Subgroups — C₂×#10618955 #13007395

Order 1280.

8006 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618955	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66051	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66011	C₂	1	2	yes	maximal, complemented
6	C₂×#66010	C₂	1	2	yes	maximal, complemented
7	C₂×#66016	C₂	1	2	yes	maximal, complemented
8	C₂×D₅×#124	C₂	1	2	yes	maximal, complemented
9	C₂×#65992	C₂	1	4	yes	maximal, complemented
10	C₂×#65991	C₂	1	4	yes	maximal, complemented
11	C₂×Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65914	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65918	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#65888	C₂	1	2	yes	maximal, complemented
16	C₂×#65891	C₂	1	2	yes	maximal, complemented
17	C₂×#65879	C₂	1	2	yes	maximal, complemented
18	C₂×#65897	C₂	1	2	yes	maximal, complemented
19	C₂²×#713	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×D₅	C₂²	1	2	yes	complemented
21	C₂²×#711	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₅	C₂²	1	2	yes	—
23	C₂²×D₄×D₅	C₂²	1	2	yes	—
24	C₅×#559	C₂²	1	16	yes	complemented
25	C₂×C₅×#127	C₂²	1	1	yes	characteristic
26	C₂×C₅×#124	C₂²	1	2	yes	complemented
27	C₂×C₅×#124	C₂²	1	2	yes	complemented
28	C₂×C₅×#123	C₂²	1	4	yes	complemented
29	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
33	C₂×#4093	C₂²	1	1	yes	characteristic
34	C₂×#4092	C₂²	1	2	yes	complemented
35	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
36	C₂×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
37	C₂×#4084	C₂²	1	2	yes	—
38	C₂×#4084	C₂²	1	2	yes	—
39	C₂×#4084	C₂²	1	2	yes	complemented
40	C₂×#4084	C₂²	1	2	yes	complemented
41	C₂×#4083	C₂²	1	4	yes	—
42	C₂×#4082	C₂²	1	2	yes	complemented
43	C₂×D₄×Dic₅	C₂²	1	2	yes	complemented
44	C₂×D₄×Dic₅	C₂²	1	2	yes	complemented
45	C₂×#4076	C₂²	1	4	yes	complemented
46	C₂×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
47	C₂²×#685	C₂²	1	4	yes	complemented
48	C₂×#4072	C₂²	1	4	yes	complemented
49	#66051	C₂²	1	16	yes	complemented
50	#66050	C₂²	1	16	yes	complemented
51	#66016	C₂²	1	32	yes	complemented
52	#66011	C₂²	1	32	yes	complemented
53	#66010	C₂²	1	32	yes	complemented
54	D₅×#124	C₂²	1	32	yes	complemented
55	#65992	C₂²	1	64	yes	complemented
56	#65991	C₂²	1	64	yes	complemented
57	#65918	C₂²	1	16	yes	complemented
58	#65914	C₂²	1	16	yes	complemented
59	Q₈×D₂₀	C₂²	1	16	yes	complemented
60	C₄×#713	C₂²	1	16	yes	complemented
61	#65897	C₂²	1	32	yes	complemented
62	#65891	C₂²	1	32	yes	complemented
63	#65888	C₂²	1	32	yes	complemented
64	#65879	C₂²	1	32	yes	complemented
65	C₂×#4044	C₂²	1	4	yes	complemented
66	C₂×#4044	C₂²	1	2	yes	complemented
67	C₂×#4043	C₂²	1	4	yes	complemented
68	C₂×#4043	C₂²	1	2	yes	complemented
69	C₂×#4041	C₂²	1	1	yes	characteristic
70	C₂×#4040	C₂²	1	2	yes	complemented
71	C₂×#4039	C₂²	1	1	yes	characteristic
72	C₂×#4039	C₂²	1	2	yes	complemented
73	C₂×#4038	C₂²	1	2	yes	complemented
74	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
75	C₂×#4038	C₂²	1	2	yes	complemented
76	C₂×#4036	C₂²	1	1	yes	characteristic, complemented
77	C₂×#4032	C₂²	1	4	yes	complemented
78	C₂×#4031	C₂²	1	4	yes	complemented
79	C₂×#4031	C₂²	1	4	yes	complemented
80	C₂×#4031	C₂²	1	4	yes	complemented
81	C₂×#4030	C₂²	1	4	yes	complemented
82	C₂×#4029	C₂²	1	4	yes	complemented
83	C₂×#4028	C₂²	1	4	yes	complemented
84	C₂×#4027	C₂²	1	4	yes	complemented
85	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
86	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
87	C₂×#4025	C₂²	1	4	yes	complemented
88	C₂×#4024	C₂²	1	4	yes	complemented
89	C₂×#4021	C₂²	1	2	yes	—
90	C₂×C₄×D₂₀	C₂²	1	2	yes	—
91	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
92	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
93	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
94	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
95	C₂×#4018	C₂²	1	2	yes	complemented
