Subgroups — C₂×C₅×#3298 #11983836

Order 1280.

2374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
3	C₅×#3298	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#483	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#448	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×#103	C₂	1	2	yes	maximal, complemented
13	C₂²×C₅×#41	—	2	1	no	—
14	C₂³×C₅×Q₈	C₂²	1	2	yes	—
15	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂³×C₅×C₈	C₂²	1	2	yes	—
18	C₅×D₄×Q₈	—	2	4	no	—
19	C₅×D₄×Q₈	C₂²	1	8	yes	complemented
20	C₅×#547	—	2	4	no	—
21	C₅×#547	C₂²	1	8	yes	—
22	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#123	—	2	2	no	—
26	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
28	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₅×#121	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	—	2	1	no	—
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₅×#487	C₂²	1	8	yes	complemented
36	C₅×#483	C₂²	1	16	yes	complemented
37	C₅×#475	C₂²	1	8	yes	complemented
38	C₅×#465	C₂²	1	16	yes	complemented
39	C₅×#461	C₂²	1	8	yes	complemented
40	C₅×#448	C₂²	1	16	yes	complemented
41	C₄×C₅×SD₁₆	C₂²	1	8	yes	complemented
42	C₅×C₈×D₄	C₂²	1	8	yes	complemented
43	C₂×C₅×#106	C₂²	1	2	yes	—
44	C₂×C₅×#106	C₂²	1	1	yes	characteristic
45	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₅×#103	C₂²	1	2	yes	—
47	C₂×C₅×#103	C₂²	1	2	yes	—
48	C₂×C₅×#103	C₂²	1	2	yes	—
49	C₂×C₅×#103	C₂²	1	2	yes	—
50	C₂×C₅×#103	C₂²	1	1	yes	characteristic
51	C₂×C₅×#103	C₂²	1	16	yes	complemented
52	C₂×C₅×#102	C₂²	1	1	yes	characteristic
53	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3298	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₅×#41	—	2	8	no	—
57	C₂×C₅×#41	—	4	8	no	—
58	C₂²×C₅×Q₈	—	2	2	no	—
59	C₂²×C₅×Q₈	—	2	1	no	—
60	C₂²×C₅×Q₈	—	2	4	no	—
61	C₂²×C₅×Q₈	—	2	8	no	—
62	C₂²×C₅×Q₈	—	4	4	no	—
63	C₂²×C₅×Q₈	C₂³	1	2	yes	—
64	C₂²×C₅×Q₈	C₂³	1	8	yes	—
65	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×D₄	—	2	2	no	—
67	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
68	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅	—	2	2	no	—
70	C₂³×C₄×C₅	—	2	2	no	—
71	C₂³×C₄×C₅	—	2	1	no	—
72	C₂³×C₄×C₅	C₂³	1	2	yes	—
73	C₂×C₅×SD₁₆	—	2	4	no	—
74	C₂×C₅×SD₁₆	—	4	4	no	—
75	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₅×SD₁₆	C₂³	1	8	yes	—
77	C₂²×C₅×C₈	—	4	4	no	—
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	2	yes	—
81	C₂²×C₅×C₈	C₂³	1	8	yes	—
82	C₅×C₄⋊Q₈	—	2	8	no	—
83	C₅×C₄⋊Q₈	—	2	2	no	—
84	C₅×C₄⋊Q₈	—	2	2	no	—
85	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
87	C₅×#123	—	2	16	no	—
88	C₅×C₂²⋊Q₈	—	2	4	no	—
89	C₅×C₂²⋊Q₈	—	2	8	no	—
90	C₅×C₂²⋊Q₈	—	2	16	no	—
91	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
92	C₅×#121	—	2	4	no	—
93	C₅×#121	C₂³	1	8	yes	—
94	C₄×C₅×Q₈	—	2	2	no	—
95	C₄×C₅×Q₈	C₂³	1	4	yes	—
96	C₄×C₅×D₄	—	2	8	no	—
97	C₄×C₅×D₄	—	2	2	no	—
98	C₄×C₅×D₄	D₄	1	4	yes	—
99	C₄×C₅×D₄	C₂³	1	4	yes	—
100	C₄×C₅×D₄	C₂³	1	4	yes	—
101	C₂×C₅×C₄⋊C₄	—	2	2	no	—
102	C₂×C₅×C₄⋊C₄	—	2	4	no	—
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	2	1	no	—
105	C₂×C₅×C₄⋊C₄	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	—	2	2	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
113	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
117	C₂×C₄²×C₅	—	2	1	no	—
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₅×#106	C₂³	1	4	yes	—
