Subgroups — C₂×C₅×#5779 #14510130

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1010	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#1007	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5779	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#918	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#916	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#915	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#909	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#578	—	3	1	no	maximal, Hall
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#1010	—	2	4	no	—
17	C₅×#1010	C₂²	1	8	yes	complemented
18	C₅×#1007	—	2	4	no	—
19	C₅×#1007	C₂²	1	8	yes	complemented
20	C₂×C₅×#239	—	2	1	no	—
21	C₂×C₅×#239	C₂²	1	2	yes	—
22	C₂×C₅×D₃×Q₈	—	2	1	no	—
23	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
24	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
25	C₂×C₅×#237	—	2	2	no	—
26	C₂×C₅×#237	C₂²	1	2	yes	—
27	C₂×C₅×#235	—	2	2	no	—
28	C₂×C₅×#235	—	2	1	no	—
29	C₂×C₅×#235	C₂²	1	1	yes	characteristic
30	C₂×C₅×#235	C₂²	1	1	yes	characteristic
31	C₂²×C₅×Dic₆	—	2	1	no	—
32	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
33	C₃×C₅×#137	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
35	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
36	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
37	C₅×#950	C₂²	1	8	yes	complemented
38	C₂×C₅×#216	C₂²	1	2	yes	—
39	C₂×C₅×#216	C₂²	1	2	yes	—
40	C₂×C₅×#216	C₂²	1	1	yes	characteristic
41	C₂×C₅×#216	C₂²	1	8	yes	complemented
42	C₂×C₅×#215	C₂²	1	1	yes	characteristic
43	C₂×C₅×#214	C₂²	1	1	yes	characteristic
44	C₂×C₅×#213	C₂²	1	1	yes	characteristic
45	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×#918	C₂²	1	16	yes	complemented
47	C₅×D₃×Q₁₆	C₂²	1	16	yes	complemented
48	C₅×#916	C₂²	1	16	yes	complemented
49	C₅×#915	C₂²	1	16	yes	complemented
50	C₅×#909	C₂²	1	8	yes	complemented
51	C₅×#907	C₂²	1	8	yes	complemented
52	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
53	C₂×C₅×#204	C₂²	1	2	yes	—
54	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
55	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
56	C₂×#5779	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
57	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
58	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
59	C₅×#578	—	3	16	no	—
60	C₂×C₅×#137	—	3	2	no	—
61	C₂×C₅×#137	—	3	2	no	—
62	C₂×C₅×#137	—	3	1	no	—
63	C₂×C₅×#137	D₃	1	1	yes	characteristic, complemented
64	C₂×C₅×#135	—	3	1	no	—
65	C₂×C₅×#135	—	3	2	no	—
66	C₂²×C₅×Q₁₆	—	3	1	no	—
67	C₂²×C₅×Q₁₆	—	3	2	no	—
68	C₂×C₅×#131	—	3	1	no	—
69	C₃×C₅×#41	—	2	2	no	—
70	C₃×C₅×#41	C₂³	1	4	yes	—
71	C₂×C₃×C₅×Q₈	—	2	1	no	—
72	C₂×C₃×C₅×Q₈	—	2	2	no	—
73	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
75	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
76	C₂×C₃×C₅×D₄	—	2	1	no	—
77	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	—	2	1	no	—
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₅×#67	—	2	1	no	—
82	C₂×C₅×#67	—	2	2	no	—
83	C₂×C₅×#67	D₄	1	2	yes	—
84	C₂²×C₅×Dic₃	—	2	1	no	—
85	C₂²×C₅×Dic₃	—	2	2	no	—
86	C₅×#239	—	2	8	no	—
87	C₅×#239	—	2	4	no	—
88	C₅×#239	C₂³	1	8	yes	—
