Subgroups — C₂×#10618991 #13006423

Order 1280.

9542 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618991	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66013	C₂	1	3	yes	maximal, complemented
4	C₂×#66010	C₂	1	6	yes	maximal, complemented
5	C₂×#66012	C₂	1	6	yes	maximal, complemented
6	C₂×#66008	C₂	1	3	yes	maximal, complemented
7	C₂×#65929	C₂	1	3	yes	maximal, complemented
8	C₂×#65924	C₂	1	3	yes	maximal, complemented
9	C₂×#65923	C₂	1	3	yes	maximal, complemented
10	C₂×D₅×#120	C₂	1	3	yes	maximal, complemented
11	C₂⁵×D₅	C₂²	1	1	yes	characteristic, complemented
12	C₂³×C₂²⋊D₅	C₂²	1	3	yes	complemented
13	C₂²×#713	C₂²	1	3	yes	complemented
14	C₂²×D₄×D₅	C₂²	1	3	yes	complemented
15	C₂²×D₄×D₅	C₂²	1	6	yes	complemented
16	C₅×H(3,𝔽₄)	C₂²	1	16	yes	complemented
17	C₂×C₅×#124	C₂²	1	3	yes	complemented
18	C₂×C₅×#124	C₂²	1	6	yes	complemented
19	C₂×C₅×#120	C₂²	1	3	yes	complemented
20	C₂×C₅×#120	C₂²	1	3	yes	complemented
21	C₂×#4099	C₂²	1	3	yes	complemented
22	C₂×#4099	C₂²	1	1	yes	characteristic, complemented
23	C₂×#4093	C₂²	1	3	yes	complemented
24	C₂×#4092	C₂²	1	6	yes	complemented
25	C₂×#4086	C₂²	1	3	yes	complemented
26	C₂×#4085	C₂²	1	6	yes	complemented
27	C₂×#4084	C₂²	1	6	yes	complemented
28	C₂×#4083	C₂²	1	3	yes	—
29	C₂×#4083	C₂²	1	6	yes	complemented
30	C₂×#4081	C₂²	1	3	yes	complemented
31	#66013	C₂²	1	48	yes	complemented
32	#66012	C₂²	1	96	yes	complemented
33	#66010	C₂²	1	96	yes	complemented
34	#66008	C₂²	1	48	yes	complemented
35	#65929	C₂²	1	48	yes	complemented
36	#65924	C₂²	1	48	yes	complemented
37	#65923	C₂²	1	48	yes	complemented
38	D₅×#120	C₂²	1	48	yes	complemented
39	C₂×#4032	C₂²	1	3	yes	complemented
40	C₂×#4030	C₂²	1	6	yes	complemented
41	C₂×#4030	C₂²	1	6	yes	complemented
42	C₂×#4030	C₂²	1	6	yes	complemented
43	C₂×#4029	C₂²	1	6	yes	complemented
44	C₂×#4029	C₂²	1	6	yes	complemented
45	C₂×#4028	C₂²	1	6	yes	complemented
46	C₂×#4028	C₂²	1	3	yes	complemented
47	C₂×#4028	C₂²	1	6	yes	complemented
48	C₂×#4027	C₂²	1	6	yes	complemented
49	C₂×D₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
50	C₂×D₅×C₂²⋊C₄	C₂²	1	6	yes	complemented
51	C₂×D₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
52	C₂×#4025	C₂²	1	6	yes	complemented
53	C₂×#4022	C₂²	1	2	yes	complemented
54	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₂₀	C₂²	1	6	yes	complemented
56	C₂×#4018	C₂²	1	3	yes	complemented
57	C₂×#3532	—	5	1	no	maximal, Sylow
58	C₂⁵×C₅	C₂³	1	1	yes	characteristic
59	C₂⁵×C₅	C₂³	1	1	yes	characteristic, complemented
60	C₂⁴×D₅	—	4	12	no	—
61	C₂⁴×D₅	C₂³	1	3	yes	—
62	C₂⁴×D₅	C₂³	1	3	yes	—
63	C₂⁴×D₅	C₂³	1	3	yes	—
64	C₂⁴×D₅	C₂³	1	8	yes	complemented
65	C₂²×C₅×Q₈	C₂³	1	3	yes	complemented
66	C₂²×C₅×D₄	C₂³	1	3	yes	—
67	C₂²×C₅×D₄	C₂³	1	6	yes	—
68	C₂²×C₂²⋊D₅	—	4	12	no	—
