Subgroups — C₅×#83988 #14454450

Order 1920.

956 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5824	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5817	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#916	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5238	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5228	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5190	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5188	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5182	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5173	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5165	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5134	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3269	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#239	C₂²	1	1	yes	characteristic
20	C₂×C₅×#237	C₂²	1	1	yes	characteristic
21	C₃×C₅×#137	—	2	4	no	—
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
27	C₅×#947	—	2	1	no	—
28	C₅×#947	C₂²	1	1	yes	characteristic
29	C₅×#946	—	2	1	no	—
30	C₅×#946	C₂²	1	1	yes	characteristic
31	C₅×#946	C₂²	1	1	yes	characteristic
32	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
33	C₅×#944	C₂²	1	1	yes	characteristic
34	C₂×C₅×#216	C₂²	1	1	yes	characteristic
35	C₂×C₅×#216	C₂²	1	1	yes	characteristic
36	C₂×C₅×#215	C₂²	1	1	yes	characteristic
37	C₅×#939	—	2	1	no	—
38	C₅×#935	—	2	1	no	—
39	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₅×#213	C₂²	1	1	yes	characteristic
41	C₅×#930	—	2	1	no	—
42	C₅×#930	C₂²	1	1	yes	characteristic
43	C₅×#929	—	2	1	no	—
44	C₄×C₅×#67	—	2	1	no	—
45	C₄×C₅×#67	C₂²	1	1	yes	characteristic
46	C₅×#924	C₂²	1	1	yes	characteristic
47	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
48	C₅×#916	—	2	4	no	—
49	C₂×C₅×#204	C₂²	1	1	yes	characteristic
50	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
51	C₅×#835	C₂²	1	1	yes	characteristic
52	C₅×#835	C₂²	1	1	yes	characteristic
53	C₅×#835	C₂²	1	1	yes	characteristic
54	C₅×#832	C₂²	1	1	yes	characteristic
55	C₅×#830	C₂²	1	1	yes	characteristic
56	C₅×#821	C₂²	1	1	yes	characteristic
57	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×#818	C₂²	1	1	yes	characteristic
59	C₅×#816	C₂²	1	1	yes	characteristic
60	C₅×#815	C₂²	1	1	yes	characteristic
61	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
62	#83988	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#137	D₃	1	1	yes	characteristic, complemented
64	C₂×C₅×#135	—	3	1	no	—
65	C₅×#548	—	3	1	no	—
66	C₅×#547	—	3	1	no	—
67	C₅×#497	—	3	1	no	—
68	C₅×#468	—	3	1	no	—
69	C₅×#467	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#462	—	3	1	no	—
72	C₅×#452	—	3	1	no	—
73	C₅×#452	—	3	1	no	—
74	C₅×#451	—	3	1	no	—
75	C₅×#449	—	3	1	no	—
76	C₅×#440	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₃×C₅×#41	—	2	2	no	—
79	C₃×C₅×#41	—	4	1	no	—
80	C₂×C₃×C₅×Q₈	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	—	2	2	no	—
82	C₂×C₃×C₅×Q₈	—	4	1	no	—
