Subgroups — C₅×D₃×#137 #11756161

Order 960.

516 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#942	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#918	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#915	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₅×#909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	3	1	no	maximal, Hall
13	C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₅×#239	C₂²	1	1	yes	characteristic
16	C₅×D₃×Q₈	—	2	1	no	—
17	C₅×D₃×Q₈	—	2	1	no	—
18	C₅×D₃×Q₈	C₂²	1	2	yes	—
19	C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
20	C₅×D₃×Q₈	C₂²	1	2	yes	complemented
21	C₅×#237	—	2	1	no	—
22	C₅×#237	C₂²	1	1	yes	characteristic
23	C₅×D₃×D₄	—	2	1	no	—
24	C₅×D₃×D₄	C₂²	1	1	yes	characteristic
25	C₅×#235	—	2	1	no	—
26	C₅×#235	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₃	—	2	1	no	—
28	C₂×C₄×C₅×D₃	—	2	1	no	—
29	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₂×C₅×Dic₆	—	2	1	no	—
31	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
33	C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
34	C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₅×#216	C₂²	1	2	yes	complemented
36	C₅×#216	C₂²	1	2	yes	complemented
37	C₅×#215	C₂²	1	2	yes	complemented
38	C₅×#214	C₂²	1	2	yes	complemented
39	C₅×#208	C₂²	1	1	yes	characteristic, complemented
40	C₅×Dic₁₂	C₂²	1	2	yes	complemented
41	C₅×#204	C₂²	1	2	yes	complemented
42	C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
43	C₅×D₃×C₈	C₂²	1	2	yes	—
44	D₃×#137	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#41	—	3	1	no	—
46	C₂²×C₅×Q₈	—	3	1	no	—
47	C₅×#137	—	3	1	no	—
48	C₅×#137	—	3	1	no	—
49	C₅×#137	—	3	2	no	—
50	C₅×#137	—	3	2	no	—
51	C₅×#137	—	3	1	no	—
52	C₅×#137	D₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×Q₁₆	—	3	2	no	—
54	C₂×C₅×SD₁₆	—	3	2	no	—
55	C₂×C₅×M₁₆	—	3	1	no	—
56	C₂²×C₅×D₃	—	2	1	no	—
57	C₂²×C₅×D₃	D₄	1	1	yes	characteristic
58	C₃×C₅×Q₈	—	2	1	no	—
59	C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₃×C₅×D₄	—	2	1	no	—
62	C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	2	1	no	—
65	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₅×#67	—	2	1	no	—
67	C₅×#67	—	2	1	no	—
68	C₅×#67	—	2	1	no	—
69	C₂×C₅×Dic₃	—	2	1	no	—
70	C₂×C₅×Dic₃	—	2	1	no	—
71	C₂×C₅×Dic₃	D₄	1	1	yes	characteristic
72	C₅×D₁₂	—	2	1	no	—
73	C₅×D₁₂	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₃	—	2	1	no	—
75	C₄×C₅×D₃	—	2	2	no	—
76	C₄×C₅×D₃	—	2	2	no	—
77	C₄×C₅×D₃	—	2	1	no	—
78	C₄×C₅×D₃	—	2	1	no	—
79	C₄×C₅×D₃	D₄	1	1	yes	characteristic
80	C₄×C₅×D₃	D₄	1	1	yes	characteristic
81	C₄×C₅×D₃	C₂³	1	1	yes	characteristic
82	C₄×C₅×D₃	C₂³	1	1	yes	characteristic
83	C₅×Dic₆	—	2	1	no	—
84	C₅×Dic₆	—	2	2	no	—
85	C₅×Dic₆	—	2	2	no	—
86	C₅×Dic₆	—	2	1	no	—
87	C₅×Dic₆	C₂³	1	2	yes	—
88	C₅×Dic₆	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₈	C₂³	1	2	yes	—
