Subgroups — C₅×#5607 #11755992

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#940	C₂	1	2	yes	maximal, complemented
5	C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#937	C₂	1	2	yes	maximal, complemented
7	C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#885	C₂	1	2	yes	maximal, complemented
11	C₅×#882	C₂	1	2	yes	maximal, complemented
12	C₅×#535	—	3	1	no	maximal, Hall
13	C₂³×C₅×D₃	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
16	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×#67	C₂²	1	2	yes	—
18	C₂×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂×C₅×#67	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×#67	C₂²	1	2	yes	complemented
21	C₂×C₅×#67	C₂²	1	2	yes	complemented
22	C₅×D₃×D₄	—	2	4	no	—
23	C₅×#235	—	2	4	no	—
24	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₁₂	C₂²	1	2	yes	complemented
27	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₅×#217	C₂²	1	2	yes	complemented
33	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
38	#5607	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#41	—	3	1	no	—
40	C₂²×C₅×D₄	—	3	1	no	—
41	C₅×#127	—	3	2	no	—
42	C₅×#124	—	3	2	no	—
43	C₅×#121	—	3	1	no	—
44	C₅×#121	—	3	1	no	—
45	C₅×#121	—	3	1	no	—
46	C₅×#121	D₃	1	1	yes	characteristic, complemented
47	C₅×#120	—	3	2	no	—
48	C₅×#120	—	3	2	no	—
49	C₅×#117	—	3	1	no	—
50	C₂³×C₃×C₅	C₂³	1	2	yes	—
51	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×D₃	—	2	4	no	—
53	C₂²×C₅×D₃	—	4	2	no	—
54	C₂²×C₅×D₃	—	4	2	no	—
55	C₂²×C₅×D₃	C₂³	1	2	yes	—
56	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
57	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₃×C₅×D₄	—	2	2	no	—
59	C₃×C₅×D₄	—	4	2	no	—
60	C₂×C₃×C₄×C₅	—	2	2	no	—
61	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₅×#67	—	2	2	no	—
65	C₅×#67	—	2	2	no	—
66	C₅×#67	—	2	4	no	—
67	C₅×#67	—	4	2	no	—
68	C₅×#67	—	4	2	no	—
69	C₂×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₅×D₁₂	—	2	2	no	—
73	C₅×D₁₂	—	2	2	no	—
74	C₅×D₁₂	—	4	2	no	—
75	C₄×C₅×D₃	—	2	2	no	—
76	C₄×C₅×D₃	D₄	1	4	yes	complemented
77	C₅×Dic₆	—	2	2	no	—
78	C₂×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#235	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
81	#940	C₂×C₅	1	2	yes	complemented
82	#938	C₂×C₅	1	1	yes	characteristic, complemented
83	#937	C₂×C₅	1	2	yes	complemented
84	#930	C₂×C₅	1	1	yes	characteristic, complemented
85	#895	C₂×C₅	1	1	yes	characteristic, complemented
86	#892	C₂×C₅	1	1	yes	characteristic, complemented
87	#885	C₂×C₅	1	2	yes	complemented
88	#882	C₂×C₅	1	2	yes	complemented
89	C₂⁴×C₅	—	3	2	no	—
90	C₅×#41	—	6	4	no	—
91	C₂×C₅×Q₈	—	3	1	no	—
92	C₂×C₅×D₄	—	3	1	no	—
93	C₂×C₅×D₄	—	3	2	no	—
94	C₂×C₅×D₄	—	3	1	no	—
95	C₂×C₅×D₄	—	3	2	no	—
96	C₂×C₅×D₄	—	3	2	no	—
97	C₂×C₅×D₄	—	3	1	no	—
98	C₂×C₅×D₄	—	3	1	no	—
99	C₂×C₅×D₄	—	3	2	no	—
100	C₂×C₅×D₄	—	6	4	no	—
101	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
102	C₂×C₅×D₄	C₂×D₃	1	2	yes	complemented
103	C₂²×C₄×C₅	—	3	1	no	—
104	C₂²×C₄×C₅	—	3	1	no	—
105	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
106	C₅×C₄⋊C₄	—	3	1	no	—
107	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
108	C₅×C₂²⋊C₄	—	3	2	no	—
109	C₅×C₂²⋊C₄	—	3	2	no	—
110	C₅×C₂²⋊C₄	—	3	2	no	—
111	C₅×C₂²⋊C₄	—	3	2	no	—