120	C₅×#106	C₂³	1	8	yes	—
121	C₅×C₄⋊C₈	C₂³	1	4	yes	—
122	C₅×#103	C₂³	1	4	yes	—
123	C₅×#103	C₂³	1	8	yes	—
124	C₅×#103	C₂³	1	8	yes	—
125	C₅×#103	C₂³	1	8	yes	—
126	C₅×#103	C₂³	1	8	yes	—
127	C₅×#102	C₂³	1	4	yes	—
128	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
129	C₄×C₅×C₈	C₂³	1	4	yes	—
130	C₂×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#547	C₂×C₅	1	1	yes	characteristic
132	#3298	C₂×C₅	1	16	yes	direct product factor
133	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×#483	C₂×C₅	1	2	yes	complemented
135	C₂×#475	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×#465	C₂×C₅	1	2	yes	complemented
137	C₂×#461	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#448	C₂×C₅	1	2	yes	complemented
139	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂²×#103	C₂×C₅	1	2	yes	complemented
142	C₂⁴×C₅	—	2	1	no	—
143	C₂⁴×C₅	C₂×D₄	1	2	yes	—
144	C₅×#41	—	4	32	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	8	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	—	2	4	no	—
149	C₂×C₅×Q₈	—	2	2	no	—
150	C₂×C₅×Q₈	—	2	16	no	—
151	C₂×C₅×Q₈	—	2	4	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	—	4	8	no	—
154	C₂×C₅×Q₈	—	4	8	no	—
155	C₂×C₅×Q₈	—	4	16	no	—
156	C₂×C₅×Q₈	—	4	4	no	—
157	C₂×C₅×Q₈	#41	1	4	yes	complemented
158	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
159	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
160	C₂×C₅×D₄	—	2	8	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	2	no	—
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	4	8	no	—
165	C₂×C₅×D₄	SD₁₆	1	8	yes	complemented
166	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
167	C₂×C₅×D₄	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	4	no	—
170	C₂²×C₄×C₅	—	2	4	no	—
171	C₂²×C₄×C₅	—	2	8	no	—
172	C₂²×C₄×C₅	—	2	8	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	2	no	—
177	C₂²×C₄×C₅	—	2	4	no	—
178	C₂²×C₄×C₅	—	4	8	no	—
179	C₂²×C₄×C₅	—	4	8	no	—
180	C₂²×C₄×C₅	—	4	4	no	—
181	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₅×SD₁₆	—	2	8	no	—
188	C₅×SD₁₆	—	4	8	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	2	2	no	—
191	C₂×C₅×C₈	—	2	4	no	—
192	C₂×C₅×C₈	—	4	8	no	—
193	C₂×C₅×C₈	C₂⁴	1	2	yes	—
194	C₂×C₅×C₈	C₂⁴	1	4	yes	—
195	C₂×C₅×C₈	C₂⁴	1	2	yes	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	8	no	—
199	C₅×C₄⋊C₄	—	2	4	no	—
200	C₅×C₄⋊C₄	—	2	4	no	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₄⋊C₄	—	2	8	no	—
203	C₅×C₄⋊C₄	—	2	4	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
206	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
207	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
208	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
209	C₅×C₂²⋊C₄	—	2	8	no	—
210	C₅×C₂²⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	2	8	no	—
212	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
213	C₄²×C₅	—	2	4	no	—
214	C₄²×C₅	C₂×D₄	1	2	yes	—
215	C₄²×C₅	C₂⁴	1	2	yes	—
216	C₂²×#41	—	2	1	no	—
217	C₂³×Q₈	C₂²×C₅	1	2	yes	—
218	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
220	C₂³×C₈	C₂²×C₅	1	2	yes	—
221	D₄×Q₈	—	2	4	no	—
222	D₄×Q₈	C₂²×C₅	1	8	yes	complemented
223	#547	—	2	4	no	—
224	#547	C₂²×C₅	1	8	yes	—
225	C₂×C₄⋊Q₈	—	2	1	no	—
226	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×#123	—	2	2	no	—