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₅×#67	—	2	1	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₂×C₅×#67	D₄	1	1	yes	characteristic
94	C₂²×C₅×Dic₃	—	2	1	no	—
95	C₂²×C₅×Dic₃	—	2	1	no	—
96	C₅×#239	—	2	2	no	—
97	C₅×#239	—	4	1	no	—
98	C₅×#237	—	2	2	no	—
99	C₅×#237	—	4	1	no	—
100	C₂×C₅×D₁₂	—	2	1	no	—
101	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
102	C₂×C₄×C₅×D₃	—	2	1	no	—
103	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
104	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
105	C₃×C₅×Q₁₆	—	2	2	no	—
106	C₃×C₅×Q₁₆	—	2	2	no	—
107	C₃×C₅×SD₁₆	—	2	2	no	—
108	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
109	C₃×C₅×M₁₆	—	2	2	no	—
110	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₅×#217	—	2	1	no	—
113	C₅×#217	—	2	1	no	—
114	C₅×#217	D₄	1	1	yes	characteristic
115	C₅×#216	—	2	2	no	—
116	C₅×#216	—	4	1	no	—
117	C₅×#215	—	4	1	no	—
118	C₅×#213	—	2	2	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
125	C₅×C₄⋊Dic₃	—	2	1	no	—
126	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
127	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
128	C₅×Dic₃⋊C₄	—	2	1	no	—
129	C₅×Dic₃⋊C₄	—	2	1	no	—
130	C₅×Dic₃⋊C₄	—	2	1	no	—
131	C₅×Dic₃⋊C₄	—	2	1	no	—
132	C₅×Dic₃⋊C₄	—	2	1	no	—
133	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
134	C₄×C₅×Dic₃	—	2	1	no	—
135	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
138	C₅×#204	—	2	2	no	—
139	C₅×D₃×C₈	—	2	2	no	—
140	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
141	#5824	C₂×C₅	1	1	yes	characteristic, complemented
142	#5817	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×#916	C₂×C₅	1	1	yes	characteristic, complemented
144	#5238	C₂×C₅	1	1	yes	characteristic, complemented
145	#5228	C₂×C₅	1	1	yes	characteristic, complemented
146	#5190	C₂×C₅	1	1	yes	characteristic, complemented
147	#5188	C₂×C₅	1	1	yes	characteristic, complemented
148	#5187	C₂×C₅	1	1	yes	characteristic, complemented
149	#5182	C₂×C₅	1	1	yes	characteristic, complemented
150	#5173	C₂×C₅	1	1	yes	characteristic, complemented
151	#5165	C₂×C₅	1	1	yes	characteristic, complemented
152	#5164	C₂×C₅	1	1	yes	characteristic, complemented
153	#5134	C₂×C₅	1	1	yes	characteristic, complemented
154	#5127	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	—	3	1	no	—
156	C₂×C₅×#41	—	3	1	no	—
157	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
158	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
159	C₅×#137	—	2	4	no	—
160	C₅×#135	—	6	4	no	—
161	C₂×C₅×Q₁₆	—	3	1	no	—
162	C₂×C₅×Q₁₆	—	3	1	no	—
163	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
164	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
165	C₂×C₅×SD₁₆	—	3	1	no	—
166	C₂×C₅×SD₁₆	—	3	1	no	—
167	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
168	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
169	C₂×C₅×D₈	—	3	1	no	—
170	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
171	C₂²×C₅×C₈	—	3	1	no	—
172	C₅×C₄⋊Q₈	—	3	1	no	—
173	C₅×#124	—	3	1	no	—
174	C₅×#124	—	6	1	no	—
175	C₅×#123	—	6	1	no	—
