Subgroups — C₂×#10619176 #13007613

Order 1280.

12366 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#4149	C₂	1	1	yes	maximal, characteristic, complemented
3	#10619176	C₂	1	32	yes	maximal, direct product factor
4	C₂×#66168	C₂	1	2	yes	maximal, complemented
5	C₂×#66163	C₂	1	6	yes	maximal, complemented
6	C₂×#66167	C₂	1	3	yes	maximal, complemented
7	C₂×#66164	C₂	1	3	yes	maximal, complemented
8	C₂×#66161	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66151	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×C₂²⋊D₅	C₂	1	6	yes	maximal, complemented
11	C₂×#66125	C₂	1	3	yes	maximal, complemented
12	C₂²×#4076	C₂	1	3	yes	maximal, complemented
13	C₂²×C₅×#41	—	2	16	no	—
14	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#41	C₂²	1	3	yes	complemented
16	C₂²×C₅×#41	C₂²	1	3	yes	complemented
17	C₂²×C₅×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×#41	C₂²	1	16	yes	complemented
19	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₅×D₄	C₂²	1	3	yes	complemented
21	C₂⁴×C₄×C₅	C₂²	1	3	yes	complemented
22	C₂³×C₂²⋊D₅	C₂²	1	6	yes	complemented
23	C₂×#4149	—	2	16	no	—
24	C₂×#4149	C₂²	1	16	yes	complemented
25	C₂²×#713	C₂²	1	2	yes	complemented
26	C₂²×D₄×D₅	C₂²	1	6	yes	complemented
27	C₂²×#709	C₂²	1	3	yes	complemented
28	C₂³×D₂₀	C₂²	1	3	yes	complemented
29	C₂×#4099	C₂²	1	6	yes	complemented
30	#66168	C₂²	1	32	yes	complemented
31	#66167	C₂²	1	48	yes	complemented
32	#66164	C₂²	1	48	yes	complemented
33	#66163	C₂²	1	96	yes	complemented
34	#66161	C₂²	1	16	yes	complemented
35	#66151	C₂²	1	32	yes	complemented
36	C₂×#4093	C₂²	1	6	yes	complemented
37	C₂×#4092	C₂²	1	6	yes	complemented
38	C₂×Q₈×Dic₅	C₂²	1	2	yes	complemented
39	C₂×#4086	C₂²	1	6	yes	complemented
40	C₂×#4085	C₂²	1	12	yes	complemented
41	D₄×C₂²⋊D₅	C₂²	1	96	yes	complemented
42	C₂×#4084	C₂²	1	6	yes	complemented
43	C₂×#4083	C₂²	1	12	yes	complemented
44	C₂×D₄×Dic₅	C₂²	1	6	yes	complemented
45	#66125	C₂²	1	48	yes	complemented
46	C₂×#4076	C₂²	1	6	yes	complemented
47	C₂×#4076	C₂²	1	3	yes	complemented
48	C₂×#4076	C₂²	1	6	yes	complemented
49	C₂×#4076	C₂²	1	6	yes	complemented
50	C₂×#4076	C₂²	1	3	yes	complemented
51	C₂×#4076	C₂²	1	48	yes	complemented
52	C₂×#4075	C₂²	1	6	yes	complemented
53	C₂×C₄×C₂²⋊D₅	C₂²	1	6	yes	complemented
54	C₂×C₄×C₂²⋊D₅	C₂²	1	6	yes	complemented
55	C₂²×#685	C₂²	1	6	yes	complemented
56	C₂×#4072	C₂²	1	3	yes	complemented
57	C₂²×C₄⋊Dic₅	C₂²	1	3	yes	complemented
58	C₂×#4070	C₂²	1	3	yes	complemented
59	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
60	C₂×#3488	—	5	1	no	maximal, Sylow
61	C₂⁵×C₅	C₂³	1	3	yes	—
62	C₂⁴×D₅	C₂³	1	6	yes	—
63	C₂×C₅×#41	—	2	128	no	—
64	C₂×C₅×#41	—	2	8	no	—
65	C₂×C₅×#41	—	2	24	no	—
66	C₂×C₅×#41	—	2	24	no	—
67	C₂×C₅×#41	D₄	1	16	yes	complemented
68	C₂×C₅×#41	C₂³	1	8	yes	—
69	C₂×C₅×#41	C₂³	1	24	yes	complemented
70	C₂×C₅×#41	C₂³	1	24	yes	complemented
71	C₂×C₅×#41	C₂³	1	8	yes	complemented
72	C₂²×C₅×Q₈	—	2	8	no	—