89	C₅×D₃×Q₈	—	2	4	no	—
90	C₅×D₃×Q₈	—	2	4	no	—
91	C₅×D₃×Q₈	—	2	8	no	—
92	C₅×D₃×Q₈	C₂³	1	8	yes	—
93	C₅×D₃×Q₈	C₂³	1	8	yes	—
94	C₅×#237	—	2	16	no	—
95	C₅×#237	—	2	4	no	—
96	C₅×#237	C₂³	1	8	yes	—
97	C₅×#235	—	2	2	no	—
98	C₅×#235	—	2	16	no	—
99	C₅×#235	—	2	8	no	—
100	C₅×#235	D₄	1	4	yes	—
101	C₅×#235	C₂³	1	4	yes	—
102	C₅×#235	C₂³	1	4	yes	—
103	C₂×C₅×D₁₂	—	2	2	no	—
104	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
105	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
106	C₂×C₄×C₅×D₃	—	2	2	no	—
107	C₂×C₄×C₅×D₃	—	2	2	no	—
108	C₂×C₄×C₅×D₃	—	2	1	no	—
109	C₂×C₄×C₅×D₃	—	2	2	no	—
110	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
111	C₂×C₅×Dic₆	—	2	1	no	—
112	C₂×C₅×Dic₆	—	2	2	no	—
113	C₂×C₅×Dic₆	—	2	2	no	—
114	C₂×C₅×Dic₆	—	2	2	no	—
115	C₂×C₅×Dic₆	—	2	8	no	—
116	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
117	C₂×C₅×Dic₆	C₂³	1	2	yes	—
118	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
119	C₂×C₅×Dic₆	C₂³	1	4	yes	—
120	C₃×C₅×Q₁₆	C₂³	1	8	yes	—
121	C₃×C₅×SD₁₆	C₂³	1	8	yes	—
122	C₃×C₅×M₁₆	C₂³	1	4	yes	—
123	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
124	C₅×#216	C₂³	1	8	yes	—
125	C₅×#216	C₂³	1	8	yes	—
126	C₅×#216	C₂³	1	4	yes	—
127	C₅×#215	C₂³	1	4	yes	—
128	C₅×#214	C₂³	1	4	yes	—
129	C₅×#213	C₂³	1	4	yes	—
130	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
133	C₅×Dic₁₂	C₂³	1	8	yes	—
134	C₅×#204	C₂³	1	8	yes	—
135	C₅×ΓL(1,𝔽₂₅)	C₂³	1	8	yes	—
136	C₅×D₃×C₈	C₂³	1	8	yes	—
137	C₂×#1010	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#1007	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
142	#5779	C₂×C₅	1	16	yes	direct product factor
143	C₂×#918	C₂×C₅	1	2	yes	complemented
144	C₂×D₃×Q₁₆	C₂×C₅	1	2	yes	complemented
145	C₂×#916	C₂×C₅	1	2	yes	complemented
146	C₂×#915	C₂×C₅	1	2	yes	complemented
147	C₂×#909	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
149	C₅×2₋¹⁺⁴	—	3	8	no	—
150	C₅×2₋¹⁺⁴	—	3	8	no	—
151	C₅×2₋¹⁺⁴	—	6	4	no	—
152	C₅×2₋¹⁺⁴	—	6	4	no	—
153	C₂×C₅×#41	—	3	1	no	—
154	C₂×C₅×#41	—	3	2	no	—
155	C₂×C₅×#41	—	3	2	no	—
156	C₂×C₅×#41	—	3	1	no	—
157	C₂×C₅×#41	—	6	2	no	—
158	C₂×C₅×#41	—	6	1	no	—
159	C₂×C₅×#41	—	6	2	no	—
160	C₂×C₅×#41	—	6	1	no	—
161	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
162	C₂²×C₅×Q₈	—	3	2	no	—
163	C₂²×C₅×Q₈	—	3	2	no	—
164	C₂²×C₅×Q₈	—	3	1	no	—
165	C₂²×C₅×Q₈	—	6	1	no	—
166	C₂²×C₅×Q₈	—	6	1	no	—
167	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
168	C₅×#137	—	3	16	no	—
169	C₅×#137	—	3	16	no	—
170	C₅×#137	—	3	8	no	—
171	C₅×#137	C₂×D₃	1	8	yes	complemented
172	C₅×#135	—	3	8	no	—
173	C₅×#135	—	3	16	no	—
174	C₂×C₅×Q₁₆	—	3	1	no	—
175	C₂×C₅×Q₁₆	—	3	2	no	—
176	C₂×C₅×Q₁₆	—	3	2	no	—
177	C₂×C₅×Q₁₆	—	3	8	no	—
178	C₂×C₅×Q₁₆	—	3	16	no	—
179	C₂×C₅×Q₁₆	—	3	2	no	—
180	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
181	C₂×C₅×SD₁₆	—	3	1	no	—
182	C₂×C₅×SD₁₆	—	3	1	no	—
183	C₂×C₅×SD₁₆	—	3	2	no	—
184	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
185	C₂×C₅×D₈	—	3	1	no	—
186	C₅×#131	—	3	8	no	—
187	C₂×C₅×M₁₆	—	3	2	no	—
188	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
189	C₂²×C₅×C₈	—	3	1	no	—
190	C₂²×C₅×C₈	—	3	2	no	—
191	C₂×#578	—	3	1	no	Sylow
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₅×D₃	—	2	1	no	—