176	C₅×#123	—	6	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×C₂²⋊Q₈	—	3	1	no	—
179	C₅×C₂²⋊Q₈	—	3	1	no	—
180	C₅×C₂²⋊Q₈	—	6	1	no	—
181	C₅×#121	—	3	1	no	—
182	C₅×#121	—	6	1	no	—
183	C₅×#121	—	6	1	no	—
184	C₄×C₅×Q₈	—	3	1	no	—
185	C₄×C₅×D₄	—	3	1	no	—
186	C₄×C₅×D₄	—	3	1	no	—
187	C₄×C₅×D₄	—	6	1	no	—
188	C₂×C₅×C₄⋊C₄	—	6	1	no	—
189	C₅×#107	—	3	1	no	—
190	C₅×C₄⋊C₈	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#103	—	3	1	no	—
194	C₅×#103	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	—	3	1	no	—
197	C₅×C₂²⋊C₈	—	3	1	no	—
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×#97	—	3	1	no	—
200	#3269	—	3	1	no	Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₅×D₃	—	2	1	no	—
204	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	—	2	1	no	—
208	C₃×C₅×Q₈	—	2	1	no	—
209	C₃×C₅×Q₈	—	2	1	no	—
210	C₃×C₅×Q₈	—	4	2	no	—
211	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	—	4	2	no	—
214	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	4	2	no	—
221	C₂×C₃×C₄×C₅	—	4	2	no	—
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₅×#67	—	4	1	no	—
225	C₅×#67	—	4	2	no	—
226	C₅×#67	—	4	2	no	—
227	C₂×C₅×Dic₃	—	2	1	no	—
228	C₂×C₅×Dic₃	—	2	1	no	—
229	C₂×C₅×Dic₃	—	2	1	no	—
230	C₂×C₅×Dic₃	—	4	2	no	—
231	C₂×C₅×Dic₃	—	4	2	no	—
232	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
233	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
234	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
235	C₅×D₁₂	—	2	1	no	—
236	C₅×D₁₂	—	2	1	no	—
237	C₅×D₁₂	—	4	2	no	—
238	C₄×C₅×D₃	—	2	1	no	—
239	C₄×C₅×D₃	—	2	1	no	—
240	C₄×C₅×D₃	—	4	2	no	—
241	C₅×Dic₆	—	2	1	no	—
242	C₅×Dic₆	—	2	1	no	—
243	C₃×C₅×C₈	—	2	1	no	—
244	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
245	C₅×C₃⋊C₈	—	2	1	no	—
246	C₅×C₃⋊C₈	—	2	1	no	—
247	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
248	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
249	C₂×#239	C₂²×C₅	1	1	yes	characteristic
250	C₂×#237	C₂²×C₅	1	1	yes	characteristic
251	C₃×#137	—	2	4	no	—
252	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
257	#947	—	2	1	no	—
258	#947	C₂²×C₅	1	1	yes	characteristic
259	#946	—	2	1	no	—
260	#946	C₂²×C₅	1	1	yes	characteristic
261	#946	C₂²×C₅	1	1	yes	characteristic
262	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
263	#944	C₂²×C₅	1	1	yes	characteristic
264	C₂×#216	C₂²×C₅	1	1	yes	characteristic
265	C₂×#216	C₂²×C₅	1	1	yes	characteristic
266	C₂×#215	C₂²×C₅	1	1	yes	characteristic
267	#939	—	2	1	no	—
268	#935	—	2	1	no	—
269	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
270	C₂×#213	C₂²×C₅	1	1	yes	characteristic
271	#930	—	2	1	no	—
272	#930	C₂²×C₅	1	1	yes	characteristic
273	#929	—	2	1	no	—
274	C₄×#67	—	2	1	no	—
275	C₄×#67	C₂²×C₅	1	1	yes	characteristic
276	#924	C₂²×C₅	1	1	yes	characteristic
277	C₂×Dic₃⋊C₄	—	2	1	no	—
278	#916	—	2	4	no	—
279	C₂×#204	C₂²×C₅	1	1	yes	characteristic
280	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
281	#835	C₂²×C₅	1	1	yes	characteristic
