Subgroups — #10618302

Order 640.

1150 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#66045	C₂	1	1	yes	maximal, characteristic, complemented
3	#66040	C₂	1	1	yes	maximal, characteristic, complemented
4	#66038	C₂	1	1	yes	maximal, characteristic, complemented
5	#66036	C₂	1	1	yes	maximal, characteristic, complemented
6	#66012	C₂	1	1	yes	maximal, characteristic, complemented
7	#66008	C₂	1	1	yes	maximal, characteristic, complemented
8	#66003	C₂	1	1	yes	maximal, characteristic, complemented
9	#66002	C₂	1	1	yes	maximal, characteristic, complemented
10	#66000	C₂	1	1	yes	maximal, characteristic, complemented
11	#65995	C₂	1	1	yes	maximal, characteristic, complemented
12	#65989	C₂	1	1	yes	maximal, characteristic, complemented
13	#65988	C₂	1	1	yes	maximal, characteristic, complemented
14	#65974	C₂	1	1	yes	maximal, characteristic, complemented
15	#65963	C₂	1	1	yes	maximal, characteristic, complemented
16	#65954	C₂	1	1	yes	maximal, characteristic, complemented
17	#65944	C₂	1	1	yes	maximal, characteristic, complemented
18	#65941	C₂	1	1	yes	maximal, characteristic, complemented
19	#65933	C₂	1	1	yes	maximal, characteristic, complemented
20	#65933	C₂	1	1	yes	maximal, characteristic, complemented
21	#65931	C₂	1	1	yes	maximal, characteristic, complemented
22	#65929	C₂	1	1	yes	maximal, characteristic, complemented
23	#65926	C₂	1	1	yes	maximal, characteristic, complemented
24	#65926	C₂	1	1	yes	maximal, characteristic, complemented
25	#65924	C₂	1	1	yes	maximal, characteristic, complemented
26	#65894	C₂	1	1	yes	maximal, characteristic, complemented
27	#65887	C₂	1	1	yes	maximal, characteristic, complemented
28	#65882	C₂	1	1	yes	maximal, characteristic, complemented
29	#65874	C₂	1	1	yes	maximal, characteristic, complemented
30	#65824	C₂	1	1	yes	maximal, characteristic, complemented
31	#65824	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₅	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊D₅	C₂²	1	1	yes	characteristic
34	C₂×#713	C₂²	1	1	yes	characteristic, complemented
35	C₂×#711	C₂²	1	1	yes	characteristic, complemented
36	C₂×#711	C₂²	1	1	yes	characteristic, complemented
37	C₂×#711	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
40	C₂×#709	C₂²	1	1	yes	characteristic, complemented
41	C₂×#709	C₂²	1	1	yes	characteristic, complemented
42	C₂×#709	C₂²	1	1	yes	characteristic, complemented
43	C₂×#709	C₂²	1	1	yes	characteristic, complemented
44	C₅×#126	C₂²	1	1	yes	characteristic, complemented
45	C₅×#126	C₂²	1	1	yes	characteristic, complemented
46	C₅×#124	C₂²	1	1	yes	characteristic, complemented
47	C₅×#124	C₂²	1	1	yes	characteristic, complemented
48	C₅×#123	C₂²	1	1	yes	characteristic, complemented
49	C₅×#123	C₂²	1	1	yes	characteristic, complemented
50	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₅×#121	C₂²	1	1	yes	characteristic, complemented
52	C₅×#121	C₂²	1	1	yes	characteristic, complemented
53	C₅×#121	C₂²	1	1	yes	characteristic, complemented
54	C₅×#120	C₂²	1	1	yes	characteristic
55	C₅×#120	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	#4099	C₂²	1	1	yes	characteristic, complemented
60	#4099	C₂²	1	1	yes	characteristic, complemented
61	#4093	C₂²	1	1	yes	characteristic, complemented
62	#4092	C₂²	1	1	yes	characteristic, complemented
63	#4090	C₂²	1	1	yes	characteristic, complemented
64	#4086	C₂²	1	1	yes	characteristic
65	#4086	C₂²	1	1	yes	characteristic
66	#4086	C₂²	1	1	yes	characteristic, complemented
67	#4086	C₂²	1	1	yes	characteristic, complemented
68	#4086	C₂²	1	1	yes	characteristic, complemented
69	#4086	C₂²	1	1	yes	characteristic, complemented
70	#4086	C₂²	1	1	yes	characteristic, complemented
71	#4085	C₂²	1	1	yes	characteristic
72	#4085	C₂²	1	1	yes	characteristic
73	#4085	C₂²	1	1	yes	characteristic
74	#4085	C₂²	1	1	yes	characteristic, complemented
75	#4085	C₂²	1	1	yes	characteristic, complemented
76	#4085	C₂²	1	1	yes	characteristic, complemented
77	#4085	C₂²	1	1	yes	characteristic, complemented
78	#4085	C₂²	1	1	yes	characteristic, complemented
79	#4085	C₂²	1	1	yes	characteristic, complemented
80	#4084	C₂²	1	1	yes	characteristic, complemented
81	#4084	C₂²	1	1	yes	characteristic, complemented
82	#4083	C₂²	1	1	yes	characteristic
83	#4083	C₂²	1	1	yes	characteristic, complemented
84	#4083	C₂²	1	1	yes	characteristic, complemented
85	#4083	C₂²	1	1	yes	characteristic, complemented
86	#4081	C₂²	1	1	yes	characteristic, complemented
87	#4076	C₂²	1	1	yes	characteristic, complemented