90	C₅×C₃⋊C₈	C₂³	1	2	yes	—
91	D₃×#41	C₂×C₅	1	1	yes	characteristic
92	C₂×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
94	#951	C₂×C₅	1	1	yes	characteristic, complemented
95	#942	C₂×C₅	1	1	yes	characteristic, complemented
96	#918	C₂×C₅	1	2	yes	complemented
97	D₃×Q₁₆	C₂×C₅	1	2	yes	complemented
98	#915	C₂×C₅	1	2	yes	complemented
99	D₃×SD₁₆	C₂×C₅	1	2	yes	complemented
100	#909	C₂×C₅	1	1	yes	characteristic, complemented
101	D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
102	C₅×#41	—	3	1	no	—
103	C₅×#41	—	3	1	no	—
104	C₅×#41	—	3	1	no	—
105	C₅×#41	—	6	1	no	—
106	C₅×#41	—	6	1	no	—
107	C₅×#41	C₂×D₃	1	1	yes	characteristic
108	C₂×C₅×Q₈	—	3	2	no	—
109	C₂×C₅×Q₈	—	3	1	no	—
110	C₂×C₅×Q₈	—	3	2	no	—
111	C₂×C₅×Q₈	—	3	1	no	—
112	C₂×C₅×Q₈	—	6	1	no	—
113	C₂×C₅×Q₈	—	6	1	no	—
114	C₂×C₅×Q₈	—	6	1	no	—
115	C₂×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
116	C₂×C₅×D₄	—	3	1	no	—
117	C₂×C₅×D₄	—	6	1	no	—
118	C₂²×C₄×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	6	1	no	—
120	C₂²×C₄×C₅	—	6	1	no	—
121	C₅×Q₁₆	—	3	2	no	—
122	C₅×Q₁₆	—	3	2	no	—
123	C₅×Q₁₆	—	3	2	no	—
124	C₅×Q₁₆	C₂×D₃	1	2	yes	complemented
125	C₅×SD₁₆	—	3	2	no	—
126	C₅×SD₁₆	—	3	2	no	—
127	C₅×SD₁₆	—	3	2	no	—
128	C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
129	C₅×M₁₆	—	3	1	no	—
130	C₅×M₁₆	—	3	2	no	—
131	C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
132	C₂×C₅×C₈	—	3	2	no	—
133	C₂×#137	—	3	1	no	Sylow
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×D₃	—	2	2	no	—
137	C₂×C₅×D₃	—	2	1	no	—
138	C₂×C₅×D₃	—	4	2	no	—
139	C₂×C₅×D₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×D₃	C₂×D₄	1	1	yes	characteristic
141	C₃×C₄×C₅	—	2	2	no	—
142	C₃×C₄×C₅	—	2	1	no	—
143	C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×Dic₃	—	2	2	no	—
146	C₅×Dic₃	—	2	1	no	—
147	C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
148	C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
149	C₃×#41	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
151	#239	C₂²×C₅	1	1	yes	characteristic
152	D₃×Q₈	—	2	1	no	—
153	D₃×Q₈	—	2	1	no	—
154	D₃×Q₈	C₂²×C₅	1	2	yes	—
155	D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
156	D₃×Q₈	C₂²×C₅	1	2	yes	complemented
157	#237	—	2	1	no	—
158	#237	C₂²×C₅	1	1	yes	characteristic
159	D₃×D₄	—	2	1	no	—
160	D₃×D₄	C₂²×C₅	1	1	yes	characteristic
161	#235	—	2	1	no	—
162	#235	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄×D₃	—	2	1	no	—
164	C₂×C₄×D₃	—	2	1	no	—
165	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
166	C₂×Dic₆	—	2	1	no	—
167	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
169	C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
170	C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
171	#216	C₂²×C₅	1	2	yes	complemented
172	#216	C₂²×C₅	1	2	yes	complemented
173	#215	C₂²×C₅	1	2	yes	complemented
