Subgroups — C₅×#5829 #11756214

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#939	C₂	1	2	yes	maximal, complemented
6	C₅×#937	C₂	1	2	yes	maximal, complemented
7	C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#929	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₅×#546	—	3	1	no	maximal, Hall
13	C₂³×C₅×D₃	C₂²	1	2	yes	—
14	C₃×C₅×#41	—	2	4	no	—
15	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂×C₅×#67	C₂²	1	2	yes	—
22	C₂×C₅×#67	C₂²	1	2	yes	complemented
23	C₂²×C₅×Dic₃	C₂²	1	2	yes	complemented
24	C₅×D₃×D₄	—	2	4	no	—
25	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₅×#217	C₂²	1	1	yes	characteristic, complemented
28	C₅×#217	C₂²	1	2	yes	complemented
29	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
32	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
33	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	#5829	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#41	D₃	1	1	yes	characteristic, complemented
40	C₂²×C₅×D₄	—	3	1	no	—
41	C₅×#124	—	3	1	no	—
42	C₅×#123	—	3	2	no	—
43	C₅×C₂²⋊Q₈	—	3	1	no	—
44	C₅×#121	—	3	2	no	—
45	C₅×#121	—	3	1	no	—
46	C₅×#120	—	3	2	no	—
47	C₄×C₅×D₄	—	3	1	no	—
48	C₄×C₅×D₄	—	3	1	no	—
49	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₅	C₂³	1	2	yes	—
52	C₂²×C₅×D₃	—	2	4	no	—
53	C₂²×C₅×D₃	—	2	4	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	C₃×C₅×Q₈	—	2	2	no	—
58	C₃×C₅×D₄	—	2	4	no	—
59	C₃×C₅×D₄	D₄	1	4	yes	complemented
60	C₂×C₃×C₄×C₅	—	2	4	no	—
61	C₂×C₃×C₄×C₅	—	2	2	no	—
62	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₅×#67	—	2	4	no	—
66	C₅×#67	—	2	2	no	—
67	C₅×#67	—	4	2	no	—
68	C₂×C₅×Dic₃	—	4	2	no	—
69	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₅×Dic₃	C₂³	1	2	yes	—
73	C₅×D₁₂	—	2	2	no	—
74	C₄×C₅×D₃	—	2	2	no	—
75	C₂×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
77	#947	C₂×C₅	1	1	yes	characteristic, complemented
78	#946	C₂×C₅	1	1	yes	characteristic, complemented
79	#939	C₂×C₅	1	2	yes	complemented
80	#937	C₂×C₅	1	2	yes	complemented
81	D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
82	#930	C₂×C₅	1	1	yes	characteristic, complemented
83	#929	C₂×C₅	1	2	yes	complemented
84	C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
86	C₂⁴×C₅	—	3	2	no	—
87	C₅×#41	—	2	4	no	—
88	C₂×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
89	C₂×C₅×D₄	—	3	1	no	—
90	C₂×C₅×D₄	—	3	2	no	—
91	C₂×C₅×D₄	—	3	2	no	—
92	C₂×C₅×D₄	—	3	1	no	—
93	C₂×C₅×D₄	—	6	4	no	—
94	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
95	C₂×C₅×D₄	C₂×D₃	1	2	yes	complemented
96	C₂²×C₄×C₅	—	3	2	no	—
97	C₂²×C₄×C₅	—	3	1	no	—
98	C₂²×C₄×C₅	C₂×D₃	1	2	yes	complemented
99	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
100	C₅×C₄⋊C₄	—	3	1	no	—
101	C₅×C₄⋊C₄	—	3	1	no	—
102	C₅×C₄⋊C₄	—	3	2	no	—
103	C₅×C₂²⋊C₄	—	3	2	no	—
104	C₅×C₂²⋊C₄	—	3	1	no	—
105	C₅×C₂²⋊C₄	—	3	1	no	—
106	C₅×C₂²⋊C₄	—	3	2	no	—
107	C₅×C₂²⋊C₄	—	3	2	no	—
108	C₅×C₂²⋊C₄	—	3	2	no	—
109	C₅×C₂²⋊C₄	—	3	2	no	—
110	C₄²×C₅	—	3	1	no	—
111	#546	—	3	1	no	Sylow
112	C₂²×C₃×C₅	—	2	2	no	—
113	C₂²×C₃×C₅	—	2	2	no	—
114	C₂²×C₃×C₅	—	2	1	no	—
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	C₂×D₄	1	4	yes	—