73	C₂²×C₅×Q₈	C₂³	1	3	yes	—
74	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×Q₈	C₂³	1	8	yes	complemented
76	C₂²×C₅×D₄	—	2	24	no	—
77	C₂²×C₅×D₄	C₂³	1	6	yes	—
78	C₂²×C₅×D₄	C₂³	1	3	yes	—
79	C₂²×C₅×D₄	C₂³	1	3	yes	—
80	C₂²×C₅×D₄	C₂³	1	24	yes	complemented
81	C₂³×C₄×C₅	—	2	24	no	—
82	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₅	C₂³	1	3	yes	—
84	C₂³×C₄×C₅	C₂³	1	3	yes	—
85	C₂³×C₄×C₅	C₂³	1	3	yes	—
86	C₂³×C₄×C₅	C₂³	1	3	yes	—
87	C₂³×C₄×C₅	C₂³	1	3	yes	—
88	C₂³×C₄×C₅	C₂³	1	24	yes	complemented
89	C₂²×C₂²⋊D₅	—	4	24	no	—
90	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
91	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
92	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
93	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
94	C₂²×C₂²⋊D₅	C₂³	1	48	yes	complemented
95	C₂³×Dic₅	C₂³	1	6	yes	—
96	#4149	—	2	128	no	—
97	C₂×#713	—	2	16	no	—
98	C₂×#713	C₂³	1	16	yes	complemented
99	C₂×D₄×D₅	—	2	48	no	—
100	C₂×D₄×D₅	C₂³	1	48	yes	complemented
101	C₂×#709	—	2	24	no	—
102	C₂×#709	C₂³	1	24	yes	complemented
103	C₂²×D₂₀	—	2	24	no	—
104	C₂²×D₂₀	C₂³	1	3	yes	—
105	C₂²×D₂₀	C₂³	1	6	yes	—
106	C₂²×D₂₀	C₂³	1	24	yes	complemented
107	C₂²×C₄×D₅	C₂³	1	6	yes	—
108	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
109	#4099	C₂³	1	48	yes	complemented
110	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
111	C₂×C₂²⋊Dic₅	C₂³	1	6	yes	—
112	C₂×C₂²⋊Dic₅	C₂³	1	6	yes	—
113	#4093	C₂³	1	48	yes	complemented
114	#4092	C₂³	1	48	yes	complemented
115	Q₈×Dic₅	C₂³	1	16	yes	complemented
116	#4086	C₂³	1	48	yes	complemented
117	#4085	C₂³	1	96	yes	complemented
118	#4084	C₂³	1	48	yes	complemented
119	#4083	C₂³	1	96	yes	complemented
120	D₄×Dic₅	C₂³	1	48	yes	complemented
121	#4076	C₂³	1	24	yes	complemented
122	#4076	C₂³	1	48	yes	complemented
123	#4076	C₂³	1	48	yes	complemented
124	#4076	C₂³	1	48	yes	complemented
125	#4076	C₂³	1	24	yes	complemented
126	#4075	C₂³	1	48	yes	complemented
127	C₄×C₂²⋊D₅	C₂³	1	48	yes	complemented
128	C₄×C₂²⋊D₅	C₂³	1	48	yes	complemented
129	C₂×#685	C₂³	1	6	yes	—
130	C₂×#685	C₂³	1	12	yes	—
131	C₂×#685	C₂³	1	6	yes	—
132	C₂×#685	C₂³	1	48	yes	complemented
133	#4072	C₂³	1	24	yes	complemented
134	C₂×C₄⋊Dic₅	C₂³	1	3	yes	—
135	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊Dic₅	C₂³	1	6	yes	—
137	C₂×C₄⋊Dic₅	C₂³	1	24	yes	complemented
138	#4070	C₂³	1	8	yes	complemented
139	#4070	C₂³	1	24	yes	complemented
140	C₂×#683	C₂³	1	2	yes	—
141	C₂×#683	C₂³	1	6	yes	—
142	C₂×C₄×Dic₅	C₂³	1	6	yes	—
143	C₂²×H(5,𝔽₂)	—	5	1	no	—
144	C₂³×#41	D₅	1	1	yes	characteristic, complemented
145	#3488	—	5	32	no	—
146	C₂×#550	—	5	2	no	—
147	C₂×#548	—	5	2	no	—
148	C₂×#546	—	5	6	no	—
149	C₂×D₄²	—	5	6	no	—
150	C₂×#537	—	5	3	no	—
151	C₂×#535	—	5	3	no	—
152	C₂×#525	—	5	3	no	—
153	C₂²×#121	—	5	3	no	—
154	C₂×#520	—	5	1	no	—
155	C₂⁴×C₅	—	2	12	no	—
156	C₂⁴×C₅	—	2	12	no	—
157	C₂⁴×C₅	—	4	6	no	—
158	C₂⁴×C₅	C₂⁴	1	3	yes	—
159	C₂⁴×C₅	C₂⁴	1	12	yes	—