174	#214	C₂²×C₅	1	2	yes	complemented
175	#208	C₂²×C₅	1	1	yes	characteristic, complemented
176	Dic₁₂	C₂²×C₅	1	2	yes	complemented
177	#204	C₂²×C₅	1	2	yes	complemented
178	ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
179	D₃×C₈	C₂²×C₅	1	2	yes	—
180	C₂³×C₅	—	3	1	no	—
181	C₂³×C₅	—	6	1	no	—
182	C₅×Q₈	—	2	1	no	—
183	C₅×Q₈	—	3	2	no	—
184	C₅×Q₈	—	3	1	no	—
185	C₅×Q₈	—	6	2	no	—
186	C₅×Q₈	—	6	2	no	—
187	C₅×Q₈	—	6	1	no	—
188	C₅×Q₈	—	6	1	no	—
189	C₅×Q₈	C₂²×D₃	1	2	yes	—
190	C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
191	C₅×D₄	—	2	1	no	—
192	C₅×D₄	—	3	1	no	—
193	C₅×D₄	—	6	1	no	—
194	C₅×D₄	—	6	1	no	—
195	C₅×D₄	—	6	1	no	—
196	C₅×D₄	—	6	1	no	—
197	C₅×D₄	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	3	1	no	—
201	C₂×C₄×C₅	—	3	1	no	—
202	C₂×C₄×C₅	—	3	1	no	—
203	C₂×C₄×C₅	—	3	1	no	—
204	C₂×C₄×C₅	—	3	1	no	—
205	C₂×C₄×C₅	—	6	1	no	—
206	C₂×C₄×C₅	—	6	1	no	—
207	C₂×C₄×C₅	—	6	2	no	—
208	C₂×C₄×C₅	—	6	2	no	—
209	C₂×C₄×C₅	—	6	1	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	6	1	no	—
212	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×C₈	—	3	2	no	—
214	C₅×C₈	C₂²×D₃	1	2	yes	—
215	C₂×#41	—	3	1	no	—
216	C₂²×Q₈	—	3	1	no	—
217	#137	—	3	1	no	—
218	#137	—	3	1	no	—
219	#137	—	3	2	no	—
220	#137	—	3	2	no	—
221	#137	—	3	1	no	—
222	#137	C₅×D₃	1	1	yes	characteristic, direct product factor
223	C₂×Q₁₆	—	3	2	no	—
224	C₂×SD₁₆	—	3	2	no	—
225	C₂×M₁₆	—	3	1	no	—
226	C₂×C₃×C₅	—	2	1	no	—
227	C₂×C₃×C₅	—	4	1	no	—
228	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₅×D₃	—	2	1	no	—
230	C₅×D₃	—	4	1	no	—
231	C₅×D₃	#137	1	2	yes	direct product factor
232	C₂²×D₃	—	2	1	no	—
233	C₂²×D₃	C₅×D₄	1	1	yes	characteristic
234	C₃×Q₈	—	2	1	no	—
235	C₃×Q₈	C₂³×C₅	1	2	yes	—
236	C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
237	C₃×D₄	—	2	1	no	—
238	C₃×D₄	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	#67	—	2	1	no	—
243	#67	—	2	1	no	—
244	#67	—	2	1	no	—
245	C₂×Dic₃	—	2	1	no	—
246	C₂×Dic₃	—	2	1	no	—
247	C₂×Dic₃	C₅×D₄	1	1	yes	characteristic
248	D₁₂	—	2	1	no	—
249	D₁₂	C₂³×C₅	1	1	yes	characteristic
250	C₄×D₃	—	2	1	no	—
251	C₄×D₃	—	2	2	no	—
252	C₄×D₃	—	2	2	no	—
253	C₄×D₃	—	2	1	no	—
254	C₄×D₃	—	2	1	no	—
255	C₄×D₃	C₅×D₄	1	1	yes	characteristic
256	C₄×D₃	C₅×D₄	1	1	yes	characteristic
257	C₄×D₃	C₂³×C₅	1	1	yes	characteristic
258	C₄×D₃	C₂³×C₅	1	1	yes	characteristic
259	Dic₆	—	2	1	no	—
260	Dic₆	—	2	2	no	—
261	Dic₆	—	2	2	no	—
262	Dic₆	—	2	1	no	—
263	Dic₆	C₂³×C₅	1	2	yes	—
264	Dic₆	C₂³×C₅	1	1	yes	characteristic
265	C₃×C₈	C₂³×C₅	1	2	yes	—
266	C₃⋊C₈	C₂³×C₅	1	2	yes	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	3	1	no	—
269	C₂²×C₅	—	3	1	no	—
270	C₂²×C₅	—	6	2	no	—
271	C₂²×C₅	—	6	1	no	—
272	C₂²×C₅	—	12	2	no	—
273	C₂²×C₅	D₃×D₄	1	1	yes	characteristic
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	3	1	no	—
277	C₄×C₅	—	3	1	no	—
