemented
20	C₂×C₅×#67	C₂²	1	2	yes	complemented
21	C₂×C₅×#67	C₂²	1	2	yes	complemented
22	C₂²×C₅×Dic₃	C₂²	1	2	yes	complemented
23	C₅×D₃×D₄	—	2	8	no	—
24	C₂×C₅×D₁₂	C₂²	1	2	yes	complemented
25	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₅×#217	C₂²	1	1	yes	characteristic, complemented
30	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
31	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
32	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
33	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
34	#5590	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₅×D₄	—	3	2	no	—
36	C₂²×C₅×D₄	—	3	2	no	—
37	C₅×#127	—	3	1	no	—
38	C₅×#121	—	3	2	no	—
39	C₅×#121	—	3	2	no	—
40	C₅×#120	—	3	1	no	—
41	C₅×#120	—	3	2	no	—
42	C₅×#120	D₃	1	1	yes	characteristic, complemented
43	C₄×C₅×D₄	—	3	2	no	—
44	C₂³×C₃×C₅	—	2	4	no	—
45	C₂³×C₃×C₅	—	4	1	no	—
46	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
48	C₂³×C₃×C₅	C₂³	1	2	yes	—
49	C₂²×C₅×D₃	—	2	4	no	—
50	C₂²×C₅×D₃	—	2	4	no	—
51	C₂²×C₅×D₃	—	2	4	no	—
52	C₂²×C₅×D₃	—	4	1	no	—
53	C₂²×C₅×D₃	—	4	2	no	—
54	C₂²×C₅×D₃	C₂³	1	2	yes	—
55	C₂²×C₅×D₃	C₂³	1	2	yes	—
56	C₃×C₅×D₄	—	2	4	no	—
57	C₃×C₅×D₄	—	4	1	no	—
58	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₅×#67	—	2	4	no	—
61	C₅×#67	—	2	4	no	—
62	C₅×#67	—	2	4	no	—
63	C₅×#67	—	2	4	no	—
64	C₅×#67	D₄	1	8	yes	complemented
65	C₂×C₅×Dic₃	—	2	4	no	—
66	C₂×C₅×Dic₃	C₂³	1	2	yes	—
67	C₂×C₅×Dic₃	C₂³	1	2	yes	—
68	C₅×D₁₂	—	2	4	no	—
69	C₅×D₁₂	—	4	1	no	—
70	C₄×C₅×D₃	—	2	4	no	—
71	C₂²×#67	C₂×C₅	1	2	yes	complemented
72	C₂×D₃×D₄	C₂×C₅	1	2	yes	complemented
73	C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
74	#940	C₂×C₅	1	1	yes	characteristic, complemented
75	#939	C₂×C₅	1	2	yes	complemented
76	#937	C₂×C₅	1	1	yes	characteristic, complemented
77	#884	C₂×C₅	1	2	yes	complemented
78	#882	C₂×C₅	1	2	yes	complemented
79	#67⋊C₄	C₂×C₅	1	2	yes	complemented
80	C₂⁴×C₅	—	3	1	no	—
81	C₂⁴×C₅	—	3	2	no	—
82	C₂⁴×C₅	C₂×D₃	1	1	yes	characteristic, complemented
83	C₂×C₅×D₄	—	3	2	no	—
84	C₂×C₅×D₄	—	3	2	no	—
85	C₂×C₅×D₄	—	3	2	no	—
86	C₂×C₅×D₄	—	3	2	no	—
87	C₂×C₅×D₄	—	3	2	no	—
88	C₂×C₅×D₄	—	3	2	no	—
89	C₂×C₅×D₄	—	3	1	no	—
90	C₂×C₅×D₄	—	6	8	no	—
91	C₂×C₅×D₄	—	6	8	no	—
92	C₂×C₅×D₄	C₂×D₃	1	2	yes	complemented
93	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
94	C₂²×C₄×C₅	—	3	2	no	—
95	C₂²×C₄×C₅	—	3	2	no	—
96	C₅×C₄⋊C₄	—	3	2	no	—
97	C₅×C₂²⋊C₄	—	3	1	no	—
98	C₅×C₂²⋊C₄	—	3	2	no	—
99	C₅×C₂²⋊C₄	—	3	2	no	—
100	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