69	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
70	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
71	C₂²×C₂²⋊D₅	C₂³	1	3	yes	—
72	C₂²×C₂²⋊D₅	C₂³	1	3	yes	—
73	C₂²×C₂²⋊D₅	C₂³	1	6	yes	complemented
74	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
75	C₂³×Dic₅	C₂³	1	3	yes	complemented
76	C₂×#713	—	4	12	no	—
77	C₂×#713	C₂³	1	24	yes	complemented
78	C₂×D₄×D₅	—	4	12	no	—
79	C₂×D₄×D₅	—	4	24	no	—
80	C₂×D₄×D₅	C₂³	1	24	yes	complemented
81	C₂×D₄×D₅	C₂³	1	48	yes	complemented
82	C₂²×D₂₀	C₂³	1	6	yes	—
83	C₂²×D₂₀	C₂³	1	3	yes	—
84	C₂²×D₂₀	C₂³	1	3	yes	complemented
85	C₂²×C₄×D₅	C₂³	1	3	yes	—
86	C₂²×C₄×D₅	C₂³	1	6	yes	—
87	C₂²×C₄×D₅	C₂³	1	6	yes	complemented
88	C₅×#124	C₂³	1	24	yes	complemented
89	C₅×#124	C₂³	1	48	yes	complemented
90	C₅×#120	C₂³	1	24	yes	complemented
91	C₅×#120	C₂³	1	24	yes	complemented
92	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂³	1	3	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂³	1	3	yes	complemented
95	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	complemented
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
97	C₂×C₄²×C₅	C₂³	1	2	yes	complemented
98	#4099	C₂³	1	24	yes	complemented
99	#4099	C₂³	1	8	yes	complemented
100	C₂×C₂²⋊Dic₅	C₂³	1	3	yes	—
101	C₂×C₂²⋊Dic₅	C₂³	1	6	yes	—
102	C₂×C₂²⋊Dic₅	C₂³	1	3	yes	complemented
103	#4093	C₂³	1	24	yes	complemented
104	#4092	C₂³	1	48	yes	complemented
105	#4086	C₂³	1	24	yes	complemented
106	#4085	C₂³	1	48	yes	complemented
107	#4084	C₂³	1	48	yes	complemented
108	#4083	C₂³	1	24	yes	—
109	#4083	C₂³	1	48	yes	complemented
110	#4081	C₂³	1	24	yes	complemented
111	C₂×#685	C₂³	1	6	yes	—
112	C₂×#685	C₂³	1	6	yes	—
113	C₂×#685	C₂³	1	6	yes	—
114	C₂×#685	C₂³	1	6	yes	complemented
115	C₂×C₄⋊Dic₅	C₂³	1	6	yes	complemented
116	C₂×#683	C₂³	1	6	yes	complemented
117	C₂×#683	C₂³	1	6	yes	complemented
118	C₂×C₄×Dic₅	C₂³	1	3	yes	complemented
119	#4032	C₂³	1	24	yes	complemented
120	#4030	C₂³	1	48	yes	complemented
121	#4030	C₂³	1	48	yes	complemented
122	#4030	C₂³	1	48	yes	complemented
123	#4029	C₂³	1	48	yes	complemented
124	#4029	C₂³	1	48	yes	complemented
125	#4028	C₂³	1	48	yes	complemented
126	#4028	C₂³	1	24	yes	complemented
127	#4028	C₂³	1	48	yes	complemented
128	#4027	C₂³	1	48	yes	complemented
129	D₅×C₂²⋊C₄	C₂³	1	48	yes	complemented
130	D₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
131	D₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
132	#4025	C₂³	1	48	yes	complemented
133	#4022	C₂³	1	16	yes	complemented
134	#4020	C₂³	1	8	yes	complemented
135	C₄×D₂₀	C₂³	1	48	yes	complemented
136	#4018	C₂³	1	24	yes	complemented
137	#3532	—	5	32	no	—
138	C₂×H(3,𝔽₄)	D₅	1	1	yes	characteristic, complemented
139	C₂×#560	—	5	3	no	—
140	C₂×#551	—	5	3	no	—
141	C₂×#546	—	5	6	no	—
