Subgroups — C₂×#10618075 #13006939

Order 1280.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618075	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66038	C₂	1	4	yes	maximal, complemented
4	C₂×#66029	C₂	1	2	yes	maximal, complemented
5	C₂×#66010	C₂	1	2	yes	maximal, complemented
6	C₂×#66000	C₂	1	4	yes	maximal, complemented
7	C₂×#65963	C₂	1	2	yes	maximal, complemented
8	C₂×#65941	C₂	1	2	yes	maximal, complemented
9	C₂×#65918	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65911	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65884	C₂	1	2	yes	maximal, complemented
13	C₂×D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#65887	C₂	1	2	yes	maximal, complemented
15	C₂×#65868	C₂	1	2	yes	maximal, complemented
16	C₂×#65859	C₂	1	2	yes	maximal, complemented
17	C₂×#65811	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65811	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#713	C₂²	1	2	yes	complemented
20	C₂²×D₄×D₅	C₂²	1	2	yes	—
21	C₂²×#709	C₂²	1	2	yes	complemented
22	C₂²×#709	C₂²	1	2	yes	complemented
23	C₂²×#709	C₂²	1	2	yes	complemented
24	C₂³×D₂₀	C₂²	1	2	yes	—
25	C₅×#529	C₂²	1	16	yes	complemented
26	C₂×C₅×#126	C₂²	1	2	yes	complemented
27	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#124	C₂²	1	1	yes	characteristic
29	C₂×C₅×#123	C₂²	1	2	yes	complemented
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₂×C₅×#117	C₂²	1	2	yes	complemented
36	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
37	C₂×#4092	C₂²	1	2	yes	complemented
38	C₂×#4086	C₂²	1	4	yes	complemented
39	C₂×#4084	C₂²	1	2	yes	—
40	C₂×#4083	C₂²	1	4	yes	complemented
41	C₂×#4076	C₂²	1	2	yes	—
42	C₂×#4076	C₂²	1	1	yes	characteristic
43	C₂×#4076	C₂²	1	2	yes	complemented
44	C₂×#4076	C₂²	1	1	yes	characteristic, complemented
45	C₂×#4076	C₂²	1	2	yes	complemented
46	C₂×#4076	C₂²	1	2	yes	complemented
47	C₂×#4070	C₂²	1	2	yes	complemented
48	#66038	C₂²	1	64	yes	complemented
49	#66029	C₂²	1	32	yes	complemented
50	#66010	C₂²	1	32	yes	complemented
51	#66000	C₂²	1	64	yes	complemented
52	#65963	C₂²	1	32	yes	complemented
53	#65941	C₂²	1	32	yes	complemented
54	#65918	C₂²	1	16	yes	complemented
55	#65911	C₂²	1	16	yes	complemented
56	#65887	C₂²	1	32	yes	complemented
57	#65885	C₂²	1	16	yes	complemented
58	#65884	C₂²	1	32	yes	complemented
59	D₄×D₂₀	C₂²	1	16	yes	complemented
60	#65868	C₂²	1	32	yes	complemented
61	#65859	C₂²	1	32	yes	complemented
62	C₂×#4044	C₂²	1	4	yes	complemented
63	C₂×#4044	C₂²	1	4	yes	complemented
64	C₂×#4042	C₂²	1	4	yes	complemented
65	C₂×#4041	C₂²	1	2	yes	—
66	C₂×#4041	C₂²	1	4	yes	complemented
67	C₂×#4041	C₂²	1	4	yes	complemented
68	C₂×#4041	C₂²	1	4	yes	complemented
69	C₂×#4041	C₂²	1	2	yes	complemented
70	C₂×#4040	C₂²	1	4	yes	complemented
71	C₂×#4039	C₂²	1	4	yes	complemented
72	C₂×#4038	C₂²	1	2	yes	complemented
73	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
74	C₂×#4031	C₂²	1	4	yes	complemented
75	C₂×#4030	C₂²	1	4	yes	complemented
76	C₂×#4030	C₂²	1	4	yes	complemented
77	C₂×#4030	C₂²	1	4	yes	complemented
78	C₂×#4029	C₂²	1	4	yes	complemented
79	C₂×#4029	C₂²	1	4	yes	complemented
80	C₂×#4028	C₂²	1	4	yes	—
81	C₂×#4028	C₂²	1	4	yes	complemented
82	C₂×#4028	C₂²	1	4	yes	complemented
83	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
84	#65811	C₂²	1	16	yes	complemented
85	#65811	C₂²	1	16	yes	complemented
86	C₂×#4021	C₂²	1	2	yes	—
87	C₂×#4021	C₂²	1	2	yes	complemented
88	C₂×#4021	C₂²	1	2	yes	complemented
89	C₂×#4020	C₂²	1	1	yes	characteristic
90	C₂×#4020	C₂²	1	1	yes	characteristic
91	C₂×#4020	C₂²	1	2	yes	complemented
92	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
93	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
94	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
96	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
97	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
98	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