195	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	—	2	2	no	—
198	C₃×C₅×Q₈	—	2	4	no	—
199	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
200	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
201	C₃×C₅×D₄	—	2	4	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	C₂⁴	1	2	yes	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	2	no	—
206	C₂×C₃×C₄×C₅	—	2	4	no	—
207	C₂×C₃×C₄×C₅	—	2	4	no	—
208	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
210	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
212	C₅×#67	—	2	4	no	—
213	C₅×#67	—	2	8	no	—
214	C₅×#67	C₂×D₄	1	8	yes	—
215	C₂×C₅×Dic₃	—	2	1	no	—
216	C₂×C₅×Dic₃	—	2	2	no	—
217	C₂×C₅×Dic₃	—	2	4	no	—
218	C₂×C₅×Dic₃	—	2	8	no	—
219	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
220	C₅×D₁₂	—	2	8	no	—
221	C₅×D₁₂	—	2	1	no	—
222	C₅×D₁₂	C₂×D₄	1	4	yes	—
223	C₅×D₁₂	C₂⁴	1	2	yes	—
224	C₄×C₅×D₃	—	2	8	no	—
225	C₄×C₅×D₃	—	2	8	no	—
226	C₄×C₅×D₃	—	2	4	no	—
227	C₄×C₅×D₃	—	2	8	no	—
228	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
229	C₄×C₅×D₃	C₂⁴	1	4	yes	—
230	C₅×Dic₆	—	2	4	no	—
231	C₅×Dic₆	—	2	2	no	—
232	C₅×Dic₆	—	2	1	no	—
233	C₅×Dic₆	—	2	8	no	—
234	C₅×Dic₆	—	2	8	no	—
235	C₅×Dic₆	C₂×D₄	1	4	yes	—
236	C₅×Dic₆	C₂⁴	1	4	yes	—
237	C₅×Dic₆	C₂⁴	1	2	yes	—
238	C₃×C₅×C₈	C₂⁴	1	4	yes	—
239	C₅×C₃⋊C₈	C₂⁴	1	2	yes	—
240	C₅×C₃⋊C₈	C₂⁴	1	2	yes	—
241	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
242	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
243	#1010	—	2	4	no	—
244	#1010	C₂²×C₅	1	8	yes	complemented
245	#1007	—	2	4	no	—
246	#1007	C₂²×C₅	1	8	yes	complemented
247	C₂×#239	—	2	1	no	—
248	C₂×#239	C₂²×C₅	1	2	yes	—
249	C₂×D₃×Q₈	—	2	1	no	—
250	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
251	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
252	C₂×#237	—	2	2	no	—
253	C₂×#237	C₂²×C₅	1	2	yes	—
254	C₂×#235	—	2	2	no	—
255	C₂×#235	—	2	1	no	—
256	C₂×#235	C₂²×C₅	1	1	yes	characteristic
257	C₂×#235	C₂²×C₅	1	1	yes	characteristic
258	C₂²×Dic₆	—	2	1	no	—
259	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
260	C₃×#137	C₂²×C₅	1	8	yes	complemented
261	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
262	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
263	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
264	#950	C₂²×C₅	1	8	yes	complemented
265	C₂×#216	C₂²×C₅	1	2	yes	—
266	C₂×#216	C₂²×C₅	1	2	yes	—
267	C₂×#216	C₂²×C₅	1	1	yes	characteristic
268	C₂×#216	C₂²×C₅	1	8	yes	complemented
269	C₂×#215	C₂²×C₅	1	1	yes	characteristic
270	C₂×#214	C₂²×C₅	1	1	yes	characteristic
271	C₂×#213	C₂²×C₅	1	1	yes	characteristic
272	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	#918	C₂²×C₅	1	16	yes	complemented
274	D₃×Q₁₆	C₂²×C₅	1	16	yes	complemented
275	#916	C₂²×C₅	1	16	yes	complemented
276	#915	C₂²×C₅	1	16	yes	complemented
277	#909	C₂²×C₅	1	8	yes	complemented
278	#907	C₂²×C₅	1	8	yes	complemented
279	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
280	C₂×#204	C₂²×C₅	1	2	yes	—
281	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
282	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
283	C₅×#41	—	2	2	no	—
284	C₅×#41	—	3	4	no	—
285	C₅×#41	—	3	4	no	—
286	C₅×#41	—	3	8	no	—