112	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
113	C₄²×C₅	—	3	2	no	—
114	#535	—	3	1	no	Sylow
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	—	2	2	no	—
117	C₂²×C₃×C₅	—	2	1	no	—
118	C₂²×C₃×C₅	—	2	2	no	—
119	C₂²×C₃×C₅	—	2	1	no	—
120	C₂²×C₃×C₅	—	2	2	no	—
121	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×D₃	—	2	1	no	—
123	C₂×C₅×D₃	—	2	1	no	—
124	C₂×C₅×D₃	—	2	1	no	—
125	C₂×C₅×D₃	—	2	2	no	—
126	C₂×C₅×D₃	—	2	1	no	—
127	C₂×C₅×D₃	—	2	2	no	—
128	C₂×C₅×D₃	—	2	1	no	—
129	C₂×C₅×D₃	—	2	2	no	—
130	C₂×C₅×D₃	—	4	8	no	—
131	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
132	C₃×C₄×C₅	—	2	1	no	—
133	C₃×C₄×C₅	—	2	2	no	—
134	C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₅×Dic₃	—	2	1	no	—
136	C₅×Dic₃	—	2	2	no	—
137	C₅×Dic₃	C₂×D₄	1	2	yes	—
138	C₂³×D₃	C₂²×C₅	1	2	yes	—
139	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
141	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
142	C₂×#67	C₂²×C₅	1	2	yes	—
143	C₂×#67	C₂²×C₅	1	1	yes	characteristic
144	C₂×#67	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₂×#67	C₂²×C₅	1	2	yes	complemented
146	C₂×#67	C₂²×C₅	1	2	yes	complemented
147	D₃×D₄	—	2	4	no	—
148	#235	—	2	4	no	—
149	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
150	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
151	C₂×D₁₂	C₂²×C₅	1	2	yes	complemented
152	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
154	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
156	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
157	#217	C₂²×C₅	1	2	yes	complemented
158	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
159	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
160	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
161	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
163	C₂³×C₅	—	3	1	no	—
164	C₂³×C₅	—	3	2	no	—
165	C₂³×C₅	—	3	1	no	—
166	C₂³×C₅	—	6	4	no	—
167	C₂³×C₅	—	12	2	no	—
168	C₂³×C₅	—	12	2	no	—
169	C₂³×C₅	C₂²×D₃	1	2	yes	—
170	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
171	C₅×Q₈	—	6	2	no	—
172	C₅×D₄	—	2	2	no	—
173	C₅×D₄	—	4	2	no	—
174	C₅×D₄	—	6	2	no	—
175	C₅×D₄	—	6	4	no	—
176	C₅×D₄	—	6	2	no	—
177	C₅×D₄	—	6	2	no	—
178	C₅×D₄	—	6	2	no	—
179	C₅×D₄	—	12	2	no	—
180	C₅×D₄	—	12	2	no	—
181	C₅×D₄	—	12	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	3	1	no	—
184	C₂×C₄×C₅	—	3	4	no	—
185	C₂×C₄×C₅	—	3	2	no	—
186	C₂×C₄×C₅	—	3	1	no	—
187	C₂×C₄×C₅	—	6	2	no	—
188	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
189	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
191	C₂×#41	—	3	1	no	—
192	C₂²×D₄	—	3	1	no	—
193	#127	—	3	2	no	—
194	#124	—	3	2	no	—
195	#121	—	3	1	no	—
196	#121	—	3	1	no	—
197	#121	—	3	1	no	—
198	#121	C₅×D₃	1	1	yes	characteristic, complemented
199	#120	—	3	2	no	—
200	#120	—	3	2	no	—
201	#117	—	3	1	no	—
202	C₂×C₃×C₅	—	4	2	no	—
203	C₂×C₃×C₅	—	4	1	no	—
204	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
207	C₅×D₃	—	2	2	no	—
208	C₅×D₃	—	4	1	no	—
209	C₅×D₃	—	4	2	no	—
210	C₂³×C₃	C₂³×C₅	1	2	yes	—
211	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
212	C₂²×D₃	—	2	4	no	—
213	C₂²×D₃	—	4	2	no	—
214	C₂²×D₃	—	4	2	no	—
215	C₂²×D₃	C₂³×C₅	1	2	yes	—
216	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