99	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
101	C₂×#3546	—	5	1	no	maximal, Sylow
102	C₂⁴×D₅	C₂³	1	4	yes	—
103	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₂²×C₅×D₄	C₂³	1	2	yes	—
106	C₂³×C₄×C₅	C₂³	1	2	yes	—
107	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
113	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
114	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
115	C₂×#713	—	4	8	no	—
116	C₂×#713	C₂³	1	16	yes	complemented
117	C₂×D₄×D₅	—	4	8	no	—
118	C₂×D₄×D₅	C₂³	1	16	yes	—
119	C₂×#709	—	4	8	no	—
120	C₂×#709	—	4	8	no	—
121	C₂×#709	—	4	8	no	—
122	C₂×#709	C₂³	1	16	yes	complemented
123	C₂×#709	C₂³	1	16	yes	complemented
124	C₂×#709	C₂³	1	16	yes	complemented
125	C₂²×D₂₀	—	4	8	no	—
126	C₂²×D₂₀	C₂³	1	1	yes	characteristic
127	C₂²×D₂₀	C₂³	1	1	yes	characteristic
128	C₂²×D₂₀	C₂³	1	2	yes	—
129	C₂²×D₂₀	C₂³	1	2	yes	—
130	C₂²×D₂₀	C₂³	1	2	yes	—
131	C₂²×D₂₀	C₂³	1	2	yes	—
132	C₂²×D₂₀	C₂³	1	2	yes	—
133	C₂²×D₂₀	C₂³	1	4	yes	—
134	C₂²×D₂₀	C₂³	1	4	yes	—
135	C₂²×D₂₀	C₂³	1	4	yes	—
136	C₂²×D₂₀	C₂³	1	16	yes	—
137	C₂²×C₄×D₅	C₂³	1	2	yes	—
138	C₂²×C₄×D₅	C₂³	1	2	yes	—
139	C₂²×C₄×D₅	C₂³	1	4	yes	—
140	C₂²×C₄×D₅	C₂³	1	4	yes	—
141	C₂²×C₄×D₅	C₂³	1	4	yes	—
142	C₂²×Dic₁₀	C₂³	1	2	yes	—
143	C₂²×Dic₁₀	C₂³	1	2	yes	—
144	C₅×#126	C₂³	1	16	yes	complemented
145	C₅×#125	C₂³	1	8	yes	complemented
146	C₅×#124	C₂³	1	8	yes	—
147	C₅×#123	C₂³	1	16	yes	complemented
148	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
149	C₅×#121	C₂³	1	8	yes	—
150	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
151	C₄×C₅×D₄	C₂³	1	8	yes	—
152	C₄×C₅×D₄	C₂³	1	16	yes	complemented
153	C₅×#117	C₂³	1	16	yes	complemented
154	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄²×C₅	C₂³	1	2	yes	—
166	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
171	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
172	#4092	C₂³	1	16	yes	complemented
173	#4086	C₂³	1	32	yes	complemented
174	#4084	C₂³	1	16	yes	—
175	#4083	C₂³	1	32	yes	complemented
176	#4076	C₂³	1	8	yes	—
177	#4076	C₂³	1	16	yes	—
178	#4076	C₂³	1	8	yes	complemented
179	#4076	C₂³	1	16	yes	complemented
180	#4076	C₂³	1	16	yes	complemented
181	#4076	C₂³	1	16	yes	complemented
182	C₂×#685	C₂³	1	2	yes	—
183	C₂×#685	C₂³	1	2	yes	—
184	C₂×#685	C₂³	1	4	yes	—
185	C₂×#685	C₂³	1	4	yes	—
186	C₂×#685	C₂³	1	2	yes	—
187	C₂×#685	C₂³	1	2	yes	—
188	C₂×#685	C₂³	1	4	yes	—
189	C₂×#685	C₂³	1	4	yes	—
190	C₂×#685	C₂³	1	4	yes	—
191	C₂×#685	C₂³	1	4	yes	—
192	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
195	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
196	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
197	#4070	C₂³	1	16	yes	complemented
198	C₂×#683	C₂³	1	4	yes	—
199	C₂×#683	C₂³	1	4	yes	—
200	C₂×C₄×Dic₅	C₂³	1	4	yes	—
201	#4044	C₂³	1	32	yes	complemented
202	#4044	C₂³	1	32	yes	complemented
203	#4042	C₂³	1	32	yes	complemented
204	#4041	C₂³	1	16	yes	—
205	#4041	C₂³	1	32	yes	complemented
206	#4041	C₂³	1	32	yes	complemented
207	#4041	C₂³	1	16	yes	complemented
208	#4041	C₂³	1	32	yes	complemented
209	#4040	C₂³	1	32	yes	complemented
210	#4039	C₂³	1	32	yes	complemented
211	#4038	C₂³	1	16	yes	complemented
212	D₅×C₄⋊C₄	C₂³	1	16	yes	complemented
213	#4031	C₂³	1	32	yes	complemented
214	#4030	C₂³	1	32	yes	complemented
215	#4030	C₂³	1	32	yes	complemented
216	#4030	C₂³	1	32	yes	complemented
217	#4029	C₂³	1	32	yes	complemented
218	#4029	C₂³	1	32	yes	complemented
219	#4028	C₂³	1	32	yes	—
220	#4028	C₂³	1	32	yes	complemented
221	#4028	C₂³	1	32	yes	complemented
222	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
223	#4021	C₂³	1	16	yes	—
224	#4021	C₂³	1	16	yes	complemented
225	#4021	C₂³	1	16	yes	complemented
226	#4020	C₂³	1	8	yes	—
227	#4020	C₂³	1	8	yes	—
228	#4020	C₂³	1	16	yes	complemented
229	C₄×D₂₀	C₂³	1	8	yes	—
230	C₄×D₂₀	C₂³	1	8	yes	complemented
231	C₄×D₂₀	C₂³	1	16	yes	complemented
232	C₄×D₂₀	C₂³	1	16	yes	complemented
233	C₄×D₂₀	C₂³	1	16	yes	complemented
234	C₄×D₂₀	C₂³	1	16	yes	complemented