96	C₂×C₄²×D₅	C₂²	1	2	yes	complemented
97	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
98	C₂×#4015	C₂²	1	2	yes	complemented
99	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
101	C₂×#3514	—	5	1	no	maximal, Sylow
102	C₂⁴×D₅	C₂³	1	4	yes	—
103	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₅×D₄	C₂³	1	2	yes	—
106	C₂²×C₅×D₄	C₂³	1	2	yes	—
107	C₂²×C₅×D₄	C₂³	1	2	yes	—
108	C₂³×C₄×C₅	C₂³	1	4	yes	—
109	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
112	C₂³×Dic₅	C₂³	1	4	yes	—
113	C₂×#713	—	2	8	no	—
114	C₂×#713	C₂³	1	8	yes	—
115	C₂×Q₈×D₅	—	4	8	no	—
116	C₂×Q₈×D₅	C₂³	1	16	yes	complemented
117	C₂×#711	—	4	8	no	—
118	C₂×#711	C₂³	1	16	yes	complemented
119	C₂×D₄×D₅	—	2	16	no	—
120	C₂×D₄×D₅	—	4	8	no	—
121	C₂×D₄×D₅	C₂³	1	16	yes	—
122	C₂×D₄×D₅	C₂³	1	16	yes	—
123	C₂²×D₂₀	C₂³	1	1	yes	characteristic
124	C₂²×D₂₀	C₂³	1	2	yes	—
125	C₂²×D₂₀	C₂³	1	2	yes	—
126	C₂²×D₂₀	C₂³	1	1	yes	characteristic
127	C₂²×C₄×D₅	C₂³	1	2	yes	—
128	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
130	C₂²×C₄×D₅	C₂³	1	2	yes	—
131	C₂²×C₄×D₅	C₂³	1	2	yes	—
132	C₂²×C₄×D₅	C₂³	1	2	yes	—
133	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
134	C₂²×C₄×D₅	C₂³	1	4	yes	—
135	C₂²×Dic₁₀	C₂³	1	2	yes	—
136	C₂²×Dic₁₀	C₂³	1	4	yes	—
137	C₅×#127	C₂³	1	8	yes	—
138	C₅×#124	C₂³	1	16	yes	complemented
139	C₅×#124	C₂³	1	16	yes	complemented
140	C₅×#123	C₂³	1	32	yes	complemented
141	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
142	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
143	C₄×C₅×D₄	C₂³	1	16	yes	complemented
144	C₄×C₅×D₄	C₂³	1	16	yes	complemented
145	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₄²×C₅	C₂³	1	2	yes	—
153	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₅	C₂³	1	2	yes	—
155	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
156	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
157	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
158	#4093	C₂³	1	8	yes	—
159	#4092	C₂³	1	8	yes	complemented
160	#4092	C₂³	1	16	yes	complemented
161	Q₈×Dic₅	C₂³	1	8	yes	complemented
162	#4084	C₂³	1	16	yes	—
163	#4084	C₂³	1	16	yes	—
164	#4084	C₂³	1	16	yes	complemented
165	#4084	C₂³	1	16	yes	complemented
166	#4083	C₂³	1	32	yes	—
167	#4082	C₂³	1	16	yes	complemented
168	D₄×Dic₅	C₂³	1	16	yes	complemented
169	D₄×Dic₅	C₂³	1	16	yes	complemented
170	#4076	C₂³	1	32	yes	complemented
171	C₄×C₂²⋊D₅	C₂³	1	32	yes	complemented
172	C₂×#685	C₂³	1	2	yes	—
173	C₂×#685	C₂³	1	2	yes	—
174	C₂×#685	C₂³	1	4	yes	—
175	C₂×#685	C₂³	1	2	yes	—
176	C₂×#685	C₂³	1	2	yes	—
177	C₂×#685	C₂³	1	2	yes	—
178	C₂×#685	C₂³	1	2	yes	—
179	C₂×#685	C₂³	1	2	yes	—
180	C₂×#685	C₂³	1	2	yes	—
181	C₂×#685	C₂³	1	4	yes	—
182	C₂×#685	C₂³	1	4	yes	—
183	C₂×#685	C₂³	1	32	yes	complemented
184	#4072	C₂³	1	32	yes	complemented
185	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
187	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
192	C₂×#683	C₂³	1	4	yes	—
193	C₂×#683	C₂³	1	2	yes	—
194	C₂×#683	C₂³	1	2	yes	—
195	C₂×C₄×Dic₅	C₂³	1	4	yes	—
196	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
197	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
198	C₂×C₄×Dic₅	C₂³	1	2	yes	—
199	C₂×C₄×Dic₅	C₂³	1	2	yes	—
200	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
201	#4044	C₂³	1	16	yes	complemented
202	#4044	C₂³	1	32	yes	complemented
203	#4043	C₂³	1	16	yes	complemented
204	#4043	C₂³	1	32	yes	complemented
205	#4041	C₂³	1	8	yes	—
206	#4040	C₂³	1	16	yes	complemented
207	#4039	C₂³	1	8	yes	—
208	#4039	C₂³	1	16	yes	complemented
209	#4038	C₂³	1	16	yes	complemented
210	#4038	C₂³	1	8	yes	complemented
211	#4038	C₂³	1	16	yes	complemented
212	#4036	C₂³	1	8	yes	complemented
213	#4032	C₂³	1	32	yes	complemented
214	#4031	C₂³	1	32	yes	complemented
215	#4031	C₂³	1	32	yes	complemented
216	#4031	C₂³	1	32	yes	complemented
217	#4030	C₂³	1	32	yes	complemented
218	#4029	C₂³	1	32	yes	complemented
219	#4028	C₂³	1	32	yes	complemented
