Subgroups — C₅×#21598 #11944318

Order 1280.

886 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1917	C₂	1	2	yes	maximal, complemented
7	C₅×#1851	C₂	1	2	yes	maximal
8	C₅×#1797	C₂	1	1	yes	maximal, characteristic
9	C₅×#1770	C₂	1	2	yes	maximal, complemented
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1753	C₂	1	2	yes	maximal
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₅×#446	—	2	4	no	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₄×C₅×M₁₆	—	2	4	no	—
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	C₂²	1	2	yes	—
26	C₂×C₅×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#391	C₄	1	1	yes	characteristic
31	C₅×#389	C₄	1	1	yes	characteristic
32	C₅×#387	C₄	1	2	yes	—
33	C₅×#385	C₄	1	2	yes	—
34	C₅×#380	C₄	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#21598	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×M₁₆	—	2	2	no	—
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	Q₈	1	4	yes	complemented
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×C₂²⋊Q₈	—	2	4	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×Q₈	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	2	yes	—
76	C₂×C₄²×C₅	C₂³	1	2	yes	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	2	4	no	—
80	C₅×C₄⋊C₈	—	2	4	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	2	no	—
83	C₅×C₂²⋊C₈	—	2	4	no	—
84	C₅×#97	—	2	2	no	—
85	C₅×#97	—	2	2	no	—
86	C₅×#97	—	2	4	no	—
87	C₄×C₅×C₈	—	2	4	no	—
88	C₄×C₅×C₈	—	2	2	no	—
89	C₄×C₅×C₈	D₄	1	4	yes	—
90	C₅×#95	C₂×C₄	1	2	yes	—
91	C₅×#95	C₂×C₄	1	2	yes	—
92	C₅×#95	C₂×C₄	1	2	yes	—
93	C₅×#95	C₂×C₄	1	2	yes	—
94	C₅×#95	C₂×C₄	1	2	yes	—
95	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
97	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
98	#1984	C₂×C₅	1	1	yes	characteristic, complemented
99	#1939	C₂×C₅	1	1	yes	characteristic, complemented
100	#1917	C₂×C₅	1	2	yes	complemented
101	#1851	C₂×C₅	1	2	yes	—
102	#1797	C₂×C₅	1	1	yes	characteristic
103	#1770	C₂×C₅	1	2	yes	complemented
104	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
105	#1753	C₂×C₅	1	2	yes	—
106	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	—	4	1	no	—
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₅	#41	1	2	yes	—
131	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₅×M₁₆	—	2	8	no	—
133	C₅×M₁₆	—	2	8	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
148	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
149	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
150	C₂×C₅×C₈	#41	1	2	yes	—
151	C₂×C₅×C₈	#41	1	2	yes	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	M₁₆	1	4	yes	complemented
158	C₅×C₂²⋊C₄	—	2	4	no	—
159	C₅×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₄²×C₅	—	2	2	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	C₂×D₄	1	2	yes	—
169	C₄²×C₅	#41	1	2	yes	—
170	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
173	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
175	#446	—	2	4	no	—
176	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
179	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
181	C₄×M₁₆	—	2	4	no	—
182	C₂×#97	C₂²×C₅	1	1	yes	characteristic
183	C₂×#97	C₂²×C₅	1	1	yes	characteristic
184	C₂×#97	C₂²×C₅	1	2	yes	—
185	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	#391	C₄×C₅	1	1	yes	characteristic
189	#389	C₄×C₅	1	1	yes	characteristic
190	#387	C₄×C₅	1	2	yes	—
191	#385	C₄×C₅	1	2	yes	—
192	#380	C₄×C₅	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
194	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
195	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
196	#336	C₂²×C₅	1	2	yes	—
197	#336	C₂²×C₅	1	2	yes	—
198	#336	C₂²×C₅	1	2	yes	—
199	#336	C₂²×C₅	1	2	yes	—
200	#336	C₂²×C₅	1	2	yes	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	—	2	1	no	—
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	—	2	1	no	—
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	C₄×Q₈	1	2	yes	—
208	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
209	C₅×Q₈	—	4	4	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	4	4	no	—
236	C₂×C₄×C₅	—	4	4	no	—
237	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
239	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
240	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
241	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
242	C₂×C₄×C₅	#131	1	2	yes	—
243	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	4	2	no	—
253	C₅×C₈	—	4	2	no	—
254	C₅×C₈	C₂²⋊Q₈	1	4	yes	complemented
255	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
256	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
257	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	C₅×Q₈	1	4	yes	complemented
265	C₂²×C₈	C₂³×C₅	1	2	yes	—
266	C₂²×C₈	C₂³×C₅	1	2	yes	—
267	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂²⋊Q₈	—	2	4	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