88	#4076	C₂²	1	1	yes	characteristic, complemented
89	#4076	C₂²	1	1	yes	characteristic, complemented
90	#4076	C₂²	1	1	yes	characteristic, complemented
91	#4075	C₂²	1	1	yes	characteristic, complemented
92	#4075	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
97	C₂×#685	C₂²	1	1	yes	characteristic, complemented
98	C₂×#683	C₂²	1	1	yes	characteristic, complemented
99	#4044	C₂²	1	1	yes	characteristic, complemented
100	#4044	C₂²	1	1	yes	characteristic, complemented
101	#4044	C₂²	1	1	yes	characteristic, complemented
102	#4042	C₂²	1	1	yes	characteristic, complemented
103	#4042	C₂²	1	1	yes	characteristic, complemented
104	#4042	C₂²	1	1	yes	characteristic, complemented
105	#4042	C₂²	1	1	yes	characteristic, complemented
106	#4041	C₂²	1	1	yes	characteristic, complemented
107	#4041	C₂²	1	1	yes	characteristic, complemented
108	#4041	C₂²	1	1	yes	characteristic, complemented
109	#4041	C₂²	1	1	yes	characteristic, complemented
110	#4041	C₂²	1	1	yes	characteristic, complemented
111	#4040	C₂²	1	1	yes	characteristic, complemented
112	#4040	C₂²	1	1	yes	characteristic, complemented
113	#4040	C₂²	1	1	yes	characteristic, complemented
114	#4040	C₂²	1	1	yes	characteristic, complemented
115	#4039	C₂²	1	1	yes	characteristic, complemented
116	#4039	C₂²	1	1	yes	characteristic, complemented
117	#4038	C₂²	1	1	yes	characteristic, complemented
118	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	#4035	C₂²	1	1	yes	characteristic, complemented
120	#4034	C₂²	1	1	yes	characteristic, complemented
121	#4033	C₂²	1	1	yes	characteristic, complemented
122	#4033	C₂²	1	1	yes	characteristic, complemented
123	#4032	C₂²	1	1	yes	characteristic, complemented
124	#4031	C₂²	1	1	yes	characteristic
125	#4031	C₂²	1	1	yes	characteristic
126	#4031	C₂²	1	1	yes	characteristic
127	#4031	C₂²	1	1	yes	characteristic, complemented
128	#4031	C₂²	1	1	yes	characteristic, complemented
129	#4031	C₂²	1	1	yes	characteristic, complemented
130	#4031	C₂²	1	1	yes	characteristic, complemented
131	#4030	C₂²	1	1	yes	characteristic
132	#4030	C₂²	1	1	yes	characteristic
133	#4030	C₂²	1	1	yes	characteristic
134	#4030	C₂²	1	1	yes	characteristic
135	#4030	C₂²	1	1	yes	characteristic
136	#4030	C₂²	1	1	yes	characteristic, complemented
137	#4030	C₂²	1	1	yes	characteristic, complemented
138	#4030	C₂²	1	1	yes	characteristic, complemented
139	#4030	C₂²	1	1	yes	characteristic, complemented
140	#4030	C₂²	1	1	yes	characteristic, complemented
141	#4030	C₂²	1	1	yes	characteristic, complemented
142	#4030	C₂²	1	1	yes	characteristic, complemented
143	#4030	C₂²	1	1	yes	characteristic, complemented
144	#4030	C₂²	1	1	yes	characteristic, complemented
145	#4030	C₂²	1	1	yes	characteristic, complemented
146	#4030	C₂²	1	1	yes	characteristic, complemented
147	#4030	C₂²	1	1	yes	characteristic, complemented
148	#4030	C₂²	1	1	yes	characteristic, complemented
149	#4029	C₂²	1	1	yes	characteristic, complemented
150	#4029	C₂²	1	1	yes	characteristic, complemented
151	#4029	C₂²	1	1	yes	characteristic, complemented
152	#4029	C₂²	1	1	yes	characteristic, complemented
153	#4028	C₂²	1	1	yes	characteristic
154	#4028	C₂²	1	1	yes	characteristic
155	#4028	C₂²	1	1	yes	characteristic, complemented
156	#4028	C₂²	1	1	yes	characteristic, complemented
157	#4028	C₂²	1	1	yes	characteristic, complemented
158	#4028	C₂²	1	1	yes	characteristic, complemented
159	#4028	C₂²	1	1	yes	characteristic, complemented
160	#4028	C₂²	1	1	yes	characteristic, complemented
161	#4027	C₂²	1	1	yes	characteristic
162	#4027	C₂²	1	1	yes	characteristic
163	#4027	C₂²	1	1	yes	characteristic, complemented
164	#4027	C₂²	1	1	yes	characteristic, complemented
165	#4027	C₂²	1	1	yes	characteristic, complemented
166	#4027	C₂²	1	1	yes	characteristic, complemented
167	#4027	C₂²	1	1	yes	characteristic, complemented
168	#4027	C₂²	1	1	yes	characteristic, complemented
169	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
171	#4025	C₂²	1	1	yes	characteristic, complemented
172	#4025	C₂²	1	1	yes	characteristic, complemented
173	#4025	C₂²	1	1	yes	characteristic, complemented
174	#4024	C₂²	1	1	yes	characteristic, complemented
175	#4024	C₂²	1	1	yes	characteristic, complemented
176	#4024	C₂²	1	1	yes	characteristic, complemented
177	#4023	C₂²	1	1	yes	characteristic, complemented
178	#4023	C₂²	1	1	yes	characteristic, complemented
179	#4022	C₂²	1	1	yes	characteristic, complemented
180	#4022	C₂²	1	1	yes	characteristic, complemented
