Subgroups — C₅×#22444 #11945164

Order 1280.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2339	C₂	1	1	yes	maximal, characteristic
6	C₅×#1971	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1809	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1788	C₂	1	1	yes	maximal, characteristic
14	C₅×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#137	—	2	4	no	—
19	C₂×C₅×#137	—	2	4	no	—
20	C₂×C₅×#137	C₄	1	8	yes	complemented
21	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₅×#440	—	2	4	no	—
31	C₄×C₅×SD₁₆	—	2	4	no	—
32	C₂×C₅×#107	C₂²	1	1	yes	characteristic
33	C₂×C₅×#106	C₂²	1	1	yes	characteristic
34	C₂×C₅×#103	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×#103	C₂²	1	1	yes	characteristic
37	C₂×C₅×#103	C₂²	1	1	yes	characteristic
38	C₂×C₅×#103	C₂²	1	1	yes	characteristic
39	C₂×C₅×#103	C₂²	1	1	yes	characteristic
40	C₂×C₅×#102	C₂²	1	1	yes	characteristic
41	C₂×C₅×#102	C₂²	1	1	yes	characteristic
42	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₅×#97	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
45	C₅×#391	—	2	1	no	—
46	C₅×#391	—	2	1	no	—
47	C₅×#391	C₂²	1	1	yes	characteristic
48	C₅×#391	C₂²	1	1	yes	characteristic
49	C₅×#391	C₂²	1	1	yes	characteristic
50	C₅×#391	C₂²	1	1	yes	characteristic
51	C₅×#386	—	2	1	no	—
52	C₅×#386	—	2	1	no	—
53	C₅×#381	—	2	1	no	—
54	C₅×#380	—	2	1	no	—
55	C₅×#380	C₂²	1	1	yes	characteristic
56	C₅×#380	C₂²	1	1	yes	characteristic
57	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₂×C₅×#95	—	2	1	no	—
60	C₅×#340	C₂²	1	1	yes	characteristic
61	C₅×#340	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	C₅×#336	C₂²	1	1	yes	characteristic
64	#22444	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂×C₅×#41	—	2	2	no	—
66	C₂×C₅×#41	—	2	2	no	—
67	C₂×C₅×#41	—	2	2	no	—
68	C₂×C₅×#41	—	4	1	no	—
69	C₂×C₅×#41	—	4	1	no	—
70	C₂×C₅×#41	C₂×C₄	1	4	yes	—
71	C₂²×C₅×Q₈	—	2	1	no	—
72	C₂²×C₅×Q₈	—	2	2	no	—
73	C₂²×C₅×Q₈	—	2	2	no	—
74	C₂²×C₅×Q₈	—	2	2	no	—
75	C₂²×C₅×Q₈	—	4	1	no	—
76	C₂²×C₅×Q₈	—	4	1	no	—
77	C₂²×C₅×Q₈	C₂×C₄	1	4	yes	complemented
78	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×D₄	—	2	1	no	—
82	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₅	—	2	1	no	—
84	C₂³×C₄×C₅	—	2	1	no	—
85	C₂³×C₄×C₅	—	2	1	no	—
86	C₂³×C₄×C₅	—	2	1	no	—
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₅×#137	—	2	32	no	—
89	C₂×C₅×Q₁₆	—	2	2	no	—
90	C₂×C₅×Q₁₆	—	2	2	no	—
91	C₂×C₅×Q₁₆	—	2	2	no	—
92	C₂×C₅×Q₁₆	—	2	2	no	—
93	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
94	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
95	C₂×C₅×SD₁₆	—	2	2	no	—
96	C₂×C₅×SD₁₆	—	2	2	no	—
97	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
98	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
99	C₂×C₅×SD₁₆	D₄	1	4	yes	—
100	C₂×C₅×SD₁₆	D₄	1	4	yes	—
101	C₂×C₅×M₁₆	—	2	2	no	—
102	C₂×C₅×M₁₆	—	2	2	no	—
103	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
104	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₅×Q₈	—	2	2	no	—
109	C₄×C₅×Q₈	—	2	2	no	—
110	C₄×C₅×Q₈	—	4	1	no	—
111	C₄×C₅×Q₈	—	4	1	no	—
112	C₄×C₅×D₄	—	2	2	no	—
113	C₄×C₅×D₄	—	2	2	no	—
114	C₄×C₅×D₄	—	4	1	no	—