282	#835	C₂²×C₅	1	1	yes	characteristic
283	#835	C₂²×C₅	1	1	yes	characteristic
284	#832	C₂²×C₅	1	1	yes	characteristic
285	#830	C₂²×C₅	1	1	yes	characteristic
286	#821	C₂²×C₅	1	1	yes	characteristic
287	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
288	#818	C₂²×C₅	1	1	yes	characteristic
289	#816	C₂²×C₅	1	1	yes	characteristic
290	#815	C₂²×C₅	1	1	yes	characteristic
291	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
292	C₅×#41	—	2	2	no	—
293	C₅×#41	—	4	1	no	—
294	C₅×#41	—	6	2	no	—
295	C₅×#41	—	6	2	no	—
296	C₅×#41	—	12	1	no	—
297	C₅×#41	—	12	1	no	—
298	C₂×C₅×Q₈	—	2	1	no	—
299	C₂×C₅×Q₈	—	2	2	no	—
300	C₂×C₅×Q₈	—	3	1	no	—
301	C₂×C₅×Q₈	—	4	1	no	—
302	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
303	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₅×D₄	—	2	1	no	—
306	C₂×C₅×D₄	—	3	1	no	—
307	C₂×C₅×D₄	—	3	1	no	—
308	C₂×C₅×D₄	—	6	1	no	—
309	C₂×C₅×D₄	—	6	1	no	—
310	C₂×C₅×D₄	—	6	1	no	—
311	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	—	2	1	no	—
313	C₂²×C₄×C₅	—	2	1	no	—
314	C₂²×C₄×C₅	—	3	1	no	—
315	C₂²×C₄×C₅	—	6	1	no	—
316	C₂²×C₄×C₅	—	6	1	no	—
317	C₂²×C₄×C₅	—	6	1	no	—
318	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₅×Q₁₆	—	2	2	no	—
320	C₅×Q₁₆	—	2	2	no	—
321	C₅×Q₁₆	—	6	2	no	—
322	C₅×Q₁₆	—	12	1	no	—
323	C₅×SD₁₆	—	2	2	no	—
324	C₅×SD₁₆	—	6	2	no	—
325	C₅×SD₁₆	—	12	1	no	—
326	C₅×SD₁₆	#67	1	4	yes	complemented
327	C₅×D₈	—	6	2	no	—
328	C₅×M₁₆	—	2	2	no	—
329	C₂×C₅×C₈	—	3	1	no	—
330	C₂×C₅×C₈	—	3	1	no	—
331	C₂×C₅×C₈	—	6	2	no	—
332	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
333	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
334	C₅×C₄⋊C₄	—	3	1	no	—
335	C₅×C₄⋊C₄	—	3	1	no	—
336	C₅×C₄⋊C₄	—	3	1	no	—
337	C₅×C₄⋊C₄	—	6	1	no	—
338	C₅×C₄⋊C₄	—	6	1	no	—
339	C₅×C₄⋊C₄	—	6	1	no	—
340	C₅×C₄⋊C₄	—	6	1	no	—
341	C₅×C₄⋊C₄	—	6	1	no	—
342	C₅×C₄⋊C₄	—	6	1	no	—
343	C₅×C₂²⋊C₄	—	3	1	no	—
344	C₅×C₂²⋊C₄	—	3	1	no	—
345	C₅×C₂²⋊C₄	—	6	1	no	—
346	C₅×C₂²⋊C₄	—	6	1	no	—
347	C₅×C₂²⋊C₄	—	6	1	no	—
348	C₅×C₂²⋊C₄	—	6	1	no	—
349	C₅×C₂²⋊C₄	—	6	1	no	—
350	C₅×C₂²⋊C₄	—	6	1	no	—
351	C₅×C₂²⋊C₄	—	6	1	no	—
352	C₄²×C₅	—	3	1	no	—
353	C₄²×C₅	—	6	1	no	—
354	C₂×#137	C₅×D₃	1	1	yes	characteristic, complemented
355	C₂×#135	—	3	1	no	—
356	#548	—	3	1	no	—
357	#547	—	3	1	no	—
358	#497	—	3	1	no	—
359	#468	—	3	1	no	—
360	#467	—	3	1	no	—
361	#463	—	3	1	no	—
362	#462	—	3	1	no	—
363	#452	—	3	1	no	—
364	#452	—	3	1	no	—
365	#451	—	3	1	no	—
366	#449	—	3	1	no	—
367	#440	—	3	1	no	—
368	#435	—	3	1	no	—
369	C₂²×C₃×C₅	—	2	2	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₅×D₃	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	—	4	1	no	—
380	C₂×C₅×D₃	—	4	1	no	—
381	C₂×C₅×D₃	—	4	1	no	—
382	C₃×C₄×C₅	—	2	2	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	—	4	1	no	—
385	C₃×C₄×C₅	—	4	1	no	—
386	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
387	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
388	C₅×Dic₃	—	2	1	no	—
389	C₅×Dic₃	—	2	1	no	—
390	C₅×Dic₃	—	2	1	no	—
391	C₅×Dic₃	—	4	1	no	—
392	C₅×Dic₃	—	4	1	no	—