181	#4021	C₂²	1	1	yes	characteristic, complemented
182	#4020	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
184	#4018	C₂²	1	1	yes	characteristic, complemented
185	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
187	#3546	—	5	1	no	maximal, Sylow
188	C₂⁴×C₅	C₂³	1	1	yes	characteristic
189	C₂³×D₅	C₂³	1	1	yes	characteristic
190	C₂³×D₅	C₂³	1	1	yes	characteristic
191	C₂³×D₅	C₂³	1	1	yes	characteristic
192	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
195	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
199	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₅	—	4	2	no	—
205	C₂×C₂²⋊D₅	—	4	2	no	—
206	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
230	C₂²×Dic₅	C₂³	1	1	yes	characteristic
231	C₂²×Dic₅	C₂³	1	1	yes	characteristic
232	C₂²×Dic₅	C₂³	1	1	yes	characteristic
233	C₂²×Dic₅	C₂³	1	1	yes	characteristic
234	C₂²×Dic₅	C₂³	1	1	yes	characteristic
235	#713	—	4	2	no	—
236	#711	—	4	2	no	—
237	#711	—	4	2	no	—
238	#711	—	4	2	no	—
239	D₄×D₅	—	4	2	no	—
240	D₄×D₅	—	4	2	no	—
241	#709	—	4	2	no	—
242	#709	—	4	2	no	—
243	#709	—	4	2	no	—
244	#709	—	4	2	no	—
245	C₂×D₂₀	C₂³	1	1	yes	characteristic
246	C₂×D₂₀	C₂³	1	1	yes	characteristic
247	C₂×D₂₀	C₂³	1	1	yes	characteristic
248	C₂×D₂₀	C₂³	1	1	yes	characteristic
249	C₂×D₂₀	C₂³	1	1	yes	characteristic
250	C₂×D₂₀	C₂³	1	1	yes	characteristic
251	C₂×D₂₀	C₂³	1	1	yes	characteristic
252	C₂×D₂₀	C₂³	1	1	yes	characteristic
253	C₂×D₂₀	C₂³	1	1	yes	characteristic
254	C₂×D₂₀	C₂³	1	1	yes	characteristic
255	C₂×D₂₀	C₂³	1	1	yes	characteristic
256	C₂×D₂₀	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
264	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
265	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
266	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
267	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
268	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
269	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
270	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
271	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
272	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
273	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₄²×C₅	C₂³	1	1	yes	characteristic
294	C₄²×C₅	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
297	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
298	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
299	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
300	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
301	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
302	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
303	#685	C₂³	1	1	yes	characteristic
304	#685	C₂³	1	1	yes	characteristic
305	#685	C₂³	1	1	yes	characteristic
306	#685	C₂³	1	1	yes	characteristic
307	#685	C₂³	1	1	yes	characteristic
308	#685	C₂³	1	1	yes	characteristic
309	#685	C₂³	1	1	yes	characteristic
310	#685	C₂³	1	1	yes	characteristic
311	#685	C₂³	1	1	yes	characteristic
312	#685	C₂³	1	1	yes	characteristic
313	#685	C₂³	1	1	yes	characteristic
314	#685	C₂³	1	1	yes	characteristic
315	#685	C₂³	1	1	yes	characteristic
316	#685	C₂³	1	1	yes	characteristic
317	#685	C₂³	1	1	yes	characteristic
318	#685	C₂³	1	1	yes	characteristic
319	#685	C₂³	1	1	yes	characteristic
320	#685	C₂³	1	1	yes	characteristic
321	#685	C₂³	1	1	yes	characteristic
322	#685	C₂³	1	1	yes	characteristic
323	#685	C₂³	1	1	yes	characteristic
324	#685	C₂³	1	1	yes	characteristic
325	#685	C₂³	1	1	yes	characteristic
326	#685	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
331	#683	C₂³	1	1	yes	characteristic
332	#683	C₂³	1	1	yes	characteristic
333	#683	C₂³	1	1	yes	characteristic
334	#683	C₂³	1	1	yes	characteristic
335	#683	C₂³	1	1	yes	characteristic
336	#683	C₂³	1	1	yes	characteristic
337	#683	C₂³	1	1	yes	characteristic
338	#683	C₂³	1	1	yes	characteristic
339	#683	C₂³	1	1	yes	characteristic
340	#683	C₂³	1	1	yes	characteristic
341	#683	C₂³	1	1	yes	characteristic
342	#683	C₂³	1	1	yes	characteristic
343	#683	C₂³	1	1	yes	characteristic
344	#683	C₂³	1	1	yes	characteristic
345	#683	C₂³	1	1	yes	characteristic
346	#683	C₂³	1	1	yes	characteristic
347	C₄×Dic₅	C₂³	1	1	yes	characteristic
348	C₄×Dic₅	C₂³	1	1	yes	characteristic
349	C₄×Dic₅	C₂³	1	1	yes	characteristic
350	C₄×Dic₅	C₂³	1	1	yes	characteristic
351	C₄×Dic₅	C₂³	1	1	yes	characteristic
352	C₄×Dic₅	C₂³	1	1	yes	characteristic
353	C₄×Dic₅	C₂³	1	1	yes	characteristic
354	C₄×Dic₅	C₂³	1	1	yes	characteristic
355	#560	—	5	1	no	—
