Subgroups — C₂×#10618246 #13006593

Order 1280.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66164	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#66162	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66151	C₂	1	2	yes	maximal, complemented
5	#10618246	C₂	1	32	yes	maximal, direct product factor
6	C₂×#66067	C₂	1	4	yes	maximal, complemented
7	C₂×#66017	C₂	1	2	yes	maximal, complemented
8	C₂×#66013	C₂	1	2	yes	maximal, complemented
9	C₂×#66000	C₂	1	2	yes	maximal, complemented
10	C₂×#65991	C₂	1	4	yes	maximal, complemented
11	C₂×#65998	C₂	1	2	yes	maximal, complemented
12	C₂×#65964	C₂	1	2	yes	maximal, complemented
13	C₂×#65975	C₂	1	2	yes	maximal, complemented
14	C₂×#65977	C₂	1	2	yes	maximal, complemented
15	C₂×#65961	C₂	1	2	yes	maximal, complemented
16	C₂×#65866	C₂	1	2	yes	maximal, complemented
17	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#713	C₂²	1	2	yes	—
20	C₂³×D₂₀	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
22	C₅×#536	C₂²	1	16	yes	complemented
23	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₅×#124	C₂²	1	2	yes	—
25	C₂×C₅×#123	C₂²	1	2	yes	complemented
26	C₂×C₅×#123	C₂²	1	2	yes	complemented
27	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
30	#66164	C₂²	1	16	yes	complemented
31	#66162	C₂²	1	16	yes	complemented
32	#66151	C₂²	1	32	yes	complemented
33	C₂×#4093	C₂²	1	2	yes	complemented
34	C₂×#4093	C₂²	1	4	yes	complemented
35	C₂×#4093	C₂²	1	2	yes	complemented
36	C₂×#4092	C₂²	1	2	yes	complemented
37	C₂×#4092	C₂²	1	4	yes	complemented
38	C₂×#4092	C₂²	1	2	yes	complemented
39	C₂×Q₈×Dic₅	C₂²	1	2	yes	complemented
40	C₂×#4086	C₂²	1	2	yes	—
41	C₂×#4084	C₂²	1	2	yes	—
42	C₂×#4083	C₂²	1	1	yes	characteristic
43	C₂×#4083	C₂²	1	2	yes	—
44	C₂×#4083	C₂²	1	1	yes	characteristic, complemented
45	C₂×#4083	C₂²	1	2	yes	complemented
46	C₂×#4081	C₂²	1	1	yes	characteristic
47	C₂×#4081	C₂²	1	1	yes	characteristic, complemented
48	C₂×#4076	C₂²	1	2	yes	—
49	C₂×#4076	C₂²	1	2	yes	complemented
50	C₂×#4076	C₂²	1	4	yes	complemented
51	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
52	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
53	C₂×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
54	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
55	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
56	#66067	C₂²	1	64	yes	complemented
57	#66017	C₂²	1	32	yes	complemented
58	#66013	C₂²	1	32	yes	complemented
59	#66000	C₂²	1	32	yes	complemented
60	#65998	C₂²	1	32	yes	complemented
61	#65991	C₂²	1	64	yes	complemented
62	#65977	C₂²	1	32	yes	complemented
63	#65975	C₂²	1	32	yes	complemented
64	#65964	C₂²	1	32	yes	complemented
65	#65961	C₂²	1	32	yes	complemented
66	#65866	C₂²	1	32	yes	complemented
67	C₂×#4044	C₂²	1	4	yes	complemented
68	C₂×#4044	C₂²	1	4	yes	complemented
69	C₂×#4043	C₂²	1	4	yes	complemented
70	C₂×#4041	C₂²	1	2	yes	—
71	C₂×#4041	C₂²	1	4	yes	—
72	C₂×#4040	C₂²	1	4	yes	complemented
73	C₂×#4040	C₂²	1	4	yes	complemented
74	C₂×#4039	C₂²	1	4	yes	complemented
75	C₂×#4039	C₂²	1	2	yes	complemented
76	C₂×#4038	C₂²	1	2	yes	complemented
77	C₂×#4034	C₂²	1	2	yes	complemented
78	C₂×#4033	C₂²	1	4	yes	complemented
79	C₂×#4031	C₂²	1	4	yes	—
80	C₂×#4031	C₂²	1	4	yes	complemented
81	C₂×#4031	C₂²	1	4	yes	complemented
82	C₂×#4030	C₂²	1	4	yes	complemented
83	C₂×#4029	C₂²	1	4	yes	complemented
84	C₂×#4028	C₂²	1	4	yes	—
85	C₂×#4028	C₂²	1	4	yes	complemented
86	C₂×#4027	C₂²	1	4	yes	complemented
87	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
88	C₂×#4025	C₂²	1	4	yes	complemented
89	C₂×#4021	C₂²	1	4	yes	complemented