235	#4015	C₂³	1	8	yes	complemented
236	#4015	C₂³	1	8	yes	complemented
237	C₄×Dic₁₀	C₂³	1	16	yes	complemented
238	#3546	—	5	32	no	—
239	C₂×#560	—	5	4	no	—
240	C₂×#556	—	5	1	no	—
241	C₂×#553	—	5	2	no	—
242	C₂×#550	—	5	1	no	—
243	C₂×#550	—	5	2	no	—
244	C₂×#547	—	5	1	no	—
245	C₂×#546	—	5	2	no	—
246	C₂×#546	—	5	2	no	—
247	C₂×D₄²	—	5	1	no	—
248	C₂×#542	—	5	2	no	—
249	C₂×#538	—	5	4	no	—
250	C₂×#537	—	5	2	no	—
251	C₂×#535	—	5	2	no	—
252	C₂×#535	—	5	2	no	—
253	C₂×#532	—	5	1	no	—
254	C₂×#532	—	5	1	no	—
255	C₂×#529	D₅	1	1	yes	characteristic, complemented
256	C₂⁴×C₅	C₂⁴	1	2	yes	—
257	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
258	C₂³×D₅	—	4	8	no	—
259	C₂³×D₅	—	4	8	no	—
260	C₂³×D₅	—	4	8	no	—
261	C₂³×D₅	C₂⁴	1	2	yes	—
262	C₂³×D₅	C₂⁴	1	4	yes	—
263	C₂³×D₅	C₂⁴	1	2	yes	—
264	C₂³×D₅	C₂⁴	1	16	yes	—
265	C₂×C₅×Q₈	—	2	4	no	—
266	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
267	C₂×C₅×D₄	—	2	4	no	—
268	C₂×C₅×D₄	—	4	4	no	—
269	C₂×C₅×D₄	C₂⁴	1	4	yes	—
270	C₂×C₅×D₄	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₅	—	2	8	no	—
272	C₂²×C₄×C₅	—	2	4	no	—
273	C₂²×C₄×C₅	—	2	4	no	—
274	C₂²×C₄×C₅	—	4	2	no	—
275	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂×C₂²⋊D₅	—	4	8	no	—
289	C₂×C₂²⋊D₅	—	4	8	no	—
290	C₂×C₂²⋊D₅	—	4	4	no	—
291	C₂×C₂²⋊D₅	—	4	4	no	—
292	C₂×C₂²⋊D₅	—	4	8	no	—
293	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
294	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
295	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
296	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
297	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
298	C₂²×Dic₅	C₂⁴	1	2	yes	—
299	C₂²×Dic₅	C₂⁴	1	4	yes	—
300	C₂²×Dic₅	C₂⁴	1	2	yes	—
301	#713	—	4	32	no	—
302	D₄×D₅	—	4	32	no	—
303	#709	—	4	32	no	—
304	#709	—	4	32	no	—
305	#709	—	4	32	no	—
306	C₂×D₂₀	—	2	4	no	—
307	C₂×D₂₀	—	2	8	no	—
308	C₂×D₂₀	—	2	4	no	—
309	C₂×D₂₀	—	2	8	no	—
310	C₂×D₂₀	—	4	32	no	—
311	C₂×D₂₀	—	4	8	no	—
312	C₂×D₂₀	—	4	4	no	—
313	C₂×D₂₀	—	4	4	no	—
314	C₂×D₂₀	—	4	8	no	—
315	C₂×D₂₀	—	4	4	no	—
316	C₂×D₂₀	—	4	8	no	—
317	C₂×D₂₀	C₂⁴	1	4	yes	—
318	C₂×D₂₀	C₂⁴	1	8	yes	—
319	C₂×D₂₀	C₂⁴	1	4	yes	—
320	C₂×D₂₀	C₂⁴	1	8	yes	—
321	C₂×D₂₀	C₂⁴	1	16	yes	—
322	C₂×D₂₀	C₂⁴	1	8	yes	—
323	C₂×D₂₀	C₂⁴	1	16	yes	—
324	C₂×D₂₀	C₂⁴	1	8	yes	—
325	C₂×D₂₀	C₂⁴	1	8	yes	—
326	C₂×D₂₀	C₂⁴	1	16	yes	—
327	C₂×C₄×D₅	—	2	8	no	—
328	C₂×C₄×D₅	—	2	8	no	—
329	C₂×C₄×D₅	—	4	8	no	—
330	C₂×C₄×D₅	—	4	8	no	—
331	C₂×C₄×D₅	—	4	8	no	—
332	C₂×C₄×D₅	C₂⁴	1	8	yes	—
333	C₂×C₄×D₅	C₂⁴	1	8	yes	—
334	C₂×C₄×D₅	C₂⁴	1	16	yes	—
335	C₂×C₄×D₅	C₂⁴	1	16	yes	—
336	C₂×C₄×D₅	C₂⁴	1	16	yes	—
337	C₂×Dic₁₀	—	2	8	no	—
338	C₂×Dic₁₀	—	4	4	no	—
339	C₂×Dic₁₀	C₂⁴	1	8	yes	—
340	C₂×Dic₁₀	C₂⁴	1	8	yes	—
341	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
342	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
343	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
344	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
345	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
346	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
347	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
350	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
352	C₄²×C₅	C₂⁴	1	4	yes	—
353	C₄²×C₅	C₂⁴	1	4	yes	—
354	C₄²×C₅	C₂⁴	1	4	yes	—
355	C₄²×C₅	C₂⁴	1	4	yes	—
356	C₄²×C₅	C₂⁴	1	8	yes	—
357	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
358	#685	C₂⁴	1	8	yes	—
359	#685	C₂⁴	1	8	yes	—
360	#685	C₂⁴	1	16	yes	—
361	#685	C₂⁴	1	16	yes	—
362	#685	C₂⁴	1	8	yes	—
363	#685	C₂⁴	1	8	yes	—
364	#685	C₂⁴	1	16	yes	—
365	#685	C₂⁴	1	16	yes	—
366	#685	C₂⁴	1	16	yes	—
367	#685	C₂⁴	1	16	yes	—
368	C₄⋊Dic₅	C₂⁴	1	4	yes	—
369	C₄⋊Dic₅	C₂⁴	1	4	yes	—
370	C₄⋊Dic₅	C₂⁴	1	8	yes	—
371	C₄⋊Dic₅	C₂⁴	1	8	yes	—
372	C₄⋊Dic₅	C₂⁴	1	8	yes	—
373	#683	C₂⁴	1	16	yes	—
374	#683	C₂⁴	1	16	yes	—
375	C₄×Dic₅	C₂⁴	1	16	yes	—
376	C₂²×#41	—	5	2	no	—
377	C₂²×#41	—	5	2	no	—
378	C₂²×#41	—	5	2	no	—
379	C₂²×#41	—	5	2	no	—
380	C₂³×D₄	—	5	2	no	—
381	C₂³×D₄	—	5	2	no	—