356	#560	—	5	1	no	—
357	#560	—	5	1	no	—
358	#560	—	5	1	no	—
359	#556	—	5	1	no	—
360	#553	—	5	1	no	—
361	#553	—	5	1	no	—
362	#550	—	5	1	no	—
363	#550	—	5	1	no	—
364	#550	—	5	1	no	—
365	#547	—	5	1	no	—
366	#546	—	5	1	no	—
367	#546	—	5	1	no	—
368	#546	—	5	1	no	—
369	#546	—	5	1	no	—
370	D₄²	—	5	1	no	—
371	#542	—	5	1	no	—
372	#542	—	5	1	no	—
373	#538	—	5	1	no	—
374	#538	—	5	1	no	—
375	#538	—	5	1	no	—
376	#538	D₅	1	1	yes	characteristic, complemented
377	#537	—	5	1	no	—
378	#537	—	5	1	no	—
379	#535	—	5	1	no	—
380	#535	—	5	1	no	—
381	#535	—	5	1	no	—
382	#535	—	5	1	no	—
383	#532	—	5	1	no	—
384	#532	—	5	1	no	—
385	#529	—	5	1	no	—
386	C₂³×C₅	—	4	1	no	—
387	C₂³×C₅	—	4	1	no	—
388	C₂³×C₅	—	4	1	no	—
389	C₂³×C₅	C₂⁴	1	1	yes	characteristic
390	C₂³×C₅	C₂⁴	1	1	yes	characteristic
391	C₂³×C₅	C₂⁴	1	1	yes	characteristic
392	C₂³×C₅	C₂⁴	1	1	yes	characteristic
393	C₂³×C₅	C₂⁴	1	1	yes	characteristic
394	C₂²×D₅	—	4	1	no	—
395	C₂²×D₅	—	4	1	no	—
396	C₂²×D₅	—	4	1	no	—
397	C₂²×D₅	—	4	1	no	—
398	C₂²×D₅	—	4	1	no	—
399	C₂²×D₅	—	4	1	no	—
400	C₂²×D₅	—	4	1	no	—
401	C₂²×D₅	—	4	1	no	—
402	C₂²×D₅	—	4	1	no	—
403	C₂²×D₅	C₂⁴	1	1	yes	characteristic
404	C₂²×D₅	C₂⁴	1	1	yes	characteristic
405	C₂²×D₅	C₂⁴	1	1	yes	characteristic
406	C₂²×D₅	C₂⁴	1	1	yes	characteristic
407	C₂²×D₅	C₂⁴	1	1	yes	characteristic
408	C₂²×D₅	C₂⁴	1	1	yes	characteristic
409	C₅×Q₈	—	4	1	no	—
410	C₅×D₄	—	4	1	no	—
411	C₅×D₄	—	4	1	no	—
412	C₅×D₄	—	4	1	no	—
413	C₅×D₄	—	4	1	no	—
414	C₅×D₄	—	4	1	no	—
415	C₅×D₄	—	4	1	no	—
416	C₅×D₄	—	4	1	no	—
417	C₂×C₄×C₅	—	4	1	no	—
418	C₂×C₄×C₅	—	4	1	no	—
419	C₂×C₄×C₅	—	4	1	no	—
420	C₂×C₄×C₅	—	4	1	no	—
421	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
426	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
427	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
428	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
431	C₂²⋊D₅	—	2	2	no	—
432	C₂²⋊D₅	—	2	2	no	—
433	C₂²⋊D₅	—	2	2	no	—
434	C₂²⋊D₅	—	2	2	no	—
435	C₂²⋊D₅	—	2	2	no	—
436	C₂²⋊D₅	—	2	2	no	—
437	C₂²⋊D₅	—	2	2	no	—
438	C₂²⋊D₅	—	4	1	no	—
439	C₂²⋊D₅	—	4	1	no	—
440	C₂²⋊D₅	—	4	1	no	—
441	C₂²⋊D₅	—	4	1	no	—
442	C₂²⋊D₅	—	4	1	no	—
443	C₂²⋊D₅	—	4	1	no	—
444	C₂²⋊D₅	—	4	1	no	—
445	C₂²⋊D₅	—	4	1	no	—
446	C₂²⋊D₅	—	4	1	no	—
447	C₂²⋊D₅	—	4	1	no	—
448	C₂²⋊D₅	—	4	1	no	—
449	C₂²⋊D₅	—	4	1	no	—
450	C₂²⋊D₅	—	4	1	no	—
451	C₂²⋊D₅	—	4	1	no	—
452	C₂²⋊D₅	—	4	1	no	—
453	C₂²⋊D₅	—	4	1	no	—
454	C₂²⋊D₅	—	4	1	no	—
455	C₂×Dic₅	—	2	2	no	—
456	C₂×Dic₅	—	2	2	no	—
457	C₂×Dic₅	—	2	2	no	—
458	C₂×Dic₅	—	4	1	no	—
459	C₂×Dic₅	—	4	1	no	—
460	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
461	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
462	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
463	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
464	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
465	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
466	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
467	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
468	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
469	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
470	D₂₀	—	4	1	no	—
471	D₂₀	—	4	1	no	—
472	D₂₀	—	4	1	no	—
473	D₂₀	—	4	1	no	—
474	D₂₀	—	4	1	no	—
475	D₂₀	—	4	1	no	—
476	D₂₀	—	4	1	no	—
477	D₂₀	—	4	1	no	—
478	D₂₀	—	4	1	no	—
479	D₂₀	—	4	1	no	—
480	D₂₀	—	4	1	no	—
481	D₂₀	—	4	1	no	—
482	C₄×D₅	—	2	2	no	—
483	C₄×D₅	—	2	2	no	—
484	C₄×D₅	—	2	2	no	—
485	C₄×D₅	—	2	2	no	—
486	C₄×D₅	—	2	2	no	—
487	C₄×D₅	—	4	1	no	—
488	C₄×D₅	—	4	1	no	—
489	C₄×D₅	—	4	1	no	—
490	C₄×D₅	—	4	1	no	—
491	C₄×D₅	—	4	1	no	—
492	C₄×D₅	—	4	1	no	—
493	C₄×D₅	—	4	1	no	—
494	Dic₁₀	—	2	2	no	—
495	Dic₁₀	—	2	2	no	—
496	Dic₁₀	—	2	2	no	—
497	Dic₁₀	—	4	1	no	—
498	C₂×#41	—	5	1	no	—
499	C₂×#41	—	5	1	no	—
500	C₂×#41	—	5	1	no	—
501	C₂×#41	—	5	1	no	—
502	C₂×#41	—	5	1	no	—
503	C₂×#41	—	5	1	no	—
504	C₂×#41	—	5	1	no	—
505	C₂×#41	—	5	1	no	—
506	C₂²×D₄	—	5	1	no	—
507	C₂²×D₄	—	5	1	no	—
508	C₂²×D₄	—	5	1	no	—
509	C₂²×D₄	—	5	1	no	—
510	C₄⋊Q₈	—	5	1	no	—
511	C₄⋊Q₈	—	5	1	no	—
512	#127	—	5	1	no	—
513	#127	—	5	1	no	—
514	#127	—	5	1	no	—
515	#127	—	5	1	no	—
516	#127	—	5	1	no	—
517	#127	—	5	1	no	—
518	#127	—	5	1	no	—
519	#127	—	5	1	no	—
520	#126	—	5	1	no	—
521	#126	—	5	1	no	—
522	#126	—	5	1	no	—
523	#126	—	5	1	no	—
524	#126	—	5	1	no	—
525	#126	—	5	1	no	—
526	#126	—	5	1	no	—
527	#126	—	5	1	no	—
528	#126	C₂×D₅	1	1	yes	characteristic, complemented
529	#126	C₂×D₅	1	1	yes	characteristic, complemented
530	#125	—	5	1	no	—
531	#124	—	5	1	no	—