142	C₂×D₄²	—	5	3	no	—
143	C₂×#538	—	5	6	no	—
144	C₂×#535	—	5	3	no	—
145	C₂×#534	—	5	3	no	—
146	C₂²×#120	—	5	3	no	—
147	C₂⁴×C₅	—	4	6	no	—
148	C₂⁴×C₅	—	4	6	no	—
149	C₂⁴×C₅	C₂⁴	1	3	yes	—
150	C₂⁴×C₅	C₂⁴	1	3	yes	—
151	C₂⁴×C₅	C₂⁴	1	4	yes	—
152	C₂⁴×C₅	C₂⁴	1	4	yes	complemented
153	C₂³×D₅	—	2	24	no	—
154	C₂³×D₅	—	2	12	no	—
155	C₂³×D₅	—	2	12	no	—
156	C₂³×D₅	—	4	48	no	—
157	C₂³×D₅	—	4	6	no	—
158	C₂³×D₅	—	4	12	no	—
159	C₂³×D₅	—	4	12	no	—
160	C₂³×D₅	—	4	64	no	—
161	C₂³×D₅	C₂⁴	1	3	yes	—
162	C₂³×D₅	C₂⁴	1	1	yes	characteristic
163	C₂³×D₅	C₂⁴	1	12	yes	—
164	C₂³×D₅	C₂⁴	1	3	yes	—
165	C₂³×D₅	C₂⁴	1	12	yes	—
166	C₂³×D₅	C₂⁴	1	12	yes	—
167	C₂×C₅×Q₈	—	4	6	no	—
168	C₂×C₅×Q₈	C₂⁴	1	12	yes	complemented
169	C₂×C₅×D₄	—	4	6	no	—
170	C₂×C₅×D₄	—	4	12	no	—
171	C₂×C₅×D₄	C₂⁴	1	12	yes	—
172	C₂×C₅×D₄	C₂⁴	1	24	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
174	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
175	C₂×C₂²⋊D₅	—	2	24	no	—
176	C₂×C₂²⋊D₅	—	4	6	no	—
177	C₂×C₂²⋊D₅	—	4	6	no	—
178	C₂×C₂²⋊D₅	—	4	12	no	—
179	C₂×C₂²⋊D₅	—	4	12	no	—
180	C₂×C₂²⋊D₅	—	4	48	no	—
181	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
182	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
183	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
184	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
185	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	complemented
186	C₂²×Dic₅	—	4	6	no	—
187	C₂²×Dic₅	C₂⁴	1	3	yes	—
188	C₂²×Dic₅	C₂⁴	1	6	yes	—
189	C₂²×Dic₅	C₂⁴	1	12	yes	complemented
190	#713	—	4	48	no	—
191	D₄×D₅	—	4	48	no	—
192	D₄×D₅	—	4	96	no	—
193	C₂×D₂₀	—	2	24	no	—
194	C₂×D₂₀	—	4	6	no	—
195	C₂×D₂₀	—	4	6	no	—
196	C₂×D₂₀	C₂⁴	1	24	yes	—
197	C₂×D₂₀	C₂⁴	1	12	yes	—
198	C₂×D₂₀	C₂⁴	1	12	yes	complemented
199	C₂×C₄×D₅	—	2	12	no	—
200	C₂×C₄×D₅	—	4	12	no	—
201	C₂×C₄×D₅	—	4	12	no	—
202	C₂×C₄×D₅	C₂⁴	1	12	yes	—
203	C₂×C₄×D₅	C₂⁴	1	24	yes	—
204	C₂×C₄×D₅	C₂⁴	1	24	yes	complemented
205	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
206	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	—
207	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	complemented
208	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	complemented
209	C₄²×C₅	C₂⁴	1	4	yes	complemented
210	C₄²×C₅	C₂⁴	1	8	yes	complemented
211	C₂²⋊Dic₅	C₂⁴	1	12	yes	—
212	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
213	C₂²⋊Dic₅	C₂⁴	1	12	yes	complemented
214	#685	C₂⁴	1	24	yes	—
215	#685	C₂⁴	1	24	yes	—
216	#685	C₂⁴	1	24	yes	—
217	#685	C₂⁴	1	24	yes	complemented
218	C₄⋊Dic₅	C₂⁴	1	24	yes	complemented
219	#683	C₂⁴	1	24	yes	complemented
220	#683	C₂⁴	1	24	yes	complemented
221	C₄×Dic₅	C₂⁴	1	12	yes	complemented
222	C₂⁶	—	5	1	no	—
223	C₂²×#41	—	5	3	no	—
224	C₂³×D₄	—	5	3	no	—
225	C₂³×D₄	—	5	3	no	—
226	C₂³×D₄	—	5	6	no	—
227	H(3,𝔽₄)	C₂×D₅	1	16	yes	complemented