393	C₅×Dic₃	—	4	1	no	—
394	C₃×#41	—	2	2	no	—
395	C₃×#41	—	4	1	no	—
396	C₂×C₃×Q₈	—	2	1	no	—
397	C₂×C₃×Q₈	—	2	2	no	—
398	C₂×C₃×Q₈	—	4	1	no	—
399	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₃×D₄	—	2	1	no	—
403	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	—	2	1	no	—
405	C₂²×C₃×C₄	—	2	1	no	—
406	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂×#67	—	2	1	no	—
408	C₂×#67	—	2	1	no	—
409	C₂×#67	C₅×D₄	1	1	yes	characteristic
410	C₂²×Dic₃	—	2	1	no	—
411	C₂²×Dic₃	—	2	1	no	—
412	#239	—	2	2	no	—
413	#239	—	4	1	no	—
414	#237	—	2	2	no	—
415	#237	—	4	1	no	—
416	C₂×D₁₂	—	2	1	no	—
417	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₄×D₃	—	2	1	no	—
419	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
420	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
421	C₃×Q₁₆	—	2	2	no	—
422	C₃×Q₁₆	—	2	2	no	—
423	C₃×SD₁₆	—	2	2	no	—
424	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
425	C₃×M₁₆	—	2	2	no	—
426	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
428	#217	—	2	1	no	—
429	#217	—	2	1	no	—
430	#217	C₅×D₄	1	1	yes	characteristic
431	#216	—	2	2	no	—
432	#216	—	4	1	no	—
433	#215	—	4	1	no	—
434	#213	—	2	2	no	—
435	(C₂×D₃)⋊C₄	—	2	1	no	—
436	(C₂×D₃)⋊C₄	—	2	1	no	—
437	(C₂×D₃)⋊C₄	—	2	1	no	—
438	(C₂×D₃)⋊C₄	—	2	1	no	—
439	(C₂×D₃)⋊C₄	—	2	1	no	—
440	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
441	C₄⋊Dic₃	—	2	1	no	—
442	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
443	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
444	Dic₃⋊C₄	—	2	1	no	—
445	Dic₃⋊C₄	—	2	1	no	—
446	Dic₃⋊C₄	—	2	1	no	—
447	Dic₃⋊C₄	—	2	1	no	—
448	Dic₃⋊C₄	—	2	1	no	—
449	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
450	C₄×Dic₃	—	2	1	no	—
451	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
454	#204	—	2	2	no	—
455	D₃×C₈	—	2	2	no	—
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	—	3	1	no	—
458	C₂³×C₅	—	6	1	no	—
459	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
460	C₅×Q₈	—	2	1	no	—
461	C₅×Q₈	—	2	1	no	—
462	C₅×Q₈	—	2	1	no	—
463	C₅×Q₈	—	2	1	no	—
464	C₅×Q₈	—	2	1	no	—
465	C₅×Q₈	—	4	2	no	—
466	C₅×Q₈	—	6	1	no	—
467	C₅×Q₈	—	6	1	no	—
468	C₅×Q₈	C₂×#67	1	2	yes	—
469	C₅×D₄	—	2	1	no	—
470	C₅×D₄	—	4	2	no	—
471	C₅×D₄	—	6	1	no	—
472	C₅×D₄	—	6	1	no	—
473	C₅×D₄	—	12	2	no	—
474	C₅×D₄	—	12	1	no	—
475	C₅×D₄	—	12	2	no	—
476	C₅×D₄	—	12	2	no	—
477	C₅×D₄	C₂×#67	1	2	yes	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	3	1	no	—
484	C₂×C₄×C₅	—	3	1	no	—
485	C₂×C₄×C₅	—	3	1	no	—
486	C₂×C₄×C₅	—	4	2	no	—
487	C₂×C₄×C₅	—	4	2	no	—
488	C₂×C₄×C₅	—	6	1	no	—
489	C₂×C₄×C₅	—	6	1	no	—
490	C₂×C₄×C₅	—	6	1	no	—
491	C₂×C₄×C₅	—	6	1	no	—
492	C₂×C₄×C₅	—	6	1	no	—
493	C₂×C₄×C₅	—	12	2	no	—
494	C₂×C₄×C₅	—	12	2	no	—
495	C₂×C₄×C₅	—	12	2	no	—
496	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
498	C₅×C₈	—	2	1	no	—
499	C₅×C₈	—	6	1	no	—
500	C₅×C₈	—	6	1	no	—
501	C₅×C₈	C₂×#67	1	2	yes	—
502	C₂×#41	—	3	1	no	—
503	C₂×#41	—	3	1	no	—
504	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