382	#560	—	5	64	no	—
383	#556	—	5	16	no	—
384	#553	—	5	32	no	—
385	#550	—	5	16	no	—
386	#550	—	5	32	no	—
387	#547	—	5	16	no	—
388	#546	—	5	32	no	—
389	#546	—	5	32	no	—
390	D₄²	—	5	16	no	—
391	#542	—	5	32	no	—
392	#538	—	5	64	no	—
393	#537	—	5	32	no	—
394	#535	—	5	32	no	—
395	#535	—	5	32	no	—
396	#532	—	5	16	no	—
397	#532	—	5	16	no	—
398	C₂×C₄⋊Q₈	—	5	1	no	—
399	C₂×C₄⋊Q₈	—	5	1	no	—
400	C₂×#127	—	5	4	no	—
401	C₂×#127	—	5	1	no	—
402	C₂×#127	—	5	1	no	—
403	C₂×#127	—	5	2	no	—
404	#529	C₂×D₅	1	16	yes	complemented
405	C₂×#126	—	5	4	no	—
406	C₂×#126	—	5	4	no	—
407	C₂×#126	C₂×D₅	1	2	yes	complemented
408	C₂×#125	C₂×D₅	1	1	yes	characteristic, complemented
409	C₂×#124	—	5	4	no	—
410	C₂×#124	—	5	2	no	—
411	C₂×#124	—	5	2	no	—
412	C₂×#124	—	5	2	no	—
413	C₂×#124	C₂×D₅	1	1	yes	characteristic
414	C₂×#123	—	5	4	no	—
415	C₂×#123	—	5	4	no	—
416	C₂×#123	—	5	4	no	—
417	C₂×#123	C₂×D₅	1	2	yes	complemented
418	C₂×C₂²⋊Q₈	—	5	2	no	—
419	C₂×C₂²⋊Q₈	—	5	2	no	—
420	C₂×C₂²⋊Q₈	—	5	4	no	—
421	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
422	C₂×#121	—	5	2	no	—
423	C₂×#121	—	5	1	no	—
424	C₂×#121	—	5	2	no	—
425	C₂×#121	—	5	2	no	—
426	C₂×#121	—	5	1	no	—
427	C₂×#121	—	5	2	no	—
428	C₂×#121	—	5	2	no	—
429	C₂×#121	—	5	2	no	—
430	C₂×#121	—	5	4	no	—
431	C₂×#121	—	5	2	no	—
432	C₂×#121	—	5	4	no	—
433	C₂×#121	—	5	4	no	—
434	C₂×#121	—	5	4	no	—
435	C₂×#121	—	5	4	no	—
436	C₂×#121	—	5	4	no	—
437	C₂×#121	C₂×D₅	1	1	yes	characteristic
438	C₂×#120	—	5	4	no	—
439	C₂×#120	—	5	4	no	—
440	C₂×#120	—	5	4	no	—
441	C₂×#120	—	5	4	no	—
442	C₂×C₄×Q₈	—	5	2	no	—
443	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
444	C₂×C₄×D₄	—	5	4	no	—
445	C₂×C₄×D₄	—	5	1	no	—
446	C₂×C₄×D₄	—	5	2	no	—
447	C₂×C₄×D₄	—	5	2	no	—
448	C₂×C₄×D₄	—	5	2	no	—
449	C₂×C₄×D₄	—	5	1	no	—
450	C₂×C₄×D₄	—	5	2	no	—
451	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
453	C₂×#117	—	5	2	no	—
454	C₂×#117	C₂×D₅	1	2	yes	complemented
455	C₂²×C₄⋊C₄	—	5	2	no	—
456	C₂²×C₂²⋊C₄	—	5	4	no	—
457	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
458	C₂³×C₅	—	2	2	no	—
459	C₂³×C₅	—	2	2	no	—
460	C₂³×C₅	—	2	4	no	—
461	C₂³×C₅	—	2	4	no	—
462	C₂³×C₅	—	2	2	no	—
463	C₂³×C₅	—	2	4	no	—
464	C₂³×C₅	C₂⁵	1	4	yes	—
465	C₂³×C₅	C₂⁵	1	2	yes	—
466	C₂³×C₅	C₂⁵	1	1	yes	characteristic
467	C₂²×D₅	—	2	4	no	—
468	C₂²×D₅	—	2	4	no	—
469	C₂²×D₅	—	2	4	no	—
470	C₂²×D₅	—	2	8	no	—
471	C₂²×D₅	—	2	8	no	—
472	C₂²×D₅	—	2	4	no	—
473	C₂²×D₅	—	2	4	no	—
474	C₂²×D₅	—	2	8	no	—
475	C₂²×D₅	—	2	4	no	—
476	C₂²×D₅	—	4	16	no	—
477	C₂²×D₅	—	4	16	no	—
478	C₂²×D₅	—	4	16	no	—
479	C₂²×D₅	—	8	32	no	—
480	C₂²×D₅	C₂⁵	1	4	yes	—
481	C₂²×D₅	C₂⁵	1	8	yes	—
482	C₂²×D₅	C₂⁵	1	4	yes	—
483	C₅×Q₈	—	2	8	no	—
484	C₅×D₄	—	2	8	no	—
485	C₅×D₄	—	4	8	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	4	no	—
489	C₂×C₄×C₅	—	2	4	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	2	4	no	—
493	C₂×C₄×C₅	—	2	16	no	—
494	C₂×C₄×C₅	—	2	8	no	—
495	C₂×C₄×C₅	—	2	8	no	—
496	C₂×C₄×C₅	—	4	4	no	—
497	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
498	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
499	C₂×C₄×C₅	C₂⁵	1	4	yes	—
500	C₂×C₄×C₅	C₂⁵	1	4	yes	—
501	C₂×C₄×C₅	C₂⁵	1	4	yes	—
502	C₂×C₄×C₅	C₂⁵	1	2	yes	—
503	C₂×C₄×C₅	C₂⁵	1	2	yes	—
504	C₂×C₄×C₅	C₂⁵	1	2	yes	—
505	C₂×C₄×C₅	C₂⁵	1	2	yes	—
506	C₂×C₄×C₅	C₂⁵	1	2	yes	—
507	C₂×C₄×C₅	C₂⁵	1	2	yes	—
508	C₂²⋊D₅	—	4	16	no	—
509	C₂²⋊D₅	—	4	16	no	—
510	C₂²⋊D₅	—	4	8	no	—
511	C₂²⋊D₅	—	4	8	no	—
512	C₂²⋊D₅	—	4	16	no	—
513	C₂×Dic₅	—	2	8	no	—
514	C₂×Dic₅	—	2	4	no	—
515	C₂×Dic₅	—	2	4	no	—
516	C₂×Dic₅	C₂⁵	1	4	yes	—
517	C₂×Dic₅	C₂⁵	1	8	yes	—
518	C₂×Dic₅	C₂⁵	1	4	yes	—
519	D₂₀	—	2	8	no	—
520	D₂₀	—	2	16	no	—
521	D₂₀	—	2	8	no	—
522	D₂₀	—	2	16	no	—
523	D₂₀	—	4	16	no	—
524	D₂₀	—	4	8	no	—
525	D₂₀	—	4	8	no	—
526	D₂₀	—	4	16	no	—
527	D₂₀	—	4	8	no	—
528	D₂₀	—	4	16	no	—
529	C₄×D₅	—	2	16	no	—
530	C₄×D₅	—	2	16	no	—
531	C₄×D₅	—	4	16	no	—
532	C₄×D₅	—	4	16	no	—
533	C₄×D₅	—	4	16	no	—
534	Dic₁₀	—	2	16	no	—
535	Dic₁₀	—	4	8	no	—