228	#560	—	5	48	no	—
229	#551	—	5	48	no	—
230	#546	—	5	96	no	—
231	D₄²	—	5	48	no	—
232	#538	—	5	96	no	—
233	#535	—	5	48	no	—
234	#534	—	5	48	no	—
235	C₂×#127	—	5	3	no	—
236	C₂×#127	—	5	1	no	—
237	C₂×#126	—	5	6	no	—
238	C₂×#126	—	5	2	no	—
239	C₂×#124	—	5	3	no	—
240	C₂×#124	C₂×D₅	1	3	yes	complemented
241	C₂×#124	C₂×D₅	1	6	yes	complemented
242	C₂×#123	—	5	3	no	—
243	C₂×#123	—	5	6	no	—
244	C₂×#123	—	5	6	no	—
245	C₂×#123	—	5	3	no	—
246	C₂×C₂²⋊Q₈	—	5	6	no	—
247	C₂×#121	—	5	6	no	—
248	C₂×#121	—	5	6	no	—
249	C₂×#121	—	5	6	no	—
250	C₂×#121	—	5	6	no	—
251	C₂×#121	—	5	6	no	—
252	C₂×#120	—	5	3	no	—
253	C₂×#120	—	5	1	no	—
254	C₂×#120	—	5	3	no	—
255	C₂×#120	—	5	6	no	—
256	C₂×#120	—	5	48	no	—
257	C₂×#120	—	5	6	no	—
258	C₂×#120	—	5	3	no	—
259	C₂×#120	—	5	6	no	—
260	C₂×#120	C₂×D₅	1	3	yes	complemented
261	C₂×#120	C₂×D₅	1	3	yes	complemented
262	C₂×C₄×D₄	—	5	6	no	—
263	C₂×C₄×D₄	—	5	6	no	—
264	C₂×#117	—	5	3	no	—
265	C₂²×C₂²⋊C₄	—	5	3	no	—
266	C₂²×C₂²⋊C₄	—	5	6	no	—
267	C₂²×C₂²⋊C₄	—	5	3	no	—
268	C₂³×C₅	—	2	6	no	—
269	C₂³×C₅	—	2	12	no	—
270	C₂³×C₅	—	2	6	no	—
271	C₂³×C₅	—	2	12	no	—
272	C₂³×C₅	—	4	12	no	—
273	C₂³×C₅	—	4	12	no	—
274	C₂³×C₅	—	4	16	no	—
275	C₂³×C₅	—	8	8	no	—
276	C₂³×C₅	C₂⁵	1	6	yes	—
277	C₂³×C₅	C₂⁵	1	6	yes	—
278	C₂³×C₅	C₂⁵	1	1	yes	characteristic
279	C₂²×D₅	—	2	12	no	—
280	C₂²×D₅	—	2	12	no	—
281	C₂²×D₅	—	2	6	no	—
282	C₂²×D₅	—	2	6	no	—
283	C₂²×D₅	—	2	48	no	—
284	C₂²×D₅	—	2	24	no	—
285	C₂²×D₅	—	2	24	no	—
286	C₂²×D₅	—	4	12	no	—
287	C₂²×D₅	—	4	24	no	—
288	C₂²×D₅	—	4	48	no	—
289	C₂²×D₅	—	4	24	no	—
290	C₂²×D₅	—	4	48	no	—
291	C₂²×D₅	—	4	128	no	—
292	C₂²×D₅	—	8	24	no	—
293	C₂²×D₅	H(5,𝔽₂)	1	12	yes	—
294	C₂²×D₅	C₂⁵	1	2	yes	—
295	C₂²×D₅	C₂⁵	1	6	yes	—
296	C₂²×D₅	C₂⁵	1	6	yes	—
297	C₅×Q₈	—	4	12	no	—
298	C₅×D₄	—	4	12	no	—
299	C₅×D₄	—	4	24	no	—
300	C₂×C₄×C₅	—	2	6	no	—
301	C₂×C₄×C₅	—	2	12	no	—
302	C₂×C₄×C₅	C₂⁵	1	6	yes	—
303	C₂×C₄×C₅	C₂⁵	1	12	yes	—
304	C₂²⋊D₅	—	2	48	no	—
305	C₂²⋊D₅	—	4	12	no	—
306	C₂²⋊D₅	—	4	12	no	—
307	C₂²⋊D₅	—	4	24	no	—
308	C₂²⋊D₅	—	4	24	no	—
309	C₂×Dic₅	—	2	6	no	—
310	C₂×Dic₅	—	2	12	no	—
311	C₂×Dic₅	—	4	12	no	—
312	C₂×Dic₅	C₂⁵	1	12	yes	—
313	C₂×Dic₅	C₂⁵	1	6	yes	—
314	D₂₀	—	2	48	no	—
315	D₂₀	—	4	12	no	—
316	D₂₀	—	4	12	no	—
317	C₄×D₅	—	2	24	no	—
318	C₄×D₅	—	4	24	no	—
319	C₄×D₅	—	4	24	no	—
320	C₂⁵	—	5	3	no	—
321	C₂⁵	—	5	3	no	—
322	C₂⁵	—	5	3	no	—
323	C₂⁵	—	5	8	no	—
324	C₂⁵	—	20	12	no	—
325	C₂⁵	C₂²×D₅	1	1	yes	characteristic
326	C₂⁵	C₂²×D₅	1	1	yes	characteristic, complemented
327	C₂×#41	—	5	24	no	—
328	C₂×#41	—	20	12	no	—
329	C₂²×Q₈	C₂²×D₅	1	3	yes	complemented
330	C₂²×D₄	—	5	6	no	—
331	C₂²×D₄	—	5	3	no	—
332	C₂²×D₄	—	5	3	no	—
333	C₂²×D₄	—	5	6	no	—
334	C₂²×D₄	—	5	6	no	—
335	C₂²×D₄	—	5	24	no	—
336	C₂²×D₄	—	5	24	no	—
337	C₂²×D₄	—	5	48	no	—