505	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
506	#137	—	2	4	no	—
507	#135	—	6	4	no	—
508	C₂×Q₁₆	—	3	1	no	—
509	C₂×Q₁₆	—	3	1	no	—
510	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
511	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
512	C₂×SD₁₆	—	3	1	no	—
513	C₂×SD₁₆	—	3	1	no	—
514	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
515	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
516	C₂×D₈	—	3	1	no	—
517	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
518	C₂²×C₈	—	3	1	no	—
519	C₄⋊Q₈	—	3	1	no	—
520	#124	—	3	1	no	—
521	#124	—	6	1	no	—
522	#123	—	6	1	no	—
523	#123	—	6	1	no	—
524	C₂²⋊Q₈	—	3	1	no	—
525	C₂²⋊Q₈	—	3	1	no	—
526	C₂²⋊Q₈	—	3	1	no	—
527	C₂²⋊Q₈	—	6	1	no	—
528	#121	—	3	1	no	—
529	#121	—	6	1	no	—
530	#121	—	6	1	no	—
531	C₄×Q₈	—	3	1	no	—
532	C₄×D₄	—	3	1	no	—
533	C₄×D₄	—	3	1	no	—
534	C₄×D₄	—	6	1	no	—
535	C₂×C₄⋊C₄	—	6	1	no	—
536	#107	—	3	1	no	—
537	C₄⋊C₈	—	3	1	no	—
538	#103	—	3	1	no	—
539	#103	—	3	1	no	—
540	#103	—	3	1	no	—
541	#103	—	3	1	no	—
542	#102	—	3	1	no	—
543	#102	—	3	1	no	—
544	C₂²⋊C₈	—	3	1	no	—
545	C₂²⋊C₈	—	3	1	no	—
546	#97	—	3	1	no	—
547	C₂×C₃×C₅	—	4	1	no	—
548	C₂×C₃×C₅	—	4	2	no	—
549	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
550	C₂×C₃×C₅	#575	1	1	yes	characteristic
551	C₂×C₃×C₅	#578	1	1	yes	characteristic
552	C₅×D₃	—	4	1	no	—
553	C₅×D₃	—	8	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂²×D₃	—	2	1	no	—
557	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
558	C₃×Q₈	—	2	1	no	—
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	2	1	no	—
561	C₃×Q₈	—	2	1	no	—
562	C₃×Q₈	—	2	1	no	—
563	C₃×Q₈	—	4	2	no	—
564	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
565	C₃×D₄	—	2	1	no	—
566	C₃×D₄	—	4	2	no	—
567	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	4	2	no	—
574	C₂×C₃×C₄	—	4	2	no	—
575	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
577	#67	—	4	1	no	—
578	#67	—	4	2	no	—
579	#67	—	4	2	no	—
580	C₂×Dic₃	—	2	1	no	—
581	C₂×Dic₃	—	2	1	no	—
582	C₂×Dic₃	—	2	1	no	—
583	C₂×Dic₃	—	4	2	no	—
584	C₂×Dic₃	—	4	2	no	—
585	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
586	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
587	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
588	D₁₂	—	2	1	no	—
589	D₁₂	—	2	1	no	—
590	D₁₂	—	4	2	no	—
591	C₄×D₃	—	2	1	no	—
592	C₄×D₃	—	2	1	no	—
593	C₄×D₃	—	4	2	no	—
594	Dic₆	—	2	1	no	—
595	Dic₆	—	2	1	no	—
596	C₃×C₈	—	2	1	no	—
597	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
598	C₃⋊C₈	—	2	1	no	—
599	C₃⋊C₈	—	2	1	no	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	1	no	—
603	C₂²×C₅	—	2	2	no	—
604	C₂²×C₅	—	4	1	no	—
605	C₂²×C₅	—	4	1	no	—
606	C₂²×C₅	—	6	1	no	—
607	C₂²×C₅	—	6	1	no	—
608	C₂²×C₅	—	6	1	no	—
609	C₂²×C₅	—	12	1	no	—
610	C₂²×C₅	—	12	1	no	—
611	C₂²×C₅	—	12	1	no	—
612	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
613	C₄×C₅	—	2	1	no	—
614	C₄×C₅	—	2	2	no	—
615	C₄×C₅	—	4	1	no	—
616	C₄×C₅	—	4	1	no	—
617	C₄×C₅	—	6	1	no	—
618	C₄×C₅	—	6	1	no	—