160	C₂⁴×C₅	C₂⁴	1	3	yes	—
161	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
162	C₂³×D₅	—	2	24	no	—
163	C₂³×D₅	—	4	12	no	—
164	C₂³×D₅	—	4	12	no	—
165	C₂³×D₅	C₂⁴	1	6	yes	—
166	C₂³×D₅	C₂⁴	1	24	yes	—
167	C₅×#41	—	2	32	no	—
168	C₅×#41	—	2	96	no	—
169	C₅×#41	—	2	96	no	—
170	C₅×#41	C₂×D₄	1	64	yes	complemented
171	C₂×C₅×Q₈	—	2	32	no	—
172	C₂×C₅×Q₈	—	2	12	no	—
173	C₂×C₅×Q₈	C₂×D₄	1	8	yes	complemented
174	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
175	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
176	C₂×C₅×D₄	—	2	24	no	—
177	C₂×C₅×D₄	—	2	96	no	—
178	C₂×C₅×D₄	—	2	12	no	—
179	C₂×C₅×D₄	C₂×D₄	1	24	yes	complemented
180	C₂×C₅×D₄	C₂⁴	1	24	yes	—
181	C₂×C₅×D₄	C₂⁴	1	12	yes	—
182	C₂×C₅×D₄	C₂⁴	1	12	yes	—
183	C₂²×C₄×C₅	—	2	12	no	—
184	C₂²×C₄×C₅	—	2	4	no	—
185	C₂²×C₄×C₅	—	2	12	no	—
186	C₂²×C₄×C₅	—	2	12	no	—
187	C₂²×C₄×C₅	—	2	12	no	—
188	C₂²×C₄×C₅	—	2	96	no	—
189	C₂²×C₄×C₅	C₂×D₄	1	24	yes	complemented
190	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
192	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
194	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
195	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
196	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
197	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
199	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
200	C₂×C₂²⋊D₅	—	2	24	no	—
201	C₂×C₂²⋊D₅	—	2	24	no	—
202	C₂×C₂²⋊D₅	—	4	24	no	—
203	C₂×C₂²⋊D₅	—	4	12	no	—
204	C₂×C₂²⋊D₅	—	4	96	no	—
205	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
206	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
207	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
208	C₂×C₂²⋊D₅	C₂⁴	1	48	yes	—
209	C₂²×Dic₅	—	4	12	no	—
210	C₂²×Dic₅	C₂⁴	1	2	yes	—
211	C₂²×Dic₅	C₂⁴	1	2	yes	—
212	C₂²×Dic₅	C₂⁴	1	6	yes	—
213	C₂²×Dic₅	C₂⁴	1	24	yes	—
214	#713	—	2	64	no	—
215	D₄×D₅	—	2	192	no	—
216	#709	—	2	96	no	—
217	C₂×D₂₀	—	2	12	no	—
218	C₂×D₂₀	—	2	24	no	—
219	C₂×D₂₀	—	2	96	no	—
220	C₂×D₂₀	C₂⁴	1	12	yes	—
221	C₂×D₂₀	C₂⁴	1	24	yes	—
222	C₂×C₄×D₅	—	2	24	no	—
223	C₂×C₄×D₅	C₂⁴	1	24	yes	—
224	C₂×Dic₁₀	—	2	4	no	—
225	C₂×Dic₁₀	C₂⁴	1	4	yes	—
226	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
227	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
228	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
229	#685	C₂⁴	1	24	yes	—
230	#685	C₂⁴	1	48	yes	—
231	#685	C₂⁴	1	24	yes	—
232	C₄⋊Dic₅	C₂⁴	1	12	yes	—
233	C₄⋊Dic₅	C₂⁴	1	4	yes	—
234	C₄⋊Dic₅	C₂⁴	1	24	yes	—
235	#683	C₂⁴	1	8	yes	—
236	#683	C₂⁴	1	24	yes	—
237	C₄×Dic₅	C₂⁴	1	24	yes	—
238	C₂×H(5,𝔽₂)	—	5	16	no	—
239	C₂×H(5,𝔽₂)	—	10	16	no	—
240	C₂²×#41	—	2	16	no	—
241	C₂²×#41	—	5	2	no	—
242	C₂²×#41	—	5	3	no	—
243	C₂²×#41	C₂×D₅	1	1	yes	characteristic
244	C₂²×#41	C₂×D₅	1	3	yes	complemented
245	C₂²×#41	C₂×D₅	1	3	yes	complemented
246	C₂²×#41	C₂×D₅	1	1	yes	characteristic, complemented
247	C₂²×#41	C₂×D₅	1	16	yes	complemented