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₂²⋊Q₈	—	2	2	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
232	C₂×#121	C₂²×C₅	1	2	yes	—
233	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
238	#487	C₂²×C₅	1	8	yes	complemented
239	#483	C₂²×C₅	1	16	yes	complemented
240	#475	C₂²×C₅	1	8	yes	complemented
241	#465	C₂²×C₅	1	16	yes	complemented
242	#461	C₂²×C₅	1	8	yes	complemented
243	#448	C₂²×C₅	1	16	yes	complemented
244	C₄×SD₁₆	C₂²×C₅	1	8	yes	complemented
245	C₈×D₄	C₂²×C₅	1	8	yes	complemented
246	C₂×#106	C₂²×C₅	1	2	yes	—
247	C₂×#106	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
249	C₂×#103	C₂²×C₅	1	2	yes	—
250	C₂×#103	C₂²×C₅	1	2	yes	—
251	C₂×#103	C₂²×C₅	1	2	yes	—
252	C₂×#103	C₂²×C₅	1	2	yes	—
253	C₂×#103	C₂²×C₅	1	1	yes	characteristic
254	C₂×#103	C₂²×C₅	1	16	yes	complemented
255	C₂×#102	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
257	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
258	C₂³×C₅	—	2	4	no	—
259	C₂³×C₅	—	2	4	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	4	2	no	—
262	C₂³×C₅	—	4	2	no	—
263	C₂³×C₅	—	4	2	no	—
264	C₂³×C₅	C₂×SD₁₆	1	8	yes	—
265	C₂³×C₅	C₂²×D₄	1	4	yes	—
266	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₅×Q₈	—	2	4	no	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	—	2	4	no	—
270	C₅×Q₈	—	2	4	no	—
271	C₅×Q₈	—	4	16	no	—
272	C₅×Q₈	—	4	4	no	—
273	C₅×Q₈	—	4	8	no	—
274	C₅×Q₈	C₂×#41	1	4	yes	complemented
275	C₅×D₄	—	2	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	4	16	no	—
278	C₅×D₄	—	4	2	no	—
279	C₅×D₄	C₂×SD₁₆	1	16	yes	complemented
280	C₂×C₄×C₅	—	2	4	no	—
281	C₂×C₄×C₅	—	2	4	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	8	no	—
285	C₂×C₄×C₅	—	2	4	no	—
286	C₂×C₄×C₅	—	2	4	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	4	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	4	no	—
291	C₂×C₄×C₅	—	4	16	no	—
292	C₂×C₄×C₅	—	4	4	no	—
293	C₂×C₄×C₅	—	4	2	no	—
294	C₂×C₄×C₅	—	4	4	no	—
295	C₂×C₄×C₅	—	4	16	no	—
296	C₂×C₄×C₅	—	4	2	no	—
297	C₂×C₄×C₅	—	4	8	no	—
298	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
299	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₅	C₂×#41	1	2	yes	—
304	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
305	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
306	C₅×C₈	—	2	2	no	—
307	C₅×C₈	—	2	2	no	—
308	C₅×C₈	—	2	4	no	—
309	C₂×#41	—	2	8	no	—
310	C₂×#41	—	4	8	no	—
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	4	no	—
314	C₂²×Q₈	—	2	8	no	—
315	C₂²×Q₈	—	4	4	no	—
316	C₂²×Q₈	C₂³×C₅	1	2	yes	—
317	C₂²×Q₈	C₂³×C₅	1	8	yes	—
318	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
321	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	C₂³×C₅	1	2	yes	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂×SD₁₆	—	4	4	no	—
328	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
329	C₂×SD₁₆	C₂³×C₅	1	8	yes	—
330	C₂²×C₈	—	4	4	no	—
331	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₅	1	2	yes	—
333	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₅	1	8	yes	—
335	C₄⋊Q₈	—	2	8	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
339	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
340	#123	—	2	16	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	8	no	—
343	C₂²⋊Q₈	—	2	16	no	—
344	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
345	#121	—	2	4	no	—