118	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×D₃	—	2	1	no	—
120	C₂×C₅×D₃	—	2	1	no	—
121	C₂×C₅×D₃	—	2	2	no	—
122	C₂×C₅×D₃	—	2	2	no	—
123	C₂×C₅×D₃	—	2	2	no	—
124	C₂×C₅×D₃	—	4	8	no	—
125	C₂×C₅×D₃	#41	1	2	yes	complemented
126	C₃×C₄×C₅	—	2	1	no	—
127	C₃×C₄×C₅	—	2	2	no	—
128	C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₅×Dic₃	—	2	1	no	—
130	C₅×Dic₃	—	2	1	no	—
131	C₅×Dic₃	—	2	1	no	—
132	C₅×Dic₃	—	2	2	no	—
133	C₂³×D₃	C₂²×C₅	1	2	yes	—
134	C₃×#41	—	2	4	no	—
135	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₃×D₄	C₂²×C₅	1	2	yes	complemented
138	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	complemented
139	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₂×#67	C₂²×C₅	1	1	yes	characteristic
141	C₂×#67	C₂²×C₅	1	2	yes	—
142	C₂×#67	C₂²×C₅	1	2	yes	complemented
143	C₂²×Dic₃	C₂²×C₅	1	2	yes	complemented
144	D₃×D₄	—	2	4	no	—
145	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
147	#217	C₂²×C₅	1	1	yes	characteristic, complemented
148	#217	C₂²×C₅	1	2	yes	complemented
149	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
151	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
152	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
153	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
154	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
155	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
156	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
157	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₂³×C₅	—	3	1	no	—
159	C₂³×C₅	—	3	2	no	—
160	C₂³×C₅	—	6	4	no	—
161	C₂³×C₅	—	6	4	no	—
162	C₂³×C₅	—	12	2	no	—
163	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂³×C₅	C₂²×D₃	1	2	yes	—
165	C₅×Q₈	—	2	2	no	—
166	C₅×D₄	—	2	4	no	—
167	C₅×D₄	—	6	2	no	—
168	C₅×D₄	—	6	4	no	—
169	C₅×D₄	—	6	2	no	—
170	C₅×D₄	—	12	2	no	—
171	C₅×D₄	#67	1	4	yes	complemented
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	3	1	no	—
175	C₂×C₄×C₅	—	3	1	no	—
176	C₂×C₄×C₅	—	3	2	no	—
177	C₂×C₄×C₅	—	3	1	no	—
178	C₂×C₄×C₅	—	6	2	no	—
179	C₂×C₄×C₅	—	12	2	no	—
180	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
182	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₂×#41	C₅×D₃	1	1	yes	characteristic, complemented
184	C₂²×D₄	—	3	1	no	—
185	#124	—	3	1	no	—
186	#123	—	3	2	no	—
187	C₂²⋊Q₈	—	3	1	no	—
188	#121	—	3	2	no	—
189	#121	—	3	1	no	—
190	#120	—	3	2	no	—
191	C₄×D₄	—	3	1	no	—
192	C₄×D₄	—	3	1	no	—
193	C₂×C₂²⋊C₄	—	3	2	no	—
194	C₂×C₃×C₅	—	2	4	no	—
195	C₂×C₃×C₅	—	4	1	no	—
196	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
199	C₅×D₃	—	2	2	no	—
200	C₅×D₃	—	4	2	no	—
201	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
202	C₂³×C₃	C₂³×C₅	1	2	yes	—
203	C₂²×D₃	—	2	4	no	—
204	C₂²×D₃	—	2	4	no	—
205	C₂²×D₃	—	4	2	no	—
206	C₂²×D₃	C₂³×C₅	1	2	yes	—
207	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
208	C₃×Q₈	—	2	2	no	—
209	C₃×D₄	—	2	4	no	—
210	C₃×D₄	C₅×D₄	1	4	yes	complemented
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
215	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	#67	—	2	4	no	—
217	#67	—	2	2	no	—
218	#67	—	4	2	no	—
219	C₂×Dic₃	—	4	2	no	—