536	C₂⁵	—	5	4	no	—
537	C₂×#41	—	5	16	no	—
538	C₂×#41	—	5	16	no	—
539	C₂×#41	—	5	16	no	—
540	C₂×#41	—	5	16	no	—
541	C₂×#41	—	20	8	no	—
542	C₂×#41	—	20	8	no	—
543	C₂×#41	—	20	8	no	—
544	C₂×#41	—	20	8	no	—
545	C₂²×Q₈	—	5	2	no	—
546	C₂²×Q₈	—	5	2	no	—
547	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
548	C₂²×D₄	—	5	2	no	—
549	C₂²×D₄	—	5	4	no	—
550	C₂²×D₄	—	5	4	no	—
551	C₂²×D₄	—	5	4	no	—
552	C₂²×D₄	—	5	2	no	—
553	C₂²×D₄	—	5	16	no	—
554	C₂²×D₄	—	5	2	no	—
555	C₂²×D₄	—	5	1	no	—
556	C₂²×D₄	—	5	2	no	—
557	C₂²×D₄	—	5	1	no	—
558	C₂²×D₄	—	5	2	no	—
559	C₂²×D₄	—	5	2	no	—
560	C₂²×D₄	—	5	4	no	—
561	C₂²×D₄	—	5	2	no	—
562	C₂²×D₄	—	5	4	no	—
563	C₂²×D₄	—	5	4	no	—
564	C₂²×D₄	—	5	16	no	—
565	C₂²×D₄	—	20	8	no	—
566	C₂²×D₄	—	20	8	no	—
567	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
568	C₂²×D₄	C₂²×D₅	1	2	yes	—
569	C₂³×C₄	—	5	2	no	—
570	C₂³×C₄	—	5	2	no	—
571	C₂³×C₄	—	5	4	no	—
572	C₂³×C₄	—	5	4	no	—
573	C₂³×C₄	—	5	4	no	—
574	C₂³×C₄	C₂²×D₅	1	2	yes	—
575	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
576	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
577	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
578	C₄⋊Q₈	—	5	8	no	—
579	C₄⋊Q₈	—	5	8	no	—
580	#127	—	5	32	no	—
581	#127	—	5	8	no	—
582	#127	—	5	8	no	—
583	#127	—	5	16	no	—
584	#126	—	5	32	no	—
585	#126	—	5	32	no	—
586	#126	C₂²×D₅	1	16	yes	complemented
587	#125	C₂²×D₅	1	8	yes	complemented
588	#124	—	5	32	no	—
589	#124	—	5	16	no	—
590	#124	—	5	16	no	—
591	#124	—	5	16	no	—
592	#124	C₂²×D₅	1	8	yes	—
593	#123	—	5	32	no	—
594	#123	—	5	32	no	—
595	#123	—	5	32	no	—
596	#123	C₂²×D₅	1	16	yes	complemented
597	C₂²⋊Q₈	—	5	16	no	—
598	C₂²⋊Q₈	—	5	16	no	—
599	C₂²⋊Q₈	—	5	32	no	—
600	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
601	#121	—	5	16	no	—
602	#121	—	5	16	no	—
603	#121	—	5	8	no	—
604	#121	—	5	8	no	—
605	#121	—	5	16	no	—
606	#121	—	5	16	no	—
607	#121	—	5	16	no	—
608	#121	—	5	32	no	—
609	#121	—	5	16	no	—
610	#121	—	5	32	no	—
611	#121	—	5	16	no	—
612	#121	—	5	32	no	—
613	#121	—	5	32	no	—
614	#121	—	5	32	no	—
615	#121	—	5	32	no	—
616	#121	C₂²×D₅	1	8	yes	—
617	#120	—	5	32	no	—
618	#120	—	5	32	no	—
619	#120	—	5	32	no	—
620	#120	—	5	32	no	—
621	C₄×Q₈	—	5	16	no	—
622	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
623	C₄×D₄	—	5	32	no	—
624	C₄×D₄	—	5	16	no	—
625	C₄×D₄	—	5	8	no	—
626	C₄×D₄	—	5	16	no	—
627	C₄×D₄	—	5	16	no	—
628	C₄×D₄	—	5	8	no	—
629	C₄×D₄	—	5	16	no	—
630	C₄×D₄	C₂²×D₅	1	8	yes	—
631	C₄×D₄	C₂²×D₅	1	16	yes	complemented
632	#117	—	5	16	no	—
633	#117	C₂²×D₅	1	16	yes	complemented
634	C₂×C₄⋊C₄	—	5	2	no	—
635	C₂×C₄⋊C₄	—	5	4	no	—
636	C₂×C₄⋊C₄	—	5	1	no	—
637	C₂×C₄⋊C₄	—	5	1	no	—
638	C₂×C₄⋊C₄	—	5	2	no	—
639	C₂×C₄⋊C₄	—	5	2	no	—
640	C₂×C₄⋊C₄	—	5	4	no	—
641	C₂×C₄⋊C₄	—	5	16	no	—
642	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
645	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
646	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
647	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
648	C₂×C₂²⋊C₄	—	5	4	no	—
649	C₂×C₂²⋊C₄	—	5	2	no	—
650	C₂×C₂²⋊C₄	—	5	4	no	—
651	C₂×C₂²⋊C₄	—	5	4	no	—
652	C₂×C₂²⋊C₄	—	5	2	no	—
653	C₂×C₂²⋊C₄	—	5	2	no	—
654	C₂×C₂²⋊C₄	—	5	4	no	—
655	C₂×C₂²⋊C₄	—	5	4	no	—
656	C₂×C₂²⋊C₄	—	5	4	no	—
657	C₂×C₂²⋊C₄	—	5	4	no	—
658	C₂×C₂²⋊C₄	—	5	2	no	—
659	C₂×C₂²⋊C₄	—	5	32	no	—
660	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
665	C₂×C₄²	—	5	4	no	—
666	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
667	C₂×C₄²	C₂²×D₅	1	2	yes	—
668	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
669	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
670	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
671	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
672	C₂²×C₅	—	2	2	no	—
673	C₂²×C₅	—	2	2	no	—
674	C₂²×C₅	—	2	4	no	—
675	C₂²×C₅	—	2	4	no	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	4	no	—
678	C₂²×C₅	—	4	8	no	—
679	C₂²×C₅	—	4	4	no	—
680	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