248	C₂³×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
249	C₂³×D₄	—	5	6	no	—
250	C₂³×D₄	—	5	6	no	—
251	C₂³×D₄	—	5	3	no	—
252	C₂³×D₄	C₂×D₅	1	3	yes	complemented
253	C₂⁴×C₄	C₂×D₅	1	3	yes	complemented
254	#550	—	5	32	no	—
255	#548	—	5	32	no	—
256	#546	—	5	96	no	—
257	D₄²	—	5	96	no	—
258	#537	—	5	48	no	—
259	#535	—	5	48	no	—
260	C₂×#127	—	5	6	no	—
261	C₂×#124	—	5	6	no	—
262	#525	—	5	48	no	—
263	C₂×#123	—	5	6	no	—
264	C₂×C₂²⋊Q₈	—	5	6	no	—
265	C₂×C₂²⋊Q₈	—	5	1	no	—
266	C₂×C₂²⋊Q₈	—	5	3	no	—
267	C₂×#121	—	5	6	no	—
268	C₂×#121	—	5	12	no	—
269	C₂×#121	—	5	3	no	—
270	C₂×#121	—	5	6	no	—
271	C₂×#121	—	5	6	no	—
272	C₂×#121	—	5	6	no	—
273	C₂×#121	—	5	3	no	—
274	C₂×#121	—	5	48	no	—
275	C₂×#120	—	5	6	no	—
276	C₂×#120	—	5	12	no	—
277	#520	—	5	16	no	—
278	C₂×C₄×Q₈	—	5	2	no	—
279	C₂×C₄×D₄	—	5	6	no	—
280	C₂×C₄×D₄	—	5	6	no	—
281	C₂×C₄×D₄	—	5	6	no	—
282	C₂×#117	—	5	3	no	—
283	C₂²×C₄⋊C₄	—	5	3	no	—
284	C₂²×C₂²⋊C₄	—	5	6	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	2	6	no	—
287	C₂³×C₅	—	2	6	no	—
288	C₂³×C₅	—	2	2	no	—
289	C₂³×C₅	—	2	24	no	—
290	C₂³×C₅	—	2	6	no	—
291	C₂³×C₅	—	2	6	no	—
292	C₂³×C₅	—	2	24	no	—
293	C₂³×C₅	—	2	6	no	—
294	C₂³×C₅	—	4	12	no	—
295	C₂³×C₅	—	4	48	no	—
296	C₂³×C₅	C₂²×D₄	1	12	yes	—
297	C₂³×C₅	H(5,𝔽₂)	1	4	yes	complemented
298	C₂³×C₅	C₂⁵	1	6	yes	—
299	C₂³×C₅	C₂⁵	1	6	yes	—
300	C₂³×C₅	C₂⁵	1	2	yes	—
301	C₂³×C₅	C₂⁵	1	1	yes	characteristic
302	C₂²×D₅	—	2	12	no	—
303	C₂²×D₅	—	2	12	no	—
304	C₂²×D₅	—	2	12	no	—
305	C₂²×D₅	—	2	48	no	—
306	C₂²×D₅	—	4	24	no	—
307	C₂²×D₅	—	4	24	no	—
308	C₂²×D₅	—	8	48	no	—
309	C₂²×D₅	C₂⁵	1	12	yes	—
310	C₅×Q₈	—	2	24	no	—
311	C₅×Q₈	C₂²×D₄	1	16	yes	complemented
312	C₅×D₄	—	2	48	no	—
313	C₅×D₄	—	2	24	no	—
314	C₅×D₄	C₂²×D₄	1	48	yes	complemented
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	6	no	—
317	C₂×C₄×C₅	—	2	24	no	—
318	C₂×C₄×C₅	—	2	8	no	—
319	C₂×C₄×C₅	—	2	24	no	—
320	C₂×C₄×C₅	—	2	24	no	—
321	C₂×C₄×C₅	—	2	24	no	—
322	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₅	C₂²×D₄	1	12	yes	—
324	C₂×C₄×C₅	C₂²×D₄	1	48	yes	complemented
325	C₂×C₄×C₅	C₂⁵	1	2	yes	—
326	C₂×C₄×C₅	C₂⁵	1	6	yes	—
327	C₂×C₄×C₅	C₂⁵	1	6	yes	—
328	C₂×C₄×C₅	C₂⁵	1	2	yes	—
329	C₂²⋊D₅	—	2	48	no	—
330	C₂²⋊D₅	—	2	48	no	—
331	C₂²⋊D₅	—	4	48	no	—
332	C₂²⋊D₅	—	4	24	no	—
333	C₂×Dic₅	—	2	4	no	—
334	C₂×Dic₅	—	2	12	no	—
335	C₂×Dic₅	—	2	4	no	—
336	C₂×Dic₅	—	4	24	no	—
337	C₂×Dic₅	C₂⁵	1	4	yes	—
338	C₂×Dic₅	C₂⁵	1	12	yes	—
339	C₂×Dic₅	C₂⁵	1	4	yes	—
340	D₂₀	—	2	24	no	—
341	D₂₀	—	2	48	no	—
342	C₄×D₅	—	2	48	no	—
343	Dic₁₀	—	2	8	no	—
344	C₂⁵	—	5	6	no	—
345	C₂⁵	C₂²×D₅	1	3	yes	—
346	H(5,𝔽₂)	—	10	128	no	—
347	C₂×#41	—	2	128	no	—
348	C₂×#41	—	2	8	no	—
349	C₂×#41	—	2	24	no	—
350	C₂×#41	—	2	24	no	—
351	C₂×#41	—	5	16	no	—
352	C₂×#41	—	5	24	no	—
353	C₂×#41	—	10	16	no	—
354	C₂×#41	—	10	24	no	—
355	C₂×#41	C₂²⋊D₅	1	16	yes	complemented
356	C₂×#41	C₂²×D₅	1	8	yes	—
357	C₂×#41	C₂²×D₅	1	24	yes	complemented
358	C₂×#41	C₂²×D₅	1	24	yes	complemented