532	#124	—	5	1	no	—
533	#124	—	5	1	no	—
534	#124	—	5	1	no	—
535	#124	—	5	1	no	—
536	#124	—	5	1	no	—
537	#124	—	5	1	no	—
538	#124	—	5	1	no	—
539	#124	—	5	1	no	—
540	#124	C₂×D₅	1	1	yes	characteristic, complemented
541	#124	C₂×D₅	1	1	yes	characteristic, complemented
542	#123	—	5	1	no	—
543	#123	—	5	1	no	—
544	#123	—	5	1	no	—
545	#123	—	5	1	no	—
546	#123	—	5	1	no	—
547	#123	—	5	1	no	—
548	#123	—	5	1	no	—
549	#123	—	5	1	no	—
550	#123	—	5	1	no	—
551	#123	—	5	1	no	—
552	#123	—	5	1	no	—
553	#123	—	5	1	no	—
554	#123	C₂×D₅	1	1	yes	characteristic, complemented
555	#123	C₂×D₅	1	1	yes	characteristic, complemented
556	C₂²⋊Q₈	—	5	1	no	—
557	C₂²⋊Q₈	—	5	1	no	—
558	C₂²⋊Q₈	—	5	1	no	—
559	C₂²⋊Q₈	—	5	1	no	—
560	C₂²⋊Q₈	—	5	1	no	—
561	C₂²⋊Q₈	—	5	1	no	—
562	C₂²⋊Q₈	—	5	1	no	—
563	C₂²⋊Q₈	—	5	1	no	—
564	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
565	#121	—	5	1	no	—
566	#121	—	5	1	no	—
567	#121	—	5	1	no	—
568	#121	—	5	1	no	—
569	#121	—	5	1	no	—
570	#121	—	5	1	no	—
571	#121	—	5	1	no	—
572	#121	—	5	1	no	—
573	#121	—	5	1	no	—
574	#121	—	5	1	no	—
575	#121	—	5	1	no	—
576	#121	—	5	1	no	—
577	#121	—	5	1	no	—
578	#121	—	5	1	no	—
579	#121	—	5	1	no	—
580	#121	—	5	1	no	—
581	#121	—	5	1	no	—
582	#121	—	5	1	no	—
583	#121	—	5	1	no	—
584	#121	—	5	1	no	—
585	#121	—	5	1	no	—
586	#121	—	5	1	no	—
587	#121	—	5	1	no	—
588	#121	—	5	1	no	—
589	#121	—	5	1	no	—
590	#121	—	5	1	no	—
591	#121	—	5	1	no	—
592	#121	—	5	1	no	—
593	#121	—	5	1	no	—
594	#121	—	5	1	no	—
595	#121	—	5	1	no	—
596	#121	—	5	1	no	—
597	#121	—	5	1	no	—
598	#121	—	5	1	no	—
599	#121	—	5	1	no	—
600	#121	—	5	1	no	—
601	#121	—	5	1	no	—
602	#121	—	5	1	no	—
603	#121	C₂×D₅	1	1	yes	characteristic, complemented
604	#121	C₂×D₅	1	1	yes	characteristic, complemented
605	#121	C₂×D₅	1	1	yes	characteristic, complemented
606	#120	—	5	1	no	—
607	#120	—	5	1	no	—
608	#120	—	5	1	no	—
609	#120	—	5	1	no	—
610	#120	—	5	1	no	—
611	#120	—	5	1	no	—
612	#120	—	5	1	no	—
613	#120	—	5	1	no	—
614	#120	—	5	1	no	—
615	#120	—	5	1	no	—
616	#120	—	5	1	no	—
617	#120	—	5	1	no	—
618	#120	—	5	1	no	—
619	#120	—	5	1	no	—
620	#120	C₂×D₅	1	1	yes	characteristic
621	#120	C₂×D₅	1	1	yes	characteristic, complemented
622	C₄×Q₈	—	5	1	no	—
623	C₄×Q₈	—	5	1	no	—
624	C₄×Q₈	—	5	1	no	—
625	C₄×D₄	—	5	1	no	—
626	C₄×D₄	—	5	1	no	—
627	C₄×D₄	—	5	1	no	—
628	C₄×D₄	—	5	1	no	—
629	C₄×D₄	—	5	1	no	—
630	C₄×D₄	—	5	1	no	—
631	C₄×D₄	—	5	1	no	—
632	C₄×D₄	—	5	1	no	—
633	C₄×D₄	—	5	1	no	—
634	C₄×D₄	—	5	1	no	—
635	C₄×D₄	—	5	1	no	—
636	C₄×D₄	—	5	1	no	—
637	C₄×D₄	—	5	1	no	—
638	C₄×D₄	—	5	1	no	—
639	C₄×D₄	—	5	1	no	—
640	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
641	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
642	#117	—	5	1	no	—
643	#117	—	5	1	no	—
644	#117	—	5	1	no	—
645	#117	—	5	1	no	—
646	C₂×C₄⋊C₄	—	5	1	no	—
647	C₂×C₄⋊C₄	—	5	1	no	—
648	C₂×C₂²⋊C₄	—	5	1	no	—
649	C₂×C₂²⋊C₄	—	5	1	no	—
650	C₂×C₂²⋊C₄	—	5	1	no	—
651	C₂×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
652	C₂×C₄²	—	5	1	no	—
653	C₂²×C₅	—	2	1	no	—
654	C₂²×C₅	—	2	1	no	—
655	C₂²×C₅	—	2	1	no	—
656	C₂²×C₅	—	2	1	no	—
657	C₂²×C₅	—	2	1	no	—
658	C₂²×C₅	—	2	1	no	—
659	C₂²×C₅	—	2	1	no	—
660	C₂²×C₅	—	2	1	no	—
661	C₂²×C₅	—	2	1	no	—
662	C₂²×C₅	—	2	1	no	—
663	C₂²×C₅	—	2	1	no	—
664	C₂²×C₅	—	2	1	no	—
665	C₂²×C₅	—	2	1	no	—
666	C₂²×C₅	—	2	1	no	—
667	C₂²×C₅	—	2	1	no	—
668	C₂²×C₅	—	8	2	no	—
669	C₂²×C₅	C₂⁵	1	1	yes	characteristic
670	C₂×D₅	—	2	1	no	—
671	C₂×D₅	—	2	1	no	—
672	C₂×D₅	—	2	1	no	—
673	C₂×D₅	—	2	1	no	—
674	C₂×D₅	—	2	1	no	—
675	C₂×D₅	—	2	1	no	—
676	C₂×D₅	—	2	1	no	—
677	C₂×D₅	—	2	1	no	—
678	C₂×D₅	—	2	1	no	—
679	C₂×D₅	—	2	1	no	—
680	C₂×D₅	—	2	1	no	—
681	C₂×D₅	—	2	1	no	—
682	C₂×D₅	—	2	1	no	—
683	C₂×D₅	—	2	1	no	—
684	C₂×D₅	—	2	1	no	—
685	C₂×D₅	—	2	1	no	—
686	C₂×D₅	—	2	1	no	—
687	C₂×D₅	—	2	1	no	—
688	C₂×D₅	—	8	2	no	—
689	C₂×D₅	—	8	2	no	—
690	C₂×D₅	—	8	2	no	—
691	C₄×C₅	—	2	1	no	—
692	C₄×C₅	—	2	1	no	—
693	C₄×C₅	—	2	1	no	—
694	C₄×C₅	—	2	1	no	—
695	C₄×C₅	—	2	1	no	—
696	C₄×C₅	—	2	1	no	—
697	C₄×C₅	—	2	1	no	—
698	C₄×C₅	—	2	1	no	—
699	C₄×C₅	—	2	1	no	—
700	C₄×C₅	—	2	1	no	—
701	Dic₅	—	2	1	no	—
702	Dic₅	—	2	1	no	—
703	Dic₅	—	2	1	no	—
704	Dic₅	—	2	1	no	—
705	Dic₅	—	2	1	no	—
706	Dic₅	—	2	1	no	—
707	Dic₅	—	2	1	no	—
708	Dic₅	—	2	1	no	—
709	Dic₅	H(5,𝔽₂)	1	2	yes	—
710	Dic₅	H(5,𝔽₂)	1	2	yes	—
711	C₂⁴	—	5	1	no	—
712	C₂⁴	—	5	1	no	—
713	C₂⁴	—	5	1	no	—
714	C₂⁴	C₂²×D₅	1	1	yes	characteristic
715	#41	—	20	2	no	—
716	#41	—	20	2	no	—
717	#41	—	20	2	no	—
718	#41	—	20	2	no	—
719	#41	—	20	2	no	—