90	C₂×#4018	C₂²	1	4	yes	complemented
91	C₂×#3540	—	5	1	no	maximal, Sylow
92	C₂⁴×D₅	C₂³	1	2	yes	—
93	C₂⁴×D₅	C₂³	1	1	yes	characteristic
94	C₂×C₅×#41	—	4	4	no	—
95	C₂×C₅×#41	C₂³	1	8	yes	—
96	C₂²×C₅×Q₈	—	4	4	no	—
97	C₂²×C₅×Q₈	C₂³	1	2	yes	—
98	C₂²×C₅×Q₈	C₂³	1	2	yes	—
99	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
100	C₂²×C₅×Q₈	C₂³	1	8	yes	complemented
101	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
102	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
103	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅	C₂³	1	2	yes	—
108	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
109	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
110	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
111	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
112	C₂³×Dic₅	C₂³	1	1	yes	characteristic
113	C₂×#713	—	4	8	no	—
114	C₂×#713	C₂³	1	16	yes	—
115	C₂²×D₂₀	—	4	4	no	—
116	C₂²×D₂₀	C₂³	1	2	yes	—
117	C₂²×D₂₀	C₂³	1	4	yes	—
118	C₂²×D₂₀	C₂³	1	4	yes	—
119	C₂²×D₂₀	C₂³	1	2	yes	—
120	C₂²×D₂₀	C₂³	1	8	yes	complemented
121	C₂²×C₄×D₅	—	4	4	no	—
122	C₂²×C₄×D₅	C₂³	1	2	yes	—
123	C₂²×C₄×D₅	C₂³	1	4	yes	—
124	C₂²×C₄×D₅	C₂³	1	4	yes	—
125	C₂²×C₄×D₅	C₂³	1	2	yes	—
126	C₂²×C₄×D₅	C₂³	1	8	yes	complemented
127	C₂²×Dic₁₀	C₂³	1	4	yes	—
128	C₅×C₄⋊Q₈	C₂³	1	16	yes	complemented
129	C₅×#124	C₂³	1	16	yes	—
130	C₅×#123	C₂³	1	16	yes	complemented
131	C₅×#123	C₂³	1	16	yes	complemented
132	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
133	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
134	C₅×#117	C₂³	1	8	yes	complemented
135	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₄²×C₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
147	#4093	C₂³	1	16	yes	complemented
148	#4093	C₂³	1	32	yes	complemented
149	#4093	C₂³	1	16	yes	complemented
150	#4092	C₂³	1	16	yes	complemented
151	#4092	C₂³	1	32	yes	complemented
152	#4092	C₂³	1	16	yes	complemented
153	Q₈×Dic₅	C₂³	1	16	yes	complemented
154	#4086	C₂³	1	16	yes	—
155	#4084	C₂³	1	16	yes	—
156	#4083	C₂³	1	8	yes	—
157	#4083	C₂³	1	16	yes	—
158	#4083	C₂³	1	8	yes	complemented
159	#4083	C₂³	1	16	yes	complemented
160	#4081	C₂³	1	8	yes	—
161	#4081	C₂³	1	8	yes	complemented
162	#4076	C₂³	1	16	yes	—
163	#4076	C₂³	1	16	yes	complemented
164	#4076	C₂³	1	32	yes	complemented
165	C₄×C₂²⋊D₅	C₂³	1	16	yes	—
166	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
167	C₄×C₂²⋊D₅	C₂³	1	32	yes	complemented
168	C₂×#685	C₂³	1	4	yes	—
169	C₂×#685	C₂³	1	4	yes	—
170	C₂×#685	C₂³	1	2	yes	—
171	C₂×#685	C₂³	1	4	yes	—
172	C₂×#685	C₂³	1	4	yes	—
173	C₂×#685	C₂³	1	4	yes	—
174	C₂×#685	C₂³	1	4	yes	—
175	C₂×#685	C₂³	1	4	yes	—
176	C₂×#685	C₂³	1	4	yes	—
177	C₂×#685	C₂³	1	2	yes	—
178	#4072	C₂³	1	8	yes	complemented
179	#4072	C₂³	1	8	yes	complemented
180	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
181	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
182	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
183	C₂×#683	C₂³	1	2	yes	—
184	C₂×#683	C₂³	1	4	yes	—
185	C₂×#683	C₂³	1	4	yes	—
186	C₂×#683	C₂³	1	2	yes	—
187	C₂×C₄×Dic₅	C₂³	1	4	yes	—
188	C₂×C₄×Dic₅	C₂³	1	4	yes	—
189	C₂×C₄×Dic₅	C₂³	1	2	yes	—
190	C₂×C₄×Dic₅	C₂³	1	2	yes	—
191	#4044	C₂³	1	32	yes	complemented
192	#4044	C₂³	1	32	yes	complemented
193	#4043	C₂³	1	32	yes	complemented
194	#4041	C₂³	1	32	yes	—
195	#4041	C₂³	1	16	yes	—
196	#4040	C₂³	1	32	yes	complemented
197	#4040	C₂³	1	32	yes	complemented
198	#4039	C₂³	1	32	yes	complemented
199	#4039	C₂³	1	16	yes	complemented
200	#4038	C₂³	1	16	yes	complemented
201	#4034	C₂³	1	16	yes	complemented