287	C₅×#41	—	3	8	no	—
288	C₅×#41	—	3	4	no	—
289	C₅×#41	—	6	16	no	—
290	C₅×#41	—	6	8	no	—
291	C₅×#41	—	6	4	no	—
292	C₅×#41	—	6	4	no	—
293	C₅×#41	—	6	16	no	—
294	C₅×#41	—	6	8	no	—
295	C₅×#41	—	6	2	no	—
296	C₅×#41	C₂²×D₃	1	4	yes	—
297	C₂×C₅×Q₈	—	2	1	no	—
298	C₂×C₅×Q₈	—	2	2	no	—
299	C₂×C₅×Q₈	—	3	1	no	—
300	C₂×C₅×Q₈	—	3	8	no	—
301	C₂×C₅×Q₈	—	3	8	no	—
302	C₂×C₅×Q₈	—	3	1	no	—
303	C₂×C₅×Q₈	—	3	2	no	—
304	C₂×C₅×Q₈	—	3	4	no	—
305	C₂×C₅×Q₈	—	6	2	no	—
306	C₂×C₅×Q₈	—	6	2	no	—
307	C₂×C₅×Q₈	—	6	8	no	—
308	C₂×C₅×Q₈	—	6	4	no	—
309	C₂×C₅×Q₈	—	6	4	no	—
310	C₂×C₅×Q₈	—	6	8	no	—
311	C₂×C₅×Q₈	—	6	1	no	—
312	C₂×C₅×Q₈	—	6	2	no	—
313	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
314	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
315	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
316	C₂×C₅×D₄	—	2	1	no	—
317	C₂×C₅×D₄	—	3	2	no	—
318	C₂×C₅×D₄	—	3	1	no	—
319	C₂×C₅×D₄	—	3	1	no	—
320	C₂×C₅×D₄	—	6	2	no	—
321	C₂×C₅×D₄	—	6	2	no	—
322	C₂×C₅×D₄	—	6	1	no	—
323	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	—	2	1	no	—
325	C₂²×C₄×C₅	—	2	1	no	—
326	C₂²×C₄×C₅	—	3	2	no	—
327	C₂²×C₄×C₅	—	6	2	no	—
328	C₂²×C₄×C₅	—	6	2	no	—
329	C₂²×C₄×C₅	—	6	2	no	—
330	C₂²×C₄×C₅	—	6	2	no	—
331	C₂²×C₄×C₅	—	6	1	no	—
332	C₂²×C₄×C₅	—	6	1	no	—
333	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
334	C₅×Q₁₆	—	3	4	no	—
335	C₅×Q₁₆	—	3	8	no	—
336	C₅×Q₁₆	—	3	8	no	—
337	C₅×Q₁₆	—	3	8	no	—
338	C₅×Q₁₆	C₂²×D₃	1	8	yes	—
339	C₅×SD₁₆	—	3	4	no	—
340	C₅×SD₁₆	—	3	4	no	—
341	C₅×SD₁₆	—	3	8	no	—
342	C₅×SD₁₆	C₂²×D₃	1	8	yes	—
343	C₅×D₈	—	3	4	no	—
344	C₅×M₁₆	—	3	8	no	—
345	C₅×M₁₆	C₂²×D₃	1	4	yes	—
346	C₂×C₅×C₈	—	3	1	no	—
347	C₂×C₅×C₈	—	3	1	no	—
348	C₂×C₅×C₈	—	3	4	no	—
349	C₂×C₅×C₈	—	3	8	no	—
350	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
351	C₂×2₋¹⁺⁴	—	3	1	no	—
352	C₂×2₋¹⁺⁴	—	3	1	no	—
353	#578	—	3	16	no	—
354	C₂×#137	—	3	2	no	—
355	C₂×#137	—	3	2	no	—
356	C₂×#137	—	3	1	no	—
357	C₂×#137	C₅×D₃	1	1	yes	characteristic, complemented
358	C₂×#135	—	3	1	no	—
359	C₂×#135	—	3	2	no	—
360	C₂²×Q₁₆	—	3	1	no	—
361	C₂²×Q₁₆	—	3	2	no	—
362	C₂×#131	—	3	1	no	—
363	C₂²×C₃×C₅	—	2	2	no	—
364	C₂²×C₃×C₅	—	2	2	no	—
365	C₂²×C₃×C₅	—	4	2	no	—
366	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
367	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₅×D₃	—	2	4	no	—
369	C₂×C₅×D₃	—	2	2	no	—
370	C₂×C₅×D₃	—	4	2	no	—
371	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
372	C₃×C₄×C₅	—	2	2	no	—
373	C₃×C₄×C₅	—	2	4	no	—
374	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
375	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
376	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
377	C₅×Dic₃	—	2	2	no	—
378	C₅×Dic₃	—	2	4	no	—
379	C₅×Dic₃	C₂²×D₄	1	4	yes	—
380	C₃×#41	—	2	2	no	—
381	C₃×#41	C₂³×C₅	1	4	yes	—
382	C₂×C₃×Q₈	—	2	1	no	—
383	C₂×C₃×Q₈	—	2	2	no	—
384	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
386	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
387	C₂×C₃×D₄	—	2	1	no	—
388	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	—	2	1	no	—
390	C₂²×C₃×C₄	—	2	1	no	—
391	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂×#67	—	2	1	no	—
393	C₂×#67	—	2	2	no	—
394	C₂×#67	C₅×D₄	1	2	yes	—
395	C₂²×Dic₃	—	2	1	no	—