681	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
682	C₂²×C₅	#585	1	2	yes	—
683	C₂²×C₅	C₂⁶	1	1	yes	characteristic
684	C₂×D₅	—	2	4	no	—
685	C₂×D₅	—	2	4	no	—
686	C₂×D₅	—	2	4	no	—
687	C₂×D₅	—	2	8	no	—
688	C₂×D₅	—	2	8	no	—
689	C₂×D₅	—	2	4	no	—
690	C₂×D₅	—	2	4	no	—
691	C₂×D₅	—	2	8	no	—
692	C₂×D₅	—	2	4	no	—
693	C₂×D₅	—	4	8	no	—
694	C₂×D₅	—	4	16	no	—
695	C₂×D₅	—	4	8	no	—
696	C₂×D₅	—	8	32	no	—
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	2	no	—
699	C₄×C₅	—	2	4	no	—
700	C₄×C₅	—	2	4	no	—
701	C₄×C₅	—	2	2	no	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	4	no	—
704	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
705	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
706	Dic₅	—	2	8	no	—
707	Dic₅	—	2	4	no	—
708	Dic₅	—	2	4	no	—
709	C₂⁴	—	5	2	no	—
710	C₂⁴	—	5	4	no	—
711	C₂⁴	—	5	2	no	—
712	C₂⁴	—	5	16	no	—
713	C₂⁴	—	20	8	no	—
714	C₂⁴	—	20	8	no	—
715	C₂⁴	—	20	8	no	—
716	C₂⁴	C₂³×D₅	1	2	yes	—
717	C₂⁴	C₂³×D₅	1	1	yes	characteristic
718	#41	—	20	32	no	—
719	#41	—	20	32	no	—
720	#41	—	20	32	no	—
721	#41	—	20	32	no	—
722	C₂×Q₈	—	2	4	no	—
723	C₂×Q₈	—	5	8	no	—
724	C₂×Q₈	—	5	8	no	—
725	C₂×Q₈	—	10	8	no	—
726	C₂×Q₈	—	20	4	no	—
727	C₂×Q₈	C₂³×D₅	1	4	yes	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	5	8	no	—
731	C₂×D₄	—	5	16	no	—
732	C₂×D₄	—	5	16	no	—
733	C₂×D₄	—	5	16	no	—
734	C₂×D₄	—	5	8	no	—
735	C₂×D₄	—	5	8	no	—
736	C₂×D₄	—	5	4	no	—
737	C₂×D₄	—	5	8	no	—
738	C₂×D₄	—	5	4	no	—
739	C₂×D₄	—	5	8	no	—
740	C₂×D₄	—	5	8	no	—
741	C₂×D₄	—	5	16	no	—
742	C₂×D₄	—	5	8	no	—
743	C₂×D₄	—	5	16	no	—
744	C₂×D₄	—	5	16	no	—
745	C₂×D₄	—	10	4	no	—
746	C₂×D₄	—	10	8	no	—
747	C₂×D₄	—	10	8	no	—
748	C₂×D₄	—	10	4	no	—
749	C₂×D₄	—	20	32	no	—
750	C₂×D₄	—	20	8	no	—
751	C₂×D₄	—	20	4	no	—
752	C₂×D₄	—	20	8	no	—
753	C₂×D₄	—	20	4	no	—
754	C₂×D₄	—	20	4	no	—
755	C₂×D₄	—	20	8	no	—
756	C₂×D₄	—	20	32	no	—
757	C₂×D₄	—	20	8	no	—
758	C₂×D₄	—	20	4	no	—
759	C₂×D₄	—	20	4	no	—
760	C₂×D₄	—	20	8	no	—
761	C₂×D₄	—	20	8	no	—
762	C₂×D₄	C₂³×D₅	1	4	yes	—
763	C₂×D₄	C₂³×D₅	1	8	yes	—
764	C₂²×C₄	—	2	8	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	5	2	no	—
769	C₂²×C₄	—	5	4	no	—
770	C₂²×C₄	—	5	2	no	—
771	C₂²×C₄	—	5	8	no	—
772	C₂²×C₄	—	5	8	no	—
773	C₂²×C₄	—	5	16	no	—
774	C₂²×C₄	—	5	16	no	—
775	C₂²×C₄	—	5	16	no	—
776	C₂²×C₄	—	10	8	no	—
777	C₂²×C₄	—	10	8	no	—
778	C₂²×C₄	—	20	8	no	—
779	C₂²×C₄	—	20	8	no	—
780	C₂²×C₄	—	20	8	no	—
781	C₂²×C₄	C₂³×D₅	1	4	yes	—
782	C₂²×C₄	C₂³×D₅	1	4	yes	—
783	C₂²×C₄	C₂³×D₅	1	8	yes	—
784	C₂²×C₄	C₂³×D₅	1	2	yes	—
785	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
786	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
787	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
789	C₂²×C₄	C₂³×D₅	1	2	yes	—
790	C₂²×C₄	C₂³×D₅	1	2	yes	—
791	C₂²×C₄	C₂³×D₅	1	4	yes	—
792	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
793	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
794	C₄⋊C₄	—	5	8	no	—
795	C₄⋊C₄	—	5	16	no	—
796	C₄⋊C₄	—	5	4	no	—
797	C₄⋊C₄	—	5	4	no	—
798	C₄⋊C₄	—	5	8	no	—
799	C₄⋊C₄	—	5	8	no	—
800	C₄⋊C₄	—	5	16	no	—
801	C₄⋊C₄	C₂³×D₅	1	4	yes	—
802	C₄⋊C₄	C₂³×D₅	1	4	yes	—
803	C₄⋊C₄	C₂³×D₅	1	8	yes	—
804	C₄⋊C₄	C₂³×D₅	1	8	yes	—
805	C₄⋊C₄	C₂³×D₅	1	8	yes	—
806	C₄⋊C₄	C₂³×D₅	1	8	yes	—
807	C₂²⋊C₄	—	5	16	no	—
808	C₂²⋊C₄	—	5	8	no	—
809	C₂²⋊C₄	—	5	16	no	—
810	C₂²⋊C₄	—	5	16	no	—
811	C₂²⋊C₄	—	5	8	no	—
812	C₂²⋊C₄	—	5	8	no	—
813	C₂²⋊C₄	—	5	16	no	—
814	C₂²⋊C₄	—	5	16	no	—
815	C₂²⋊C₄	—	5	16	no	—
816	C₂²⋊C₄	—	5	16	no	—
817	C₂²⋊C₄	—	5	8	no	—
818	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
819	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
820	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
821	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
822	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
823	C₄²	—	5	16	no	—
824	C₄²	C₂³×D₅	1	4	yes	—
825	C₄²	C₂³×D₅	1	4	yes	—
826	C₄²	C₂³×D₅	1	4	yes	—
827	C₄²	C₂³×D₅	1	4	yes	—
828	C₄²	C₂³×D₅	1	8	yes	—
829	C₂×C₅	—	4	4	no	—