278	C₄×C₅	—	6	1	no	—
279	C₄×C₅	—	6	2	no	—
280	C₄×C₅	D₃×D₄	1	1	yes	characteristic
281	C₄×C₅	C₂³×D₃	1	1	yes	characteristic
282	#41	—	3	1	no	—
283	#41	—	3	1	no	—
284	#41	—	3	1	no	—
285	#41	—	6	1	no	—
286	#41	—	6	1	no	—
287	#41	C₂×C₅×D₃	1	1	yes	characteristic
288	C₂×Q₈	—	3	2	no	—
289	C₂×Q₈	—	3	1	no	—
290	C₂×Q₈	—	3	2	no	—
291	C₂×Q₈	—	3	1	no	—
292	C₂×Q₈	—	6	1	no	—
293	C₂×Q₈	—	6	1	no	—
294	C₂×Q₈	—	6	1	no	—
295	C₂×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
296	C₂×D₄	—	3	1	no	—
297	C₂×D₄	—	6	1	no	—
298	C₂²×C₄	—	3	1	no	—
299	C₂²×C₄	—	6	1	no	—
300	C₂²×C₄	—	6	1	no	—
301	Q₁₆	—	3	2	no	—
302	Q₁₆	—	3	2	no	—
303	Q₁₆	—	3	2	no	—
304	Q₁₆	C₂×C₅×D₃	1	2	yes	complemented
305	SD₁₆	—	3	2	no	—
306	SD₁₆	—	3	2	no	—
307	SD₁₆	—	3	2	no	—
308	SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
309	M₁₆	—	3	1	no	—
310	M₁₆	—	3	2	no	—
311	M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
312	C₂×C₈	—	3	2	no	—
313	C₃×C₅	C₂×#137	1	1	yes	characteristic, complemented, Hall
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂×D₃	—	2	2	no	—
317	C₂×D₃	—	2	1	no	—
318	C₂×D₃	—	4	2	no	—
319	C₂×D₃	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×D₃	C₂×C₅×D₄	1	1	yes	characteristic
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
325	Dic₃	—	2	2	no	—
326	Dic₃	—	2	1	no	—
327	Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
328	Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	3	2	no	—
331	C₂×C₅	—	4	1	no	—
332	C₂×C₅	—	6	1	no	—
333	C₂×C₅	—	12	1	no	—
334	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
335	C₂³	—	3	1	no	—
336	C₂³	—	6	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	3	2	no	—
339	Q₈	—	3	1	no	—
340	Q₈	—	6	2	no	—
341	Q₈	—	6	2	no	—
342	Q₈	—	6	1	no	—
343	Q₈	—	6	1	no	—
344	Q₈	C₂²×C₅×D₃	1	2	yes	—
345	Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
346	D₄	—	2	1	no	—
347	D₄	—	3	1	no	—
348	D₄	—	6	1	no	—
349	D₄	—	6	1	no	—
350	D₄	—	6	1	no	—
351	D₄	—	6	1	no	—
352	D₄	C₂²×C₅×D₃	1	1	yes	characteristic
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	3	1	no	—
356	C₂×C₄	—	3	1	no	—
357	C₂×C₄	—	3	1	no	—
358	C₂×C₄	—	3	1	no	—
359	C₂×C₄	—	3	1	no	—
360	C₂×C₄	—	6	1	no	—
361	C₂×C₄	—	6	1	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	2	no	—
364	C₂×C₄	—	6	1	no	—
365	C₂×C₄	—	6	1	no	—
366	C₂×C₄	—	6	1	no	—
367	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	C₈	—	3	2	no	—
369	C₈	C₂²×C₅×D₃	1	2	yes	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	4	1	no	—
372	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
373	D₃	—	2	1	no	—
374	D₃	—	4	1	no	—
375	D₃	C₅×#137	1	2	yes	direct product factor
376	C₅	D₃×#137	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	2	1	no	—
378	C₂²	—	3	1	no	—
379	C₂²	—	3	1	no	—
380	C₂²	—	6	2	no	—
381	C₂²	—	6	1	no	—
382	C₂²	—	12	2	no	—
383	C₂²	C₅×D₃×D₄	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	3	1	no	—