101	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
102	C₄²×C₅	—	3	1	no	—
103	D₄²	—	3	1	no	Sylow
104	C₂²×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	—	2	2	no	—
107	C₂²×C₃×C₅	—	2	2	no	—
108	C₂²×C₃×C₅	—	2	1	no	—
109	C₂²×C₃×C₅	—	2	1	no	—
110	C₂²×C₃×C₅	—	4	4	no	—
111	C₂²×C₃×C₅	C₂×D₄	1	4	yes	complemented
112	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×C₅×D₃	—	2	2	no	—
114	C₂×C₅×D₃	—	2	2	no	—
115	C₂×C₅×D₃	—	2	2	no	—
116	C₂×C₅×D₃	—	2	2	no	—
117	C₂×C₅×D₃	—	2	2	no	—
118	C₂×C₅×D₃	—	4	4	no	—
119	C₂×C₅×D₃	—	4	8	no	—
120	C₂×C₅×D₃	C₂×D₄	1	4	yes	complemented
121	C₃×C₄×C₅	—	2	2	no	—
122	C₃×C₄×C₅	—	2	1	no	—
123	C₅×Dic₃	—	2	2	no	—
124	C₅×Dic₃	C₂×D₄	1	4	yes	complemented
125	C₂⁴×C₃	C₂²×C₅	1	1	yes	characteristic, complemented
126	C₂³×D₃	C₂²×C₅	1	2	yes	complemented
127	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
128	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
129	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₂×#67	—	2	8	no	—
131	C₂×#67	C₂²×C₅	1	2	yes	—
132	C₂×#67	C₂²×C₅	1	2	yes	complemented
133	C₂×#67	C₂²×C₅	1	2	yes	complemented
134	C₂×#67	C₂²×C₅	1	2	yes	complemented
135	C₂×#67	C₂²×C₅	1	2	yes	complemented
136	C₂²×Dic₃	C₂²×C₅	1	2	yes	complemented
137	D₃×D₄	—	2	8	no	—
138	C₂×D₁₂	C₂²×C₅	1	2	yes	complemented
139	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
141	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
142	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
143	#217	C₂²×C₅	1	1	yes	characteristic, complemented
144	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
145	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
146	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
147	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₂³×C₅	—	2	4	no	—
149	C₂³×C₅	—	3	2	no	—
150	C₂³×C₅	—	3	2	no	—
151	C₂³×C₅	—	4	1	no	—
152	C₂³×C₅	—	6	4	no	—
153	C₂³×C₅	—	6	4	no	—
154	C₂³×C₅	—	6	4	no	—
155	C₂³×C₅	—	12	2	no	—
156	C₂³×C₅	—	12	1	no	—
157	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₂³×C₅	C₂²×D₃	1	2	yes	—
160	C₅×D₄	—	2	4	no	—
161	C₅×D₄	—	3	8	no	—
162	C₅×D₄	—	4	1	no	—
163	C₅×D₄	—	6	4	no	—
164	C₅×D₄	—	6	4	no	—
165	C₅×D₄	—	6	4	no	—
166	C₅×D₄	—	6	4	no	—
167	C₅×D₄	—	6	4	no	—
168	C₅×D₄	—	12	1	no	—
169	C₂×C₄×C₅	—	3	2	no	—
170	C₂×C₄×C₅	—	3	2	no	—
171	C₂×C₄×C₅	—	6	4	no	—
172	C₂×C₄×C₅	—	6	4	no	—
173	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
175	C₂²×D₄	—	3	2	no	—
176	C₂²×D₄	—	3	2	no	—
177	#127	—	3	1	no	—
178	#121	—	3	2	no	—
179	#121	—	3	2	no	—