830	C₂×C₅	—	4	2	no	—
831	C₂×C₅	#3546	1	4	yes	complemented
832	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
833	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
834	C₂×C₅	C₂×#585	1	1	yes	characteristic
835	D₅	—	4	4	no	—
836	D₅	—	4	8	no	—
837	D₅	—	4	4	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	5	4	no	—
845	C₂³	—	5	8	no	—
846	C₂³	—	5	4	no	—
847	C₂³	—	10	4	no	—
848	C₂³	—	10	4	no	—
849	C₂³	—	10	4	no	—
850	C₂³	—	10	8	no	—
851	C₂³	—	10	8	no	—
852	C₂³	—	10	4	no	—
853	C₂³	—	10	4	no	—
854	C₂³	—	10	8	no	—
855	C₂³	—	10	4	no	—
856	C₂³	—	20	16	no	—
857	C₂³	—	20	16	no	—
858	C₂³	—	20	16	no	—
859	C₂³	—	40	32	no	—
860	C₂³	C₂⁴×D₅	1	4	yes	—
861	C₂³	C₂⁴×D₅	1	2	yes	—
862	C₂³	C₂⁴×D₅	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	10	16	no	—
865	Q₈	—	20	8	no	—
866	D₄	—	2	8	no	—
867	D₄	—	4	8	no	—
868	D₄	—	10	8	no	—
869	D₄	—	10	16	no	—
870	D₄	—	10	16	no	—
871	D₄	—	10	8	no	—
872	D₄	—	20	16	no	—
873	D₄	—	20	8	no	—
874	D₄	—	20	16	no	—
875	D₄	—	20	8	no	—
876	D₄	—	20	8	no	—
877	D₄	—	20	16	no	—
878	D₄	—	20	16	no	—
879	D₄	—	20	8	no	—
880	D₄	—	20	8	no	—
881	D₄	—	20	16	no	—
882	D₄	—	20	16	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	4	no	—
890	C₂×C₄	—	2	16	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	5	4	no	—
895	C₂×C₄	—	5	8	no	—
896	C₂×C₄	—	5	4	no	—
897	C₂×C₄	—	10	4	no	—
898	C₂×C₄	—	10	4	no	—
899	C₂×C₄	—	10	8	no	—
900	C₂×C₄	—	10	16	no	—
901	C₂×C₄	—	10	16	no	—
902	C₂×C₄	—	20	16	no	—
903	C₂×C₄	—	20	16	no	—
904	C₂×C₄	—	20	16	no	—
905	C₂×C₄	#4149	1	4	yes	—
906	C₂×C₄	#4149	1	4	yes	—
907	C₂×C₄	C₂⁴×D₅	1	4	yes	—
908	C₂×C₄	C₂⁴×D₅	1	2	yes	—
909	C₂×C₄	C₂⁴×D₅	1	2	yes	—
910	C₂×C₄	C₂⁴×D₅	1	2	yes	—
911	C₂×C₄	C₂⁴×D₅	1	2	yes	—
912	C₂×C₄	C₂⁴×D₅	1	4	yes	—
913	C₂×C₄	C₂⁴×D₅	1	4	yes	—
914	C₂×C₄	C₂⁴×D₅	1	2	yes	—
915	C₂×C₄	C₂⁴×D₅	1	2	yes	—
916	C₅	C₂×#3546	1	1	yes	characteristic, complemented, Sylow
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	8	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	10	4	no	—
926	C₂²	—	10	4	no	—
927	C₂²	—	10	4	no	—
928	C₂²	—	10	8	no	—
929	C₂²	—	10	8	no	—
930	C₂²	—	10	4	no	—
931	C₂²	—	10	4	no	—
932	C₂²	—	10	8	no	—
933	C₂²	—	10	4	no	—
934	C₂²	—	20	8	no	—
935	C₂²	—	20	16	no	—
936	C₂²	—	20	8	no	—
937	C₂²	—	40	32	no	—
938	C₂²	C₂×#4149	1	2	yes	—
939	C₂²	C₂×#4149	1	2	yes	—
940	C₂²	#66283	1	2	yes	—
941	C₂²	C₂⁵×D₅	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	10	4	no	—
950	C₄	—	10	4	no	—
951	C₄	—	10	8	no	—
952	C₄	C₂×#4149	1	4	yes	—
953	C₄	C₂×#4149	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	2	no	—
956	C₂	—	20	4	no	—
957	C₂	—	20	8	no	—
958	C₂	—	20	4	no	—
959	C₂	#10618075	1	4	yes	direct product factor
960	C₂	C₂²×#4149	1	1	yes	characteristic
961	C₂	C₂²×#4149	1	1	yes	characteristic
962	C₂	C₂×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#529	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#529	D₅
hypocenter	C₅	C₂×#3546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#529	C₂	semidirect
2. #10618075	C₂	direct (N × H)
3. C₂×#66038	C₂	semidirect
4. C₂×#66029	C₂	semidirect
5. C₂×#66010	C₂	semidirect
6. C₂×#66000	C₂	semidirect
7. C₂×#65963	C₂	semidirect
8. C₂×#65941	C₂	semidirect
9. C₂×#65918	C₂	semidirect
10. C₂×#65911	C₂	semidirect
11. C₂×#65885	C₂	semidirect
12. C₂×#65884	C₂	semidirect
13. C₂×D₄×D₂₀	C₂	semidirect
14. C₂×#65887	C₂	semidirect
15. C₂×#65868	C₂	semidirect
16. C₂×#65859	C₂	semidirect
17. C₂×#65811	C₂	semidirect
18. C₂×#65811	C₂	semidirect
19. C₂²×#713	C₂²	semidirect
21. C₂²×#709	C₂²	semidirect
22. C₂²×#709	C₂²	semidirect
23. C₂²×#709	C₂²	semidirect
25. C₅×#529	C₂²	semidirect
26. C₂×C₅×#126	C₂²	semidirect
27. C₂×C₅×#125	C₂²	semidirect
29. C₂×C₅×#123	C₂²	semidirect
30. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₄×C₅×Q₈	C₂²	semidirect
34. C₂×C₄×C₅×D₄	C₂²	semidirect
35. C₂×C₅×#117	C₂²	semidirect
36. C₂²×C₄²×C₅	C₂²	semidirect
37. C₂×#4092	C₂²	semidirect
38. C₂×#4086	C₂²	semidirect
40. C₂×#4083	C₂²	semidirect