346	#121	C₂³×C₅	1	8	yes	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	C₂³×C₅	1	4	yes	—
349	C₄×D₄	—	2	8	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	C₅×D₄	1	4	yes	—
352	C₄×D₄	C₂³×C₅	1	4	yes	—
353	C₄×D₄	C₂³×C₅	1	4	yes	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
365	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
372	#106	C₂³×C₅	1	4	yes	—
373	#106	C₂³×C₅	1	8	yes	—
374	C₄⋊C₈	C₂³×C₅	1	4	yes	—
375	#103	C₂³×C₅	1	4	yes	—
376	#103	C₂³×C₅	1	8	yes	—
377	#103	C₂³×C₅	1	8	yes	—
378	#103	C₂³×C₅	1	8	yes	—
379	#103	C₂³×C₅	1	8	yes	—
380	#102	C₂³×C₅	1	4	yes	—
381	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
382	C₄×C₈	C₂³×C₅	1	4	yes	—
383	C₂²×C₅	—	2	4	no	—
384	C₂²×C₅	—	2	16	no	—
385	C₂²×C₅	—	2	4	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	—	4	2	no	—
388	C₂²×C₅	—	4	2	no	—
389	C₂²×C₅	—	8	4	no	—
390	C₂²×C₅	#546	1	2	yes	—
391	C₂²×C₅	C₂²×SD₁₆	1	8	yes	—
392	C₂²×C₅	C₂²×SD₁₆	1	2	yes	—
393	C₂²×C₅	#578	1	2	yes	—
394	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₅	—	2	4	no	—
396	C₄×C₅	—	2	4	no	—
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	4	4	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	4	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	#546	1	2	yes	—
403	C₄×C₅	C₂²×SD₁₆	1	4	yes	—
404	C₄×C₅	C₂²×#41	1	1	yes	characteristic
405	C₄×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
406	C₂⁴	—	2	1	no	—
407	C₂⁴	C₂×C₅×D₄	1	2	yes	—
408	#41	—	4	32	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	8	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	16	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	4	8	no	—
418	C₂×Q₈	—	4	8	no	—
419	C₂×Q₈	—	4	16	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×Q₈	C₅×#41	1	4	yes	complemented
422	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
423	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	C₅×SD₁₆	1	8	yes	complemented
430	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
431	C₂×D₄	C₂⁴×C₅	1	2	yes	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	8	no	—
443	C₂²×C₄	—	4	8	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
447	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
448	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
451	SD₁₆	—	2	8	no	—
452	SD₁₆	—	4	8	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	4	no	—
456	C₂×C₈	—	4	8	no	—
457	C₂×C₈	C₂⁴×C₅	1	2	yes	—
458	C₂×C₈	C₂⁴×C₅	1	2	yes	—
459	C₂×C₈	C₂⁴×C₅	1	4	yes	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
471	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
472	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
477	C₄²	—	2	4	no	—
478	C₄²	C₂×C₅×D₄	1	2	yes	—
479	C₄²	C₂⁴×C₅	1	2	yes	—
480	C₂×C₅	—	2	8	no	—
481	C₂×C₅	—	8	2	no	—
482	C₂×C₅	#3298	1	4	yes	direct product factor
483	C₂×C₅	C₂×#546	1	1	yes	characteristic
484	C₂×C₅	C₂³×SD₁₆	1	1	yes	characteristic
485	C₂×C₅	C₂×#578	1	1	yes	characteristic
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	C₂×C₅×SD₁₆	1	8	yes	—
493	C₂³	C₂²×C₅×D₄	1	4	yes	—
494	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
495	Q₈	—	2	4	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	4	16	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	8	no	—
502	Q₈	C₂×C₅×#41	1	4	yes	complemented
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	4	16	no	—