220	#4027	C₂³	1	32	yes	complemented
221	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
222	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
223	#4025	C₂³	1	32	yes	complemented
224	#4024	C₂³	1	32	yes	complemented
225	#4021	C₂³	1	16	yes	—
226	C₄×D₂₀	C₂³	1	8	yes	—
227	C₄×D₂₀	C₂³	1	8	yes	—
228	C₄×D₂₀	C₂³	1	16	yes	—
229	C₄×D₂₀	C₂³	1	16	yes	complemented
230	C₄×D₂₀	C₂³	1	16	yes	complemented
231	#4018	C₂³	1	16	yes	complemented
232	C₄²×D₅	C₂³	1	8	yes	complemented
233	C₄²×D₅	C₂³	1	16	yes	complemented
234	#4015	C₂³	1	8	yes	complemented
235	#4015	C₂³	1	16	yes	complemented
236	C₄×Dic₁₀	C₂³	1	16	yes	complemented
237	#3514	—	5	32	no	—
238	C₂×#559	D₅	1	1	yes	characteristic, complemented
239	C₂×#556	—	5	1	no	—
240	C₂×#555	—	5	2	no	—
241	C₂×#551	—	5	4	no	—
242	C₂×D₄×Q₈	—	5	1	no	—
243	C₂×#548	—	5	2	no	—
244	C₂×#546	—	5	2	no	—
245	C₂×#546	—	5	2	no	—
246	C₂×D₄²	—	5	1	no	—
247	C₂×#542	—	5	2	no	—
248	C₂×#538	—	5	4	no	—
249	C₂×#532	—	5	1	no	—
250	C₂×#529	—	5	1	no	—
251	C₂×#529	—	5	2	no	—
252	C₂²×#124	—	5	2	no	—
253	C₂×#518	—	5	2	no	—
254	C₂×C₄×#41	—	5	1	no	—
255	C₂⁴×C₅	C₂⁴	1	4	yes	—
256	C₂³×D₅	—	2	16	no	—
257	C₂³×D₅	—	4	8	no	—
258	C₂³×D₅	—	4	8	no	—
259	C₂³×D₅	C₂⁴	1	1	yes	characteristic
260	C₂³×D₅	C₂⁴	1	2	yes	—
261	C₂³×D₅	C₂⁴	1	2	yes	—
262	C₂³×D₅	C₂⁴	1	16	yes	—
263	C₂×C₅×Q₈	—	2	4	no	—
264	C₂×C₅×Q₈	—	2	4	no	—
265	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
266	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
267	C₂×C₅×D₄	—	2	8	no	—
268	C₂×C₅×D₄	—	2	8	no	—
269	C₂×C₅×D₄	—	4	4	no	—
270	C₂×C₅×D₄	C₂⁴	1	8	yes	—
271	C₂×C₅×D₄	C₂⁴	1	8	yes	—
272	C₂×C₅×D₄	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₅	—	4	8	no	—
274	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
280	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₂²⋊D₅	—	2	16	no	—
283	C₂×C₂²⋊D₅	—	4	8	no	—
284	C₂×C₂²⋊D₅	—	4	8	no	—
285	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
286	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
287	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
288	C₂²×Dic₅	—	4	8	no	—
289	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
290	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
291	C₂²×Dic₅	C₂⁴	1	4	yes	—
292	C₂²×Dic₅	C₂⁴	1	2	yes	—
293	C₂²×Dic₅	C₂⁴	1	2	yes	—
294	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
295	C₂²×Dic₅	C₂⁴	1	16	yes	—
296	#713	—	2	32	no	—
297	Q₈×D₅	—	4	32	no	—
298	#711	—	4	32	no	—
299	D₄×D₅	—	2	64	no	—
300	D₄×D₅	—	4	32	no	—
301	C₂×D₂₀	—	2	8	no	—
302	C₂×D₂₀	—	2	4	no	—
303	C₂×D₂₀	—	4	4	no	—
304	C₂×D₂₀	#41	1	8	yes	complemented
305	C₂×D₂₀	C₂⁴	1	4	yes	—
306	C₂×D₂₀	C₂⁴	1	8	yes	—
307	C₂×D₂₀	C₂⁴	1	8	yes	—
308	C₂×D₂₀	C₂⁴	1	4	yes	—
309	C₂×C₄×D₅	—	2	8	no	—
310	C₂×C₄×D₅	—	2	8	no	—
311	C₂×C₄×D₅	—	2	4	no	—
312	C₂×C₄×D₅	—	2	8	no	—
313	C₂×C₄×D₅	—	2	4	no	—
314	C₂×C₄×D₅	—	4	4	no	—
315	C₂×C₄×D₅	—	4	2	no	—
316	C₂×C₄×D₅	—	4	8	no	—
317	C₂×C₄×D₅	C₂⁴	1	8	yes	—
318	C₂×C₄×D₅	C₂⁴	1	8	yes	—
319	C₂×C₄×D₅	C₂⁴	1	4	yes	—
320	C₂×C₄×D₅	C₂⁴	1	4	yes	—
321	C₂×C₄×D₅	C₂⁴	1	8	yes	—
322	C₂×C₄×D₅	C₂⁴	1	16	yes	—
323	C₂×C₄×D₅	C₂⁴	1	8	yes	—
324	C₂×C₄×D₅	C₂⁴	1	4	yes	—
325	C₂×Dic₁₀	—	2	8	no	—
326	C₂×Dic₁₀	—	4	8	no	—
327	C₂×Dic₁₀	C₂⁴	1	8	yes	—
328	C₂×Dic₁₀	C₂⁴	1	16	yes	—
329	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
331	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
332	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
333	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₄²×C₅	C₂⁴	1	8	yes	—
337	C₄²×C₅	C₂⁴	1	8	yes	—
338	C₄²×C₅	C₂⁴	1	4	yes	—
339	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
340	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
341	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
342	#685	C₂⁴	1	8	yes	—
343	#685	C₂⁴	1	8	yes	—
344	#685	C₂⁴	1	16	yes	—
345	#685	C₂⁴	1	8	yes	—
346	#685	C₂⁴	1	8	yes	—
347	#685	C₂⁴	1	8	yes	—
348	#685	C₂⁴	1	8	yes	—
349	#685	C₂⁴	1	8	yes	—