619	C₄×C₅	—	6	1	no	—
620	C₄×C₅	—	12	1	no	—
621	C₄×C₅	—	12	1	no	—
622	C₄×C₅	—	12	1	no	—
623	C₄×C₅	#1004	1	1	yes	characteristic
624	C₄×C₅	C₂²×#67	1	1	yes	characteristic
625	#41	—	2	2	no	—
626	#41	—	4	1	no	—
627	#41	—	6	2	no	—
628	#41	—	6	2	no	—
629	#41	—	12	1	no	—
630	#41	—	12	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	3	1	no	—
634	C₂×Q₈	—	4	1	no	—
635	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
636	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	3	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	6	1	no	—
642	C₂×D₄	—	6	1	no	—
643	C₂×D₄	—	6	1	no	—
644	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	3	1	no	—
648	C₂²×C₄	—	6	1	no	—
649	C₂²×C₄	—	6	1	no	—
650	C₂²×C₄	—	6	1	no	—
651	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
652	Q₁₆	—	2	2	no	—
653	Q₁₆	—	2	2	no	—
654	Q₁₆	—	6	2	no	—
655	Q₁₆	—	12	1	no	—
656	SD₁₆	—	2	2	no	—
657	SD₁₆	—	6	2	no	—
658	SD₁₆	—	12	1	no	—
659	SD₁₆	C₅×#67	1	4	yes	complemented
660	D₈	—	6	2	no	—
661	M₁₆	—	2	2	no	—
662	C₂×C₈	—	3	1	no	—
663	C₂×C₈	—	3	1	no	—
664	C₂×C₈	—	6	2	no	—
665	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
666	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	3	1	no	—
669	C₄⋊C₄	—	3	1	no	—
670	C₄⋊C₄	—	6	1	no	—
671	C₄⋊C₄	—	6	1	no	—
672	C₄⋊C₄	—	6	1	no	—
673	C₄⋊C₄	—	6	1	no	—
674	C₄⋊C₄	—	6	1	no	—
675	C₄⋊C₄	—	6	1	no	—
676	C₂²⋊C₄	—	3	1	no	—
677	C₂²⋊C₄	—	3	1	no	—
678	C₂²⋊C₄	—	6	1	no	—
679	C₂²⋊C₄	—	6	1	no	—
680	C₂²⋊C₄	—	6	1	no	—
681	C₂²⋊C₄	—	6	1	no	—
682	C₂²⋊C₄	—	6	1	no	—
683	C₂²⋊C₄	—	6	1	no	—
684	C₂²⋊C₄	—	6	1	no	—
685	C₄²	—	3	1	no	—
686	C₄²	—	6	1	no	—
687	C₃×C₅	#3269	1	1	yes	characteristic, complemented, Hall
688	C₂²×C₃	—	2	2	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	1	no	—
691	C₂²×C₃	—	2	1	no	—
692	C₂²×C₃	—	4	1	no	—
693	C₂²×C₃	—	4	1	no	—
694	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
695	C₂×D₃	—	2	1	no	—
696	C₂×D₃	—	2	1	no	—
697	C₂×D₃	—	2	1	no	—
698	C₂×D₃	—	4	1	no	—
699	C₂×D₃	—	4	1	no	—
700	C₂×D₃	—	4	1	no	—
701	C₃×C₄	—	2	2	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	4	1	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
706	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
707	Dic₃	—	2	1	no	—
708	Dic₃	—	2	1	no	—
709	Dic₃	—	2	1	no	—
710	Dic₃	—	4	1	no	—
711	Dic₃	—	4	1	no	—
712	Dic₃	—	4	1	no	—
713	C₂×C₅	—	4	1	no	—
714	C₂×C₅	—	4	2	no	—
715	C₂×C₅	—	12	1	no	—
716	C₂×C₅	—	24	1	no	—
717	C₂×C₅	#5777	1	1	yes	characteristic
718	C₂×C₅	#5779	1	1	yes	characteristic
719	C₂×C₅	D₄×#67	1	1	yes	characteristic
720	C₂³	—	2	1	no	—
721	C₂³	—	3	1	no	—
722	C₂³	—	6	1	no	—
723	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	6	1	no	—
731	Q₈	—	6	1	no	—
732	Q₈	C₂×C₅×#67	1	2	yes	—
733	D₄	—	2	1	no	—
734	D₄	—	4	2	no	—
735	D₄	—	6	1	no	—
736	D₄	—	6	1	no	—
737	D₄	—	12	2	no	—
738	D₄	—	12	1	no	—
739	D₄	—	12	2	no	—
740	D₄	—	12	2	no	—
741	D₄	C₂×C₅×#67	1	2	yes	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	3	1	no	—
748	C₂×C₄	—	3	1	no	—
749	C₂×C₄	—	3	1	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	6	1	no	—