202	#4033	C₂³	1	32	yes	complemented
203	#4031	C₂³	1	32	yes	—
204	#4031	C₂³	1	32	yes	complemented
205	#4031	C₂³	1	32	yes	complemented
206	#4030	C₂³	1	32	yes	complemented
207	#4029	C₂³	1	32	yes	complemented
208	#4028	C₂³	1	32	yes	—
209	#4028	C₂³	1	32	yes	complemented
210	#4027	C₂³	1	32	yes	complemented
211	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
212	#4025	C₂³	1	32	yes	complemented
213	#4021	C₂³	1	32	yes	complemented
214	#4018	C₂³	1	32	yes	complemented
215	#3540	—	5	32	no	—
216	C₂×H(3,𝔽₄)	—	5	2	no	—
217	C₂×#560	—	5	2	no	—
218	C₂×#559	—	5	2	no	—
219	C₂×#556	—	5	2	no	—
220	C₂×#555	—	5	2	no	—
221	C₂×#551	—	5	2	no	—
222	C₂×#548	—	5	2	no	—
223	C₂×#546	—	5	2	no	—
224	C₂×#542	—	5	4	no	—
225	C₂×#542	—	5	2	no	—
226	C₂×#538	—	5	4	no	—
227	C₂×#536	D₅	1	1	yes	characteristic, complemented
228	C₂×#535	—	5	1	no	—
229	C₂×#525	—	5	1	no	—
230	C₂×#525	—	5	2	no	—
231	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
234	C₂³×D₅	—	4	2	no	—
235	C₂³×D₅	—	4	4	no	—
236	C₂³×D₅	—	4	4	no	—
237	C₂³×D₅	—	4	8	no	—
238	C₂³×D₅	C₂⁴	1	2	yes	—
239	C₂³×D₅	C₂⁴	1	4	yes	—
240	C₂³×D₅	C₂⁴	1	4	yes	—
241	C₂³×D₅	C₂⁴	1	8	yes	—
242	C₅×#41	—	4	16	no	—
243	C₂×C₅×Q₈	—	2	8	no	—
244	C₂×C₅×Q₈	—	4	4	no	—
245	C₂×C₅×Q₈	—	4	2	no	—
246	C₂×C₅×Q₈	—	4	16	no	—
247	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
248	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
249	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
250	C₂×C₅×D₄	—	4	2	no	—
251	C₂×C₅×D₄	—	4	2	no	—
252	C₂×C₅×D₄	—	4	2	no	—
253	C₂×C₅×D₄	C₂⁴	1	4	yes	—
254	C₂×C₅×D₄	C₂⁴	1	4	yes	—
255	C₂×C₅×D₄	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₅	—	2	4	no	—
257	C₂²×C₄×C₅	—	2	4	no	—
258	C₂²×C₄×C₅	—	2	4	no	—
259	C₂²×C₄×C₅	—	4	4	no	—
260	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
269	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₂²⋊D₅	—	4	4	no	—
271	C₂×C₂²⋊D₅	—	4	8	no	—
272	C₂×C₂²⋊D₅	—	4	8	no	—
273	C₂×C₂²⋊D₅	—	4	4	no	—
274	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
275	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
276	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
277	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
278	C₂²×Dic₅	—	4	2	no	—
279	C₂²×Dic₅	C₂⁴	1	2	yes	—
280	C₂²×Dic₅	C₂⁴	1	2	yes	—
281	C₂²×Dic₅	C₂⁴	1	2	yes	—
282	C₂²×Dic₅	C₂⁴	1	4	yes	—
283	C₂²×Dic₅	C₂⁴	1	4	yes	—
284	#713	—	4	32	no	—
285	C₂×D₂₀	—	2	8	no	—
286	C₂×D₂₀	—	4	16	no	—
287	C₂×D₂₀	—	4	4	no	—
288	C₂×D₂₀	—	4	8	no	—
289	C₂×D₂₀	—	4	8	no	—
290	C₂×D₂₀	C₂⁴	1	8	yes	—
291	C₂×D₂₀	C₂⁴	1	8	yes	—
292	C₂×D₂₀	C₂⁴	1	16	yes	—
293	C₂×D₂₀	C₂⁴	1	16	yes	—
294	C₂×C₄×D₅	—	2	8	no	—
295	C₂×C₄×D₅	—	4	16	no	—
296	C₂×C₄×D₅	—	4	4	no	—
297	C₂×C₄×D₅	—	4	8	no	—
298	C₂×C₄×D₅	—	4	8	no	—
299	C₂×C₄×D₅	C₂⁴	1	8	yes	—
300	C₂×C₄×D₅	C₂⁴	1	8	yes	—
301	C₂×C₄×D₅	C₂⁴	1	16	yes	—
302	C₂×C₄×D₅	C₂⁴	1	16	yes	—
303	C₂×Dic₁₀	—	4	8	no	—
304	C₂×Dic₁₀	C₂⁴	1	16	yes	—
305	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
307	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
308	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
309	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
310	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
311	C₄²×C₅	C₂⁴	1	8	yes	—
312	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
313	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
314	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
315	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
316	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
317	#685	C₂⁴	1	16	yes	—
318	#685	C₂⁴	1	16	yes	—
319	#685	C₂⁴	1	8	yes	—