350	#685	C₂⁴	1	8	yes	—
351	#685	C₂⁴	1	16	yes	—
352	#685	C₂⁴	1	16	yes	—
353	C₄⋊Dic₅	C₂⁴	1	4	yes	—
354	C₄⋊Dic₅	C₂⁴	1	8	yes	—
355	C₄⋊Dic₅	C₂⁴	1	4	yes	—
356	C₄⋊Dic₅	C₂⁴	1	16	yes	—
357	C₄⋊Dic₅	C₂⁴	1	8	yes	—
358	C₄⋊Dic₅	C₂⁴	1	8	yes	—
359	C₄⋊Dic₅	C₂⁴	1	8	yes	—
360	#683	C₂⁴	1	16	yes	—
361	#683	C₂⁴	1	8	yes	—
362	#683	C₂⁴	1	8	yes	—
363	C₄×Dic₅	C₂⁴	1	16	yes	—
364	C₄×Dic₅	C₂⁴	1	4	yes	—
365	C₄×Dic₅	C₂⁴	1	4	yes	—
366	C₄×Dic₅	C₂⁴	1	8	yes	—
367	C₄×Dic₅	C₂⁴	1	8	yes	—
368	C₄×Dic₅	C₂⁴	1	4	yes	—
369	C₂²×#41	—	5	1	no	—
370	C₂²×#41	—	5	2	no	—
371	C₂³×Q₈	—	5	2	no	—
372	C₂³×D₄	—	5	2	no	—
373	C₂³×D₄	—	5	2	no	—
374	#559	C₂×D₅	1	16	yes	complemented
375	#556	—	5	16	no	—
376	#555	—	5	32	no	—
377	#551	—	5	64	no	—
378	D₄×Q₈	—	5	16	no	—
379	#548	—	5	32	no	—
380	#546	—	5	32	no	—
381	#546	—	5	32	no	—
382	D₄²	—	5	16	no	—
383	#542	—	5	32	no	—
384	#538	—	5	64	no	—
385	#532	—	5	16	no	—
386	C₂×C₄⋊Q₈	—	5	1	no	—
387	C₂×C₄⋊Q₈	—	5	2	no	—
388	C₂×#127	C₂×D₅	1	1	yes	characteristic
389	#529	—	5	16	no	—
390	#529	—	5	32	no	—
391	C₂×#126	—	5	2	no	—
392	C₂×#126	—	5	4	no	—
393	C₂×#126	—	5	4	no	—
394	C₂×#125	—	5	1	no	—
395	C₂×#124	—	5	1	no	—
396	C₂×#124	—	5	2	no	—
397	C₂×#124	—	5	32	no	—
398	C₂×#124	—	5	4	no	—
399	C₂×#124	—	5	4	no	—
400	C₂×#124	—	5	4	no	—
401	C₂×#124	—	5	2	no	—
402	C₂×#124	C₂×D₅	1	2	yes	complemented
403	C₂×#124	C₂×D₅	1	2	yes	complemented
404	C₂×#123	—	5	2	no	—
405	C₂×#123	—	5	4	no	—
406	C₂×#123	—	5	4	no	—
407	C₂×#123	C₂×D₅	1	4	yes	complemented
408	C₂×C₂²⋊Q₈	—	5	1	no	—
409	C₂×C₂²⋊Q₈	—	5	2	no	—
410	C₂×C₂²⋊Q₈	—	5	2	no	—
411	C₂×C₂²⋊Q₈	—	5	4	no	—
412	C₂×C₂²⋊Q₈	—	5	4	no	—
413	C₂×#121	—	5	2	no	—
414	C₂×#121	—	5	2	no	—
415	C₂×#121	—	5	2	no	—
416	C₂×#121	—	5	2	no	—
417	C₂×#121	—	5	4	no	—
418	C₂×#121	—	5	1	no	—
419	C₂×#121	—	5	4	no	—
420	C₂×#120	—	5	4	no	—
421	C₂×#120	—	5	4	no	—
422	#518	—	5	32	no	—
423	C₄×#41	—	5	16	no	—
424	C₂×C₄×Q₈	—	5	1	no	—
425	C₂×C₄×Q₈	—	5	2	no	—
426	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
427	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
428	C₂×C₄×D₄	—	5	2	no	—
429	C₂×C₄×D₄	—	5	2	no	—
430	C₂×C₄×D₄	—	5	4	no	—
431	C₂×C₄×D₄	—	5	1	no	—
432	C₂×C₄×D₄	—	5	2	no	—
433	C₂×C₄×D₄	—	5	4	no	—
434	C₂×C₄×D₄	—	5	1	no	—
435	C₂×C₄×D₄	—	5	2	no	—
436	C₂×C₄×D₄	—	5	1	no	—
437	C₂×C₄×D₄	—	5	2	no	—
438	C₂×C₄×D₄	—	5	2	no	—
439	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
440	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
441	C₂×#117	—	5	4	no	—
442	C₂×#117	—	5	2	no	—
443	C₂×#117	—	5	1	no	—
444	C₂×#117	—	5	2	no	—
445	C₂×#117	—	5	2	no	—
446	C₂²×C₂²⋊C₄	—	5	4	no	—
447	C₂²×C₂²⋊C₄	—	5	4	no	—
448	C₂²×C₂²⋊C₄	—	5	4	no	—
449	C₂²×C₄²	—	5	2	no	—
450	C₂²×C₄²	—	5	1	no	—
451	C₂³×C₅	—	2	8	no	—
452	C₂³×C₅	—	2	8	no	—
453	C₂³×C₅	—	2	8	no	—
454	C₂³×C₅	C₂⁵	1	8	yes	—
455	C₂³×C₅	C₂⁵	1	1	yes	characteristic
456	C₂²×D₅	—	2	4	no	—
457	C₂²×D₅	—	2	4	no	—
458	C₂²×D₅	—	2	2	no	—
459	C₂²×D₅	—	2	4	no	—
460	C₂²×D₅	—	2	2	no	—
461	C₂²×D₅	—	2	4	no	—
462	C₂²×D₅	—	2	2	no	—
463	C₂²×D₅	—	2	4	no	—
464	C₂²×D₅	—	2	32	no	—
465	C₂²×D₅	—	4	16	no	—
466	C₂²×D₅	—	4	16	no	—
467	C₂²×D₅	—	8	32	no	—
468	C₂²×D₅	C₂×#41	1	8	yes	—
469	C₂²×D₅	C₂⁵	1	4	yes	—
470	C₂²×D₅	C₂⁵	1	2	yes	—
471	C₂²×D₅	C₂⁵	1	4	yes	—
472	C₅×Q₈	—	2	8	no	—
473	C₅×Q₈	—	2	8	no	—
474	C₅×D₄	—	2	16	no	—
475	C₅×D₄	—	2	16	no	—
476	C₅×D₄	—	4	8	no	—
477	C₂×C₄×C₅	—	2	4	no	—
478	C₂×C₄×C₅	—	2	4	no	—
479	C₂×C₄×C₅	—	2	4	no	—
480	C₂×C₄×C₅	—	2	2	no	—
481	C₂×C₄×C₅	—	2	4	no	—
482	C₂×C₄×C₅	—	4	16	no	—
483	C₂×C₄×C₅	C₂×#41	1	4	yes	—
484	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
485	C₂×C₄×C₅	C₂⁵	1	4	yes	—
486	C₂×C₄×C₅	C₂⁵	1	4	yes	—
487	C₂×C₄×C₅	C₂⁵	1	2	yes	—
488	C₂×C₄×C₅	C₂⁵	1	4	yes	—
489	C₂×C₄×C₅	C₂⁵	1	4	yes	—
490	C₂×C₄×C₅	C₂⁵	1	2	yes	—
491	C₂×C₄×C₅	C₂⁵	1	2	yes	—
492	C₂²⋊D₅	—	2	32	no	—
493	C₂²⋊D₅	—	4	16	no	—
494	C₂²⋊D₅	—	4	16	no	—
495	C₂×Dic₅	—	2	2	no	—
496	C₂×Dic₅	—	2	4	no	—
497	C₂×Dic₅	—	2	8	no	—
498	C₂×Dic₅	—	2	4	no	—
499	C₂×Dic₅	—	2	2	no	—