359	C₂×#41	C₂²×D₅	1	8	yes	complemented
360	C₂²×Q₈	—	2	8	no	—
361	C₂²×Q₈	—	5	1	no	—
362	C₂²×Q₈	C₂²×D₅	1	3	yes	—
363	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
364	C₂²×Q₈	C₂²×D₅	1	8	yes	complemented
365	C₂²×D₄	—	2	24	no	—
366	C₂²×D₄	—	5	6	no	—
367	C₂²×D₄	—	5	6	no	—
368	C₂²×D₄	—	5	6	no	—
369	C₂²×D₄	—	5	12	no	—
370	C₂²×D₄	—	5	48	no	—
371	C₂²×D₄	—	5	48	no	—
372	C₂²×D₄	—	5	3	no	—
373	C₂²×D₄	—	5	6	no	—
374	C₂²×D₄	—	5	24	no	—
375	C₂²×D₄	—	10	48	no	—
376	C₂²×D₄	—	10	24	no	—
377	C₂²×D₄	—	20	24	no	—
378	C₂²×D₄	C₂²×D₅	1	6	yes	—
379	C₂²×D₄	C₂²×D₅	1	3	yes	—
380	C₂²×D₄	C₂²×D₅	1	3	yes	—
381	C₂²×D₄	C₂²×D₅	1	24	yes	complemented
382	C₂³×C₄	—	2	24	no	—
383	C₂³×C₄	—	5	6	no	—
384	C₂³×C₄	—	5	6	no	—
385	C₂³×C₄	C₂²×D₅	1	3	yes	—
386	C₂³×C₄	C₂²×D₅	1	3	yes	—
387	C₂³×C₄	C₂²×D₅	1	3	yes	—
388	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
389	C₂³×C₄	C₂²×D₅	1	3	yes	—
390	C₂³×C₄	C₂²×D₅	1	3	yes	—
391	C₂³×C₄	C₂²×D₅	1	24	yes	complemented
392	#127	—	5	48	no	—
393	#124	—	5	48	no	—
394	#123	—	5	48	no	—
395	C₂²⋊Q₈	—	5	48	no	—
396	C₂²⋊Q₈	—	5	8	no	—
397	C₂²⋊Q₈	—	5	24	no	—
398	#121	—	5	96	no	—
399	#121	—	5	48	no	—
400	#121	—	5	24	no	—
401	#121	—	5	48	no	—
402	#121	—	5	48	no	—
403	#121	—	5	48	no	—
404	#121	—	5	24	no	—
405	#120	—	5	48	no	—
406	#120	—	5	96	no	—
407	C₄×Q₈	—	5	16	no	—
408	C₄×D₄	—	5	48	no	—
409	C₄×D₄	—	5	48	no	—
410	C₄×D₄	—	5	48	no	—
411	#117	—	5	24	no	—
412	C₂×C₄⋊C₄	—	5	3	no	—
413	C₂×C₄⋊C₄	—	5	6	no	—
414	C₂×C₄⋊C₄	—	5	24	no	—
415	C₂×C₄⋊C₄	—	5	1	no	—
416	C₂×C₄⋊C₄	—	5	2	no	—
417	C₂×C₄⋊C₄	—	5	6	no	—
418	C₂×C₂²⋊C₄	—	5	6	no	—
419	C₂×C₂²⋊C₄	—	5	2	no	—
420	C₂×C₂²⋊C₄	—	5	6	no	—
421	C₂×C₂²⋊C₄	—	5	6	no	—
422	C₂×C₂²⋊C₄	—	5	12	no	—
423	C₂×C₂²⋊C₄	—	5	48	no	—
424	C₂×C₂²⋊C₄	—	5	6	no	—
425	C₂×C₄²	—	5	6	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	6	no	—
428	C₂²×C₅	—	2	6	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	24	no	—
431	C₂²×C₅	—	2	8	no	—
432	C₂²×C₅	—	2	6	no	—
433	C₂²×C₅	—	2	6	no	—
434	C₂²×C₅	—	2	6	no	—
435	C₂²×C₅	—	4	48	no	—
436	C₂²×C₅	—	4	12	no	—
437	C₂²×C₅	C₂³×D₄	1	12	yes	—
438	C₂²×C₅	C₂³×D₄	1	2	yes	—
439	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	complemented
441	C₂²×C₅	#585	1	2	yes	—
442	C₂²×C₅	C₂⁶	1	1	yes	characteristic
443	C₂×D₅	—	2	12	no	—
444	C₂×D₅	—	2	12	no	—
445	C₂×D₅	—	2	12	no	—
446	C₂×D₅	—	4	24	no	—
447	C₂×D₅	—	8	48	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	6	no	—
450	C₄×C₅	C₂³×D₄	1	4	yes	—
451	C₄×C₅	C₂³×D₄	1	12	yes	—
452	Dic₅	—	2	4	no	—
453	Dic₅	—	2	12	no	—
454	Dic₅	—	2	4	no	—
455	C₂⁴	—	2	12	no	—
456	C₂⁴	—	2	12	no	—
457	C₂⁴	—	4	6	no	—
458	C₂⁴	—	5	6	no	—
459	C₂⁴	—	5	24	no	—
460	C₂⁴	—	10	24	no	—
461	C₂⁴	—	20	12	no	—
462	C₂⁴	—	20	12	no	—
463	C₂⁴	C₂³×D₅	1	3	yes	—
464	C₂⁴	C₂³×D₅	1	12	yes	—
465	C₂⁴	C₂³×D₅	1	1	yes	characteristic
466	C₂⁴	C₂³×D₅	1	3	yes	—
467	#41	—	2	32	no	—
468	#41	—	2	96	no	—
469	#41	—	2	96	no	—
470	#41	—	10	64	no	—
471	#41	—	10	96	no	—
472	#41	C₂×C₂²⋊D₅	1	64	yes	complemented