338	C₂²×D₄	—	5	6	no	—
339	C₂²×D₄	—	5	3	no	—
340	C₂²×D₄	—	5	3	no	—
341	C₂²×D₄	—	20	12	no	—
342	C₂²×D₄	—	20	24	no	—
343	C₂²×D₄	—	20	12	no	—
344	C₂²×D₄	C₂²×D₅	1	6	yes	—
345	C₂²×D₄	C₂²×D₅	1	3	yes	—
346	C₂³×C₄	—	5	3	no	—
347	C₂³×C₄	—	5	3	no	—
348	C₂³×C₄	—	5	6	no	—
349	C₂³×C₄	—	5	6	no	—
350	#127	—	5	24	no	—
351	#127	—	5	8	no	—
352	#126	—	5	48	no	—
353	#126	—	5	16	no	—
354	#124	—	5	24	no	—
355	#124	C₂²×D₅	1	24	yes	complemented
356	#124	C₂²×D₅	1	48	yes	complemented
357	#123	—	5	24	no	—
358	#123	—	5	48	no	—
359	#123	—	5	24	no	—
360	#123	—	5	48	no	—
361	C₂²⋊Q₈	—	5	48	no	—
362	#121	—	5	48	no	—
363	#121	—	5	48	no	—
364	#121	—	5	48	no	—
365	#121	—	5	48	no	—
366	#121	—	5	48	no	—
367	#120	—	5	24	no	—
368	#120	—	5	8	no	—
369	#120	—	5	48	no	—
370	#120	—	5	24	no	—
371	#120	—	5	48	no	—
372	#120	—	5	24	no	—
373	#120	—	5	48	no	—
374	#120	C₂²×D₅	1	24	yes	complemented
375	#120	C₂²×D₅	1	24	yes	complemented
376	C₄×D₄	—	5	48	no	—
377	C₄×D₄	—	5	48	no	—
378	#117	—	5	24	no	—
379	C₂×C₄⋊C₄	—	5	6	no	—
380	C₂×C₄⋊C₄	—	5	6	no	—
381	C₂×C₄⋊C₄	—	5	6	no	—
382	C₂×C₂²⋊C₄	—	5	3	no	—
383	C₂×C₂²⋊C₄	—	5	6	no	—
384	C₂×C₂²⋊C₄	—	5	3	no	—
385	C₂×C₂²⋊C₄	—	5	6	no	—
386	C₂×C₂²⋊C₄	—	5	6	no	—
387	C₂×C₂²⋊C₄	—	5	6	no	—
388	C₂×C₂²⋊C₄	—	5	6	no	—
389	C₂×C₂²⋊C₄	—	5	24	no	—
390	C₂×C₂²⋊C₄	—	5	48	no	—
391	C₂×C₂²⋊C₄	—	5	24	no	—
392	C₂×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
393	C₂×C₂²⋊C₄	C₂²×D₅	1	3	yes	—
394	C₂×C₂²⋊C₄	C₂²×D₅	1	3	yes	complemented
395	C₂×C₂²⋊C₄	C₂²×D₅	1	6	yes	complemented
396	C₂×C₄²	—	5	3	no	—
397	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
398	C₂×C₄²	C₂²×D₅	1	2	yes	complemented
399	C₂²×C₅	—	2	6	no	—
400	C₂²×C₅	—	2	12	no	—
401	C₂²×C₅	—	2	6	no	—
402	C₂²×C₅	—	2	12	no	—
403	C₂²×C₅	—	4	16	no	—
404	C₂²×C₅	—	4	12	no	—
405	C₂²×C₅	—	4	12	no	—
406	C₂²×C₅	—	8	8	no	—
407	C₂²×C₅	C₂×H(5,𝔽₂)	1	6	yes	—
408	C₂²×C₅	C₂⁶	1	1	yes	characteristic
409	C₂×D₅	—	2	12	no	—
410	C₂×D₅	—	2	24	no	—
411	C₂×D₅	—	2	12	no	—
412	C₂×D₅	—	2	6	no	—
413	C₂×D₅	—	2	6	no	—
414	C₂×D₅	—	4	48	no	—
415	C₂×D₅	—	4	48	no	—
416	C₂×D₅	—	4	4	no	—
417	C₂×D₅	—	4	12	no	—
418	C₂×D₅	—	8	24	no	—
419	C₂×D₅	C₂×H(5,𝔽₂)	1	12	yes	—
420	C₄×C₅	—	2	6	no	—
421	C₄×C₅	—	2	12	no	—
422	Dic₅	—	2	6	no	—
423	Dic₅	—	2	12	no	—
424	C₂⁴	—	4	6	no	—
425	C₂⁴	—	4	6	no	—
426	C₂⁴	—	5	3	no	—
427	C₂⁴	—	5	1	no	—
428	C₂⁴	—	5	3	no	—
429	C₂⁴	—	5	12	no	—
430	C₂⁴	—	5	12	no	—
431	C₂⁴	—	5	12	no	—
432	C₂⁴	—	10	24	no	—
433	C₂⁴	—	10	12	no	—
434	C₂⁴	—	10	12	no	—
435	C₂⁴	—	20	6	no	—
436	C₂⁴	—	20	12	no	—
437	C₂⁴	—	20	12	no	—
438	C₂⁴	—	20	48	no	—
439	C₂⁴	—	20	64	no	—
440	C₂⁴	C₂³×D₅	1	3	yes	—
441	C₂⁴	C₂³×D₅	1	3	yes	—
442	C₂⁴	C₂³×D₅	1	4	yes	—
443	C₂⁴	C₂³×D₅	1	4	yes	complemented
444	#41	—	20	48	no	—
445	C₂×Q₈	—	4	6	no	—
446	C₂×Q₈	C₂³×D₅	1	12	yes	complemented
447	C₂×D₄	—	4	6	no	—