320	#685	C₂⁴	1	16	yes	—
321	#685	C₂⁴	1	16	yes	—
322	#685	C₂⁴	1	16	yes	—
323	#685	C₂⁴	1	16	yes	—
324	#685	C₂⁴	1	16	yes	—
325	#685	C₂⁴	1	16	yes	—
326	#685	C₂⁴	1	8	yes	—
327	C₄⋊Dic₅	C₂⁴	1	16	yes	—
328	C₄⋊Dic₅	C₂⁴	1	8	yes	—
329	C₄⋊Dic₅	C₂⁴	1	8	yes	—
330	#683	C₂⁴	1	8	yes	—
331	#683	C₂⁴	1	16	yes	—
332	#683	C₂⁴	1	16	yes	—
333	#683	C₂⁴	1	8	yes	—
334	C₄×Dic₅	C₂⁴	1	16	yes	—
335	C₄×Dic₅	C₂⁴	1	16	yes	—
336	C₄×Dic₅	C₂⁴	1	8	yes	—
337	C₄×Dic₅	C₂⁴	1	8	yes	—
338	C₂²×#41	—	5	2	no	—
339	C₂²×#41	C₂×D₅	1	1	yes	characteristic
340	C₂³×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
341	C₂³×D₄	—	5	1	no	—
342	C₂⁴×C₄	—	5	1	no	—
343	H(3,𝔽₄)	—	5	32	no	—
344	#560	—	5	32	no	—
345	#559	—	5	32	no	—
346	#556	—	5	32	no	—
347	#555	—	5	32	no	—
348	#551	—	5	32	no	—
349	#548	—	5	32	no	—
350	#546	—	5	32	no	—
351	#542	—	5	64	no	—
352	#542	—	5	32	no	—
353	#538	—	5	64	no	—
354	#536	C₂×D₅	1	16	yes	complemented
355	#535	—	5	16	no	—
356	C₂×C₄⋊Q₈	—	5	2	no	—
357	C₂×C₄⋊Q₈	C₂×D₅	1	2	yes	complemented
358	C₂×#127	—	5	2	no	—
359	C₂×#126	—	5	4	no	—
360	C₂×#126	—	5	4	no	—
361	C₂×#126	—	5	4	no	—
362	C₂×#124	—	5	2	no	—
363	C₂×#124	—	5	2	no	—
364	C₂×#124	—	5	4	no	—
365	C₂×#124	—	5	4	no	—
366	C₂×#124	—	5	4	no	—
367	C₂×#124	—	5	4	no	—
368	C₂×#124	—	5	4	no	—
369	C₂×#124	C₂×D₅	1	2	yes	—
370	#525	—	5	16	no	—
371	#525	—	5	32	no	—
372	C₂×#123	—	5	1	no	—
373	C₂×#123	—	5	1	no	—
374	C₂×#123	—	5	4	no	—
375	C₂×#123	—	5	4	no	—
376	C₂×#123	—	5	4	no	—
377	C₂×#123	C₂×D₅	1	2	yes	complemented
378	C₂×#123	C₂×D₅	1	2	yes	complemented
379	C₂×C₂²⋊Q₈	—	5	2	no	—
380	C₂×C₂²⋊Q₈	—	5	2	no	—
381	C₂×C₂²⋊Q₈	—	5	4	no	—
382	C₂×C₂²⋊Q₈	—	5	4	no	—
383	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
384	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
385	C₂×#121	—	5	2	no	—
386	C₂×#121	—	5	2	no	—
387	C₂×#121	—	5	2	no	—
388	C₂×#121	—	5	4	no	—
389	C₂×#121	—	5	2	no	—
390	C₂×#121	—	5	4	no	—
391	C₂×#121	—	5	4	no	—
392	C₂×#120	—	5	1	no	—
393	C₂×#120	—	5	2	no	—
394	C₂×#120	—	5	1	no	—
395	C₂×#120	—	5	2	no	—
396	C₂×#120	—	5	4	no	—
397	C₂×#120	—	5	4	no	—
398	C₂×C₄×Q₈	—	5	2	no	—
399	C₂×C₄×Q₈	—	5	4	no	—
400	C₂×C₄×D₄	—	5	2	no	—
401	C₂×C₄×D₄	—	5	2	no	—
402	C₂×C₄×D₄	—	5	4	no	—
403	C₂×C₄×D₄	—	5	4	no	—
404	C₂×C₄×D₄	—	5	2	no	—
405	C₂×C₄×D₄	—	5	4	no	—
406	C₂×#117	—	5	1	no	—
407	C₂×#117	—	5	1	no	—
408	C₂×#117	—	5	2	no	—
409	C₂×#117	—	5	4	no	—
410	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
411	C₂²×C₂²⋊C₄	—	5	4	no	—
412	C₂³×C₅	—	2	2	no	—
413	C₂³×C₅	—	2	2	no	—
414	C₂³×C₅	—	2	2	no	—
415	C₂³×C₅	—	2	4	no	—
416	C₂³×C₅	—	2	4	no	—
417	C₂³×C₅	—	2	4	no	—
418	C₂³×C₅	C₂⁵	1	2	yes	—
419	C₂³×C₅	C₂⁵	1	2	yes	—
420	C₂³×C₅	C₂⁵	1	2	yes	—
421	C₂³×C₅	C₂⁵	1	1	yes	characteristic
422	C₂²×D₅	—	2	4	no	—
423	C₂²×D₅	—	2	8	no	—
424	C₂²×D₅	—	2	8	no	—
425	C₂²×D₅	—	2	4	no	—
426	C₂²×D₅	—	2	8	no	—
427	C₂²×D₅	—	2	4	no	—
428	C₂²×D₅	—	4	4	no	—
429	C₂²×D₅	—	4	8	no	—
430	C₂²×D₅	—	4	8	no	—
431	C₂²×D₅	—	4	16	no	—
432	C₂²×D₅	—	4	16	no	—
433	C₂²×D₅	—	8	16	no	—
434	C₂²×D₅	C₂⁵	1	4	yes	—
435	C₂²×D₅	C₂⁵	1	8	yes	—
436	C₅×Q₈	—	2	16	no	—
437	C₅×Q₈	—	4	8	no	—
438	C₅×Q₈	—	4	4	no	—
439	C₅×D₄	—	4	4	no	—
440	C₅×D₄	—	4	4	no	—
441	C₅×D₄	—	4	4	no	—
442	C₂×C₄×C₅	—	2	2	no	—
443	C₂×C₄×C₅	—	2	8	no	—
444	C₂×C₄×C₅	—	2	2	no	—
445	C₂×C₄×C₅	—	2	2	no	—
446	C₂×C₄×C₅	—	2	8	no	—
447	C₂×C₄×C₅	—	2	8	no	—
448	C₂×C₄×C₅	—	2	8	no	—
449	C₂×C₄×C₅	—	2	8	no	—
450	C₂×C₄×C₅	—	4	8	no	—
451	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
452	C₂×C₄×C₅	C₂⁵	1	2	yes	—
453	C₂×C₄×C₅	C₂⁵	1	8	yes	—
454	C₂×C₄×C₅	C₂⁵	1	8	yes	—
455	C₂×C₄×C₅	C₂⁵	1	2	yes	—
456	C₂×C₄×C₅	C₂⁵	1	2	yes	—