473	C₂×Q₈	—	2	32	no	—
474	C₂×Q₈	—	2	12	no	—
475	C₂×Q₈	—	5	4	no	—
476	C₂×Q₈	—	10	4	no	—
477	C₂×Q₈	C₂×C₂²⋊D₅	1	8	yes	complemented
478	C₂×Q₈	C₂³×D₅	1	12	yes	—
479	C₂×Q₈	C₂³×D₅	1	4	yes	—
480	C₂×D₄	—	2	24	no	—
481	C₂×D₄	—	2	96	no	—
482	C₂×D₄	—	2	12	no	—
483	C₂×D₄	—	5	24	no	—
484	C₂×D₄	—	5	24	no	—
485	C₂×D₄	—	5	24	no	—
486	C₂×D₄	—	5	48	no	—
487	C₂×D₄	—	5	12	no	—
488	C₂×D₄	—	5	24	no	—
489	C₂×D₄	—	10	24	no	—
490	C₂×D₄	—	10	24	no	—
491	C₂×D₄	—	10	192	no	—
492	C₂×D₄	—	10	12	no	—
493	C₂×D₄	—	10	24	no	—
494	C₂×D₄	—	10	96	no	—
495	C₂×D₄	—	20	24	no	—
496	C₂×D₄	—	20	12	no	—
497	C₂×D₄	—	20	96	no	—
498	C₂×D₄	C₂×C₂²⋊D₅	1	24	yes	complemented
499	C₂×D₄	C₂³×D₅	1	24	yes	—
500	C₂×D₄	C₂³×D₅	1	12	yes	—
501	C₂×D₄	C₂³×D₅	1	12	yes	—
502	C₂²×C₄	—	2	12	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	12	no	—
505	C₂²×C₄	—	2	12	no	—
506	C₂²×C₄	—	2	12	no	—
507	C₂²×C₄	—	2	96	no	—
508	C₂²×C₄	—	5	2	no	—
509	C₂²×C₄	—	5	6	no	—
510	C₂²×C₄	—	5	2	no	—
511	C₂²×C₄	—	5	24	no	—
512	C₂²×C₄	—	5	24	no	—
513	C₂²×C₄	—	10	24	no	—
514	C₂²×C₄	—	20	12	no	—
515	C₂²×C₄	C₂×C₂²⋊D₅	1	24	yes	complemented
516	C₂²×C₄	C₂³×D₅	1	12	yes	—
517	C₂²×C₄	C₂³×D₅	1	12	yes	—
518	C₂²×C₄	C₂³×D₅	1	12	yes	—
519	C₂²×C₄	C₂³×D₅	1	4	yes	—
520	C₂²×C₄	C₂³×D₅	1	12	yes	—
521	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
522	C₂²×C₄	C₂³×D₅	1	3	yes	—
523	C₂²×C₄	C₂³×D₅	1	3	yes	—
524	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
525	C₂²×C₄	C₂³×D₅	1	12	yes	—
526	C₄⋊C₄	—	5	12	no	—
527	C₄⋊C₄	—	5	24	no	—
528	C₄⋊C₄	—	5	4	no	—
529	C₄⋊C₄	—	5	8	no	—
530	C₄⋊C₄	—	5	24	no	—
531	C₂²⋊C₄	—	5	24	no	—
532	C₂²⋊C₄	—	5	8	no	—
533	C₂²⋊C₄	—	5	24	no	—
534	C₂²⋊C₄	—	5	24	no	—
535	C₂²⋊C₄	—	5	48	no	—
536	C₂²⋊C₄	—	5	24	no	—
537	C₄²	—	5	24	no	—
538	C₂×C₅	—	2	12	no	—
539	C₂×C₅	—	2	4	no	—
540	C₂×C₅	—	4	6	no	—
541	C₂×C₅	#3488	1	4	yes	complemented
542	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
543	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂×C₅	C₂×#585	1	1	yes	characteristic
545	D₅	—	4	12	no	—
546	C₂³	—	2	6	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	6	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	6	no	—
551	C₂³	—	2	24	no	—
552	C₂³	—	2	6	no	—
553	C₂³	—	2	24	no	—
554	C₂³	—	2	6	no	—
555	C₂³	—	4	12	no	—
556	C₂³	—	4	48	no	—
557	C₂³	—	5	12	no	—
558	C₂³	—	10	12	no	—
559	C₂³	—	10	12	no	—
560	C₂³	—	10	12	no	—
561	C₂³	—	10	48	no	—
562	C₂³	—	20	24	no	—
563	C₂³	—	20	24	no	—
564	C₂³	—	40	48	no	—
565	C₂³	#4149	1	4	yes	complemented
566	C₂³	C₂²×C₂²⋊D₅	1	12	yes	—
567	C₂³	C₂⁴×D₅	1	6	yes	—
568	C₂³	C₂⁴×D₅	1	2	yes	—
569	C₂³	C₂⁴×D₅	1	6	yes	—
570	C₂³	C₂⁴×D₅	1	1	yes	characteristic
571	Q₈	—	2	24	no	—
572	Q₈	—	10	8	no	—
573	Q₈	C₂²×C₂²⋊D₅	1	16	yes	complemented
574	D₄	—	2	48	no	—
575	D₄	—	2	24	no	—
576	D₄	—	10	48	no	—
577	D₄	—	10	48	no	—
578	D₄	—	10	24	no	—
579	D₄	—	10	48	no	—
580	D₄	—	20	48	no	—
581	D₄	—	20	24	no	—
582	D₄	C₂²×C₂²⋊D₅	1	48	yes	complemented