448	C₂×D₄	—	4	12	no	—
449	C₂×D₄	—	5	24	no	—
450	C₂×D₄	—	5	12	no	—
451	C₂×D₄	—	5	12	no	—
452	C₂×D₄	—	5	24	no	—
453	C₂×D₄	—	5	24	no	—
454	C₂×D₄	—	5	24	no	—
455	C₂×D₄	—	5	12	no	—
456	C₂×D₄	—	5	12	no	—
457	C₂×D₄	—	10	24	no	—
458	C₂×D₄	—	10	24	no	—
459	C₂×D₄	—	20	6	no	—
460	C₂×D₄	—	20	6	no	—
461	C₂×D₄	—	20	48	no	—
462	C₂×D₄	—	20	6	no	—
463	C₂×D₄	—	20	6	no	—
464	C₂×D₄	—	20	12	no	—
465	C₂×D₄	—	20	12	no	—
466	C₂×D₄	—	20	96	no	—
467	C₂×D₄	—	20	48	no	—
468	C₂×D₄	C₂³×D₅	1	24	yes	—
469	C₂×D₄	C₂³×D₅	1	12	yes	—
470	C₂²×C₄	—	5	6	no	—
471	C₂²×C₄	—	5	3	no	—
472	C₂²×C₄	—	5	12	no	—
473	C₂²×C₄	—	5	12	no	—
474	C₂²×C₄	—	5	24	no	—
475	C₂²×C₄	—	5	24	no	—
476	C₂²×C₄	—	10	12	no	—
477	C₂²×C₄	—	20	12	no	—
478	C₂²×C₄	—	20	12	no	—
479	C₂²×C₄	—	20	6	no	—
480	C₂²×C₄	C₂³×D₅	1	3	yes	—
481	C₂²×C₄	C₂³×D₅	1	6	yes	—
482	C₄⋊C₄	—	5	24	no	—
483	C₄⋊C₄	—	5	24	no	—
484	C₄⋊C₄	—	5	24	no	—
485	C₂²⋊C₄	—	5	12	no	—
486	C₂²⋊C₄	—	5	24	no	—
487	C₂²⋊C₄	—	5	12	no	—
488	C₂²⋊C₄	—	5	24	no	—
489	C₂²⋊C₄	—	5	24	no	—
490	C₂²⋊C₄	—	5	24	no	—
491	C₂²⋊C₄	—	5	24	no	—
492	C₂²⋊C₄	C₂³×D₅	1	24	yes	—
493	C₂²⋊C₄	C₂³×D₅	1	12	yes	—
494	C₂²⋊C₄	C₂³×D₅	1	12	yes	complemented
495	C₂²⋊C₄	C₂³×D₅	1	24	yes	complemented
496	C₄²	—	5	12	no	—
497	C₄²	C₂³×D₅	1	4	yes	complemented
498	C₄²	C₂³×D₅	1	8	yes	complemented
499	C₂×C₅	—	4	6	no	—
500	C₂×C₅	—	4	6	no	—
501	C₂×C₅	#3532	1	4	yes	complemented
502	C₂×C₅	C₂²×H(5,𝔽₂)	1	3	yes	—
503	D₅	—	2	12	no	—
504	D₅	—	4	2	no	—
505	D₅	—	4	6	no	—
506	C₂³	—	2	6	no	—
507	C₂³	—	2	12	no	—
508	C₂³	—	2	6	no	—
509	C₂³	—	2	12	no	—
510	C₂³	—	4	12	no	—
511	C₂³	—	4	12	no	—
512	C₂³	—	4	16	no	—
513	C₂³	—	5	12	no	—
514	C₂³	—	5	6	no	—
515	C₂³	—	5	2	no	—
516	C₂³	—	5	6	no	—
517	C₂³	—	8	8	no	—
518	C₂³	—	10	48	no	—
519	C₂³	—	10	24	no	—
520	C₂³	—	10	24	no	—
521	C₂³	—	10	12	no	—
522	C₂³	—	10	12	no	—
523	C₂³	—	10	6	no	—
524	C₂³	—	10	6	no	—
525	C₂³	—	20	12	no	—
526	C₂³	—	20	24	no	—
527	C₂³	—	20	24	no	—
528	C₂³	—	20	48	no	—
529	C₂³	—	20	48	no	—
530	C₂³	—	20	128	no	—
531	C₂³	—	40	24	no	—
532	C₂³	C₂⁴×D₅	1	6	yes	—
533	C₂³	C₂⁴×D₅	1	6	yes	—
534	C₂³	C₂⁴×D₅	1	1	yes	characteristic
535	Q₈	—	4	12	no	—
536	D₄	—	4	12	no	—
537	D₄	—	4	24	no	—
538	D₄	—	10	48	no	—
539	D₄	—	10	48	no	—
540	D₄	—	20	12	no	—
541	D₄	—	20	12	no	—
542	D₄	—	20	12	no	—
543	D₄	—	20	12	no	—
544	D₄	—	20	24	no	—
545	D₄	—	20	24	no	—
546	C₂×C₄	—	2	6	no	—
547	C₂×C₄	—	2	12	no	—
548	C₂×C₄	—	5	12	no	—
549	C₂×C₄	—	5	6	no	—
550	C₂×C₄	—	10	24	no	—
551	C₂×C₄	—	10	6	no	—
552	C₂×C₄	—	10	12	no	—
553	C₂×C₄	—	20	24	no	—
554	C₂×C₄	—	20	24	no	—
555	C₂×C₄	—	20	12	no	—
556	C₂×C₄	C₂⁴×D₅	1	6	yes	—
557	C₂×C₄	C₂⁴×D₅	1	12	yes	—
558	C₅	C₂×#3532	1	1	yes	characteristic, complemented, Sylow
559	C₂²	—	2	6	no	—
560	C₂²	—	2	12	no	—
561	C₂²	—	2	6	no	—
562	C₂²	—	2	12	no	—
563	C₂²	—	4	16	no	—