396	C₂²×Dic₃	—	2	2	no	—
397	#239	—	2	8	no	—
398	#239	—	2	4	no	—
399	#239	C₂³×C₅	1	8	yes	—
400	D₃×Q₈	—	2	4	no	—
401	D₃×Q₈	—	2	4	no	—
402	D₃×Q₈	—	2	8	no	—
403	D₃×Q₈	C₂³×C₅	1	8	yes	—
404	D₃×Q₈	C₂³×C₅	1	8	yes	—
405	#237	—	2	16	no	—
406	#237	—	2	4	no	—
407	#237	C₂³×C₅	1	8	yes	—
408	#235	—	2	2	no	—
409	#235	—	2	16	no	—
410	#235	—	2	8	no	—
411	#235	C₅×D₄	1	4	yes	—
412	#235	C₂³×C₅	1	4	yes	—
413	#235	C₂³×C₅	1	4	yes	—
414	C₂×D₁₂	—	2	2	no	—
415	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
416	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₄×D₃	—	2	2	no	—
418	C₂×C₄×D₃	—	2	2	no	—
419	C₂×C₄×D₃	—	2	1	no	—
420	C₂×C₄×D₃	—	2	2	no	—
421	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
422	C₂×Dic₆	—	2	1	no	—
423	C₂×Dic₆	—	2	2	no	—
424	C₂×Dic₆	—	2	2	no	—
425	C₂×Dic₆	—	2	2	no	—
426	C₂×Dic₆	—	2	8	no	—
427	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
428	C₂×Dic₆	C₂³×C₅	1	2	yes	—
429	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
430	C₂×Dic₆	C₂³×C₅	1	4	yes	—
431	C₃×Q₁₆	C₂³×C₅	1	8	yes	—
432	C₃×SD₁₆	C₂³×C₅	1	8	yes	—
433	C₃×M₁₆	C₂³×C₅	1	4	yes	—
434	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
435	#216	C₂³×C₅	1	8	yes	—
436	#216	C₂³×C₅	1	8	yes	—
437	#216	C₂³×C₅	1	4	yes	—
438	#215	C₂³×C₅	1	4	yes	—
439	#214	C₂³×C₅	1	4	yes	—
440	#213	C₂³×C₅	1	4	yes	—
441	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
444	Dic₁₂	C₂³×C₅	1	8	yes	—
445	#204	C₂³×C₅	1	8	yes	—
446	ΓL(1,𝔽₂₅)	C₂³×C₅	1	8	yes	—
447	D₃×C₈	C₂³×C₅	1	8	yes	—
448	C₂³×C₅	—	2	1	no	—
449	C₂³×C₅	—	3	2	no	—
450	C₂³×C₅	—	6	1	no	—
451	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
452	C₅×Q₈	—	2	4	no	—
453	C₅×Q₈	—	2	2	no	—
454	C₅×Q₈	—	2	1	no	—
455	C₅×Q₈	—	3	4	no	—
456	C₅×Q₈	—	3	2	no	—
457	C₅×Q₈	—	3	4	no	—
458	C₅×Q₈	—	6	8	no	—
459	C₅×Q₈	—	6	8	no	—
460	C₅×Q₈	—	6	4	no	—
461	C₅×Q₈	—	6	2	no	—
462	C₅×Q₈	—	6	1	no	—
463	C₅×Q₈	C₂³×D₃	1	2	yes	—
464	C₅×Q₈	C₂³×D₃	1	4	yes	—
465	C₅×D₄	—	2	4	no	—
466	C₅×D₄	—	2	1	no	—
467	C₅×D₄	—	3	8	no	—
468	C₅×D₄	—	3	4	no	—
469	C₅×D₄	—	3	2	no	—
470	C₅×D₄	—	6	8	no	—
471	C₅×D₄	—	6	8	no	—
472	C₅×D₄	—	6	4	no	—
473	C₅×D₄	—	6	1	no	—
474	C₅×D₄	C₂³×D₃	1	2	yes	—
475	C₂×C₄×C₅	—	2	4	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	2	no	—
478	C₂×C₄×C₅	—	2	4	no	—
479	C₂×C₄×C₅	—	3	2	no	—
480	C₂×C₄×C₅	—	3	4	no	—
481	C₂×C₄×C₅	—	3	4	no	—
482	C₂×C₄×C₅	—	6	8	no	—
483	C₂×C₄×C₅	—	6	8	no	—
484	C₂×C₄×C₅	—	6	8	no	—
485	C₂×C₄×C₅	—	6	8	no	—
486	C₂×C₄×C₅	—	6	4	no	—
487	C₂×C₄×C₅	—	6	1	no	—
488	C₂×C₄×C₅	—	6	2	no	—
489	C₂×C₄×C₅	—	6	4	no	—
490	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
491	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
492	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
493	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
494	C₅×C₈	—	3	2	no	—
495	C₅×C₈	—	3	2	no	—
496	C₅×C₈	C₂³×D₃	1	4	yes	—
497	2₋¹⁺⁴	—	3	8	no	—
498	2₋¹⁺⁴	—	3	8	no	—
499	2₋¹⁺⁴	—	6	4	no	—
500	2₋¹⁺⁴	—	6	4	no	—
501	C₂×#41	—	3	1	no	—
502	C₂×#41	—	3	2	no	—
503	C₂×#41	—	3	2	no	—
504	C₂×#41	—	3	1	no	—
505	C₂×#41	—	6	2	no	—
506	C₂×#41	—	6	1	no	—
507	C₂×#41	—	6	2	no	—
508	C₂×#41	—	6	1	no	—
509	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
510	C₂²×Q₈	—	3	2	no	—
511	C₂²×Q₈	—	3	2	no	—