457	C₂×C₄×C₅	C₂⁵	1	2	yes	—
458	C₂²⋊D₅	—	4	8	no	—
459	C₂²⋊D₅	—	4	16	no	—
460	C₂²⋊D₅	—	4	16	no	—
461	C₂²⋊D₅	—	4	8	no	—
462	C₂×Dic₅	—	2	4	no	—
463	C₂×Dic₅	—	2	4	no	—
464	C₂×Dic₅	—	2	8	no	—
465	C₂×Dic₅	—	2	4	no	—
466	C₂×Dic₅	—	4	4	no	—
467	C₂×Dic₅	C₂⁵	1	8	yes	—
468	C₂×Dic₅	C₂⁵	1	4	yes	—
469	C₂×Dic₅	C₂⁵	1	4	yes	—
470	C₂×Dic₅	C₂⁵	1	4	yes	—
471	D₂₀	—	2	16	no	—
472	D₂₀	—	4	8	no	—
473	D₂₀	—	4	16	no	—
474	D₂₀	—	4	16	no	—
475	C₄×D₅	—	2	16	no	—
476	C₄×D₅	—	4	8	no	—
477	C₄×D₅	—	4	16	no	—
478	C₄×D₅	—	4	16	no	—
479	Dic₁₀	—	4	16	no	—
480	C₂⁵	—	5	2	no	—
481	C₂⁵	—	5	1	no	—
482	C₂×#41	—	4	4	no	—
483	C₂×#41	—	5	16	no	—
484	C₂×#41	—	20	8	no	—
485	C₂×#41	C₂²×D₅	1	8	yes	—
486	C₂²×Q₈	—	4	4	no	—
487	C₂²×Q₈	—	5	4	no	—
488	C₂²×Q₈	C₂²×D₅	1	2	yes	—
489	C₂²×Q₈	C₂²×D₅	1	2	yes	—
490	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
491	C₂²×Q₈	C₂²×D₅	1	8	yes	complemented
492	C₂²×D₄	—	5	2	no	—
493	C₂²×D₄	—	5	4	no	—
494	C₂²×D₄	—	5	2	no	—
495	C₂²×D₄	—	5	4	no	—
496	C₂²×D₄	—	5	2	no	—
497	C₂²×D₄	—	5	4	no	—
498	C₂²×D₄	—	5	4	no	—
499	C₂²×D₄	—	5	2	no	—
500	C₂²×D₄	—	5	8	no	—
501	C₂²×D₄	—	20	4	no	—
502	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
503	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
504	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
505	C₂³×C₄	—	5	1	no	—
506	C₂³×C₄	—	5	2	no	—
507	C₂³×C₄	—	5	4	no	—
508	C₂³×C₄	—	5	4	no	—
509	C₂³×C₄	—	5	2	no	—
510	C₂³×C₄	—	5	8	no	—
511	C₂³×C₄	—	20	4	no	—
512	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
513	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
514	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
515	C₂³×C₄	C₂²×D₅	1	2	yes	—
516	C₄⋊Q₈	—	5	16	no	—
517	C₄⋊Q₈	C₂²×D₅	1	16	yes	complemented
518	#127	—	5	16	no	—
519	#126	—	5	32	no	—
520	#126	—	5	32	no	—
521	#126	—	5	32	no	—
522	#124	—	5	16	no	—
523	#124	—	5	16	no	—
524	#124	—	5	32	no	—
525	#124	—	5	32	no	—
526	#124	—	5	32	no	—
527	#124	—	5	32	no	—
528	#124	—	5	32	no	—
529	#124	C₂²×D₅	1	16	yes	—
530	#123	—	5	8	no	—
531	#123	—	5	8	no	—
532	#123	—	5	32	no	—
533	#123	—	5	32	no	—
534	#123	—	5	32	no	—
535	#123	C₂²×D₅	1	16	yes	complemented
536	#123	C₂²×D₅	1	16	yes	complemented
537	C₂²⋊Q₈	—	5	16	no	—
538	C₂²⋊Q₈	—	5	16	no	—
539	C₂²⋊Q₈	—	5	32	no	—
540	C₂²⋊Q₈	—	5	32	no	—
541	C₂²⋊Q₈	C₂²×D₅	1	16	yes	complemented
542	C₂²⋊Q₈	C₂²×D₅	1	16	yes	complemented
543	#121	—	5	16	no	—
544	#121	—	5	16	no	—
545	#121	—	5	16	no	—
546	#121	—	5	32	no	—
547	#121	—	5	16	no	—
548	#121	—	5	32	no	—
549	#121	—	5	32	no	—
550	#120	—	5	8	no	—
551	#120	—	5	8	no	—
552	#120	—	5	16	no	—
553	#120	—	5	16	no	—
554	#120	—	5	32	no	—
555	#120	—	5	32	no	—
556	C₄×Q₈	—	5	16	no	—
557	C₄×Q₈	—	5	32	no	—
558	C₄×D₄	—	5	16	no	—
559	C₄×D₄	—	5	16	no	—
560	C₄×D₄	—	5	32	no	—
561	C₄×D₄	—	5	32	no	—
562	C₄×D₄	—	5	16	no	—
563	C₄×D₄	—	5	32	no	—
564	#117	—	5	8	no	—
565	#117	—	5	8	no	—
566	#117	—	5	16	no	—
567	#117	—	5	32	no	—
568	#117	C₂²×D₅	1	8	yes	complemented
569	C₂×C₄⋊C₄	—	5	2	no	—
570	C₂×C₄⋊C₄	—	5	2	no	—
571	C₂×C₄⋊C₄	—	5	2	no	—
572	C₂×C₄⋊C₄	—	5	4	no	—
573	C₂×C₄⋊C₄	—	5	4	no	—
574	C₂×C₄⋊C₄	—	5	2	no	—
575	C₂×C₄⋊C₄	—	5	4	no	—
576	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
577	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
578	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
579	C₂×C₂²⋊C₄	—	5	2	no	—
580	C₂×C₂²⋊C₄	—	5	2	no	—
581	C₂×C₂²⋊C₄	—	5	1	no	—
582	C₂×C₂²⋊C₄	—	5	1	no	—
583	C₂×C₂²⋊C₄	—	5	2	no	—
584	C₂×C₂²⋊C₄	—	5	4	no	—
585	C₂×C₂²⋊C₄	—	5	4	no	—
586	C₂×C₂²⋊C₄	—	5	4	no	—
587	C₂×C₂²⋊C₄	—	5	4	no	—
588	C₂×C₂²⋊C₄	—	5	2	no	—
589	C₂×C₂²⋊C₄	—	5	4	no	—
590	C₂×C₂²⋊C₄	—	5	4	no	—