387	C₄	—	3	1	no	—
388	C₄	—	6	1	no	—
389	C₄	—	6	2	no	—
390	C₄	C₅×D₃×D₄	1	1	yes	characteristic
391	C₄	C₂³×C₅×D₃	1	1	yes	characteristic
392	C₃	C₂×C₅×#137	1	1	yes	characteristic, complemented, Sylow
393	C₂	—	2	1	no	—
394	C₂	—	3	2	no	—
395	C₂	—	4	1	no	—
396	C₂	—	6	1	no	—
397	C₂	—	12	1	no	—
398	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#137	C₂
socle	C₂×C₃×C₅	C₂²×D₄
prime radical	C₅×D₃×#41	C₂
hypercenter	C₅×#137	D₃
hypocenter	C₃	C₂×C₅×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#137

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×Q₈	C₂	semidirect
3. C₃×C₅×#137	C₂	semidirect
4. C₅×#951	C₂	semidirect
5. C₅×#942	C₂	semidirect
6. C₅×#918	C₂	semidirect
7. C₅×D₃×Q₁₆	C₂	semidirect
8. C₅×#915	C₂	semidirect
9. C₅×D₃×SD₁₆	C₂	semidirect
10. C₅×#909	C₂	semidirect
11. C₅×D₃×M₁₆	C₂	semidirect
14. C₂×C₃×C₅×Q₈	C₂²	semidirect
20. C₅×D₃×Q₈	C₂²	semidirect
31. C₂×C₅×Dic₆	C₂²	semidirect
32. C₃×C₅×Q₁₆	C₂²	semidirect
33. C₃×C₅×SD₁₆	C₂²	semidirect
34. C₃×C₅×M₁₆	C₂²	semidirect
35. C₅×#216	C₂²	semidirect
36. C₅×#216	C₂²	semidirect
37. C₅×#215	C₂²	semidirect
38. C₅×#214	C₂²	semidirect
39. C₅×#208	C₂²	semidirect
40. C₅×Dic₁₂	C₂²	semidirect
41. C₅×#204	C₂²	semidirect
42. C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
44. D₃×#137	C₅	direct (N × H)
52. C₅×#137	D₃	direct (N × H)
92. C₂×D₃×Q₈	C₂×C₅	semidirect
93. C₃×#137	C₂×C₅	semidirect
94. #951	C₂×C₅	semidirect
95. #942	C₂×C₅	semidirect
96. #918	C₂×C₅	semidirect
97. D₃×Q₁₆	C₂×C₅	semidirect
98. #915	C₂×C₅	semidirect
99. D₃×SD₁₆	C₂×C₅	semidirect
100. #909	C₂×C₅	semidirect
101. D₃×M₁₆	C₂×C₅	semidirect
115. C₂×C₅×Q₈	C₂×D₃	semidirect
124. C₅×Q₁₆	C₂×D₃	semidirect
128. C₅×SD₁₆	C₂×D₃	semidirect
131. C₅×M₁₆	C₂×D₃	semidirect
150. C₂×C₃×Q₈	C₂²×C₅	semidirect
156. D₃×Q₈	C₂²×C₅	semidirect
167. C₂×Dic₆	C₂²×C₅	semidirect
168. C₃×Q₁₆	C₂²×C₅	semidirect
169. C₃×SD₁₆	C₂²×C₅	semidirect
170. C₃×M₁₆	C₂²×C₅	semidirect
171. #216	C₂²×C₅	semidirect
172. #216	C₂²×C₅	semidirect
173. #215	C₂²×C₅	semidirect
174. #214	C₂²×C₅	semidirect
175. #208	C₂²×C₅	semidirect
176. Dic₁₂	C₂²×C₅	semidirect
177. #204	C₂²×C₅	semidirect
178. ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
222. #137	C₅×D₃	direct (N × H)
231. C₅×D₃	#137	direct (N × H)
295. C₂×Q₈	C₂×C₅×D₃	semidirect
304. Q₁₆	C₂×C₅×D₃	semidirect
308. SD₁₆	C₂×C₅×D₃	semidirect
311. M₁₆	C₂×C₅×D₃	semidirect
313. C₃×C₅	C₂×#137	semidirect
375. D₃	C₅×#137	direct (N × H)
376. C₅	D₃×#137	direct (N × H)
392. C₃	C₂×C₅×#137	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#41	2
C₂×C₅×D₃×Q₈	2
C₃×C₅×#137	2
C₅×#951	2
C₅×#942	2
C₅×#918	2
C₅×D₃×Q₁₆	2
C₅×#915	2
C₅×D₃×SD₁₆	2
C₅×#909	2
C₅×D₃×M₁₆	2
C₂×C₅×#137	3
D₃×#137	5

Subgroups — C5×D3×#137 #11756161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#137 #11756161