512	C₂²×Q₈	—	3	1	no	—
513	C₂²×Q₈	—	6	1	no	—
514	C₂²×Q₈	—	6	1	no	—
515	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
516	#137	—	3	16	no	—
517	#137	—	3	16	no	—
518	#137	—	3	8	no	—
519	#137	C₂×C₅×D₃	1	8	yes	complemented
520	#135	—	3	8	no	—
521	#135	—	3	16	no	—
522	C₂×Q₁₆	—	3	1	no	—
523	C₂×Q₁₆	—	3	2	no	—
524	C₂×Q₁₆	—	3	2	no	—
525	C₂×Q₁₆	—	3	8	no	—
526	C₂×Q₁₆	—	3	16	no	—
527	C₂×Q₁₆	—	3	2	no	—
528	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
529	C₂×SD₁₆	—	3	1	no	—
530	C₂×SD₁₆	—	3	1	no	—
531	C₂×SD₁₆	—	3	2	no	—
532	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
533	C₂×D₈	—	3	1	no	—
534	#131	—	3	8	no	—
535	C₂×M₁₆	—	3	2	no	—
536	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
537	C₂²×C₈	—	3	1	no	—
538	C₂²×C₈	—	3	2	no	—
539	C₂×C₃×C₅	—	2	2	no	—
540	C₂×C₃×C₅	—	4	2	no	—
541	C₂×C₃×C₅	#578	1	2	yes	complemented
542	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
543	C₅×D₃	—	2	4	no	—
544	C₅×D₃	—	4	2	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
547	C₂²×D₃	—	2	1	no	—
548	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
549	C₃×Q₈	—	2	1	no	—
550	C₃×Q₈	—	2	2	no	—
551	C₃×Q₈	—	2	4	no	—
552	C₃×Q₈	C₂⁴×C₅	1	2	yes	—
553	C₃×Q₈	C₂⁴×C₅	1	4	yes	—
554	C₃×D₄	—	2	4	no	—
555	C₃×D₄	—	2	1	no	—
556	C₃×D₄	C₂⁴×C₅	1	2	yes	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	4	no	—
560	C₂×C₃×C₄	—	2	4	no	—
561	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
563	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
565	#67	—	2	4	no	—
566	#67	—	2	8	no	—
567	#67	C₂×C₅×D₄	1	8	yes	—
568	C₂×Dic₃	—	2	1	no	—
569	C₂×Dic₃	—	2	2	no	—
570	C₂×Dic₃	—	2	4	no	—
571	C₂×Dic₃	—	2	8	no	—
572	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
573	D₁₂	—	2	8	no	—
574	D₁₂	—	2	1	no	—
575	D₁₂	C₂×C₅×D₄	1	4	yes	—
576	D₁₂	C₂⁴×C₅	1	2	yes	—
577	C₄×D₃	—	2	8	no	—
578	C₄×D₃	—	2	8	no	—
579	C₄×D₃	—	2	4	no	—
580	C₄×D₃	—	2	8	no	—
581	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
582	C₄×D₃	C₂⁴×C₅	1	4	yes	—
583	Dic₆	—	2	4	no	—
584	Dic₆	—	2	2	no	—
585	Dic₆	—	2	1	no	—
586	Dic₆	—	2	8	no	—
587	Dic₆	—	2	8	no	—
588	Dic₆	C₂×C₅×D₄	1	4	yes	—
589	Dic₆	C₂⁴×C₅	1	4	yes	—
590	Dic₆	C₂⁴×C₅	1	2	yes	—
591	C₃×C₈	C₂⁴×C₅	1	4	yes	—
592	C₃⋊C₈	C₂⁴×C₅	1	2	yes	—
593	C₃⋊C₈	C₂⁴×C₅	1	2	yes	—
594	C₂²×C₅	—	2	2	no	—
595	C₂²×C₅	—	2	2	no	—
596	C₂²×C₅	—	3	4	no	—
597	C₂²×C₅	—	4	2	no	—
598	C₂²×C₅	—	6	4	no	—
599	C₂²×C₅	—	6	2	no	—
600	C₂²×C₅	—	12	2	no	—
601	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
602	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	2	4	no	—
605	C₄×C₅	—	3	4	no	—
606	C₄×C₅	—	6	2	no	—
607	C₄×C₅	—	6	4	no	—
608	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
609	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
610	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
611	#41	—	2	2	no	—
612	#41	—	3	4	no	—
613	#41	—	3	4	no	—
614	#41	—	3	8	no	—
615	#41	—	3	8	no	—
616	#41	—	3	4	no	—
617	#41	—	6	16	no	—
618	#41	—	6	8	no	—
619	#41	—	6	4	no	—
620	#41	—	6	4	no	—
621	#41	—	6	16	no	—
622	#41	—	6	8	no	—
623	#41	—	6	2	no	—
624	#41	C₂²×C₅×D₃	1	4	yes	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	3	1	no	—
628	C₂×Q₈	—	3	8	no	—
629	C₂×Q₈	—	3	8	no	—
630	C₂×Q₈	—	3	1	no	—