500	C₂×Dic₅	—	2	2	no	—
501	C₂×Dic₅	—	4	16	no	—
502	C₂×Dic₅	C₂⁵	1	2	yes	—
503	C₂×Dic₅	C₂⁵	1	2	yes	—
504	C₂×Dic₅	C₂⁵	1	4	yes	—
505	C₂×Dic₅	C₂⁵	1	2	yes	—
506	C₂×Dic₅	C₂⁵	1	4	yes	—
507	C₂×Dic₅	C₂⁵	1	8	yes	—
508	D₂₀	—	2	16	no	—
509	D₂₀	—	2	8	no	—
510	D₂₀	—	4	8	no	—
511	D₂₀	C₂×#41	1	16	yes	complemented
512	C₄×D₅	—	2	16	no	—
513	C₄×D₅	—	2	16	no	—
514	C₄×D₅	—	2	8	no	—
515	C₄×D₅	—	2	16	no	—
516	C₄×D₅	—	2	8	no	—
517	C₄×D₅	—	4	8	no	—
518	C₄×D₅	—	4	4	no	—
519	C₄×D₅	—	4	16	no	—
520	Dic₁₀	—	2	16	no	—
521	Dic₁₀	—	4	16	no	—
522	C₂⁵	—	5	4	no	—
523	C₂×#41	—	5	8	no	—
524	C₂×#41	—	5	16	no	—
525	C₂×#41	—	10	8	no	—
526	C₂×#41	—	20	8	no	—
527	C₂²×Q₈	—	5	16	no	—
528	C₂²×Q₈	—	5	2	no	—
529	C₂²×Q₈	—	5	4	no	—
530	C₂²×Q₈	—	20	8	no	—
531	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
532	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
533	C₂²×D₄	—	5	4	no	—
534	C₂²×D₄	—	5	4	no	—
535	C₂²×D₄	—	5	4	no	—
536	C₂²×D₄	—	5	16	no	—
537	C₂²×D₄	—	5	16	no	—
538	C₂²×D₄	—	5	1	no	—
539	C₂²×D₄	—	5	2	no	—
540	C₂²×D₄	—	5	1	no	—
541	C₂²×D₄	—	5	2	no	—
542	C₂²×D₄	—	10	16	no	—
543	C₂²×D₄	—	20	8	no	—
544	C₂²×D₄	C₂²×D₅	1	2	yes	—
545	C₂²×D₄	C₂²×D₅	1	2	yes	—
546	C₂²×D₄	C₂²×D₅	1	2	yes	—
547	C₂³×C₄	—	5	4	no	—
548	C₂³×C₄	—	5	2	no	—
549	C₂³×C₄	—	5	2	no	—
550	C₂³×C₄	—	5	1	no	—
551	C₂³×C₄	—	5	2	no	—
552	C₂³×C₄	—	5	1	no	—
553	C₂³×C₄	—	5	2	no	—
554	C₂³×C₄	—	5	4	no	—
555	C₂³×C₄	—	5	1	no	—
556	C₂³×C₄	C₂²×D₅	1	4	yes	—
557	C₄⋊Q₈	—	5	8	no	—
558	C₄⋊Q₈	—	5	16	no	—
559	#127	C₂²×D₅	1	8	yes	—
560	#126	—	5	16	no	—
561	#126	—	5	32	no	—
562	#126	—	5	32	no	—
563	#125	—	5	8	no	—
564	#124	—	5	8	no	—
565	#124	—	5	16	no	—
566	#124	—	5	32	no	—
567	#124	—	5	32	no	—
568	#124	—	5	32	no	—
569	#124	—	5	16	no	—
570	#124	C₂²×D₅	1	16	yes	complemented
571	#124	C₂²×D₅	1	16	yes	complemented
572	#123	—	5	16	no	—
573	#123	—	5	32	no	—
574	#123	—	5	32	no	—
575	#123	C₂²×D₅	1	32	yes	complemented
576	C₂²⋊Q₈	—	5	8	no	—
577	C₂²⋊Q₈	—	5	16	no	—
578	C₂²⋊Q₈	—	5	16	no	—
579	C₂²⋊Q₈	—	5	32	no	—
580	C₂²⋊Q₈	—	5	32	no	—
581	#121	—	5	16	no	—
582	#121	—	5	16	no	—
583	#121	—	5	16	no	—
584	#121	—	5	16	no	—
585	#121	—	5	32	no	—
586	#121	—	5	8	no	—
587	#121	—	5	32	no	—
588	#120	—	5	32	no	—
589	#120	—	5	32	no	—
590	C₄×Q₈	—	5	8	no	—
591	C₄×Q₈	—	5	16	no	—
592	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
593	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
594	C₄×D₄	—	5	16	no	—
595	C₄×D₄	—	5	16	no	—
596	C₄×D₄	—	5	32	no	—
597	C₄×D₄	—	5	8	no	—
598	C₄×D₄	—	5	16	no	—
599	C₄×D₄	—	5	32	no	—
600	C₄×D₄	—	5	8	no	—
601	C₄×D₄	—	5	16	no	—
602	C₄×D₄	—	5	16	no	—
603	C₄×D₄	—	5	8	no	—
604	C₄×D₄	—	5	16	no	—
605	C₄×D₄	C₂²×D₅	1	16	yes	complemented
606	C₄×D₄	C₂²×D₅	1	16	yes	complemented
607	#117	—	5	32	no	—
608	#117	—	5	16	no	—
609	#117	—	5	8	no	—
610	#117	—	5	16	no	—
611	#117	—	5	16	no	—
612	C₂×C₄⋊C₄	—	5	2	no	—
613	C₂×C₄⋊C₄	—	5	2	no	—
614	C₂×C₄⋊C₄	—	5	2	no	—
615	C₂×C₄⋊C₄	—	5	2	no	—
616	C₂×C₄⋊C₄	—	5	1	no	—
617	C₂×C₄⋊C₄	—	5	2	no	—
618	C₂×C₄⋊C₄	—	5	4	no	—
619	C₂×C₄⋊C₄	—	5	1	no	—
620	C₂×C₄⋊C₄	—	5	2	no	—
621	C₂×C₄⋊C₄	—	5	4	no	—
622	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
624	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
626	C₂×C₂²⋊C₄	—	5	4	no	—
627	C₂×C₂²⋊C₄	—	5	4	no	—
628	C₂×C₂²⋊C₄	—	5	4	no	—
629	C₂×C₂²⋊C₄	—	5	2	no	—
630	C₂×C₂²⋊C₄	—	5	2	no	—
631	C₂×C₂²⋊C₄	—	5	4	no	—
632	C₂×C₂²⋊C₄	—	5	2	no	—
633	C₂×C₂²⋊C₄	—	5	2	no	—
634	C₂×C₂²⋊C₄	—	5	4	no	—
635	C₂×C₂²⋊C₄	—	5	32	no	—
636	C₂×C₂²⋊C₄	—	5	4	no	—
637	C₂×C₂²⋊C₄	—	5	2	no	—
638	C₂×C₂²⋊C₄	—	5	2	no	—
639	C₂×C₂²⋊C₄	—	5	2	no	—
640	C₂×C₂²⋊C₄	—	5	2	no	—
641	C₂×C₂²⋊C₄	—	5	32	no	—
642	C₂×C₂²⋊C₄	—	5	32	no	—
643	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
645	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
646	C₂×C₄²	—	5	2	no	—
647	C₂×C₄²	—	5	1	no	—
648	C₂×C₄²	—	5	4	no	—
649	C₂×C₄²	—	5	1	no	—
650	C₂×C₄²	—	5	2	no	—
651	C₂×C₄²	—	5	1	no	—
652	C₂×C₄²	—	5	16	no	—
653	C₂×C₄²	—	5	8	no	—