217	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
218	C₃×D₄	—	2	2	no	—
219	C₃×D₄	—	4	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	#67	—	2	2	no	—
225	#67	—	2	2	no	—
226	#67	—	2	4	no	—
227	#67	—	4	2	no	—
228	#67	—	4	2	no	—
229	C₂×Dic₃	C₂³×C₅	1	2	yes	—
230	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
231	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
232	D₁₂	—	2	2	no	—
233	D₁₂	—	2	2	no	—
234	D₁₂	—	4	2	no	—
235	C₄×D₃	—	2	2	no	—
236	C₄×D₃	C₅×D₄	1	4	yes	complemented
237	Dic₆	—	2	2	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	3	2	no	—
245	C₂²×C₅	—	6	1	no	—
246	C₂²×C₅	—	6	1	no	—
247	C₂²×C₅	—	6	1	no	—
248	C₂²×C₅	—	6	2	no	—
249	C₂²×C₅	—	6	1	no	—
250	C₂²×C₅	—	6	2	no	—
251	C₂²×C₅	—	6	1	no	—
252	C₂²×C₅	—	6	2	no	—
253	C₂²×C₅	—	12	8	no	—
254	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	3	2	no	—
258	C₄×C₅	—	6	1	no	—
259	C₄×C₅	—	6	2	no	—
260	C₄×C₅	D₃×D₄	1	2	yes	—
261	C₂⁴	—	3	2	no	—
262	#41	—	6	4	no	—
263	C₂×Q₈	—	3	1	no	—
264	C₂×D₄	—	3	1	no	—
265	C₂×D₄	—	3	2	no	—
266	C₂×D₄	—	3	1	no	—
267	C₂×D₄	—	3	2	no	—
268	C₂×D₄	—	3	2	no	—
269	C₂×D₄	—	3	1	no	—
270	C₂×D₄	—	3	1	no	—
271	C₂×D₄	—	3	2	no	—
272	C₂×D₄	—	6	4	no	—
273	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
274	C₂×D₄	C₂×C₅×D₃	1	2	yes	complemented
275	C₂²×C₄	—	3	1	no	—
276	C₂²×C₄	—	3	1	no	—
277	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
278	C₄⋊C₄	—	3	1	no	—
279	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
280	C₂²⋊C₄	—	3	2	no	—
281	C₂²⋊C₄	—	3	2	no	—
282	C₂²⋊C₄	—	3	2	no	—
283	C₂²⋊C₄	—	3	2	no	—
284	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
285	C₄²	—	3	2	no	—
286	C₃×C₅	#535	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	2	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
294	C₂×D₃	—	2	1	no	—
295	C₂×D₃	—	2	1	no	—
296	C₂×D₃	—	2	1	no	—
297	C₂×D₃	—	2	2	no	—
298	C₂×D₃	—	2	1	no	—
299	C₂×D₃	—	2	2	no	—
300	C₂×D₃	—	2	1	no	—
301	C₂×D₃	—	2	2	no	—
302	C₂×D₃	—	4	8	no	—
303	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	C₂×C₅×D₄	1	2	yes	—
307	Dic₃	—	2	1	no	—
308	Dic₃	—	2	2	no	—
309	Dic₃	C₂×C₅×D₄	1	2	yes	—
310	C₂×C₅	—	4	2	no	—
311	C₂×C₅	—	4	1	no	—
312	C₂×C₅	—	6	2	no	—
313	C₂×C₅	—	12	2	no	—
314	C₂×C₅	—	12	1	no	—
315	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
316	C₂×C₅	#1004	1	1	yes	characteristic
317	C₂×C₅	#1009	1	1	yes	characteristic
318	C₂³	—	3	1	no	—
319	C₂³	—	3	2	no	—
320	C₂³	—	3	1	no	—
321	C₂³	—	6	4	no	—
322	C₂³	—	12	2	no	—
323	C₂³	—	12	2	no	—
324	C₂³	C₂²×C₅×D₃	1	2	yes	—
325	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
326	Q₈	—	6	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	6	2	no	—
330	D₄	—	6	4	no	—
331	D₄	—	6	2	no	—
332	D₄	—	6	2	no	—
333	D₄	—	6	2	no	—
334	D₄	—	12	2	no	—
335	D₄	—	12	2	no	—
336	D₄	—	12	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	3	1	no	—
339	C₂×C₄	—	3	4	no	—
340	C₂×C₄	—	3	2	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
344	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₂×C₃	—	4	2	no	—
347	C₂×C₃	—	4	1	no	—
348	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
349	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
351	D₃	—	2	2	no	—
352	D₃	—	4	2	no	—
353	D₃	—	4	1	no	—