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	6	no	—
585	C₂×C₄	—	2	24	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	24	no	—
588	C₂×C₄	—	2	24	no	—
589	C₂×C₄	—	2	24	no	—
590	C₂×C₄	—	5	4	no	—
591	C₂×C₄	—	5	12	no	—
592	C₂×C₄	—	5	4	no	—
593	C₂×C₄	—	10	12	no	—
594	C₂×C₄	—	10	4	no	—
595	C₂×C₄	—	10	4	no	—
596	C₂×C₄	—	10	48	no	—
597	C₂×C₄	—	20	24	no	—
598	C₂×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
599	C₂×C₄	C₂²×C₂²⋊D₅	1	12	yes	—
600	C₂×C₄	C₂²×C₂²⋊D₅	1	48	yes	complemented
601	C₂×C₄	C₂⁴×D₅	1	2	yes	—
602	C₂×C₄	C₂⁴×D₅	1	6	yes	—
603	C₂×C₄	C₂⁴×D₅	1	6	yes	—
604	C₂×C₄	C₂⁴×D₅	1	2	yes	—
605	C₅	C₂×#3488	1	1	yes	characteristic, complemented, Sylow
606	C₂²	—	2	8	no	—
607	C₂²	—	2	24	no	—
608	C₂²	—	2	6	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	6	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	6	no	—
613	C₂²	—	2	6	no	—
614	C₂²	—	2	6	no	—
615	C₂²	—	4	48	no	—
616	C₂²	—	4	12	no	—
617	C₂²	—	10	12	no	—
618	C₂²	—	10	12	no	—
619	C₂²	—	10	12	no	—
620	C₂²	—	20	24	no	—
621	C₂²	—	40	48	no	—
622	C₂²	C₂×#4149	1	2	yes	—
623	C₂²	C₂×#4149	1	4	yes	complemented
624	C₂²	#66283	1	2	yes	—
625	C₂²	C₂³×C₂²⋊D₅	1	12	yes	—
626	C₂²	C₂³×C₂²⋊D₅	1	2	yes	—
627	C₂²	C₂⁵×D₅	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	6	no	—
630	C₄	—	10	12	no	—
631	C₄	—	10	4	no	—
632	C₄	—	10	4	no	—
633	C₄	C₂³×C₂²⋊D₅	1	4	yes	—
634	C₄	C₂³×C₂²⋊D₅	1	12	yes	—
635	C₂	—	2	4	no	—
636	C₂	—	2	12	no	—
637	C₂	—	4	6	no	—
638	C₂	—	20	12	no	—
639	C₂	#10619176	1	4	yes	direct product factor
640	C₂	C₂²×#4149	1	1	yes	characteristic
641	C₂	C₂×#66283	1	1	yes	characteristic
642	C₂	C₂⁴×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂³×C₅×#41	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂³×#41	D₅
hypocenter	C₅	C₂×#3488
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×#41	C₂	semidirect
2. C₂²×#4149	C₂	semidirect
3. #10619176	C₂	direct (N × H)
4. C₂×#66168	C₂	semidirect
5. C₂×#66163	C₂	semidirect
6. C₂×#66167	C₂	semidirect
7. C₂×#66164	C₂	semidirect
8. C₂×#66161	C₂	semidirect
9. C₂×#66151	C₂	semidirect
10. C₂×D₄×C₂²⋊D₅	C₂	semidirect
11. C₂×#66125	C₂	semidirect
12. C₂²×#4076	C₂	semidirect
15. C₂²×C₅×#41	C₂²	semidirect
16. C₂²×C₅×#41	C₂²	semidirect
17. C₂²×C₅×#41	C₂²	semidirect
18. C₂²×C₅×#41	C₂²	semidirect
19. C₂³×C₅×Q₈	C₂²	semidirect
20. C₂³×C₅×D₄	C₂²	semidirect
21. C₂⁴×C₄×C₅	C₂²	semidirect
22. C₂³×C₂²⋊D₅	C₂²	semidirect
24. C₂×#4149	C₂²	semidirect
25. C₂²×#713	C₂²	semidirect
26. C₂²×D₄×D₅	C₂²	semidirect
27. C₂²×#709	C₂²	semidirect
28. C₂³×D₂₀	C₂²	semidirect
29. C₂×#4099	C₂²	semidirect
30. #66168	C₂²	semidirect
31. #66167	C₂²	semidirect
32. #66164	C₂²	semidirect
33. #66163	C₂²	semidirect
34. #66161	C₂²	semidirect
35. #66151	C₂²	semidirect
36. C₂×#4093	C₂²	semidirect
37. C₂×#4092	C₂²	semidirect
38. C₂×Q₈×Dic₅	C₂²	semidirect
39. C₂×#4086	C₂²	semidirect
40. C₂×#4085	C₂²	semidirect
41. D₄×C₂²⋊D₅	C₂²	semidirect
42. C₂×#4084	C₂²	semidirect