591	C₂×C₂²⋊C₄	—	5	4	no	—
592	C₂×C₂²⋊C₄	—	5	2	no	—
593	C₂×C₂²⋊C₄	—	5	4	no	—
594	C₂×C₂²⋊C₄	—	5	32	no	—
595	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
598	C₂×C₄²	—	5	4	no	—
599	C₂×C₄²	—	5	2	no	—
600	C₂×C₄²	—	5	2	no	—
601	C₂×C₄²	—	5	4	no	—
602	C₂×C₄²	C₂²×D₅	1	2	yes	—
603	C₂²×C₅	—	2	2	no	—
604	C₂²×C₅	—	2	2	no	—
605	C₂²×C₅	—	2	2	no	—
606	C₂²×C₅	—	2	4	no	—
607	C₂²×C₅	—	2	4	no	—
608	C₂²×C₅	—	2	4	no	—
609	C₂²×C₅	—	4	4	no	—
610	C₂²×C₅	—	4	4	no	—
611	C₂²×C₅	—	4	4	no	—
612	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
613	C₂²×C₅	#585	1	4	yes	—
614	C₂²×C₅	C₂⁶	1	1	yes	characteristic
615	C₂×D₅	—	2	4	no	—
616	C₂×D₅	—	2	8	no	—
617	C₂×D₅	—	2	8	no	—
618	C₂×D₅	—	2	4	no	—
619	C₂×D₅	—	2	8	no	—
620	C₂×D₅	—	2	4	no	—
621	C₂×D₅	—	4	16	no	—
622	C₂×D₅	—	4	8	no	—
623	C₂×D₅	—	4	16	no	—
624	C₂×D₅	—	8	16	no	—
625	C₄×C₅	—	2	2	no	—
626	C₄×C₅	—	2	8	no	—
627	C₄×C₅	—	2	2	no	—
628	C₄×C₅	—	2	2	no	—
629	C₄×C₅	—	2	8	no	—
630	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
631	Dic₅	—	2	4	no	—
632	Dic₅	—	2	4	no	—
633	Dic₅	—	2	8	no	—
634	Dic₅	—	2	4	no	—
635	C₂⁴	—	5	2	no	—
636	C₂⁴	—	5	4	no	—
637	C₂⁴	—	5	8	no	—
638	C₂⁴	—	5	4	no	—
639	C₂⁴	—	20	2	no	—
640	C₂⁴	—	20	4	no	—
641	C₂⁴	—	20	4	no	—
642	C₂⁴	—	20	8	no	—
643	C₂⁴	C₂³×D₅	1	1	yes	characteristic
644	C₂⁴	C₂³×D₅	1	1	yes	characteristic
645	C₂⁴	C₂³×D₅	1	1	yes	characteristic
646	#41	—	4	16	no	—
647	#41	—	20	32	no	—
648	C₂×Q₈	—	2	8	no	—
649	C₂×Q₈	—	4	4	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×Q₈	—	4	16	no	—
652	C₂×Q₈	—	5	16	no	—
653	C₂×Q₈	—	20	8	no	—
654	C₂×Q₈	C₂³×D₅	1	8	yes	—
655	C₂×Q₈	C₂³×D₅	1	8	yes	—
656	C₂×Q₈	C₂³×D₅	1	4	yes	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	5	8	no	—
661	C₂×D₄	—	5	16	no	—
662	C₂×D₄	—	5	8	no	—
663	C₂×D₄	—	5	16	no	—
664	C₂×D₄	—	5	8	no	—
665	C₂×D₄	—	5	16	no	—
666	C₂×D₄	—	5	16	no	—
667	C₂×D₄	—	5	8	no	—
668	C₂×D₄	—	10	8	no	—
669	C₂×D₄	—	20	16	no	—
670	C₂×D₄	—	20	4	no	—
671	C₂×D₄	—	20	8	no	—
672	C₂×D₄	—	20	8	no	—
673	C₂×D₄	—	20	4	no	—
674	C₂×D₄	—	20	8	no	—
675	C₂×D₄	—	20	8	no	—
676	C₂×D₄	—	20	4	no	—
677	C₂×D₄	C₂³×D₅	1	4	yes	—
678	C₂×D₄	C₂³×D₅	1	4	yes	—
679	C₂×D₄	C₂³×D₅	1	4	yes	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	4	4	no	—
684	C₂²×C₄	—	5	2	no	—
685	C₂²×C₄	—	5	4	no	—
686	C₂²×C₄	—	5	2	no	—
687	C₂²×C₄	—	5	2	no	—
688	C₂²×C₄	—	5	4	no	—
689	C₂²×C₄	—	5	8	no	—
690	C₂²×C₄	—	5	16	no	—
691	C₂²×C₄	—	5	16	no	—
692	C₂²×C₄	—	5	8	no	—
693	C₂²×C₄	—	10	8	no	—
694	C₂²×C₄	—	20	16	no	—
695	C₂²×C₄	—	20	4	no	—
696	C₂²×C₄	—	20	8	no	—
697	C₂²×C₄	—	20	8	no	—
698	C₂²×C₄	—	20	2	no	—
699	C₂²×C₄	C₂³×D₅	1	4	yes	—
700	C₂²×C₄	C₂³×D₅	1	4	yes	—
701	C₂²×C₄	C₂³×D₅	1	4	yes	—
702	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
703	C₂²×C₄	C₂³×D₅	1	4	yes	—
704	C₂²×C₄	C₂³×D₅	1	4	yes	—
705	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
706	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
707	C₂²×C₄	C₂³×D₅	1	8	yes	—
708	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
709	C₄⋊C₄	—	5	8	no	—
710	C₄⋊C₄	—	5	8	no	—
711	C₄⋊C₄	—	5	8	no	—
712	C₄⋊C₄	—	5	16	no	—
713	C₄⋊C₄	—	5	16	no	—
714	C₄⋊C₄	—	5	8	no	—
715	C₄⋊C₄	—	5	16	no	—
716	C₄⋊C₄	C₂³×D₅	1	8	yes	—
717	C₄⋊C₄	C₂³×D₅	1	16	yes	—
718	C₄⋊C₄	C₂³×D₅	1	16	yes	—
719	C₂²⋊C₄	—	5	8	no	—
720	C₂²⋊C₄	—	5	8	no	—
721	C₂²⋊C₄	—	5	4	no	—
722	C₂²⋊C₄	—	5	4	no	—
723	C₂²⋊C₄	—	5	8	no	—
724	C₂²⋊C₄	—	5	16	no	—
725	C₂²⋊C₄	—	5	16	no	—
726	C₂²⋊C₄	—	5	16	no	—
727	C₂²⋊C₄	—	5	16	no	—
728	C₂²⋊C₄	—	5	8	no	—
729	C₂²⋊C₄	—	5	16	no	—
730	C₂²⋊C₄	—	5	16	no	—
731	C₂²⋊C₄	—	5	16	no	—
732	C₂²⋊C₄	—	5	8	no	—
733	C₂²⋊C₄	—	5	16	no	—