180	#120	—	3	1	no	—
181	#120	—	3	2	no	—
182	#120	C₅×D₃	1	1	yes	characteristic, complemented
183	C₄×D₄	—	3	2	no	—
184	C₂×C₃×C₅	—	2	4	no	—
185	C₂×C₃×C₅	—	4	1	no	—
186	C₂×C₃×C₅	—	4	1	no	—
187	C₂×C₃×C₅	C₂²×D₄	1	2	yes	—
188	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
189	C₅×D₃	—	2	4	no	—
190	C₅×D₃	—	4	2	no	—
191	C₂³×C₃	—	2	4	no	—
192	C₂³×C₃	—	4	1	no	—
193	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
194	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
195	C₂³×C₃	C₂³×C₅	1	2	yes	—
196	C₂²×D₃	—	2	4	no	—
197	C₂²×D₃	—	2	4	no	—
198	C₂²×D₃	—	2	4	no	—
199	C₂²×D₃	—	4	1	no	—
200	C₂²×D₃	—	4	2	no	—
201	C₂²×D₃	C₂³×C₅	1	2	yes	—
202	C₂²×D₃	C₂³×C₅	1	2	yes	—
203	C₃×D₄	—	2	4	no	—
204	C₃×D₄	—	4	1	no	—
205	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
207	#67	—	2	4	no	—
208	#67	—	2	4	no	—
209	#67	—	2	4	no	—
210	#67	—	2	4	no	—
211	#67	C₅×D₄	1	8	yes	complemented
212	C₂×Dic₃	—	2	4	no	—
213	C₂×Dic₃	C₂³×C₅	1	2	yes	—
214	C₂×Dic₃	C₂³×C₅	1	2	yes	—
215	D₁₂	—	2	4	no	—
216	D₁₂	—	4	1	no	—
217	C₄×D₃	—	2	4	no	—
218	C₂²×C₅	—	2	2	no	—
219	C₂²×C₅	—	2	2	no	—
220	C₂²×C₅	—	2	2	no	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	3	4	no	—
225	C₂²×C₅	—	4	4	no	—
226	C₂²×C₅	—	6	2	no	—
227	C₂²×C₅	—	6	2	no	—
228	C₂²×C₅	—	6	2	no	—
229	C₂²×C₅	—	6	2	no	—
230	C₂²×C₅	—	6	2	no	—
231	C₂²×C₅	—	12	8	no	—
232	C₂²×C₅	—	12	4	no	—
233	C₂²×C₅	D₃×D₄	1	4	yes	complemented
234	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
235	C₄×C₅	—	2	2	no	—
236	C₄×C₅	—	2	1	no	—
237	C₄×C₅	—	3	4	no	—
238	C₄×C₅	—	6	2	no	—
239	C₂⁴	—	3	1	no	—
240	C₂⁴	—	3	2	no	—
241	C₂⁴	C₂×C₅×D₃	1	1	yes	characteristic, complemented
242	C₂×D₄	—	3	2	no	—
243	C₂×D₄	—	3	2	no	—
244	C₂×D₄	—	3	2	no	—
245	C₂×D₄	—	3	2	no	—
246	C₂×D₄	—	3	2	no	—
247	C₂×D₄	—	3	2	no	—
248	C₂×D₄	—	3	1	no	—
249	C₂×D₄	—	6	8	no	—
250	C₂×D₄	—	6	8	no	—
251	C₂×D₄	C₂×C₅×D₃	1	2	yes	complemented
252	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
253	C₂²×C₄	—	3	2	no	—
254	C₂²×C₄	—	3	2	no	—
255	C₄⋊C₄	—	3	2	no	—
256	C₂²⋊C₄	—	3	1	no	—
257	C₂²⋊C₄	—	3	2	no	—
258	C₂²⋊C₄	—	3	2	no	—
259	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
260	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
261	C₄²	—	3	1	no	—
262	C₃×C₅	D₄²	1	1	yes	characteristic, complemented, Hall
263	C₂²×C₃	—	2	2	no	—
264	C₂²×C₃	—	2	2	no	—
265	C₂²×C₃	—	2	2	no	—
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	4	4	no	—
270	C₂²×C₃	C₂×C₅×D₄	1	4	yes	complemented
271	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