631	C₂×Q₈	—	3	2	no	—
632	C₂×Q₈	—	3	4	no	—
633	C₂×Q₈	—	6	2	no	—
634	C₂×Q₈	—	6	2	no	—
635	C₂×Q₈	—	6	8	no	—
636	C₂×Q₈	—	6	4	no	—
637	C₂×Q₈	—	6	4	no	—
638	C₂×Q₈	—	6	8	no	—
639	C₂×Q₈	—	6	1	no	—
640	C₂×Q₈	—	6	2	no	—
641	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
642	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
643	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	3	2	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	6	2	no	—
649	C₂×D₄	—	6	2	no	—
650	C₂×D₄	—	6	1	no	—
651	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	3	2	no	—
655	C₂²×C₄	—	6	2	no	—
656	C₂²×C₄	—	6	2	no	—
657	C₂²×C₄	—	6	2	no	—
658	C₂²×C₄	—	6	2	no	—
659	C₂²×C₄	—	6	1	no	—
660	C₂²×C₄	—	6	1	no	—
661	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
662	Q₁₆	—	3	4	no	—
663	Q₁₆	—	3	8	no	—
664	Q₁₆	—	3	8	no	—
665	Q₁₆	—	3	8	no	—
666	Q₁₆	C₂²×C₅×D₃	1	8	yes	—
667	SD₁₆	—	3	4	no	—
668	SD₁₆	—	3	4	no	—
669	SD₁₆	—	3	8	no	—
670	SD₁₆	C₂²×C₅×D₃	1	8	yes	—
671	D₈	—	3	4	no	—
672	M₁₆	—	3	8	no	—
673	M₁₆	C₂²×C₅×D₃	1	4	yes	—
674	C₂×C₈	—	3	1	no	—
675	C₂×C₈	—	3	1	no	—
676	C₂×C₈	—	3	4	no	—
677	C₂×C₈	—	3	8	no	—
678	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
679	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
680	C₂²×C₃	—	2	2	no	—
681	C₂²×C₃	—	2	2	no	—
682	C₂²×C₃	—	4	2	no	—
683	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
684	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
685	C₂×D₃	—	2	4	no	—
686	C₂×D₃	—	2	2	no	—
687	C₂×D₃	—	4	2	no	—
688	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
689	C₃×C₄	—	2	2	no	—
690	C₃×C₄	—	2	4	no	—
691	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
692	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
693	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
694	Dic₃	—	2	2	no	—
695	Dic₃	—	2	4	no	—
696	Dic₃	C₂²×C₅×D₄	1	4	yes	—
697	C₂×C₅	—	2	2	no	—
698	C₂×C₅	—	4	2	no	—
699	C₂×C₅	—	6	4	no	—
700	C₂×C₅	—	12	2	no	—
701	C₂×C₅	#5779	1	2	yes	direct product factor
702	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
703	C₂³	—	2	1	no	—
704	C₂³	—	3	2	no	—
705	C₂³	—	6	1	no	—
706	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	3	4	no	—
711	Q₈	—	3	2	no	—
712	Q₈	—	3	4	no	—
713	Q₈	—	6	8	no	—
714	Q₈	—	6	8	no	—
715	Q₈	—	6	4	no	—
716	Q₈	—	6	1	no	—
717	Q₈	—	6	2	no	—
718	Q₈	C₂³×C₅×D₃	1	2	yes	—
719	Q₈	C₂³×C₅×D₃	1	4	yes	—
720	D₄	—	2	4	no	—
721	D₄	—	2	1	no	—
722	D₄	—	3	8	no	—
723	D₄	—	3	4	no	—
724	D₄	—	3	2	no	—
725	D₄	—	6	8	no	—
726	D₄	—	6	8	no	—
727	D₄	—	6	4	no	—
728	D₄	—	6	1	no	—
729	D₄	C₂³×C₅×D₃	1	2	yes	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	3	2	no	—
735	C₂×C₄	—	3	4	no	—
736	C₂×C₄	—	3	4	no	—
737	C₂×C₄	—	6	8	no	—
738	C₂×C₄	—	6	8	no	—
739	C₂×C₄	—	6	8	no	—
740	C₂×C₄	—	6	8	no	—
741	C₂×C₄	—	6	1	no	—
742	C₂×C₄	—	6	2	no	—
743	C₂×C₄	—	6	4	no	—
744	C₂×C₄	—	6	4	no	—
745	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
746	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
747	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
748	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
749	C₈	—	3	2	no	—
750	C₈	—	3	2	no	—
751	C₈	C₂³×C₅×D₃	1	4	yes	—
752	C₂×C₃	—	2	2	no	—
753	C₂×C₃	—	4	2	no	—
754	C₂×C₃	C₅×#578	1	2	yes	complemented