564	C₂²	—	4	12	no	—
565	C₂²	—	4	12	no	—
566	C₂²	—	5	12	no	—
567	C₂²	—	8	8	no	—
568	C₂²	—	10	12	no	—
569	C₂²	—	10	24	no	—
570	C₂²	—	10	12	no	—
571	C₂²	—	10	6	no	—
572	C₂²	—	10	6	no	—
573	C₂²	—	20	48	no	—
574	C₂²	—	20	48	no	—
575	C₂²	—	20	4	no	—
576	C₂²	—	20	12	no	—
577	C₂²	—	40	24	no	—
578	C₂²	D₅×H(5,𝔽₂)	1	6	yes	—
579	C₂²	C₂⁵×D₅	1	1	yes	characteristic
580	C₄	—	2	6	no	—
581	C₄	—	2	12	no	—
582	C₄	—	10	6	no	—
583	C₄	—	10	12	no	—
584	C₂	—	4	6	no	—
585	C₂	—	4	6	no	—
586	C₂	—	10	12	no	—
587	C₂	—	20	2	no	—
588	C₂	—	20	6	no	—
589	C₂	#10618991	1	4	yes	direct product factor
590	C₂	C₂×D₅×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×H(3,𝔽₄)	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₅
hypocenter	C₅	C₂×#3532
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×H(3,𝔽₄)	C₂	semidirect
2. #10618991	C₂	direct (N × H)
3. C₂×#66013	C₂	semidirect
4. C₂×#66010	C₂	semidirect
5. C₂×#66012	C₂	semidirect
6. C₂×#66008	C₂	semidirect
7. C₂×#65929	C₂	semidirect
8. C₂×#65924	C₂	semidirect
9. C₂×#65923	C₂	semidirect
10. C₂×D₅×#120	C₂	semidirect
11. C₂⁵×D₅	C₂²	semidirect
12. C₂³×C₂²⋊D₅	C₂²	semidirect
13. C₂²×#713	C₂²	semidirect
14. C₂²×D₄×D₅	C₂²	semidirect
15. C₂²×D₄×D₅	C₂²	semidirect
16. C₅×H(3,𝔽₄)	C₂²	semidirect
17. C₂×C₅×#124	C₂²	semidirect
18. C₂×C₅×#124	C₂²	semidirect
19. C₂×C₅×#120	C₂²	semidirect
20. C₂×C₅×#120	C₂²	semidirect
21. C₂×#4099	C₂²	semidirect
22. C₂×#4099	C₂²	semidirect
23. C₂×#4093	C₂²	semidirect
24. C₂×#4092	C₂²	semidirect
25. C₂×#4086	C₂²	semidirect
26. C₂×#4085	C₂²	semidirect
27. C₂×#4084	C₂²	semidirect
29. C₂×#4083	C₂²	semidirect
30. C₂×#4081	C₂²	semidirect
31. #66013	C₂²	semidirect
32. #66012	C₂²	semidirect
33. #66010	C₂²	semidirect
34. #66008	C₂²	semidirect
35. #65929	C₂²	semidirect
36. #65924	C₂²	semidirect
37. #65923	C₂²	semidirect
38. D₅×#120	C₂²	semidirect
39. C₂×#4032	C₂²	semidirect
40. C₂×#4030	C₂²	semidirect
41. C₂×#4030	C₂²	semidirect
42. C₂×#4030	C₂²	semidirect
43. C₂×#4029	C₂²	semidirect
44. C₂×#4029	C₂²	semidirect
45. C₂×#4028	C₂²	semidirect
46. C₂×#4028	C₂²	semidirect
47. C₂×#4028	C₂²	semidirect
48. C₂×#4027	C₂²	semidirect
49. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
50. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
51. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
52. C₂×#4025	C₂²	semidirect
53. C₂×#4022	C₂²	semidirect
54. C₂×#4020	C₂²	semidirect
55. C₂×C₄×D₂₀	C₂²	semidirect
56. C₂×#4018	C₂²	semidirect
59. C₂⁵×C₅	C₂³	semidirect
64. C₂⁴×D₅	C₂³	semidirect
65. C₂²×C₅×Q₈	C₂³	semidirect
73. C₂²×C₂²⋊D₅	C₂³	semidirect
74. C₂²×C₂²⋊D₅	C₂³	semidirect
75. C₂³×Dic₅	C₂³	semidirect
77. C₂×#713	C₂³	semidirect
80. C₂×D₄×D₅	C₂³	semidirect
81. C₂×D₄×D₅	C₂³	semidirect
84. C₂²×D₂₀	C₂³	semidirect