734	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
735	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
736	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
737	C₄²	—	5	16	no	—
738	C₄²	—	5	8	no	—
739	C₄²	—	5	8	no	—
740	C₄²	—	5	16	no	—
741	C₄²	C₂³×D₅	1	8	yes	—
742	C₂×C₅	—	4	2	no	—
743	C₂×C₅	—	4	2	no	—
744	C₂×C₅	—	4	2	no	—
745	C₂×C₅	#3540	1	4	yes	complemented
746	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂×C₅	C₂×#585	1	2	yes	—
748	D₅	—	4	4	no	—
749	D₅	—	4	8	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	5	4	no	—
757	C₂³	—	5	8	no	—
758	C₂³	—	10	4	no	—
759	C₂³	—	10	8	no	—
760	C₂³	—	10	8	no	—
761	C₂³	—	10	4	no	—
762	C₂³	—	10	4	no	—
763	C₂³	—	10	8	no	—
764	C₂³	—	20	4	no	—
765	C₂³	—	20	8	no	—
766	C₂³	—	20	8	no	—
767	C₂³	—	20	16	no	—
768	C₂³	—	20	16	no	—
769	C₂³	—	40	16	no	—
770	C₂³	C₂⁴×D₅	1	2	yes	—
771	C₂³	C₂⁴×D₅	1	2	yes	—
772	C₂³	C₂⁴×D₅	1	2	yes	—
773	C₂³	C₂⁴×D₅	1	1	yes	characteristic
774	Q₈	—	2	16	no	—
775	Q₈	—	4	8	no	—
776	Q₈	—	4	4	no	—
777	Q₈	—	20	16	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	10	16	no	—
782	D₄	—	20	8	no	—
783	D₄	—	20	16	no	—
784	D₄	—	20	16	no	—
785	D₄	—	20	8	no	—
786	D₄	—	20	16	no	—
787	D₄	—	20	16	no	—
788	D₄	—	20	8	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	5	4	no	—
799	C₂×C₄	—	5	8	no	—
800	C₂×C₄	—	5	4	no	—
801	C₂×C₄	—	5	4	no	—
802	C₂×C₄	—	10	4	no	—
803	C₂×C₄	—	10	4	no	—
804	C₂×C₄	—	10	8	no	—
805	C₂×C₄	—	10	4	no	—
806	C₂×C₄	—	10	16	no	—
807	C₂×C₄	—	20	8	no	—
808	C₂×C₄	—	20	16	no	—
809	C₂×C₄	—	20	16	no	—
810	C₂×C₄	—	20	4	no	—
811	C₂×C₄	#4144	1	4	yes	—
812	C₂×C₄	C₂⁴×D₅	1	2	yes	—
813	C₂×C₄	C₂⁴×D₅	1	8	yes	—
814	C₂×C₄	C₂⁴×D₅	1	8	yes	—
815	C₂×C₄	C₂⁴×D₅	1	2	yes	—
816	C₂×C₄	C₂⁴×D₅	1	2	yes	—
817	C₂×C₄	C₂⁴×D₅	1	2	yes	—
818	C₅	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	10	4	no	—
829	C₂²	—	10	8	no	—
830	C₂²	—	10	8	no	—
831	C₂²	—	10	4	no	—
832	C₂²	—	10	4	no	—
833	C₂²	—	10	8	no	—
834	C₂²	—	20	16	no	—
835	C₂²	—	20	8	no	—
836	C₂²	—	20	16	no	—
837	C₂²	—	40	16	no	—
838	C₂²	C₂×#4144	1	2	yes	—
839	C₂²	#66287	1	4	yes	—
840	C₂²	C₂⁵×D₅	1	1	yes	characteristic
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	8	no	—
845	C₄	—	2	8	no	—
846	C₄	—	10	4	no	—
847	C₄	—	10	4	no	—
848	C₄	—	10	8	no	—
849	C₄	—	10	4	no	—
850	C₄	C₂×#4144	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	20	4	no	—
855	C₂	—	20	8	no	—
856	C₂	#10618246	1	4	yes	direct product factor
857	C₂	C₂²×#4144	1	1	yes	characteristic
858	C₂	C₂×#66287	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#536	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#536	D₅
hypocenter	C₅	C₂×#3540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#536	C₂	semidirect
2. C₂×#66164	C₂	semidirect
3. C₂×#66162	C₂	semidirect
4. C₂×#66151	C₂	semidirect
5. #10618246	C₂	direct (N × H)
6. C₂×#66067	C₂	semidirect
7. C₂×#66017	C₂	semidirect
8. C₂×#66013	C₂	semidirect
9. C₂×#66000	C₂	semidirect
10. C₂×#65991	C₂	semidirect
11. C₂×#65998	C₂	semidirect
12. C₂×#65964	C₂	semidirect
13. C₂×#65975	C₂	semidirect
14. C₂×#65977	C₂	semidirect
15. C₂×#65961	C₂	semidirect
16. C₂×#65866	C₂	semidirect
18. C₂³×C₅×Q₈	C₂²	semidirect
20. C₂³×D₂₀	C₂²	semidirect
21. C₂³×C₄×D₅	C₂²	semidirect
22. C₅×#536	C₂²	semidirect
23. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₅×#123	C₂²	semidirect
26. C₂×C₅×#123	C₂²	semidirect
27. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₅×#117	C₂²	semidirect
30. #66164	C₂²	semidirect
31. #66162	C₂²	semidirect
32. #66151	C₂²	semidirect
33. C₂×#4093	C₂²	semidirect
34. C₂×#4093	C₂²	semidirect
35. C₂×#4093	C₂²	semidirect