43. C₂×#4076	C₂²	semidirect
44. C₂×#4076	C₂²	semidirect
45. C₂×#4076	C₂²	semidirect
46. C₂×#4076	C₂²	semidirect
47. C₂×#4070	C₂²	semidirect
48. #66038	C₂²	semidirect
49. #66029	C₂²	semidirect
50. #66010	C₂²	semidirect
51. #66000	C₂²	semidirect
52. #65963	C₂²	semidirect
53. #65941	C₂²	semidirect
54. #65918	C₂²	semidirect
55. #65911	C₂²	semidirect
56. #65887	C₂²	semidirect
57. #65885	C₂²	semidirect
58. #65884	C₂²	semidirect
59. D₄×D₂₀	C₂²	semidirect
60. #65868	C₂²	semidirect
61. #65859	C₂²	semidirect
62. C₂×#4044	C₂²	semidirect
63. C₂×#4044	C₂²	semidirect
64. C₂×#4042	C₂²	semidirect
66. C₂×#4041	C₂²	semidirect
67. C₂×#4041	C₂²	semidirect
68. C₂×#4041	C₂²	semidirect
69. C₂×#4041	C₂²	semidirect
70. C₂×#4040	C₂²	semidirect
71. C₂×#4039	C₂²	semidirect
72. C₂×#4038	C₂²	semidirect
73. C₂×D₅×C₄⋊C₄	C₂²	semidirect
74. C₂×#4031	C₂²	semidirect
75. C₂×#4030	C₂²	semidirect
76. C₂×#4030	C₂²	semidirect
77. C₂×#4030	C₂²	semidirect
78. C₂×#4029	C₂²	semidirect
79. C₂×#4029	C₂²	semidirect
81. C₂×#4028	C₂²	semidirect
82. C₂×#4028	C₂²	semidirect
83. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
84. #65811	C₂²	semidirect
85. #65811	C₂²	semidirect
87. C₂×#4021	C₂²	semidirect
88. C₂×#4021	C₂²	semidirect
91. C₂×#4020	C₂²	semidirect
93. C₂×C₄×D₂₀	C₂²	semidirect
94. C₂×C₄×D₂₀	C₂²	semidirect
95. C₂×C₄×D₂₀	C₂²	semidirect
96. C₂×C₄×D₂₀	C₂²	semidirect
97. C₂×C₄×D₂₀	C₂²	semidirect
98. C₂×#4015	C₂²	semidirect
99. C₂×#4015	C₂²	semidirect
100. C₂×C₄×Dic₁₀	C₂²	semidirect
116. C₂×#713	C₂³	semidirect
122. C₂×#709	C₂³	semidirect
123. C₂×#709	C₂³	semidirect
124. C₂×#709	C₂³	semidirect
144. C₅×#126	C₂³	semidirect
145. C₅×#125	C₂³	semidirect
147. C₅×#123	C₂³	semidirect
148. C₅×C₂²⋊Q₈	C₂³	semidirect
150. C₄×C₅×Q₈	C₂³	semidirect
152. C₄×C₅×D₄	C₂³	semidirect
153. C₅×#117	C₂³	semidirect
170. C₂×C₄²×C₅	C₂³	semidirect
172. #4092	C₂³	semidirect
173. #4086	C₂³	semidirect
175. #4083	C₂³	semidirect
178. #4076	C₂³	semidirect
179. #4076	C₂³	semidirect
180. #4076	C₂³	semidirect
181. #4076	C₂³	semidirect
197. #4070	C₂³	semidirect
201. #4044	C₂³	semidirect
202. #4044	C₂³	semidirect
203. #4042	C₂³	semidirect
205. #4041	C₂³	semidirect
206. #4041	C₂³	semidirect
207. #4041	C₂³	semidirect
208. #4041	C₂³	semidirect
209. #4040	C₂³	semidirect
210. #4039	C₂³	semidirect
211. #4038	C₂³	semidirect
212. D₅×C₄⋊C₄	C₂³	semidirect
213. #4031	C₂³	semidirect
214. #4030	C₂³	semidirect
215. #4030	C₂³	semidirect
216. #4030	C₂³	semidirect
217. #4029	C₂³	semidirect
218. #4029	C₂³	semidirect
220. #4028	C₂³	semidirect
221. #4028	C₂³	semidirect
222. D₅×C₂²⋊C₄	C₂³	semidirect
224. #4021	C₂³	semidirect
225. #4021	C₂³	semidirect
228. #4020	C₂³	semidirect
230. C₄×D₂₀	C₂³	semidirect
231. C₄×D₂₀	C₂³	semidirect
232. C₄×D₂₀	C₂³	semidirect
233. C₄×D₂₀	C₂³	semidirect
234. C₄×D₂₀	C₂³	semidirect
235. #4015	C₂³	semidirect
236. #4015	C₂³	semidirect
237. C₄×Dic₁₀	C₂³	semidirect
255. C₂×#529	D₅	semidirect
404. #529	C₂×D₅	semidirect
407. C₂×#126	C₂×D₅	semidirect
408. C₂×#125	C₂×D₅	semidirect
417. C₂×#123	C₂×D₅	semidirect
421. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
443. C₂×C₄×Q₈	C₂×D₅	semidirect
452. C₂×C₄×D₄	C₂×D₅	semidirect
454. C₂×#117	C₂×D₅	semidirect
457. C₂²×C₄²	C₂×D₅	semidirect
586. #126	C₂²×D₅	semidirect
587. #125	C₂²×D₅	semidirect
596. #123	C₂²×D₅	semidirect
600. C₂²⋊Q₈	C₂²×D₅	semidirect
622. C₄×Q₈	C₂²×D₅	semidirect
631. C₄×D₄	C₂²×D₅	semidirect
633. #117	C₂²×D₅	semidirect
671. C₂×C₄²	C₂²×D₅	semidirect
831. C₂×C₅	#3546	semidirect
916. C₅	C₂×#3546	semidirect
959. C₂	#10618075	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×#529	2
#10618075	2
C₂×#66038	2
C₂×#66029	2
C₂×#66010	2
C₂×#66000	2
C₂×#65963	2
C₂×#65941	2
C₂×#65918	2
C₂×#65911	2
C₂×#65885	2
C₂×#65884	2
C₂×D₄×D₂₀	2
C₂×#65887	2
C₂×#65868	2
C₂×#65859	2
C₂×#65811	2
C₂×#3546	5

Subgroups — C2×#10618075 #13006939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618075 #13006939