506	D₄	—	4	2	no	—
507	D₄	C₂×C₅×SD₁₆	1	16	yes	complemented
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	16	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	16	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
527	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
528	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
529	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
531	C₂×C₄	C₂×C₅×#41	1	2	yes	—
532	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
533	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	4	no	—
537	C₅	C₂×#3298	1	1	yes	characteristic, direct product factor, Sylow
538	C₂²	—	2	16	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	8	4	no	—
545	C₂²	C₅×#546	1	2	yes	—
546	C₂²	C₂²×C₅×SD₁₆	1	8	yes	—
547	C₂²	C₂²×C₅×SD₁₆	1	2	yes	—
548	C₂²	C₅×#578	1	2	yes	—
549	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
550	C₄	—	2	4	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	2	no	—
557	C₄	C₅×#546	1	2	yes	—
558	C₄	C₂²×C₅×SD₁₆	1	4	yes	—
559	C₄	C₂²×C₅×#41	1	1	yes	characteristic
560	C₄	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂	—	2	8	no	—
562	C₂	—	8	2	no	—
563	C₂	C₅×#3298	1	4	yes	direct product factor
564	C₂	C₂×C₅×#546	1	1	yes	characteristic
565	C₂	C₂³×C₅×SD₁₆	1	1	yes	characteristic
566	C₂	C₂×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₄×Q₈	C₂	semidirect
3. C₅×#3298	C₂	direct (N × H)
4. C₂×C₅×#487	C₂	semidirect
5. C₂×C₅×#483	C₂	semidirect
6. C₂×C₅×#475	C₂	semidirect
7. C₂×C₅×#465	C₂	semidirect
8. C₂×C₅×#461	C₂	semidirect
9. C₂×C₅×#448	C₂	semidirect
10. C₂×C₄×C₅×SD₁₆	C₂	semidirect
11. C₂×C₅×C₈×D₄	C₂	semidirect
12. C₂²×C₅×#103	C₂	semidirect
19. C₅×D₄×Q₈	C₂²	semidirect
35. C₅×#487	C₂²	semidirect
36. C₅×#483	C₂²	semidirect
37. C₅×#475	C₂²	semidirect
38. C₅×#465	C₂²	semidirect
39. C₅×#461	C₂²	semidirect
40. C₅×#448	C₂²	semidirect
41. C₄×C₅×SD₁₆	C₂²	semidirect
42. C₅×C₈×D₄	C₂²	semidirect
51. C₂×C₅×#103	C₂²	semidirect
55. C₂×#3298	C₅	direct (N × H)
130. C₂×D₄×Q₈	C₂×C₅	semidirect
132. #3298	C₂×C₅	direct (N × H)
133. C₂×#487	C₂×C₅	semidirect
134. C₂×#483	C₂×C₅	semidirect
135. C₂×#475	C₂×C₅	semidirect
136. C₂×#465	C₂×C₅	semidirect
137. C₂×#461	C₂×C₅	semidirect
138. C₂×#448	C₂×C₅	semidirect
139. C₂×C₄×SD₁₆	C₂×C₅	semidirect
140. C₂×C₈×D₄	C₂×C₅	semidirect
141. C₂²×#103	C₂×C₅	semidirect
157. C₂×C₅×Q₈	#41	semidirect
165. C₂×C₅×D₄	SD₁₆	semidirect
222. D₄×Q₈	C₂²×C₅	semidirect
238. #487	C₂²×C₅	semidirect
239. #483	C₂²×C₅	semidirect
240. #475	C₂²×C₅	semidirect
241. #465	C₂²×C₅	semidirect
242. #461	C₂²×C₅	semidirect
243. #448	C₂²×C₅	semidirect
244. C₄×SD₁₆	C₂²×C₅	semidirect
245. C₈×D₄	C₂²×C₅	semidirect
254. C₂×#103	C₂²×C₅	semidirect
274. C₅×Q₈	C₂×#41	semidirect
279. C₅×D₄	C₂×SD₁₆	semidirect
421. C₂×Q₈	C₅×#41	semidirect
429. C₂×D₄	C₅×SD₁₆	semidirect
482. C₂×C₅	#3298	direct (N × H)
502. Q₈	C₂×C₅×#41	semidirect
507. D₄	C₂×C₅×SD₁₆	semidirect
537. C₅	C₂×#3298	direct (N × H)
563. C₂	C₅×#3298	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×D₄×Q₈	2
C₂×C₅×#547	2
C₅×#3298	2
C₂×C₅×#487	2
C₂×C₅×#483	2
C₂×C₅×#475	2
C₂×C₅×#465	2
C₂×C₅×#461	2
C₂×C₅×#448	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×C₈×D₄	2
C₂²×C₅×#103	2
C₂×#3298	5

Subgroups — C2×C5×#3298 #11983836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3298 #11983836