220	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
221	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
222	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
223	C₂×Dic₃	C₂³×C₅	1	2	yes	—
224	D₁₂	—	2	2	no	—
225	C₄×D₃	—	2	2	no	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	3	2	no	—
232	C₂²×C₅	—	6	1	no	—
233	C₂²×C₅	—	6	1	no	—
234	C₂²×C₅	—	6	2	no	—
235	C₂²×C₅	—	6	2	no	—
236	C₂²×C₅	—	6	2	no	—
237	C₂²×C₅	—	12	8	no	—
238	C₂²×C₅	C₂×#67	1	4	yes	—
239	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	6	1	no	—
243	C₄×C₅	—	6	1	no	—
244	C₄×C₅	—	6	2	no	—
245	C₄×C₅	—	6	1	no	—
246	C₄×C₅	C₂×#67	1	2	yes	—
247	C₂⁴	—	3	2	no	—
248	#41	—	2	4	no	—
249	C₂×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
250	C₂×D₄	—	3	1	no	—
251	C₂×D₄	—	3	2	no	—
252	C₂×D₄	—	3	2	no	—
253	C₂×D₄	—	3	1	no	—
254	C₂×D₄	—	6	4	no	—
255	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
256	C₂×D₄	C₂×C₅×D₃	1	2	yes	complemented
257	C₂²×C₄	—	3	2	no	—
258	C₂²×C₄	—	3	1	no	—
259	C₂²×C₄	C₂×C₅×D₃	1	2	yes	complemented
260	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
261	C₄⋊C₄	—	3	1	no	—
262	C₄⋊C₄	—	3	1	no	—
263	C₄⋊C₄	—	3	2	no	—
264	C₂²⋊C₄	—	3	2	no	—
265	C₂²⋊C₄	—	3	1	no	—
266	C₂²⋊C₄	—	3	1	no	—
267	C₂²⋊C₄	—	3	2	no	—
268	C₂²⋊C₄	—	3	2	no	—
269	C₂²⋊C₄	—	3	2	no	—
270	C₂²⋊C₄	—	3	2	no	—
271	C₄²	—	3	1	no	—
272	C₃×C₅	#546	1	1	yes	characteristic, complemented, Hall
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	C₂×C₅×D₄	1	4	yes	—
279	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
280	C₂×D₃	—	2	1	no	—
281	C₂×D₃	—	2	1	no	—
282	C₂×D₃	—	2	2	no	—
283	C₂×D₃	—	2	2	no	—
284	C₂×D₃	—	2	2	no	—
285	C₂×D₃	—	4	8	no	—
286	C₂×D₃	C₅×#41	1	2	yes	complemented
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	C₂×C₅×D₄	1	2	yes	—
290	Dic₃	—	2	1	no	—
291	Dic₃	—	2	1	no	—
292	Dic₃	—	2	1	no	—
293	Dic₃	—	2	2	no	—
294	C₂×C₅	—	2	4	no	—
295	C₂×C₅	—	4	1	no	—
296	C₂×C₅	—	6	2	no	—
297	C₂×C₅	—	12	2	no	—
298	C₂×C₅	D₃×#41	1	1	yes	characteristic
299	C₂×C₅	#1009	1	1	yes	characteristic
300	C₂×C₅	C₂²×#67	1	1	yes	characteristic
301	C₂³	—	3	1	no	—
302	C₂³	—	3	2	no	—
303	C₂³	—	6	4	no	—
304	C₂³	—	6	4	no	—
305	C₂³	—	12	2	no	—
306	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
307	C₂³	C₂²×C₅×D₃	1	2	yes	—
308	Q₈	—	2	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	6	2	no	—
311	D₄	—	6	4	no	—
312	D₄	—	6	2	no	—
313	D₄	—	12	2	no	—
314	D₄	C₅×#67	1	4	yes	complemented
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	3	1	no	—
318	C₂×C₄	—	3	1	no	—
319	C₂×C₄	—	3	2	no	—
320	C₂×C₄	—	3	1	no	—
321	C₂×C₄	—	6	2	no	—
322	C₂×C₄	—	12	2	no	—
323	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
325	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₂×C₃	—	2	4	no	—
327	C₂×C₃	—	4	1	no	—
328	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
329	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
330	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
331	D₃	—	2	2	no	—
332	D₃	—	4	2	no	—
333	C₅	#5829	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	3	2	no	—
340	C₂²	—	6	1	no	—
341	C₂²	—	6	1	no	—
342	C₂²	—	6	2	no	—
343	C₂²	—	6	2	no	—
344	C₂²	—	6	2	no	—