36. C₂×#4092	C₂²	semidirect
37. C₂×#4092	C₂²	semidirect
38. C₂×#4092	C₂²	semidirect
39. C₂×Q₈×Dic₅	C₂²	semidirect
44. C₂×#4083	C₂²	semidirect
45. C₂×#4083	C₂²	semidirect
47. C₂×#4081	C₂²	semidirect
49. C₂×#4076	C₂²	semidirect
50. C₂×#4076	C₂²	semidirect
52. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
53. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
54. C₂×#4072	C₂²	semidirect
55. C₂×#4072	C₂²	semidirect
56. #66067	C₂²	semidirect
57. #66017	C₂²	semidirect
58. #66013	C₂²	semidirect
59. #66000	C₂²	semidirect
60. #65998	C₂²	semidirect
61. #65991	C₂²	semidirect
62. #65977	C₂²	semidirect
63. #65975	C₂²	semidirect
64. #65964	C₂²	semidirect
65. #65961	C₂²	semidirect
66. #65866	C₂²	semidirect
67. C₂×#4044	C₂²	semidirect
68. C₂×#4044	C₂²	semidirect
69. C₂×#4043	C₂²	semidirect
72. C₂×#4040	C₂²	semidirect
73. C₂×#4040	C₂²	semidirect
74. C₂×#4039	C₂²	semidirect
75. C₂×#4039	C₂²	semidirect
76. C₂×#4038	C₂²	semidirect
77. C₂×#4034	C₂²	semidirect
78. C₂×#4033	C₂²	semidirect
80. C₂×#4031	C₂²	semidirect
81. C₂×#4031	C₂²	semidirect
82. C₂×#4030	C₂²	semidirect
83. C₂×#4029	C₂²	semidirect
85. C₂×#4028	C₂²	semidirect
86. C₂×#4027	C₂²	semidirect
87. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
88. C₂×#4025	C₂²	semidirect
89. C₂×#4021	C₂²	semidirect
90. C₂×#4018	C₂²	semidirect
100. C₂²×C₅×Q₈	C₂³	semidirect
120. C₂²×D₂₀	C₂³	semidirect
126. C₂²×C₄×D₅	C₂³	semidirect
128. C₅×C₄⋊Q₈	C₂³	semidirect
130. C₅×#123	C₂³	semidirect
131. C₅×#123	C₂³	semidirect
132. C₅×C₂²⋊Q₈	C₂³	semidirect
133. C₅×C₂²⋊Q₈	C₂³	semidirect
134. C₅×#117	C₂³	semidirect
147. #4093	C₂³	semidirect
148. #4093	C₂³	semidirect
149. #4093	C₂³	semidirect
150. #4092	C₂³	semidirect
151. #4092	C₂³	semidirect
152. #4092	C₂³	semidirect
153. Q₈×Dic₅	C₂³	semidirect
158. #4083	C₂³	semidirect
159. #4083	C₂³	semidirect
161. #4081	C₂³	semidirect
163. #4076	C₂³	semidirect
164. #4076	C₂³	semidirect
166. C₄×C₂²⋊D₅	C₂³	semidirect
167. C₄×C₂²⋊D₅	C₂³	semidirect
178. #4072	C₂³	semidirect
179. #4072	C₂³	semidirect
191. #4044	C₂³	semidirect
192. #4044	C₂³	semidirect
193. #4043	C₂³	semidirect
196. #4040	C₂³	semidirect
197. #4040	C₂³	semidirect
198. #4039	C₂³	semidirect
199. #4039	C₂³	semidirect
200. #4038	C₂³	semidirect
201. #4034	C₂³	semidirect
202. #4033	C₂³	semidirect
204. #4031	C₂³	semidirect
205. #4031	C₂³	semidirect
206. #4030	C₂³	semidirect
207. #4029	C₂³	semidirect
209. #4028	C₂³	semidirect
210. #4027	C₂³	semidirect
211. D₅×C₂²⋊C₄	C₂³	semidirect
212. #4025	C₂³	semidirect
213. #4021	C₂³	semidirect
214. #4018	C₂³	semidirect
227. C₂×#536	D₅	semidirect
340. C₂³×Q₈	C₂×D₅	semidirect
354. #536	C₂×D₅	semidirect
357. C₂×C₄⋊Q₈	C₂×D₅	semidirect
377. C₂×#123	C₂×D₅	semidirect
378. C₂×#123	C₂×D₅	semidirect
383. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
384. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
410. C₂×#117	C₂×D₅	semidirect
491. C₂²×Q₈	C₂²×D₅	semidirect
517. C₄⋊Q₈	C₂²×D₅	semidirect
535. #123	C₂²×D₅	semidirect
536. #123	C₂²×D₅	semidirect
541. C₂²⋊Q₈	C₂²×D₅	semidirect
542. C₂²⋊Q₈	C₂²×D₅	semidirect
568. #117	C₂²×D₅	semidirect
745. C₂×C₅	#3540	semidirect
818. C₅	C₂×#3540	semidirect
856. C₂	#10618246	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×#536	2
C₂×#66164	2
C₂×#66162	2
C₂×#66151	2
#10618246	2
C₂×#66067	2
C₂×#66017	2
C₂×#66013	2
C₂×#66000	2
C₂×#65991	2
C₂×#65998	2
C₂×#65964	2
C₂×#65975	2
C₂×#65977	2
C₂×#65961	2
C₂×#65866	2
C₂×#3540	5

Subgroups — C2×#10618246 #13006593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618246 #13006593