654	C₂×C₄²	C₂²×D₅	1	2	yes	—
655	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
656	C₂×C₄²	C₂²×D₅	1	2	yes	—
657	C₂²×C₅	—	2	8	no	—
658	C₂²×C₅	—	2	8	no	—
659	C₂²×C₅	—	2	8	no	—
660	C₂²×C₅	—	4	16	no	—
661	C₂²×C₅	C₂²×#41	1	2	yes	—
662	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
663	C₂²×C₅	#585	1	2	yes	—
664	C₂²×C₅	C₂⁶	1	1	yes	characteristic
665	C₂×D₅	—	2	4	no	—
666	C₂×D₅	—	2	4	no	—
667	C₂×D₅	—	2	16	no	—
668	C₂×D₅	—	2	2	no	—
669	C₂×D₅	—	2	4	no	—
670	C₂×D₅	—	2	2	no	—
671	C₂×D₅	—	2	4	no	—
672	C₂×D₅	—	2	2	no	—
673	C₂×D₅	—	2	4	no	—
674	C₂×D₅	—	4	4	no	—
675	C₂×D₅	—	4	8	no	—
676	C₂×D₅	—	8	32	no	—
677	C₂×D₅	C₂²×#41	1	8	yes	—
678	C₄×C₅	—	2	4	no	—
679	C₄×C₅	—	2	4	no	—
680	C₄×C₅	—	2	4	no	—
681	C₄×C₅	—	2	2	no	—
682	C₄×C₅	—	2	4	no	—
683	C₄×C₅	C₂²×#41	1	4	yes	—
684	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
685	Dic₅	—	2	2	no	—
686	Dic₅	—	2	4	no	—
687	Dic₅	—	2	8	no	—
688	Dic₅	—	2	4	no	—
689	Dic₅	—	2	2	no	—
690	Dic₅	—	2	2	no	—
691	C₂⁴	—	5	2	no	—
692	C₂⁴	—	5	2	no	—
693	C₂⁴	—	5	1	no	—
694	C₂⁴	—	5	16	no	—
695	C₂⁴	—	10	16	no	—
696	C₂⁴	—	20	8	no	—
697	C₂⁴	—	20	8	no	—
698	C₂⁴	C₂³×D₅	1	4	yes	—
699	#41	—	10	32	no	—
700	#41	—	20	32	no	—
701	C₂×Q₈	—	2	4	no	—
702	C₂×Q₈	—	2	4	no	—
703	C₂×Q₈	—	5	8	no	—
704	C₂×Q₈	—	5	16	no	—
705	C₂×Q₈	—	10	8	no	—
706	C₂×Q₈	—	20	8	no	—
707	C₂×Q₈	—	20	32	no	—
708	C₂×Q₈	C₂³×D₅	1	4	yes	—
709	C₂×Q₈	C₂³×D₅	1	4	yes	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	5	16	no	—
714	C₂×D₄	—	5	16	no	—
715	C₂×D₄	—	5	16	no	—
716	C₂×D₄	—	5	8	no	—
717	C₂×D₄	—	5	4	no	—
718	C₂×D₄	—	5	8	no	—
719	C₂×D₄	—	5	4	no	—
720	C₂×D₄	—	5	8	no	—
721	C₂×D₄	—	10	8	no	—
722	C₂×D₄	—	10	64	no	—
723	C₂×D₄	—	10	16	no	—
724	C₂×D₄	—	10	4	no	—
725	C₂×D₄	—	20	4	no	—
726	C₂×D₄	—	20	32	no	—
727	C₂×D₄	—	20	8	no	—
728	C₂×D₄	—	20	8	no	—
729	C₂×D₄	C₂³×D₅	1	8	yes	—
730	C₂×D₄	C₂³×D₅	1	8	yes	—
731	C₂×D₄	C₂³×D₅	1	8	yes	—
732	C₂²×C₄	—	4	8	no	—
733	C₂²×C₄	—	5	1	no	—
734	C₂²×C₄	—	5	1	no	—
735	C₂²×C₄	—	5	2	no	—
736	C₂²×C₄	—	5	1	no	—
737	C₂²×C₄	—	5	2	no	—
738	C₂²×C₄	—	5	4	no	—
739	C₂²×C₄	—	5	16	no	—
740	C₂²×C₄	—	5	8	no	—
741	C₂²×C₄	—	5	4	no	—
742	C₂²×C₄	—	5	8	no	—
743	C₂²×C₄	—	5	4	no	—
744	C₂²×C₄	—	5	8	no	—
745	C₂²×C₄	—	5	8	no	—
746	C₂²×C₄	—	5	4	no	—
747	C₂²×C₄	—	5	16	no	—
748	C₂²×C₄	—	10	8	no	—
749	C₂²×C₄	—	10	8	no	—
750	C₂²×C₄	—	10	4	no	—
751	C₂²×C₄	—	10	8	no	—
752	C₂²×C₄	—	10	4	no	—
753	C₂²×C₄	—	20	8	no	—
754	C₂²×C₄	—	20	4	no	—
755	C₂²×C₄	—	20	2	no	—
756	C₂²×C₄	—	20	8	no	—
757	C₂²×C₄	C₂³×D₅	1	2	yes	—
758	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
759	C₂²×C₄	C₂³×D₅	1	2	yes	—
760	C₂²×C₄	C₂³×D₅	1	2	yes	—
761	C₂²×C₄	C₂³×D₅	1	2	yes	—
762	C₂²×C₄	C₂³×D₅	1	16	yes	—
763	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
765	C₄⋊C₄	—	5	8	no	—
766	C₄⋊C₄	—	5	8	no	—
767	C₄⋊C₄	—	5	8	no	—
768	C₄⋊C₄	—	5	8	no	—
769	C₄⋊C₄	—	5	4	no	—
770	C₄⋊C₄	—	5	8	no	—
771	C₄⋊C₄	—	5	16	no	—
772	C₄⋊C₄	—	5	4	no	—
773	C₄⋊C₄	—	5	8	no	—
774	C₄⋊C₄	—	5	16	no	—
775	C₄⋊C₄	C₂³×D₅	1	4	yes	—
776	C₄⋊C₄	C₂³×D₅	1	8	yes	—
777	C₄⋊C₄	C₂³×D₅	1	4	yes	—
778	C₄⋊C₄	C₂³×D₅	1	8	yes	—
779	C₂²⋊C₄	—	5	16	no	—
780	C₂²⋊C₄	—	5	16	no	—
781	C₂²⋊C₄	—	5	16	no	—
782	C₂²⋊C₄	—	5	8	no	—
783	C₂²⋊C₄	—	5	8	no	—
784	C₂²⋊C₄	—	5	16	no	—
785	C₂²⋊C₄	—	5	8	no	—
786	C₂²⋊C₄	—	5	8	no	—
787	C₂²⋊C₄	—	5	16	no	—
788	C₂²⋊C₄	—	5	16	no	—
789	C₂²⋊C₄	—	5	8	no	—
790	C₂²⋊C₄	—	5	8	no	—
791	C₂²⋊C₄	—	5	8	no	—
792	C₂²⋊C₄	—	5	8	no	—
793	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
794	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
795	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
796	C₄²	—	5	4	no	—
797	C₄²	—	5	8	no	—
798	C₄²	—	5	4	no	—
799	C₄²	—	5	4	no	—
800	C₄²	—	5	8	no	—
801	C₄²	—	5	16	no	—
802	C₄²	C₂³×D₅	1	4	yes	—
803	C₄²	C₂³×D₅	1	8	yes	—
804	C₄²	C₂³×D₅	1	8	yes	—
805	C₂×C₅	—	4	8	no	—
806	C₂×C₅	#3514	1	4	yes	complemented
807	C₂×C₅	C₂³×#41	1	1	yes	characteristic
808	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