115	C₄×C₅×D₄	—	4	1	no	—
116	C₂×C₅×C₄⋊C₄	—	2	1	no	—
117	C₂×C₅×C₄⋊C₄	—	2	1	no	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₅	—	2	1	no	—
129	C₂×C₄²×C₅	—	2	1	no	—
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₅×#107	—	2	2	no	—
133	C₅×#106	—	2	2	no	—
134	C₅×#103	—	2	2	no	—
135	C₅×#103	—	2	2	no	—
136	C₅×#103	—	4	1	no	—
137	C₅×#103	—	4	1	no	—
138	C₅×#103	—	4	1	no	—
139	C₅×#103	—	4	1	no	—
140	C₅×#102	—	2	2	no	—
141	C₅×#102	—	2	2	no	—
142	C₅×C₂²⋊C₈	—	2	2	no	—
143	C₅×#97	—	2	2	no	—
144	C₄×C₅×C₈	—	2	2	no	—
145	C₅×#95	—	2	1	no	—
146	C₅×#95	—	2	1	no	—
147	C₅×#95	—	2	1	no	—
148	C₅×#95	—	2	1	no	—
149	C₅×#95	—	2	1	no	—
150	C₅×#95	—	2	1	no	—
151	C₅×#95	—	2	1	no	—
152	C₅×#95	—	2	1	no	—
153	C₅×#95	—	2	1	no	—
154	C₅×#95	—	2	1	no	—
155	C₅×#95	D₄	1	1	yes	characteristic
156	C₅×#95	D₄	1	1	yes	characteristic
157	C₂²×#137	C₂×C₅	1	1	yes	characteristic
158	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
160	Q₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
161	#2339	C₂×C₅	1	1	yes	characteristic
162	#1971	C₂×C₅	1	1	yes	characteristic, complemented
163	#1969	C₂×C₅	1	1	yes	characteristic, complemented
164	#1878	C₂×C₅	1	1	yes	characteristic, complemented
165	#1878	C₂×C₅	1	1	yes	characteristic, complemented
166	#1877	C₂×C₅	1	1	yes	characteristic, complemented
167	#1877	C₂×C₅	1	1	yes	characteristic, complemented
168	#1809	C₂×C₅	1	1	yes	characteristic, complemented
169	#1788	C₂×C₅	1	1	yes	characteristic
170	#1787	C₂×C₅	1	1	yes	characteristic, complemented
171	#1753	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂⁴×C₅	—	2	1	no	—
173	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
174	C₅×#41	—	2	8	no	—
175	C₅×#41	—	4	4	no	—
176	C₅×#41	—	4	4	no	—
177	C₅×#41	—	4	4	no	—
178	C₂×C₅×Q₈	—	2	4	no	—
179	C₂×C₅×Q₈	—	2	1	no	—
180	C₂×C₅×Q₈	—	2	1	no	—
181	C₂×C₅×Q₈	—	2	1	no	—
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	—	2	1	no	—
184	C₂×C₅×Q₈	—	2	8	no	—
185	C₂×C₅×Q₈	—	2	1	no	—
186	C₂×C₅×Q₈	—	2	1	no	—
187	C₂×C₅×Q₈	—	2	1	no	—
188	C₂×C₅×Q₈	—	2	1	no	—
189	C₂×C₅×Q₈	—	2	1	no	—
190	C₂×C₅×Q₈	—	2	1	no	—
191	C₂×C₅×Q₈	—	2	1	no	—
192	C₂×C₅×Q₈	—	2	1	no	—
193	C₂×C₅×Q₈	—	4	2	no	—
194	C₂×C₅×Q₈	—	4	2	no	—
195	C₂×C₅×Q₈	—	4	4	no	—
196	C₂×C₅×Q₈	—	4	4	no	—
197	C₂×C₅×Q₈	—	4	4	no	—
198	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
199	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
200	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
201	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
202	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
203	C₂×C₅×D₄	—	2	4	no	—
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	—	4	2	no	—
208	C₂×C₅×D₄	—	4	2	no	—
209	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
210	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
211	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	1	no	—
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	4	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	2	4	no	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	4	2	no	—
226	C₂²×C₄×C₅	—	4	2	no	—
227	C₂²×C₄×C₅	—	4	2	no	—
228	C₂²×C₄×C₅	—	4	2	no	—