720	#41	—	20	2	no	—
721	#41	—	20	2	no	—
722	#41	—	20	2	no	—
723	C₂×Q₈	—	5	1	no	—
724	C₂×Q₈	—	5	1	no	—
725	C₂×Q₈	—	5	1	no	—
726	C₂×Q₈	—	5	1	no	—
727	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
728	C₂×D₄	—	5	1	no	—
729	C₂×D₄	—	5	1	no	—
730	C₂×D₄	—	5	1	no	—
731	C₂×D₄	—	5	1	no	—
732	C₂×D₄	—	5	1	no	—
733	C₂×D₄	—	5	1	no	—
734	C₂×D₄	—	5	1	no	—
735	C₂×D₄	—	5	1	no	—
736	C₂×D₄	—	5	1	no	—
737	C₂×D₄	—	5	1	no	—
738	C₂×D₄	—	5	1	no	—
739	C₂×D₄	—	5	1	no	—
740	C₂×D₄	—	5	1	no	—
741	C₂×D₄	—	5	1	no	—
742	C₂×D₄	—	5	1	no	—
743	C₂×D₄	—	5	1	no	—
744	C₂×D₄	—	5	1	no	—
745	C₂×D₄	—	5	1	no	—
746	C₂×D₄	—	5	1	no	—
747	C₂×D₄	—	5	1	no	—
748	C₂×D₄	—	5	1	no	—
749	C₂×D₄	—	5	1	no	—
750	C₂×D₄	—	5	1	no	—
751	C₂×D₄	—	5	1	no	—
752	C₂×D₄	—	5	1	no	—
753	C₂×D₄	—	5	1	no	—
754	C₂×D₄	—	5	1	no	—
755	C₂×D₄	—	5	1	no	—
756	C₂×D₄	—	5	1	no	—
757	C₂×D₄	—	5	1	no	—
758	C₂×D₄	—	5	1	no	—
759	C₂×D₄	—	5	1	no	—
760	C₂×D₄	—	5	1	no	—
761	C₂×D₄	—	5	1	no	—
762	C₂×D₄	—	5	1	no	—
763	C₂×D₄	—	5	1	no	—
764	C₂×D₄	—	20	2	no	—
765	C₂×D₄	—	20	2	no	—
766	C₂×D₄	—	20	2	no	—
767	C₂×D₄	—	20	2	no	—
768	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
769	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
770	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
771	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
772	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
773	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
774	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
775	C₂²×C₄	—	5	1	no	—
776	C₂²×C₄	—	5	1	no	—
777	C₂²×C₄	—	5	1	no	—
778	C₂²×C₄	—	5	1	no	—
779	C₂²×C₄	—	5	1	no	—
780	C₂²×C₄	—	5	1	no	—
781	C₂²×C₄	—	5	1	no	—
782	C₂²×C₄	—	5	1	no	—
783	C₂²×C₄	—	5	1	no	—
784	C₂²×C₄	—	5	1	no	—
785	C₂²×C₄	—	5	1	no	—
786	C₂²×C₄	—	5	1	no	—
787	C₂²×C₄	—	5	1	no	—
788	C₂²×C₄	—	5	1	no	—
789	C₂²×C₄	—	5	1	no	—
790	C₂²×C₄	—	5	1	no	—
791	C₂²×C₄	—	5	1	no	—
792	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
793	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
794	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
795	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
796	C₄⋊C₄	—	5	1	no	—
797	C₄⋊C₄	—	5	1	no	—
798	C₄⋊C₄	—	5	1	no	—
799	C₄⋊C₄	—	5	1	no	—
800	C₄⋊C₄	—	5	1	no	—
801	C₄⋊C₄	—	5	1	no	—
802	C₄⋊C₄	—	5	1	no	—
803	C₄⋊C₄	—	5	1	no	—
804	C₄⋊C₄	—	5	1	no	—
805	C₄⋊C₄	—	5	1	no	—
806	C₄⋊C₄	—	5	1	no	—
807	C₄⋊C₄	—	5	1	no	—
808	C₄⋊C₄	—	5	1	no	—
809	C₄⋊C₄	—	5	1	no	—
810	C₄⋊C₄	—	5	1	no	—
811	C₄⋊C₄	—	5	1	no	—
812	C₄⋊C₄	—	5	1	no	—
813	C₄⋊C₄	—	5	1	no	—
814	C₄⋊C₄	—	5	1	no	—
815	C₄⋊C₄	—	5	1	no	—
816	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
817	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
818	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
819	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
820	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
822	C₂²⋊C₄	—	5	1	no	—
823	C₂²⋊C₄	—	5	1	no	—
824	C₂²⋊C₄	—	5	1	no	—
825	C₂²⋊C₄	—	5	1	no	—
826	C₂²⋊C₄	—	5	1	no	—
827	C₂²⋊C₄	—	5	1	no	—
828	C₂²⋊C₄	—	5	1	no	—
829	C₂²⋊C₄	—	5	1	no	—
830	C₂²⋊C₄	—	5	1	no	—
831	C₂²⋊C₄	—	5	1	no	—
832	C₂²⋊C₄	—	5	1	no	—
833	C₂²⋊C₄	—	5	1	no	—
834	C₂²⋊C₄	—	5	1	no	—
835	C₂²⋊C₄	—	5	1	no	—
836	C₂²⋊C₄	—	5	1	no	—
837	C₂²⋊C₄	—	5	1	no	—
838	C₂²⋊C₄	—	5	1	no	—
839	C₂²⋊C₄	—	5	1	no	—
840	C₂²⋊C₄	—	5	1	no	—
841	C₂²⋊C₄	—	5	1	no	—
842	C₂²⋊C₄	—	5	1	no	—
843	C₂²⋊C₄	—	5	1	no	—
844	C₂²⋊C₄	—	5	1	no	—
845	C₂²⋊C₄	—	5	1	no	—
846	C₂²⋊C₄	—	5	1	no	—
847	C₂²⋊C₄	—	5	1	no	—
848	C₂²⋊C₄	—	5	1	no	—
849	C₂²⋊C₄	—	5	1	no	—
850	C₂²⋊C₄	—	5	1	no	—
851	C₂²⋊C₄	—	5	1	no	—
852	C₂²⋊C₄	—	5	1	no	—
853	C₂²⋊C₄	—	5	1	no	—
854	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
855	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
856	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
857	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
858	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
859	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
860	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
868	C₄²	—	5	1	no	—
869	C₄²	—	5	1	no	—
870	C₄²	—	5	1	no	—
871	C₄²	—	5	1	no	—
872	C₄²	—	5	1	no	—
873	C₄²	—	5	1	no	—
874	C₄²	—	5	1	no	—
875	C₄²	—	5	1	no	—
876	C₄²	C₂²×D₅	1	1	yes	characteristic
877	C₄²	C₂²×D₅	1	1	yes	characteristic
878	C₂×C₅	—	4	1	no	—
879	C₂×C₅	—	4	1	no	—
880	C₂×C₅	—	4	1	no	—
881	C₂×C₅	—	4	1	no	—
882	C₂×C₅	—	4	1	no	—
883	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
884	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂×C₅	#585	1	1	yes	characteristic