755	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
756	D₃	—	2	4	no	—
757	D₃	—	4	2	no	—
758	C₅	C₂×#5779	1	1	yes	characteristic, direct product factor, Sylow
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	3	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	6	4	no	—
764	C₂²	—	6	2	no	—
765	C₂²	—	12	2	no	—
766	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
767	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
768	C₄	—	2	2	no	—
769	C₄	—	2	4	no	—
770	C₄	—	3	4	no	—
771	C₄	—	6	2	no	—
772	C₄	—	6	4	no	—
773	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
774	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
775	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
776	C₃	C₂×C₅×#578	1	1	yes	characteristic, complemented, Sylow
777	C₂	—	2	2	no	—
778	C₂	—	4	2	no	—
779	C₂	—	6	4	no	—
780	C₂	—	12	2	no	—
781	C₂	C₅×#5779	1	2	yes	direct product factor
782	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#137	D₃
hypocenter	C₃	C₂×C₅×#578
LCS	G ▷ 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×C₅×#1010	C₂	semidirect
2. C₂×C₅×#1007	C₂	semidirect
3. C₂×C₃×C₅×#137	C₂	semidirect
4. C₂×C₅×#950	C₂	semidirect
5. C₂²×C₅×#216	C₂	semidirect
6. C₅×#5779	C₂	direct (N × H)
7. C₂×C₅×#918	C₂	semidirect
8. C₂×C₅×D₃×Q₁₆	C₂	semidirect
9. C₂×C₅×#916	C₂	semidirect
10. C₂×C₅×#915	C₂	semidirect
11. C₂×C₅×#909	C₂	semidirect
12. C₂×C₅×#907	C₂	semidirect
17. C₅×#1010	C₂²	semidirect
19. C₅×#1007	C₂²	semidirect
33. C₃×C₅×#137	C₂²	semidirect
37. C₅×#950	C₂²	semidirect
41. C₂×C₅×#216	C₂²	semidirect
46. C₅×#918	C₂²	semidirect
47. C₅×D₃×Q₁₆	C₂²	semidirect
48. C₅×#916	C₂²	semidirect
49. C₅×#915	C₂²	semidirect
50. C₅×#909	C₂²	semidirect
51. C₅×#907	C₂²	semidirect
56. C₂×#5779	C₅	direct (N × H)
63. C₂×C₅×#137	D₃	semidirect
137. C₂×#1010	C₂×C₅	semidirect
138. C₂×#1007	C₂×C₅	semidirect
139. C₂×C₃×#137	C₂×C₅	semidirect
140. C₂×#950	C₂×C₅	semidirect
141. C₂²×#216	C₂×C₅	semidirect
142. #5779	C₂×C₅	direct (N × H)
143. C₂×#918	C₂×C₅	semidirect
144. C₂×D₃×Q₁₆	C₂×C₅	semidirect
145. C₂×#916	C₂×C₅	semidirect
146. C₂×#915	C₂×C₅	semidirect
147. C₂×#909	C₂×C₅	semidirect
148. C₂×#907	C₂×C₅	semidirect
171. C₅×#137	C₂×D₃	semidirect
244. #1010	C₂²×C₅	semidirect
246. #1007	C₂²×C₅	semidirect
260. C₃×#137	C₂²×C₅	semidirect
264. #950	C₂²×C₅	semidirect
268. C₂×#216	C₂²×C₅	semidirect
273. #918	C₂²×C₅	semidirect
274. D₃×Q₁₆	C₂²×C₅	semidirect
275. #916	C₂²×C₅	semidirect
276. #915	C₂²×C₅	semidirect
277. #909	C₂²×C₅	semidirect
278. #907	C₂²×C₅	semidirect
357. C₂×#137	C₅×D₃	semidirect
519. #137	C₂×C₅×D₃	semidirect
541. C₂×C₃×C₅	#578	semidirect
679. C₃×C₅	C₂×#578	semidirect
701. C₂×C₅	#5779	direct (N × H)
754. C₂×C₃	C₅×#578	semidirect
758. C₅	C₂×#5779	direct (N × H)
776. C₃	C₂×C₅×#578	semidirect
781. C₂	C₅×#5779	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#1010	2
C₂×C₅×#1007	2
C₂×C₃×C₅×#137	2
C₂×C₅×#950	2
C₂²×C₅×#216	2
C₅×#5779	2
C₂×C₅×#918	2
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×#916	2
C₂×C₅×#915	2
C₂×C₅×#909	2
C₂×C₅×#907	2
C₂×C₅×#578	3
C₂×#5779	5

Subgroups — C2×C5×#5779 #14510130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5779 #14510130