809	C₂×C₅	C₂×#585	1	1	yes	characteristic
810	D₅	—	2	8	no	—
811	D₅	—	4	2	no	—
812	D₅	—	4	4	no	—
813	C₂³	—	2	8	no	—
814	C₂³	—	2	8	no	—
815	C₂³	—	2	8	no	—
816	C₂³	—	5	8	no	—
817	C₂³	—	5	4	no	—
818	C₂³	—	5	4	no	—
819	C₂³	—	5	2	no	—
820	C₂³	—	10	32	no	—
821	C₂³	—	10	4	no	—
822	C₂³	—	10	4	no	—
823	C₂³	—	10	2	no	—
824	C₂³	—	10	4	no	—
825	C₂³	—	10	2	no	—
826	C₂³	—	10	4	no	—
827	C₂³	—	10	2	no	—
828	C₂³	—	10	4	no	—
829	C₂³	—	20	16	no	—
830	C₂³	—	20	16	no	—
831	C₂³	—	40	32	no	—
832	C₂³	C₂⁴×D₅	1	8	yes	—
833	C₂³	C₂⁴×D₅	1	1	yes	characteristic
834	Q₈	—	2	8	no	—
835	Q₈	—	2	8	no	—
836	Q₈	—	10	16	no	—
837	Q₈	—	20	16	no	—
838	D₄	—	2	16	no	—
839	D₄	—	2	16	no	—
840	D₄	—	4	8	no	—
841	D₄	—	5	16	no	—
842	D₄	—	10	16	no	—
843	D₄	—	10	32	no	—
844	D₄	—	10	8	no	—
845	D₄	—	20	8	no	—
846	D₄	—	20	16	no	—
847	D₄	—	20	16	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	16	no	—
854	C₂×C₄	—	5	2	no	—
855	C₂×C₄	—	5	2	no	—
856	C₂×C₄	—	5	4	no	—
857	C₂×C₄	—	5	2	no	—
858	C₂×C₄	—	5	4	no	—
859	C₂×C₄	—	5	8	no	—
860	C₂×C₄	—	10	16	no	—
861	C₂×C₄	—	10	2	no	—
862	C₂×C₄	—	10	4	no	—
863	C₂×C₄	—	10	2	no	—
864	C₂×C₄	—	10	4	no	—
865	C₂×C₄	—	10	8	no	—
866	C₂×C₄	—	10	2	no	—
867	C₂×C₄	—	10	16	no	—
868	C₂×C₄	—	10	8	no	—
869	C₂×C₄	—	10	16	no	—
870	C₂×C₄	—	10	8	no	—
871	C₂×C₄	—	20	16	no	—
872	C₂×C₄	—	20	8	no	—
873	C₂×C₄	—	20	4	no	—
874	C₂×C₄	—	20	16	no	—
875	C₂×C₄	D₅×#41	1	4	yes	—
876	C₂×C₄	#4149	1	4	yes	—
877	C₂×C₄	C₂⁴×D₅	1	4	yes	—
878	C₂×C₄	C₂⁴×D₅	1	2	yes	—
879	C₂×C₄	C₂⁴×D₅	1	4	yes	—
880	C₂×C₄	C₂⁴×D₅	1	4	yes	—
881	C₂×C₄	C₂⁴×D₅	1	4	yes	—
882	C₂×C₄	C₂⁴×D₅	1	2	yes	—
883	C₂×C₄	C₂⁴×D₅	1	2	yes	—
884	C₅	C₂×#3514	1	1	yes	characteristic, complemented, Sylow
885	C₂²	—	2	8	no	—
886	C₂²	—	2	8	no	—
887	C₂²	—	2	8	no	—
888	C₂²	—	4	16	no	—
889	C₂²	—	5	8	no	—
890	C₂²	—	10	4	no	—
891	C₂²	—	10	4	no	—
892	C₂²	—	10	16	no	—
893	C₂²	—	10	2	no	—
894	C₂²	—	10	4	no	—
895	C₂²	—	10	2	no	—
896	C₂²	—	10	4	no	—
897	C₂²	—	10	2	no	—
898	C₂²	—	10	4	no	—
899	C₂²	—	20	8	no	—
900	C₂²	—	20	4	no	—
901	C₂²	—	40	32	no	—
902	C₂²	C₂×D₅×#41	1	2	yes	—
903	C₂²	C₂×#4149	1	2	yes	—
904	C₂²	#66285	1	2	yes	—
905	C₂²	C₂⁵×D₅	1	1	yes	characteristic
906	C₄	—	2	4	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	10	2	no	—
912	C₄	—	10	4	no	—
913	C₄	—	10	2	no	—
914	C₄	—	10	4	no	—
915	C₄	—	10	8	no	—
916	C₄	—	10	2	no	—
917	C₄	C₂×D₅×#41	1	4	yes	—
918	C₄	C₂×#4149	1	4	yes	—
919	C₂	—	4	8	no	—
920	C₂	—	10	8	no	—
921	C₂	—	20	4	no	—
922	C₂	—	20	2	no	—
923	C₂	#10618955	1	4	yes	direct product factor
924	C₂	C₂²×D₅×#41	1	1	yes	characteristic
925	C₂	C₂²×#4149	1	1	yes	characteristic
926	C₂	C₂×#66285	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#559	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#559	D₅
hypocenter	C₅	C₂×#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#559

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#559	C₂	semidirect
2. #10618955	C₂	direct (N × H)
3. C₂×#66051	C₂	semidirect
4. C₂×#66050	C₂	semidirect
5. C₂×#66011	C₂	semidirect
6. C₂×#66010	C₂	semidirect
7. C₂×#66016	C₂	semidirect
8. C₂×D₅×#124	C₂	semidirect
9. C₂×#65992	C₂	semidirect
10. C₂×#65991	C₂	semidirect
11. C₂×Q₈×D₂₀	C₂	semidirect
12. C₂×#65914	C₂	semidirect
13. C₂×#65918	C₂	semidirect
14. C₂×C₄×#713	C₂	semidirect
15. C₂×#65888	C₂	semidirect
16. C₂×#65891	C₂	semidirect
17. C₂×#65879	C₂	semidirect
18. C₂×#65897	C₂	semidirect
20. C₂²×Q₈×D₅	C₂²	semidirect
21. C₂²×#711	C₂²	semidirect
24. C₅×#559	C₂²	semidirect
26. C₂×C₅×#124	C₂²	semidirect
27. C₂×C₅×#124	C₂²	semidirect
28. C₂×C₅×#123	C₂²	semidirect
29. C₂×C₄×C₅×Q₈	C₂²	semidirect
30. C₂×C₄×C₅×Q₈	C₂²	semidirect
31. C₂×C₄×C₅×D₄	C₂²	semidirect
32. C₂×C₄×C₅×D₄	C₂²	semidirect
34. C₂×#4092	C₂²	semidirect
35. C₂×#4092	C₂²	semidirect
36. C₂×Q₈×Dic₅	C₂²	semidirect
39. C₂×#4084	C₂²	semidirect
40. C₂×#4084	C₂²	semidirect
42. C₂×#4082	C₂²	semidirect
43. C₂×D₄×Dic₅	C₂²	semidirect
44. C₂×D₄×Dic₅	C₂²	semidirect