43. C₂×#4083	C₂²	semidirect
44. C₂×D₄×Dic₅	C₂²	semidirect
45. #66125	C₂²	semidirect
46. C₂×#4076	C₂²	semidirect
47. C₂×#4076	C₂²	semidirect
48. C₂×#4076	C₂²	semidirect
49. C₂×#4076	C₂²	semidirect
50. C₂×#4076	C₂²	semidirect
51. C₂×#4076	C₂²	semidirect
52. C₂×#4075	C₂²	semidirect
53. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
54. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
55. C₂²×#685	C₂²	semidirect
56. C₂×#4072	C₂²	semidirect
57. C₂²×C₄⋊Dic₅	C₂²	semidirect
58. C₂×#4070	C₂²	semidirect
59. C₂×#4070	C₂²	semidirect
67. C₂×C₅×#41	D₄	semidirect
69. C₂×C₅×#41	C₂³	semidirect
70. C₂×C₅×#41	C₂³	semidirect
71. C₂×C₅×#41	C₂³	semidirect
75. C₂²×C₅×Q₈	C₂³	semidirect
80. C₂²×C₅×D₄	C₂³	semidirect
88. C₂³×C₄×C₅	C₂³	semidirect
94. C₂²×C₂²⋊D₅	C₂³	semidirect
98. C₂×#713	C₂³	semidirect
100. C₂×D₄×D₅	C₂³	semidirect
102. C₂×#709	C₂³	semidirect
106. C₂²×D₂₀	C₂³	semidirect
109. #4099	C₂³	semidirect
113. #4093	C₂³	semidirect
114. #4092	C₂³	semidirect
115. Q₈×Dic₅	C₂³	semidirect
116. #4086	C₂³	semidirect
117. #4085	C₂³	semidirect
118. #4084	C₂³	semidirect
119. #4083	C₂³	semidirect
120. D₄×Dic₅	C₂³	semidirect
121. #4076	C₂³	semidirect
122. #4076	C₂³	semidirect
123. #4076	C₂³	semidirect
124. #4076	C₂³	semidirect
125. #4076	C₂³	semidirect
126. #4075	C₂³	semidirect
127. C₄×C₂²⋊D₅	C₂³	semidirect
128. C₄×C₂²⋊D₅	C₂³	semidirect
132. C₂×#685	C₂³	semidirect
133. #4072	C₂³	semidirect
137. C₂×C₄⋊Dic₅	C₂³	semidirect
138. #4070	C₂³	semidirect
139. #4070	C₂³	semidirect
144. C₂³×#41	D₅	semidirect
170. C₅×#41	C₂×D₄	semidirect
173. C₂×C₅×Q₈	C₂×D₄	semidirect
179. C₂×C₅×D₄	C₂×D₄	semidirect
189. C₂²×C₄×C₅	C₂×D₄	semidirect
244. C₂²×#41	C₂×D₅	semidirect
245. C₂²×#41	C₂×D₅	semidirect
246. C₂²×#41	C₂×D₅	semidirect
247. C₂²×#41	C₂×D₅	semidirect
248. C₂³×Q₈	C₂×D₅	semidirect
252. C₂³×D₄	C₂×D₅	semidirect
253. C₂⁴×C₄	C₂×D₅	semidirect
297. C₂³×C₅	H(5,𝔽₂)	semidirect
311. C₅×Q₈	C₂²×D₄	semidirect
314. C₅×D₄	C₂²×D₄	semidirect
324. C₂×C₄×C₅	C₂²×D₄	semidirect
355. C₂×#41	C₂²⋊D₅	semidirect
357. C₂×#41	C₂²×D₅	semidirect
358. C₂×#41	C₂²×D₅	semidirect
359. C₂×#41	C₂²×D₅	semidirect
364. C₂²×Q₈	C₂²×D₅	semidirect
381. C₂²×D₄	C₂²×D₅	semidirect
391. C₂³×C₄	C₂²×D₅	semidirect
440. C₂²×C₅	C₂×H(5,𝔽₂)	semidirect
472. #41	C₂×C₂²⋊D₅	semidirect
477. C₂×Q₈	C₂×C₂²⋊D₅	semidirect
498. C₂×D₄	C₂×C₂²⋊D₅	semidirect
515. C₂²×C₄	C₂×C₂²⋊D₅	semidirect
541. C₂×C₅	#3488	semidirect
565. C₂³	#4149	semidirect
573. Q₈	C₂²×C₂²⋊D₅	semidirect
582. D₄	C₂²×C₂²⋊D₅	semidirect
600. C₂×C₄	C₂²×C₂²⋊D₅	semidirect
605. C₅	C₂×#3488	semidirect
623. C₂²	C₂×#4149	semidirect
639. C₂	#10619176	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×#41	2
C₂²×#4149	2
#10619176	2
C₂×#66168	2
C₂×#66163	2
C₂×#66167	2
C₂×#66164	2
C₂×#66161	2
C₂×#66151	2
C₂×D₄×C₂²⋊D₅	2
C₂×#66125	2
C₂²×#4076	2
C₂×#3488	5

Subgroups — C2×#10619176 #13007613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10619176 #13007613