272	C₂×D₃	—	2	2	no	—
273	C₂×D₃	—	2	2	no	—
274	C₂×D₃	—	2	2	no	—
275	C₂×D₃	—	2	2	no	—
276	C₂×D₃	—	2	2	no	—
277	C₂×D₃	—	4	4	no	—
278	C₂×D₃	—	4	8	no	—
279	C₂×D₃	C₂×C₅×D₄	1	4	yes	complemented
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	2	1	no	—
282	Dic₃	—	2	2	no	—
283	Dic₃	C₂×C₅×D₄	1	4	yes	complemented
284	C₂×C₅	—	2	4	no	—
285	C₂×C₅	—	4	1	no	—
286	C₂×C₅	—	4	1	no	—
287	C₂×C₅	—	6	4	no	—
288	C₂×C₅	—	12	2	no	—
289	C₂×C₅	C₂×D₃×D₄	1	2	yes	—
290	C₂×C₅	#1004	1	1	yes	characteristic
291	C₂³	—	2	4	no	—
292	C₂³	—	3	2	no	—
293	C₂³	—	3	2	no	—
294	C₂³	—	4	1	no	—
295	C₂³	—	6	4	no	—
296	C₂³	—	6	4	no	—
297	C₂³	—	6	4	no	—
298	C₂³	—	12	2	no	—
299	C₂³	—	12	1	no	—
300	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₂³	C₂²×C₅×D₃	1	2	yes	—
303	D₄	—	2	4	no	—
304	D₄	—	3	8	no	—
305	D₄	—	4	1	no	—
306	D₄	—	6	4	no	—
307	D₄	—	6	4	no	—
308	D₄	—	6	4	no	—
309	D₄	—	6	4	no	—
310	D₄	—	6	4	no	—
311	D₄	—	12	1	no	—
312	C₂×C₄	—	3	2	no	—
313	C₂×C₄	—	3	2	no	—
314	C₂×C₄	—	6	4	no	—
315	C₂×C₄	—	6	4	no	—
316	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
318	C₂×C₃	—	2	4	no	—
319	C₂×C₃	—	4	1	no	—
320	C₂×C₃	—	4	1	no	—
321	C₂×C₃	C₂²×C₅×D₄	1	2	yes	—
322	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
323	D₃	—	2	4	no	—
324	D₃	—	4	2	no	—
325	C₅	#5590	1	1	yes	characteristic, direct product factor, Sylow
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	3	4	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	6	2	no	—
335	C₂²	—	6	2	no	—
336	C₂²	—	6	2	no	—
337	C₂²	—	6	2	no	—
338	C₂²	—	6	2	no	—
339	C₂²	—	12	8	no	—
340	C₂²	—	12	4	no	—
341	C₂²	C₅×D₃×D₄	1	4	yes	complemented
342	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	2	1	no	—
345	C₄	—	3	4	no	—
346	C₄	—	6	2	no	—
347	C₃	C₅×D₄²	1	1	yes	characteristic, complemented, Sylow
348	C₂	—	2	4	no	—
349	C₂	—	4	1	no	—
350	C₂	—	4	1	no	—
351	C₂	—	6	4	no	—
352	C₂	—	12	2	no	—
353	C₂	C₂×C₅×D₃×D₄	1	2	yes	—
354	C₂	C₅×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×#120	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#120	D₃
hypocenter	C₃	C₅×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#67	C₂	semidirect
2. C₂×C₅×D₃×D₄	C₂	semidirect
3. C₃×C₅×#120	C₂	semidirect
4. C₅×#940	C₂	semidirect
5. C₅×#939	C₂	semidirect
6. C₅×#937	C₂	semidirect
7. C₅×#884	C₂	semidirect
8. C₅×#882	C₂	semidirect
9. C₅×#67⋊C₄	C₂	semidirect
11. C₂⁴×C₃×C₅	C₂²	semidirect
12. C₂³×C₅×D₃	C₂²	semidirect
13. C₂³×C₅×D₃	C₂²	semidirect
14. C₂×C₃×C₅×D₄	C₂²	semidirect
15. C₂×C₃×C₅×D₄	C₂²	semidirect
18. C₂×C₅×#67	C₂²	semidirect