229	C₂²×C₄×C₅	—	4	2	no	—
230	C₂²×C₄×C₅	—	4	2	no	—
231	C₂²×C₄×C₅	—	4	2	no	—
232	C₂²×C₄×C₅	—	4	2	no	—
233	C₂²×C₄×C₅	—	8	1	no	—
234	C₂²×C₄×C₅	—	8	1	no	—
235	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₅	#41	1	2	yes	—
242	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₅×Q₁₆	—	2	8	no	—
244	C₅×Q₁₆	—	2	8	no	—
245	C₅×SD₁₆	—	2	8	no	—
246	C₅×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
247	C₅×M₁₆	—	2	8	no	—
248	C₂×C₅×C₈	—	2	1	no	—
249	C₂×C₅×C₈	—	2	1	no	—
250	C₂×C₅×C₈	—	2	1	no	—
251	C₂×C₅×C₈	—	2	1	no	—
252	C₂×C₅×C₈	—	2	1	no	—
253	C₂×C₅×C₈	—	2	1	no	—
254	C₂×C₅×C₈	—	2	1	no	—
255	C₂×C₅×C₈	—	2	1	no	—
256	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
257	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
258	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
259	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
260	C₅×C₄⋊C₄	—	2	1	no	—
261	C₅×C₄⋊C₄	—	2	1	no	—
262	C₅×C₄⋊C₄	—	2	1	no	—
263	C₅×C₄⋊C₄	—	2	1	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	—	2	1	no	—
266	C₅×C₄⋊C₄	—	2	1	no	—
267	C₅×C₄⋊C₄	—	2	1	no	—
268	C₅×C₄⋊C₄	—	4	2	no	—
269	C₅×C₄⋊C₄	—	4	2	no	—
270	C₅×C₂²⋊C₄	—	2	2	no	—
271	C₅×C₂²⋊C₄	—	4	1	no	—
272	C₅×C₂²⋊C₄	—	4	2	no	—
273	C₅×C₂²⋊C₄	—	4	2	no	—
274	C₅×C₂²⋊C₄	—	4	2	no	—
275	C₅×C₂²⋊C₄	—	8	1	no	—
276	C₄²×C₅	—	2	1	no	—
277	C₄²×C₅	—	2	1	no	—
278	C₄²×C₅	—	2	1	no	—
279	C₄²×C₅	—	2	1	no	—
280	C₄²×C₅	—	4	2	no	—
281	C₄²×C₅	—	4	2	no	—
282	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
283	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
284	C₂×#137	—	2	4	no	—
285	C₂×#137	—	2	4	no	—
286	C₂×#137	C₄×C₅	1	8	yes	complemented
287	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
288	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
289	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
290	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
296	#440	—	2	4	no	—
297	C₄×SD₁₆	—	2	4	no	—
298	C₂×#107	C₂²×C₅	1	1	yes	characteristic
299	C₂×#106	C₂²×C₅	1	1	yes	characteristic
300	C₂×#103	C₂²×C₅	1	1	yes	characteristic
301	C₂×#103	C₂²×C₅	1	1	yes	characteristic
302	C₂×#103	C₂²×C₅	1	1	yes	characteristic
303	C₂×#103	C₂²×C₅	1	1	yes	characteristic
304	C₂×#103	C₂²×C₅	1	1	yes	characteristic
305	C₂×#103	C₂²×C₅	1	1	yes	characteristic
306	C₂×#102	C₂²×C₅	1	1	yes	characteristic
307	C₂×#102	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
309	C₂×#97	C₂²×C₅	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
311	#391	—	2	1	no	—
312	#391	—	2	1	no	—
313	#391	C₂²×C₅	1	1	yes	characteristic
314	#391	C₂²×C₅	1	1	yes	characteristic
315	#391	C₂²×C₅	1	1	yes	characteristic
316	#391	C₂²×C₅	1	1	yes	characteristic
317	#386	—	2	1	no	—
318	#386	—	2	1	no	—
319	#381	—	2	1	no	—
320	#380	—	2	1	no	—
321	#380	C₂²×C₅	1	1	yes	characteristic
322	#380	C₂²×C₅	1	1	yes	characteristic
323	C₄×C₂²⋊C₄	—	2	1	no	—
324	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
325	C₂×#95	—	2	1	no	—
326	#340	C₂²×C₅	1	1	yes	characteristic
327	#340	C₂²×C₅	1	1	yes	characteristic
328	#336	C₂²×C₅	1	1	yes	characteristic
329	#336	C₂²×C₅	1	1	yes	characteristic
330	C₂³×C₅	—	2	2	no	—