753	C₂×C₄	—	6	1	no	—
754	C₂×C₄	—	6	1	no	—
755	C₂×C₄	—	6	1	no	—
756	C₂×C₄	—	6	1	no	—
757	C₂×C₄	—	12	2	no	—
758	C₂×C₄	—	12	2	no	—
759	C₂×C₄	—	12	2	no	—
760	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
762	C₈	—	2	1	no	—
763	C₈	—	6	1	no	—
764	C₈	—	6	1	no	—
765	C₈	C₂×C₅×#67	1	2	yes	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	2	no	—
768	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
769	C₂×C₃	C₅×#575	1	1	yes	characteristic
770	C₂×C₃	C₅×#578	1	1	yes	characteristic
771	D₃	—	4	1	no	—
772	D₃	—	8	1	no	—
773	C₅	#83988	1	1	yes	characteristic, direct product factor, Sylow
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	6	1	no	—
781	C₂²	—	6	1	no	—
782	C₂²	—	6	1	no	—
783	C₂²	—	12	1	no	—
784	C₂²	—	12	1	no	—
785	C₂²	—	12	1	no	—
786	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	2	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	6	1	no	—
792	C₄	—	6	1	no	—
793	C₄	—	6	1	no	—
794	C₄	—	12	1	no	—
795	C₄	—	12	1	no	—
796	C₄	—	12	1	no	—
797	C₄	C₅×#1004	1	1	yes	characteristic
798	C₄	C₂²×C₅×#67	1	1	yes	characteristic
799	C₃	C₅×#3269	1	1	yes	characteristic, complemented, Sylow
800	C₂	—	4	1	no	—
801	C₂	—	4	2	no	—
802	C₂	—	12	1	no	—
803	C₂	—	24	1	no	—
804	C₂	C₅×#5777	1	1	yes	characteristic
805	C₂	C₅×#5779	1	1	yes	characteristic
806	C₂	C₅×D₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#137	D₃
hypocenter	C₃	C₅×#3269
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#137

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
2. C₅×#5824	C₂	semidirect
3. C₅×#5817	C₂	semidirect
4. C₂×C₅×#916	C₂	semidirect
5. C₅×#5238	C₂	semidirect
6. C₅×#5228	C₂	semidirect
7. C₅×#5190	C₂	semidirect
8. C₅×#5188	C₂	semidirect
9. C₅×#5187	C₂	semidirect
10. C₅×#5182	C₂	semidirect
11. C₅×#5173	C₂	semidirect
12. C₅×#5165	C₂	semidirect
13. C₅×#5164	C₂	semidirect
14. C₅×#5134	C₂	semidirect
15. C₅×#5127	C₂	semidirect
62. #83988	C₅	direct (N × H)
63. C₂×C₅×#137	D₃	semidirect
108. C₃×C₅×SD₁₆	D₄	semidirect
140. C₂×C₃×#137	C₂×C₅	semidirect
141. #5824	C₂×C₅	semidirect
142. #5817	C₂×C₅	semidirect
143. C₂×#916	C₂×C₅	semidirect
144. #5238	C₂×C₅	semidirect
145. #5228	C₂×C₅	semidirect
146. #5190	C₂×C₅	semidirect
147. #5188	C₂×C₅	semidirect
148. #5187	C₂×C₅	semidirect
149. #5182	C₂×C₅	semidirect
150. #5173	C₂×C₅	semidirect
151. #5165	C₂×C₅	semidirect
152. #5164	C₂×C₅	semidirect
153. #5134	C₂×C₅	semidirect
154. #5127	C₂×C₅	semidirect
326. C₅×SD₁₆	#67	semidirect
354. C₂×#137	C₅×D₃	semidirect
424. C₃×SD₁₆	C₅×D₄	semidirect
659. SD₁₆	C₅×#67	semidirect
687. C₃×C₅	#3269	semidirect
773. C₅	#83988	direct (N × H)
799. C₃	C₅×#3269	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×#137	2
C₅×#5824	2
C₅×#5817	2
C₂×C₅×#916	2
C₅×#5238	2
C₅×#5228	2
C₅×#5190	2
C₅×#5188	2
C₅×#5187	2
C₅×#5182	2
C₅×#5173	2
C₅×#5165	2
C₅×#5164	2
C₅×#5134	2
C₅×#5127	2
C₅×#3269	3
#83988	5

Subgroups — C5×#83988 #14454450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83988 #14454450