19. C₂×C₅×#67	C₂²	semidirect
20. C₂×C₅×#67	C₂²	semidirect
21. C₂×C₅×#67	C₂²	semidirect
22. C₂²×C₅×Dic₃	C₂²	semidirect
24. C₂×C₅×D₁₂	C₂²	semidirect
25. C₂×C₅×D₁₂	C₂²	semidirect
26. C₂×C₄×C₅×D₃	C₂²	semidirect
27. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₅×#217	C₂²	semidirect
30. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
31. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₅×Dic₃⋊C₄	C₂²	semidirect
33. C₄×C₅×Dic₃	C₂²	semidirect
34. #5590	C₅	direct (N × H)
42. C₅×#120	D₃	semidirect
64. C₅×#67	D₄	semidirect
71. C₂²×#67	C₂×C₅	semidirect
72. C₂×D₃×D₄	C₂×C₅	semidirect
73. C₃×#120	C₂×C₅	semidirect
74. #940	C₂×C₅	semidirect
75. #939	C₂×C₅	semidirect
76. #937	C₂×C₅	semidirect
77. #884	C₂×C₅	semidirect
78. #882	C₂×C₅	semidirect
79. #67⋊C₄	C₂×C₅	semidirect
82. C₂⁴×C₅	C₂×D₃	semidirect
92. C₂×C₅×D₄	C₂×D₃	semidirect
93. C₂×C₅×D₄	C₂×D₃	semidirect
100. C₅×C₂²⋊C₄	C₂×D₃	semidirect
101. C₅×C₂²⋊C₄	C₂×D₃	semidirect
111. C₂²×C₃×C₅	C₂×D₄	semidirect
120. C₂×C₅×D₃	C₂×D₄	semidirect
124. C₅×Dic₃	C₂×D₄	semidirect
125. C₂⁴×C₃	C₂²×C₅	semidirect
126. C₂³×D₃	C₂²×C₅	semidirect
127. C₂³×D₃	C₂²×C₅	semidirect
128. C₂×C₃×D₄	C₂²×C₅	semidirect
129. C₂×C₃×D₄	C₂²×C₅	semidirect
132. C₂×#67	C₂²×C₅	semidirect
133. C₂×#67	C₂²×C₅	semidirect
134. C₂×#67	C₂²×C₅	semidirect
135. C₂×#67	C₂²×C₅	semidirect
136. C₂²×Dic₃	C₂²×C₅	semidirect
138. C₂×D₁₂	C₂²×C₅	semidirect
139. C₂×D₁₂	C₂²×C₅	semidirect
140. C₂×C₄×D₃	C₂²×C₅	semidirect
141. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
142. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
143. #217	C₂²×C₅	semidirect
144. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
145. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
146. Dic₃⋊C₄	C₂²×C₅	semidirect
147. C₄×Dic₃	C₂²×C₅	semidirect
182. #120	C₅×D₃	semidirect
211. #67	C₅×D₄	semidirect
233. C₂²×C₅	D₃×D₄	semidirect
241. C₂⁴	C₂×C₅×D₃	semidirect
251. C₂×D₄	C₂×C₅×D₃	semidirect
252. C₂×D₄	C₂×C₅×D₃	semidirect
259. C₂²⋊C₄	C₂×C₅×D₃	semidirect
260. C₂²⋊C₄	C₂×C₅×D₃	semidirect
262. C₃×C₅	D₄²	semidirect
270. C₂²×C₃	C₂×C₅×D₄	semidirect
279. C₂×D₃	C₂×C₅×D₄	semidirect
283. Dic₃	C₂×C₅×D₄	semidirect
325. C₅	#5590	direct (N × H)
341. C₂²	C₅×D₃×D₄	semidirect
347. C₃	C₅×D₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#67	2
C₂×C₅×D₃×D₄	2
C₃×C₅×#120	2
C₅×#940	2
C₅×#939	2
C₅×#937	2
C₅×#884	2
C₅×#882	2
C₅×#67⋊C₄	2
C₅×D₄²	3
#5590	5

Subgroups — C5×#5590 #11755975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5590 #11755975