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	1	no	—
334	C₂³×C₅	—	2	1	no	—
335	C₂³×C₅	—	2	1	no	—
336	C₂³×C₅	—	2	1	no	—
337	C₂³×C₅	—	2	1	no	—
338	C₂³×C₅	—	2	1	no	—
339	C₂³×C₅	—	4	1	no	—
340	C₂³×C₅	—	4	1	no	—
341	C₂³×C₅	—	4	1	no	—
342	C₂³×C₅	—	4	1	no	—
343	C₂³×C₅	C₄×D₄	1	2	yes	—
344	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₅×Q₈	—	2	2	no	—
346	C₅×Q₈	—	2	2	no	—
347	C₅×Q₈	—	2	2	no	—
348	C₅×Q₈	—	2	2	no	—
349	C₅×Q₈	—	2	2	no	—
350	C₅×Q₈	—	2	2	no	—
351	C₅×Q₈	—	2	2	no	—
352	C₅×Q₈	—	4	8	no	—
353	C₅×Q₈	—	4	1	no	—
354	C₅×Q₈	—	4	1	no	—
355	C₅×Q₈	—	4	1	no	—
356	C₅×Q₈	—	4	1	no	—
357	C₅×Q₈	C₂×C₂²⋊C₄	1	4	yes	—
358	C₅×D₄	—	2	2	no	—
359	C₅×D₄	—	2	2	no	—
360	C₅×D₄	—	2	2	no	—
361	C₅×D₄	—	4	8	no	—
362	C₅×D₄	C₂×C₂²⋊C₄	1	4	yes	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	2	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	4	8	no	—
386	C₂×C₄×C₅	—	4	8	no	—
387	C₂×C₄×C₅	—	4	1	no	—
388	C₂×C₄×C₅	—	4	1	no	—
389	C₂×C₄×C₅	—	4	1	no	—
390	C₂×C₄×C₅	—	4	1	no	—
391	C₂×C₄×C₅	—	4	1	no	—
392	C₂×C₄×C₅	—	4	1	no	—
393	C₂×C₄×C₅	—	4	1	no	—
394	C₂×C₄×C₅	—	4	1	no	—
395	C₂×C₄×C₅	—	4	1	no	—
396	C₂×C₄×C₅	—	4	1	no	—
397	C₂×C₄×C₅	—	4	1	no	—
398	C₂×C₄×C₅	—	4	1	no	—
399	C₂×C₄×C₅	—	4	1	no	—
400	C₂×C₄×C₅	—	4	1	no	—
401	C₂×C₄×C₅	—	4	1	no	—
402	C₂×C₄×C₅	—	4	1	no	—
403	C₂×C₄×C₅	—	8	4	no	—
404	C₂×C₄×C₅	—	8	4	no	—
405	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
406	C₂×C₄×C₅	#137	1	2	yes	complemented
407	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
411	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
413	C₅×C₈	—	2	2	no	—
414	C₅×C₈	—	4	1	no	—
415	C₅×C₈	—	4	1	no	—
416	C₅×C₈	C₂×C₂²⋊C₄	1	4	yes	—
417	C₂×#41	—	2	2	no	—
418	C₂×#41	—	2	2	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	—	4	1	no	—
421	C₂×#41	—	4	1	no	—
422	C₂×#41	C₂×C₄×C₅	1	4	yes	—
423	C₂²×Q₈	—	2	1	no	—
424	C₂²×Q₈	—	2	2	no	—
425	C₂²×Q₈	—	2	2	no	—
426	C₂²×Q₈	—	2	2	no	—
427	C₂²×Q₈	—	4	1	no	—
428	C₂²×Q₈	—	4	1	no	—
429	C₂²×Q₈	C₂×C₄×C₅	1	4	yes	complemented
430	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
440	#137	—	2	32	no	—
441	C₂×Q₁₆	—	2	2	no	—
442	C₂×Q₁₆	—	2	2	no	—
443	C₂×Q₁₆	—	2	2	no	—
444	C₂×Q₁₆	—	2	2	no	—
445	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
446	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
450	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
451	C₂×SD₁₆	C₅×D₄	1	4	yes	—
452	C₂×SD₁₆	C₅×D₄	1	4	yes	—
453	C₂×M₁₆	—	2	2	no	—
454	C₂×M₁₆	—	2	2	no	—
455	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
456	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	4	1	no	—
463	C₄×Q₈	—	4	1	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	4	1	no	—
467	C₄×D₄	—	4	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
480	C₂×C₄²	—	2	1	no	—
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
484	#107	—	2	2	no	—
485	#106	—	2	2	no	—
486	#103	—	2	2	no	—
487	#103	—	2	2	no	—
488	#103	—	4	1	no	—
489	#103	—	4	1	no	—
490	#103	—	4	1	no	—
491	#103	—	4	1	no	—
492	#102	—	2	2	no	—
493	#102	—	2	2	no	—
494	C₂²⋊C₈	—	2	2	no	—
495	#97	—	2	2	no	—
496	C₄×C₈	—	2	2	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	C₅×D₄	1	1	yes	characteristic