276	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
277	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₅	1	2	yes	—
287	C₂×C₄²	C₂³×C₅	1	2	yes	—
288	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
290	C₄⋊C₈	—	2	4	no	—
291	C₄⋊C₈	—	2	4	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	4	no	—
295	#97	—	2	2	no	—
296	#97	—	2	2	no	—
297	#97	—	2	4	no	—
298	C₄×C₈	—	2	4	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	C₅×D₄	1	4	yes	—
301	#95	C₂×C₄×C₅	1	2	yes	—
302	#95	C₂×C₄×C₅	1	2	yes	—
303	#95	C₂×C₄×C₅	1	2	yes	—
304	#95	C₂×C₄×C₅	1	2	yes	—
305	#95	C₂×C₄×C₅	1	2	yes	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	4	1	no	—
312	C₂²×C₅	—	4	1	no	—
313	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
315	C₂²×C₅	C₄×#41	1	1	yes	characteristic
316	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
317	C₂²×C₅	C₂×#131	1	1	yes	characteristic
318	C₂²×C₅	#568	1	1	yes	characteristic
319	C₂²×C₅	#568	1	1	yes	characteristic
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	2	4	no	—
322	C₄×C₅	—	2	2	no	—
323	C₄×C₅	—	4	1	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	4	1	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	#436	1	4	yes	—
329	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
330	C₄×C₅	#525	1	1	yes	characteristic
331	C₄×C₅	#529	1	1	yes	characteristic
332	C₄×C₅	#533	1	1	yes	characteristic
333	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
357	C₂²×C₄	C₅×#41	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
359	M₁₆	—	2	8	no	—
360	M₁₆	—	2	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
374	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
376	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
377	C₂×C₈	C₅×#41	1	2	yes	—
378	C₂×C₈	C₅×#41	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₅×M₁₆	1	4	yes	complemented
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	2	no	—
395	C₄²	C₂×C₅×D₄	1	2	yes	—
396	C₄²	C₅×#41	1	2	yes	—
397	C₂×C₅	—	4	2	no	—
398	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
399	C₂×C₅	C₂×#436	1	1	yes	characteristic
400	C₂×C₅	#2930	1	1	yes	characteristic
401	C₂×C₅	#2962	1	1	yes	characteristic
402	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
403	C₂×C₅	#2969	1	1	yes	characteristic
404	C₂×C₅	#2970	1	1	yes	characteristic
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	C₄×C₅×Q₈	1	2	yes	—
412	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
413	Q₈	—	4	4	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
442	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
443	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
444	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
445	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
446	C₂×C₄	C₅×#131	1	2	yes	—
447	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
450	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
452	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₈	C₅×C₂²⋊Q₈	1	4	yes	complemented
459	C₅	#21598	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
468	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
469	C₂²	C₄×C₅×#41	1	1	yes	characteristic
470	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₅×#131	1	1	yes	characteristic
472	C₂²	C₅×#568	1	1	yes	characteristic
473	C₂²	C₅×#568	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	C₅×#436	1	4	yes	—
483	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
484	C₄	C₅×#525	1	1	yes	characteristic
485	C₄	C₅×#529	1	1	yes	characteristic
486	C₄	C₅×#533	1	1	yes	characteristic
487	C₂	—	4	2	no	—
488	C₂	C₄×C₅×C₂²⋊Q₈	1	1	yes	characteristic
489	C₂	C₂×C₅×#436	1	1	yes	characteristic
490	C₂	C₅×#2930	1	1	yes	characteristic
491	C₂	C₅×#2962	1	1	yes	characteristic
492	C₂	C₅×Q₈×M₁₆	1	1	yes	characteristic
493	C₂	C₅×#2969	1	1	yes	characteristic
494	C₂	C₅×#2970	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#446	C₂	semidirect
4. C₅×#1984	C₂	semidirect
5. C₅×#1939	C₂	semidirect
6. C₅×#1917	C₂	semidirect
9. C₅×#1770	C₂	semidirect
10. C₅×C₈×C₄⋊C₄	C₂	semidirect
43. #21598	C₅	direct (N × H)
53. C₂×C₅×M₁₆	Q₈	semidirect
95. C₂×#446	C₂×C₅	semidirect
98. #1984	C₂×C₅	semidirect
99. #1939	C₂×C₅	semidirect
100. #1917	C₂×C₅	semidirect
103. #1770	C₂×C₅	semidirect
104. C₈×C₄⋊C₄	C₂×C₅	semidirect
157. C₅×C₄⋊C₄	M₁₆	semidirect
254. C₅×C₈	C₂²⋊Q₈	semidirect
264. C₂×M₁₆	C₅×Q₈	semidirect
384. C₄⋊C₄	C₅×M₁₆	semidirect
458. C₈	C₅×C₂²⋊Q₈	semidirect
459. C₅	#21598	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×#446	2
C₂×C₄×C₅×M₁₆	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#1984	2
C₅×#1939	2
C₅×#1917	2
C₅×#1851	2
C₅×#1797	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₅×#1753	2
#21598	5

Subgroups — C5×#21598 #11944318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21598 #11944318