345	C₂²	—	12	8	no	—
346	C₂²	C₂×C₅×#67	1	4	yes	—
347	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	6	1	no	—
351	C₄	—	6	1	no	—
352	C₄	—	6	2	no	—
353	C₄	—	6	1	no	—
354	C₄	C₂×C₅×#67	1	2	yes	—
355	C₃	C₅×#546	1	1	yes	characteristic, complemented, Sylow
356	C₂	—	2	4	no	—
357	C₂	—	4	1	no	—
358	C₂	—	6	2	no	—
359	C₂	—	12	2	no	—
360	C₂	C₅×D₃×#41	1	1	yes	characteristic
361	C₂	C₅×#1009	1	1	yes	characteristic
362	C₂	C₂²×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#41	D₃
hypocenter	C₃	C₅×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#41	C₂	semidirect
2. C₂×C₅×D₃×D₄	C₂	semidirect
3. C₅×#947	C₂	semidirect
4. C₅×#946	C₂	semidirect
5. C₅×#939	C₂	semidirect
6. C₅×#937	C₂	semidirect
7. C₅×D₄×Dic₃	C₂	semidirect
8. C₅×#930	C₂	semidirect
9. C₅×#929	C₂	semidirect
10. C₄×C₅×#67	C₂	semidirect
11. C₂×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
15. C₂×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×C₃×C₅×D₄	C₂²	semidirect
18. C₂²×C₃×C₄×C₅	C₂²	semidirect
19. C₂²×C₃×C₄×C₅	C₂²	semidirect
22. C₂×C₅×#67	C₂²	semidirect
23. C₂²×C₅×Dic₃	C₂²	semidirect
27. C₅×#217	C₂²	semidirect
28. C₅×#217	C₂²	semidirect
31. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₅×C₄⋊Dic₃	C₂²	semidirect
35. C₅×Dic₃⋊C₄	C₂²	semidirect
36. C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₄×C₅×Dic₃	C₂²	semidirect
38. #5829	C₅	direct (N × H)
39. C₂×C₅×#41	D₃	semidirect
59. C₃×C₅×D₄	D₄	semidirect
75. C₂×C₃×#41	C₂×C₅	semidirect
76. C₂×D₃×D₄	C₂×C₅	semidirect
77. #947	C₂×C₅	semidirect
78. #946	C₂×C₅	semidirect
79. #939	C₂×C₅	semidirect
80. #937	C₂×C₅	semidirect
81. D₄×Dic₃	C₂×C₅	semidirect
82. #930	C₂×C₅	semidirect
83. #929	C₂×C₅	semidirect
84. C₄×#67	C₂×C₅	semidirect
85. C₂×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
88. C₂×C₅×Q₈	C₂×D₃	semidirect
95. C₂×C₅×D₄	C₂×D₃	semidirect
98. C₂²×C₄×C₅	C₂×D₃	semidirect
99. C₂²×C₄×C₅	C₂×D₃	semidirect
125. C₂×C₅×D₃	#41	semidirect
135. C₂×C₃×Q₈	C₂²×C₅	semidirect
137. C₂×C₃×D₄	C₂²×C₅	semidirect
138. C₂²×C₃×C₄	C₂²×C₅	semidirect
139. C₂²×C₃×C₄	C₂²×C₅	semidirect
142. C₂×#67	C₂²×C₅	semidirect
143. C₂²×Dic₃	C₂²×C₅	semidirect
147. #217	C₂²×C₅	semidirect
148. #217	C₂²×C₅	semidirect
151. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
152. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
153. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
154. C₄⋊Dic₃	C₂²×C₅	semidirect
155. Dic₃⋊C₄	C₂²×C₅	semidirect
156. Dic₃⋊C₄	C₂²×C₅	semidirect
157. C₄×Dic₃	C₂²×C₅	semidirect
171. C₅×D₄	#67	semidirect
183. C₂×#41	C₅×D₃	semidirect
210. C₃×D₄	C₅×D₄	semidirect
249. C₂×Q₈	C₂×C₅×D₃	semidirect
256. C₂×D₄	C₂×C₅×D₃	semidirect
259. C₂²×C₄	C₂×C₅×D₃	semidirect
260. C₂²×C₄	C₂×C₅×D₃	semidirect
272. C₃×C₅	#546	semidirect
286. C₂×D₃	C₅×#41	semidirect
314. D₄	C₅×#67	semidirect
333. C₅	#5829	direct (N × H)
355. C₃	C₅×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#41	2
C₂×C₅×D₃×D₄	2
C₅×#947	2
C₅×#946	2
C₅×#939	2
C₅×#937	2
C₅×D₄×Dic₃	2
C₅×#930	2
C₅×#929	2
C₄×C₅×#67	2
C₂×C₅×(C₂×D₃)⋊C₄	2
C₅×#546	3
#5829	5

Subgroups — C5×#5829 #11756214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5829 #11756214