886	D₅	—	4	1	no	—
887	D₅	—	4	1	no	—
888	D₅	—	4	1	no	—
889	D₅	—	4	1	no	—
890	D₅	—	4	1	no	—
891	D₅	—	4	1	no	—
892	C₂³	—	4	1	no	—
893	C₂³	—	4	1	no	—
894	C₂³	—	4	1	no	—
895	C₂³	—	5	1	no	—
896	C₂³	—	5	1	no	—
897	C₂³	—	5	1	no	—
898	C₂³	—	5	1	no	—
899	C₂³	—	5	1	no	—
900	C₂³	—	5	1	no	—
901	C₂³	—	20	1	no	—
902	C₂³	—	20	1	no	—
903	C₂³	—	20	1	no	—
904	C₂³	—	20	1	no	—
905	C₂³	—	20	1	no	—
906	C₂³	—	20	1	no	—
907	C₂³	—	20	1	no	—
908	C₂³	—	20	1	no	—
909	C₂³	—	20	1	no	—
910	C₂³	C₂³×D₅	1	1	yes	characteristic
911	C₂³	C₂³×D₅	1	1	yes	characteristic
912	C₂³	C₂³×D₅	1	1	yes	characteristic
913	C₂³	C₂³×D₅	1	1	yes	characteristic
914	C₂³	C₂³×D₅	1	1	yes	characteristic
915	Q₈	—	4	1	no	—
916	Q₈	—	10	2	no	—
917	Q₈	—	10	2	no	—
918	Q₈	—	10	2	no	—
919	Q₈	—	20	1	no	—
920	D₄	—	4	1	no	—
921	D₄	—	4	1	no	—
922	D₄	—	4	1	no	—
923	D₄	—	4	1	no	—
924	D₄	—	4	1	no	—
925	D₄	—	4	1	no	—
926	D₄	—	4	1	no	—
927	D₄	—	10	2	no	—
928	D₄	—	10	2	no	—
929	D₄	—	10	2	no	—
930	D₄	—	10	2	no	—
931	D₄	—	10	2	no	—
932	D₄	—	10	2	no	—
933	D₄	—	10	2	no	—
934	D₄	—	20	1	no	—
935	D₄	—	20	1	no	—
936	D₄	—	20	1	no	—
937	D₄	—	20	1	no	—
938	D₄	—	20	1	no	—
939	D₄	—	20	1	no	—
940	D₄	—	20	1	no	—
941	D₄	—	20	1	no	—
942	D₄	—	20	1	no	—
943	D₄	—	20	1	no	—
944	D₄	—	20	1	no	—
945	D₄	—	20	1	no	—
946	D₄	—	20	1	no	—
947	D₄	—	20	1	no	—
948	D₄	—	20	1	no	—
949	D₄	—	20	1	no	—
950	D₄	—	20	1	no	—
951	D₄	—	20	1	no	—
952	D₄	—	20	1	no	—
953	D₄	—	20	1	no	—
954	D₄	—	20	1	no	—
955	D₄	—	20	1	no	—
956	D₄	—	20	1	no	—
957	D₄	—	20	1	no	—
958	D₄	—	20	1	no	—
959	D₄	—	20	1	no	—
960	D₄	—	20	1	no	—
961	D₄	—	20	1	no	—
962	D₄	—	20	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	5	1	no	—
968	C₂×C₄	—	5	1	no	—
969	C₂×C₄	—	5	1	no	—
970	C₂×C₄	—	5	1	no	—
971	C₂×C₄	—	5	1	no	—
972	C₂×C₄	—	5	1	no	—
973	C₂×C₄	—	5	1	no	—
974	C₂×C₄	—	5	1	no	—
975	C₂×C₄	—	5	1	no	—
976	C₂×C₄	—	5	1	no	—
977	C₂×C₄	—	10	2	no	—
978	C₂×C₄	—	10	2	no	—
979	C₂×C₄	—	10	2	no	—
980	C₂×C₄	—	10	2	no	—
981	C₂×C₄	—	10	2	no	—
982	C₂×C₄	—	10	2	no	—
983	C₂×C₄	—	10	2	no	—
984	C₂×C₄	—	10	2	no	—
985	C₂×C₄	—	20	1	no	—
986	C₂×C₄	—	20	1	no	—
987	C₂×C₄	—	20	1	no	—
988	C₂×C₄	—	20	1	no	—
989	C₂×C₄	—	20	1	no	—
990	C₂×C₄	—	20	1	no	—
991	C₂×C₄	—	20	1	no	—
992	C₂×C₄	—	20	1	no	—
993	C₂×C₄	—	20	1	no	—
994	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
995	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
996	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
997	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
1004	C₅	#3546	1	1	yes	characteristic, complemented, Sylow
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	8	2	no	—
1021	C₂²	—	10	1	no	—
1022	C₂²	—	10	1	no	—
1023	C₂²	—	10	1	no	—
1024	C₂²	—	10	1	no	—
1025	C₂²	—	10	1	no	—
1026	C₂²	—	10	1	no	—
1027	C₂²	—	10	1	no	—
1028	C₂²	—	10	1	no	—
1029	C₂²	—	10	1	no	—
1030	C₂²	—	10	1	no	—
1031	C₂²	—	10	1	no	—
1032	C₂²	—	10	1	no	—
1033	C₂²	—	10	1	no	—
1034	C₂²	—	10	1	no	—
1035	C₂²	—	10	1	no	—
1036	C₂²	—	10	1	no	—
1037	C₂²	—	10	1	no	—
1038	C₂²	—	10	1	no	—
1039	C₂²	—	40	2	no	—
1040	C₂²	—	40	2	no	—
1041	C₂²	—	40	2	no	—
1042	C₂²	C₂⁴×D₅	1	1	yes	characteristic
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	5	2	no	—
1054	C₄	—	5	2	no	—
1055	C₄	—	10	1	no	—
1056	C₄	—	10	1	no	—
1057	C₄	—	10	1	no	—
1058	C₄	—	10	1	no	—
1059	C₄	—	10	1	no	—
1060	C₄	—	10	1	no	—
1061	C₄	—	10	1	no	—
1062	C₄	—	10	1	no	—
1063	C₂	—	4	1	no	—
1064	C₂	—	4	1	no	—
1065	C₂	—	4	1	no	—
1066	C₂	—	4	1	no	—
1067	C₂	—	4	1	no	—
1068	C₂	—	20	1	no	—
1069	C₂	—	20	1	no	—
1070	C₂	—	20	1	no	—
1071	C₂	—	20	1	no	—
1072	C₂	—	20	1	no	—
1073	C₂	—	20	1	no	—
1074	C₂	#66283	1	1	yes	characteristic
1075	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
1076	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#538	C₂
hypercenter	#538	D₅
hypocenter	C₅	#3546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. C₅×#538	C₂	semidirect
2. #66045	C₂	semidirect
3. #66040	C₂	semidirect
4. #66038	C₂	semidirect
5. #66036	C₂	semidirect
6. #66012	C₂	semidirect
7. #66008	C₂	semidirect
8. #66003	C₂	semidirect
9. #66002	C₂	semidirect
10. #66000	C₂	semidirect
11. #65995	C₂	semidirect
12. #65989	C₂	semidirect
13. #65988	C₂	semidirect
14. #65974	C₂	semidirect
15. #65963	C₂	semidirect
16. #65954	C₂	semidirect
17. #65944	C₂	semidirect
18. #65941	C₂	semidirect
19. #65933	C₂	semidirect
20. #65933	C₂	semidirect
21. #65931	C₂	semidirect
22. #65929	C₂	semidirect
23. #65926	C₂	semidirect
24. #65926	C₂	semidirect
25. #65924	C₂	semidirect
26. #65894	C₂	semidirect