508	#95	C₅×D₄	1	1	yes	characteristic
509	C₂²×C₅	—	2	2	no	—
510	C₂²×C₅	—	2	4	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	2	2	no	—
513	C₂²×C₅	—	4	2	no	—
514	C₂²×C₅	—	4	2	no	—
515	C₂²×C₅	—	4	2	no	—
516	C₂²×C₅	—	4	1	no	—
517	C₂²×C₅	—	4	1	no	—
518	C₂²×C₅	—	4	2	no	—
519	C₂²×C₅	—	4	2	no	—
520	C₂²×C₅	—	4	1	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	4	2	no	—
523	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
524	C₂²×C₅	D₄²	1	1	yes	characteristic
525	C₂²×C₅	D₄²	1	1	yes	characteristic
526	C₂²×C₅	C₂×#137	1	1	yes	characteristic
527	C₂²×C₅	#575	1	1	yes	characteristic
528	C₂²×C₅	#577	1	1	yes	characteristic
529	C₂²×C₅	#578	1	1	yes	characteristic
530	C₄×C₅	—	2	2	no	—
531	C₄×C₅	—	2	4	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	4	2	no	—
534	C₄×C₅	—	4	2	no	—
535	C₄×C₅	—	4	1	no	—
536	C₄×C₅	—	4	1	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	8	1	no	—
539	C₄×C₅	—	8	1	no	—
540	C₄×C₅	—	8	1	no	—
541	C₄×C₅	—	8	1	no	—
542	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
543	C₄×C₅	#518	1	1	yes	characteristic
544	C₄×C₅	#546	1	1	yes	characteristic
545	C₄×C₅	#546	1	1	yes	characteristic
546	C₂⁴	—	2	1	no	—
547	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
548	#41	—	2	8	no	—
549	#41	—	4	4	no	—
550	#41	—	4	4	no	—
551	#41	—	4	4	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	8	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	4	2	no	—
568	C₂×Q₈	—	4	2	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	—	4	4	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
573	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
574	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
575	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
576	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
584	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
585	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	8	1	no	—
608	C₂²×C₄	—	8	1	no	—
609	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
610	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
612	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
615	C₂²×C₄	C₅×#41	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
617	Q₁₆	—	2	8	no	—
618	Q₁₆	—	2	8	no	—
619	SD₁₆	—	2	8	no	—
620	SD₁₆	C₅×C₂²⋊C₄	1	16	yes	complemented
621	M₁₆	—	2	8	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
631	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
632	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
633	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	4	1	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	8	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	4	2	no	—
655	C₄²	—	4	2	no	—
656	C₂×C₅	—	4	2	no	—
657	C₂×C₅	—	4	4	no	—
658	C₂×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic
659	C₂×C₅	C₄×#137	1	1	yes	characteristic
660	C₂×C₅	#2947	1	1	yes	characteristic
661	C₂×C₅	#3266	1	1	yes	characteristic
662	C₂×C₅	#3269	1	1	yes	characteristic
663	C₂×C₅	#3275	1	1	yes	characteristic
664	C₂×C₅	#3276	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	C₄×C₅×D₄	1	2	yes	—