87. C₂²×C₄×D₅	C₂³	semidirect
88. C₅×#124	C₂³	semidirect
89. C₅×#124	C₂³	semidirect
90. C₅×#120	C₂³	semidirect
91. C₅×#120	C₂³	semidirect
94. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
95. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
96. C₂×C₄²×C₅	C₂³	semidirect
97. C₂×C₄²×C₅	C₂³	semidirect
98. #4099	C₂³	semidirect
99. #4099	C₂³	semidirect
102. C₂×C₂²⋊Dic₅	C₂³	semidirect
103. #4093	C₂³	semidirect
104. #4092	C₂³	semidirect
105. #4086	C₂³	semidirect
106. #4085	C₂³	semidirect
107. #4084	C₂³	semidirect
109. #4083	C₂³	semidirect
110. #4081	C₂³	semidirect
114. C₂×#685	C₂³	semidirect
115. C₂×C₄⋊Dic₅	C₂³	semidirect
116. C₂×#683	C₂³	semidirect
117. C₂×#683	C₂³	semidirect
118. C₂×C₄×Dic₅	C₂³	semidirect
119. #4032	C₂³	semidirect
120. #4030	C₂³	semidirect
121. #4030	C₂³	semidirect
122. #4030	C₂³	semidirect
123. #4029	C₂³	semidirect
124. #4029	C₂³	semidirect
125. #4028	C₂³	semidirect
126. #4028	C₂³	semidirect
127. #4028	C₂³	semidirect
128. #4027	C₂³	semidirect
129. D₅×C₂²⋊C₄	C₂³	semidirect
130. D₅×C₂²⋊C₄	C₂³	semidirect
131. D₅×C₂²⋊C₄	C₂³	semidirect
132. #4025	C₂³	semidirect
133. #4022	C₂³	semidirect
134. #4020	C₂³	semidirect
135. C₄×D₂₀	C₂³	semidirect
136. #4018	C₂³	semidirect
138. C₂×H(3,𝔽₄)	D₅	semidirect
152. C₂⁴×C₅	C₂⁴	semidirect
168. C₂×C₅×Q₈	C₂⁴	semidirect
185. C₂×C₂²⋊D₅	C₂⁴	semidirect
189. C₂²×Dic₅	C₂⁴	semidirect
198. C₂×D₂₀	C₂⁴	semidirect
204. C₂×C₄×D₅	C₂⁴	semidirect
207. C₅×C₂²⋊C₄	C₂⁴	semidirect
208. C₅×C₂²⋊C₄	C₂⁴	semidirect
209. C₄²×C₅	C₂⁴	semidirect
210. C₄²×C₅	C₂⁴	semidirect
213. C₂²⋊Dic₅	C₂⁴	semidirect
217. #685	C₂⁴	semidirect
218. C₄⋊Dic₅	C₂⁴	semidirect
219. #683	C₂⁴	semidirect
220. #683	C₂⁴	semidirect
221. C₄×Dic₅	C₂⁴	semidirect
227. H(3,𝔽₄)	C₂×D₅	semidirect
240. C₂×#124	C₂×D₅	semidirect
241. C₂×#124	C₂×D₅	semidirect
260. C₂×#120	C₂×D₅	semidirect
261. C₂×#120	C₂×D₅	semidirect
326. C₂⁵	C₂²×D₅	semidirect
329. C₂²×Q₈	C₂²×D₅	semidirect
355. #124	C₂²×D₅	semidirect
356. #124	C₂²×D₅	semidirect
374. #120	C₂²×D₅	semidirect
375. #120	C₂²×D₅	semidirect
394. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
395. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
397. C₂×C₄²	C₂²×D₅	semidirect
398. C₂×C₄²	C₂²×D₅	semidirect
443. C₂⁴	C₂³×D₅	semidirect
446. C₂×Q₈	C₂³×D₅	semidirect
494. C₂²⋊C₄	C₂³×D₅	semidirect
495. C₂²⋊C₄	C₂³×D₅	semidirect
497. C₄²	C₂³×D₅	semidirect
498. C₄²	C₂³×D₅	semidirect
501. C₂×C₅	#3532	semidirect
558. C₅	C₂×#3532	semidirect
589. C₂	#10618991	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×H(3,𝔽₄)	2
#10618991	2
C₂×#66013	2
C₂×#66010	2
C₂×#66012	2
C₂×#66008	2
C₂×#65929	2
C₂×#65924	2
C₂×#65923	2
C₂×D₅×#120	2
C₂×#3532	5

Subgroups — C2×#10618991 #13006423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618991 #13006423