27. #65887	C₂	semidirect
28. #65882	C₂	semidirect
29. #65874	C₂	semidirect
30. #65824	C₂	semidirect
31. #65824	C₂	semidirect
34. C₂×#713	C₂²	semidirect
35. C₂×#711	C₂²	semidirect
36. C₂×#711	C₂²	semidirect
37. C₂×#711	C₂²	semidirect
40. C₂×#709	C₂²	semidirect
41. C₂×#709	C₂²	semidirect
42. C₂×#709	C₂²	semidirect
43. C₂×#709	C₂²	semidirect
44. C₅×#126	C₂²	semidirect
45. C₅×#126	C₂²	semidirect
46. C₅×#124	C₂²	semidirect
47. C₅×#124	C₂²	semidirect
48. C₅×#123	C₂²	semidirect
49. C₅×#123	C₂²	semidirect
50. C₅×C₂²⋊Q₈	C₂²	semidirect
51. C₅×#121	C₂²	semidirect
52. C₅×#121	C₂²	semidirect
53. C₅×#121	C₂²	semidirect
55. C₅×#120	C₂²	semidirect
56. C₄×C₅×D₄	C₂²	semidirect
57. C₄×C₅×D₄	C₂²	semidirect
58. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
59. #4099	C₂²	semidirect
60. #4099	C₂²	semidirect
61. #4093	C₂²	semidirect
62. #4092	C₂²	semidirect
63. #4090	C₂²	semidirect
66. #4086	C₂²	semidirect
67. #4086	C₂²	semidirect
68. #4086	C₂²	semidirect
69. #4086	C₂²	semidirect
70. #4086	C₂²	semidirect
74. #4085	C₂²	semidirect
75. #4085	C₂²	semidirect
76. #4085	C₂²	semidirect
77. #4085	C₂²	semidirect
78. #4085	C₂²	semidirect
79. #4085	C₂²	semidirect
80. #4084	C₂²	semidirect
81. #4084	C₂²	semidirect
83. #4083	C₂²	semidirect
84. #4083	C₂²	semidirect
85. #4083	C₂²	semidirect
86. #4081	C₂²	semidirect
87. #4076	C₂²	semidirect
88. #4076	C₂²	semidirect
89. #4076	C₂²	semidirect
90. #4076	C₂²	semidirect
91. #4075	C₂²	semidirect
92. #4075	C₂²	semidirect
93. C₄×C₂²⋊D₅	C₂²	semidirect
94. C₄×C₂²⋊D₅	C₂²	semidirect
95. C₄×C₂²⋊D₅	C₂²	semidirect
96. C₄×C₂²⋊D₅	C₂²	semidirect
97. C₂×#685	C₂²	semidirect
98. C₂×#683	C₂²	semidirect
99. #4044	C₂²	semidirect
100. #4044	C₂²	semidirect
101. #4044	C₂²	semidirect
102. #4042	C₂²	semidirect
103. #4042	C₂²	semidirect
104. #4042	C₂²	semidirect
105. #4042	C₂²	semidirect
106. #4041	C₂²	semidirect
107. #4041	C₂²	semidirect
108. #4041	C₂²	semidirect
109. #4041	C₂²	semidirect
110. #4041	C₂²	semidirect
111. #4040	C₂²	semidirect
112. #4040	C₂²	semidirect
113. #4040	C₂²	semidirect
114. #4040	C₂²	semidirect
115. #4039	C₂²	semidirect
116. #4039	C₂²	semidirect
117. #4038	C₂²	semidirect
118. D₅×C₄⋊C₄	C₂²	semidirect
119. #4035	C₂²	semidirect
120. #4034	C₂²	semidirect
121. #4033	C₂²	semidirect
122. #4033	C₂²	semidirect
123. #4032	C₂²	semidirect
127. #4031	C₂²	semidirect
128. #4031	C₂²	semidirect
129. #4031	C₂²	semidirect
130. #4031	C₂²	semidirect
136. #4030	C₂²	semidirect
137. #4030	C₂²	semidirect
138. #4030	C₂²	semidirect
139. #4030	C₂²	semidirect
140. #4030	C₂²	semidirect
141. #4030	C₂²	semidirect
142. #4030	C₂²	semidirect
143. #4030	C₂²	semidirect
144. #4030	C₂²	semidirect
145. #4030	C₂²	semidirect
146. #4030	C₂²	semidirect
147. #4030	C₂²	semidirect
148. #4030	C₂²	semidirect
149. #4029	C₂²	semidirect
150. #4029	C₂²	semidirect
151. #4029	C₂²	semidirect
152. #4029	C₂²	semidirect
155. #4028	C₂²	semidirect
156. #4028	C₂²	semidirect
157. #4028	C₂²	semidirect
158. #4028	C₂²	semidirect
159. #4028	C₂²	semidirect
160. #4028	C₂²	semidirect
163. #4027	C₂²	semidirect
164. #4027	C₂²	semidirect
165. #4027	C₂²	semidirect
166. #4027	C₂²	semidirect
167. #4027	C₂²	semidirect
168. #4027	C₂²	semidirect
169. D₅×C₂²⋊C₄	C₂²	semidirect
170. D₅×C₂²⋊C₄	C₂²	semidirect
171. #4025	C₂²	semidirect
172. #4025	C₂²	semidirect
173. #4025	C₂²	semidirect
174. #4024	C₂²	semidirect
175. #4024	C₂²	semidirect
176. #4024	C₂²	semidirect
177. #4023	C₂²	semidirect
178. #4023	C₂²	semidirect
179. #4022	C₂²	semidirect
180. #4022	C₂²	semidirect
181. #4021	C₂²	semidirect
182. #4020	C₂²	semidirect
183. C₄×D₂₀	C₂²	semidirect
184. #4018	C₂²	semidirect
185. C₄²×D₅	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
376. #538	D₅	semidirect
528. #126	C₂×D₅	semidirect
529. #126	C₂×D₅	semidirect
540. #124	C₂×D₅	semidirect
541. #124	C₂×D₅	semidirect
554. #123	C₂×D₅	semidirect
555. #123	C₂×D₅	semidirect
564. C₂²⋊Q₈	C₂×D₅	semidirect
603. #121	C₂×D₅	semidirect
604. #121	C₂×D₅	semidirect
605. #121	C₂×D₅	semidirect
621. #120	C₂×D₅	semidirect
640. C₄×D₄	C₂×D₅	semidirect
641. C₄×D₄	C₂×D₅	semidirect
651. C₂×C₂²⋊C₄	C₂×D₅	semidirect
1004. C₅	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₅×#538	2
#66045	2
#66040	2
#66038	2
#66036	2
#66012	2
#66008	2
#66003	2
#66002	2
#66000	2
#65995	2
#65989	2
#65988	2
#65974	2
#65963	2
#65954	2
#65944	2
#65941	2
#65933	2
#65931	2
#65929	2
#65926	2
#65924	2
#65894	2
#65887	2
#65882	2
#65874	2
#65824	2
#3546	5