679	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	—	4	1	no	—
692	Q₈	C₂×C₅×C₂²⋊C₄	1	4	yes	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	4	8	no	—
697	D₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
741	C₂×C₄	C₅×#137	1	2	yes	complemented
742	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
743	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
744	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
745	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
746	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
748	C₈	—	2	2	no	—
749	C₈	—	4	1	no	—
750	C₈	—	4	1	no	—
751	C₈	C₂×C₅×C₂²⋊C₄	1	4	yes	—
752	C₅	#22444	1	1	yes	characteristic, direct product factor, Sylow
753	C₂²	—	2	2	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
768	C₂²	C₅×D₄²	1	1	yes	characteristic
769	C₂²	C₅×D₄²	1	1	yes	characteristic
770	C₂²	C₂×C₅×#137	1	1	yes	characteristic
771	C₂²	C₅×#575	1	1	yes	characteristic
772	C₂²	C₅×#577	1	1	yes	characteristic
773	C₂²	C₅×#578	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	4	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
787	C₄	C₅×#518	1	1	yes	characteristic
788	C₄	C₅×#546	1	1	yes	characteristic
789	C₄	C₅×#546	1	1	yes	characteristic
790	C₂	—	4	2	no	—
791	C₂	—	4	4	no	—
792	C₂	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic
793	C₂	C₄×C₅×#137	1	1	yes	characteristic
794	C₂	C₅×#2947	1	1	yes	characteristic
795	C₂	C₅×#3266	1	1	yes	characteristic
796	C₂	C₅×#3269	1	1	yes	characteristic
797	C₂	C₅×#3275	1	1	yes	characteristic
798	C₂	C₅×#3276	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#440	C₂	semidirect
3. C₂×C₄×C₅×SD₁₆	C₂	semidirect
4. C₅×Q₈×C₂²⋊C₄	C₂	semidirect
6. C₅×#1971	C₂	semidirect
7. C₅×#1969	C₂	semidirect
8. C₅×#1878	C₂	semidirect
9. C₅×#1878	C₂	semidirect
10. C₅×#1877	C₂	semidirect
11. C₅×#1877	C₂	semidirect
12. C₅×#1809	C₂	semidirect
14. C₅×#1787	C₂	semidirect
15. C₅×#1753	C₂	semidirect
20. C₂×C₅×#137	C₄	semidirect
64. #22444	C₅	direct (N × H)
77. C₂²×C₅×Q₈	C₂×C₄	semidirect
93. C₂×C₅×Q₁₆	C₂×C₄	semidirect
94. C₂×C₅×Q₁₆	C₂×C₄	semidirect
103. C₂×C₅×M₁₆	C₂×C₄	semidirect
158. C₂×#440	C₂×C₅	semidirect
159. C₂×C₄×SD₁₆	C₂×C₅	semidirect
160. Q₈×C₂²⋊C₄	C₂×C₅	semidirect
162. #1971	C₂×C₅	semidirect
163. #1969	C₂×C₅	semidirect
164. #1878	C₂×C₅	semidirect
165. #1878	C₂×C₅	semidirect
166. #1877	C₂×C₅	semidirect
167. #1877	C₂×C₅	semidirect
168. #1809	C₂×C₅	semidirect
170. #1787	C₂×C₅	semidirect
171. #1753	C₂×C₅	semidirect
246. C₅×SD₁₆	C₂²⋊C₄	semidirect
286. C₂×#137	C₄×C₅	semidirect
406. C₂×C₄×C₅	#137	semidirect
429. C₂²×Q₈	C₂×C₄×C₅	semidirect
445. C₂×Q₁₆	C₂×C₄×C₅	semidirect
446. C₂×Q₁₆	C₂×C₄×C₅	semidirect
455. C₂×M₁₆	C₂×C₄×C₅	semidirect
620. SD₁₆	C₅×C₂²⋊C₄	semidirect
741. C₂×C₄	C₅×#137	semidirect
752. C₅	#22444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#137	2
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#2339	2
C₅×#1971	2
C₅×#1969	2
C₅×#1878	2
C₅×#1877	2
C₅×#1809	2
C₅×#1788	2
C₅×#1787	2
C₅×#1753	2
#22444	5

Subgroups — C5×#22444 #11945164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22444 #11945164