354	C₅	#5607	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	1	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	3	2	no	—
362	C₂²	—	6	1	no	—
363	C₂²	—	6	1	no	—
364	C₂²	—	6	1	no	—
365	C₂²	—	6	2	no	—
366	C₂²	—	6	1	no	—
367	C₂²	—	6	2	no	—
368	C₂²	—	6	1	no	—
369	C₂²	—	6	2	no	—
370	C₂²	—	12	8	no	—
371	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	3	2	no	—
375	C₄	—	6	1	no	—
376	C₄	—	6	2	no	—
377	C₄	C₅×D₃×D₄	1	2	yes	—
378	C₃	C₅×#535	1	1	yes	characteristic, complemented, Sylow
379	C₂	—	4	2	no	—
380	C₂	—	4	1	no	—
381	C₂	—	6	2	no	—
382	C₂	—	12	2	no	—
383	C₂	—	12	1	no	—
384	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
385	C₂	C₅×#1004	1	1	yes	characteristic
386	C₂	C₅×#1009	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×#121	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#121	D₃
hypocenter	C₃	C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×D₄	C₂	semidirect
2. C₂×C₅×#235	C₂	semidirect
3. C₃×C₅×#121	C₂	semidirect
4. C₅×#940	C₂	semidirect
5. C₅×#938	C₂	semidirect
6. C₅×#937	C₂	semidirect
7. C₅×#930	C₂	semidirect
8. C₅×#895	C₂	semidirect
9. C₅×#892	C₂	semidirect
10. C₅×#885	C₂	semidirect
11. C₅×#882	C₂	semidirect
15. C₂×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₃×C₄×C₅	C₂²	semidirect
19. C₂×C₅×#67	C₂²	semidirect
20. C₂×C₅×#67	C₂²	semidirect
21. C₂×C₅×#67	C₂²	semidirect
26. C₂×C₅×D₁₂	C₂²	semidirect
28. C₂×C₄×C₅×D₃	C₂²	semidirect
29. C₂×C₅×Dic₆	C₂²	semidirect
30. C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
32. C₅×#217	C₂²	semidirect
34. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₅×C₄⋊Dic₃	C₂²	semidirect
37. C₄×C₅×Dic₃	C₂²	semidirect
38. #5607	C₅	direct (N × H)
46. C₅×#121	D₃	semidirect
76. C₄×C₅×D₃	D₄	semidirect
78. C₂×D₃×D₄	C₂×C₅	semidirect
79. C₂×#235	C₂×C₅	semidirect
80. C₃×#121	C₂×C₅	semidirect
81. #940	C₂×C₅	semidirect
82. #938	C₂×C₅	semidirect
83. #937	C₂×C₅	semidirect
84. #930	C₂×C₅	semidirect
85. #895	C₂×C₅	semidirect
86. #892	C₂×C₅	semidirect
87. #885	C₂×C₅	semidirect
88. #882	C₂×C₅	semidirect
102. C₂×C₅×D₄	C₂×D₃	semidirect
105. C₂²×C₄×C₅	C₂×D₃	semidirect
107. C₅×C₄⋊C₄	C₂×D₃	semidirect
112. C₅×C₂²⋊C₄	C₂×D₃	semidirect
140. C₂×C₃×D₄	C₂²×C₅	semidirect
141. C₂²×C₃×C₄	C₂²×C₅	semidirect
144. C₂×#67	C₂²×C₅	semidirect
145. C₂×#67	C₂²×C₅	semidirect
146. C₂×#67	C₂²×C₅	semidirect
151. C₂×D₁₂	C₂²×C₅	semidirect
153. C₂×C₄×D₃	C₂²×C₅	semidirect
154. C₂×Dic₆	C₂²×C₅	semidirect
155. C₃×C₄⋊C₄	C₂²×C₅	semidirect
156. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
157. #217	C₂²×C₅	semidirect
159. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
160. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
161. C₄⋊Dic₃	C₂²×C₅	semidirect
162. C₄×Dic₃	C₂²×C₅	semidirect
198. #121	C₅×D₃	semidirect
236. C₄×D₃	C₅×D₄	semidirect
274. C₂×D₄	C₂×C₅×D₃	semidirect
277. C₂²×C₄	C₂×C₅×D₃	semidirect
279. C₄⋊C₄	C₂×C₅×D₃	semidirect
284. C₂²⋊C₄	C₂×C₅×D₃	semidirect
286. C₃×C₅	#535	semidirect
354. C₅	#5607	direct (N × H)
378. C₃	C₅×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₄	2
C₂×C₅×#235	2
C₃×C₅×#121	2
C₅×#940	2
C₅×#938	2
C₅×#937	2
C₅×#930	2
C₅×#895	2
C₅×#892	2
C₅×#885	2
C₅×#882	2
C₅×#535	3
#5607	5

Subgroups — C5×#5607 #11755992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5607 #11755992