45. C₂×#4076	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
47. C₂²×#685	C₂²	semidirect
48. C₂×#4072	C₂²	semidirect
49. #66051	C₂²	semidirect
50. #66050	C₂²	semidirect
51. #66016	C₂²	semidirect
52. #66011	C₂²	semidirect
53. #66010	C₂²	semidirect
54. D₅×#124	C₂²	semidirect
55. #65992	C₂²	semidirect
56. #65991	C₂²	semidirect
57. #65918	C₂²	semidirect
58. #65914	C₂²	semidirect
59. Q₈×D₂₀	C₂²	semidirect
60. C₄×#713	C₂²	semidirect
61. #65897	C₂²	semidirect
62. #65891	C₂²	semidirect
63. #65888	C₂²	semidirect
64. #65879	C₂²	semidirect
65. C₂×#4044	C₂²	semidirect
66. C₂×#4044	C₂²	semidirect
67. C₂×#4043	C₂²	semidirect
68. C₂×#4043	C₂²	semidirect
70. C₂×#4040	C₂²	semidirect
72. C₂×#4039	C₂²	semidirect
73. C₂×#4038	C₂²	semidirect
74. C₂×#4038	C₂²	semidirect
75. C₂×#4038	C₂²	semidirect
76. C₂×#4036	C₂²	semidirect
77. C₂×#4032	C₂²	semidirect
78. C₂×#4031	C₂²	semidirect
79. C₂×#4031	C₂²	semidirect
80. C₂×#4031	C₂²	semidirect
81. C₂×#4030	C₂²	semidirect
82. C₂×#4029	C₂²	semidirect
83. C₂×#4028	C₂²	semidirect
84. C₂×#4027	C₂²	semidirect
85. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
86. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
87. C₂×#4025	C₂²	semidirect
88. C₂×#4024	C₂²	semidirect
93. C₂×C₄×D₂₀	C₂²	semidirect
94. C₂×C₄×D₂₀	C₂²	semidirect
95. C₂×#4018	C₂²	semidirect
96. C₂×C₄²×D₅	C₂²	semidirect
97. C₂×C₄²×D₅	C₂²	semidirect
98. C₂×#4015	C₂²	semidirect
99. C₂×#4015	C₂²	semidirect
100. C₂×C₄×Dic₁₀	C₂²	semidirect
116. C₂×Q₈×D₅	C₂³	semidirect
118. C₂×#711	C₂³	semidirect
138. C₅×#124	C₂³	semidirect
139. C₅×#124	C₂³	semidirect
140. C₅×#123	C₂³	semidirect
141. C₄×C₅×Q₈	C₂³	semidirect
142. C₄×C₅×Q₈	C₂³	semidirect
143. C₄×C₅×D₄	C₂³	semidirect
144. C₄×C₅×D₄	C₂³	semidirect
159. #4092	C₂³	semidirect
160. #4092	C₂³	semidirect
161. Q₈×Dic₅	C₂³	semidirect
164. #4084	C₂³	semidirect
165. #4084	C₂³	semidirect
167. #4082	C₂³	semidirect
168. D₄×Dic₅	C₂³	semidirect
169. D₄×Dic₅	C₂³	semidirect
170. #4076	C₂³	semidirect
171. C₄×C₂²⋊D₅	C₂³	semidirect
183. C₂×#685	C₂³	semidirect
184. #4072	C₂³	semidirect
201. #4044	C₂³	semidirect
202. #4044	C₂³	semidirect
203. #4043	C₂³	semidirect
204. #4043	C₂³	semidirect
206. #4040	C₂³	semidirect
208. #4039	C₂³	semidirect
209. #4038	C₂³	semidirect
210. #4038	C₂³	semidirect
211. #4038	C₂³	semidirect
212. #4036	C₂³	semidirect
213. #4032	C₂³	semidirect
214. #4031	C₂³	semidirect
215. #4031	C₂³	semidirect
216. #4031	C₂³	semidirect
217. #4030	C₂³	semidirect
218. #4029	C₂³	semidirect
219. #4028	C₂³	semidirect
220. #4027	C₂³	semidirect
221. D₅×C₂²⋊C₄	C₂³	semidirect
222. D₅×C₂²⋊C₄	C₂³	semidirect
223. #4025	C₂³	semidirect
224. #4024	C₂³	semidirect
229. C₄×D₂₀	C₂³	semidirect
230. C₄×D₂₀	C₂³	semidirect
231. #4018	C₂³	semidirect
232. C₄²×D₅	C₂³	semidirect
233. C₄²×D₅	C₂³	semidirect
234. #4015	C₂³	semidirect
235. #4015	C₂³	semidirect
236. C₄×Dic₁₀	C₂³	semidirect
238. C₂×#559	D₅	semidirect
304. C₂×D₂₀	#41	semidirect
374. #559	C₂×D₅	semidirect
402. C₂×#124	C₂×D₅	semidirect
403. C₂×#124	C₂×D₅	semidirect
407. C₂×#123	C₂×D₅	semidirect
426. C₂×C₄×Q₈	C₂×D₅	semidirect
427. C₂×C₄×Q₈	C₂×D₅	semidirect
439. C₂×C₄×D₄	C₂×D₅	semidirect
440. C₂×C₄×D₄	C₂×D₅	semidirect
511. D₂₀	C₂×#41	semidirect
570. #124	C₂²×D₅	semidirect
571. #124	C₂²×D₅	semidirect
575. #123	C₂²×D₅	semidirect
592. C₄×Q₈	C₂²×D₅	semidirect
593. C₄×Q₈	C₂²×D₅	semidirect
605. C₄×D₄	C₂²×D₅	semidirect
606. C₄×D₄	C₂²×D₅	semidirect
806. C₂×C₅	#3514	semidirect
884. C₅	C₂×#3514	semidirect
923. C₂	#10618955	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×#559	2
#10618955	2
C₂×#66051	2
C₂×#66050	2
C₂×#66011	2
C₂×#66010	2
C₂×#66016	2
C₂×D₅×#124	2
C₂×#65992	2
C₂×#65991	2
C₂×Q₈×D₂₀	2
C₂×#65914	2
C₂×#65918	2
C₂×C₄×#713	2
C₂×#65888	2
C₂×#65891	2
C₂×#65879	2
C₂×#65897	2
C₂×#3514	5

Subgroups — C2×#10618955 #13007395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618955 #13007395