Subgroups — C₅×#22886 #11945606

Order 1280.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3002	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2933	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2880	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₂×C₅×#135	C₂²	1	1	yes	characteristic
19	C₂×C₅×#131	C₂²	1	1	yes	characteristic
20	C₂×C₅×#131	C₂²	1	1	yes	characteristic
21	C₂×C₅×#131	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₅×#525	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#452	C₄	1	1	yes	characteristic, complemented
26	C₅×#452	C₄	1	1	yes	characteristic, complemented
27	C₅×#451	C₄	1	1	yes	characteristic, complemented
28	C₅×#450	C₄	1	1	yes	characteristic, complemented
29	C₅×#449	C₄	1	1	yes	characteristic, complemented
30	C₅×#449	C₄	1	1	yes	characteristic, complemented
31	C₅×#448	C₄	1	1	yes	characteristic, complemented
32	C₅×#447	C₄	1	1	yes	characteristic, complemented
33	C₅×#444	—	2	4	no	—
34	C₅×#436	—	2	1	no	—
35	C₅×#435	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×C₈×D₄	—	2	1	no	—
38	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
40	C₅×#424	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×#104	—	2	4	no	—
42	C₂×C₅×#104	C₂²	1	1	yes	characteristic
43	C₂×C₅×#104	C₂²	1	1	yes	characteristic
44	C₂×C₅×#104	C₂²	1	1	yes	characteristic
45	C₂×C₅×#104	C₂²	1	1	yes	characteristic
46	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
48	C₅×#416	C₂²	1	1	yes	characteristic
49	C₅×#416	C₂²	1	1	yes	characteristic
50	C₅×#408	—	2	1	no	—
51	C₅×#408	—	2	1	no	—
52	C₅×#408	C₂²	1	1	yes	characteristic
53	C₅×#408	C₂²	1	1	yes	characteristic
54	C₅×#408	C₂²	1	1	yes	characteristic, complemented
55	C₅×#407	—	2	1	no	—
56	C₅×#407	C₂²	1	1	yes	characteristic
57	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
58	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×#405	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
63	C₅×#341	C₂²	1	1	yes	characteristic, complemented
64	C₅×#341	C₂²	1	1	yes	characteristic, complemented
65	C₅×#339	C₂²	1	1	yes	characteristic, complemented
66	C₅×#339	C₂²	1	1	yes	characteristic, complemented
67	C₅×#336	C₂²	1	1	yes	characteristic, complemented
68	C₅×#336	C₂²	1	1	yes	characteristic, complemented
69	#22886	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₅×#41	—	2	1	no	—
71	C₂×C₅×#41	—	2	1	no	—
72	C₂×C₅×#41	—	2	2	no	—
73	C₂×C₅×#41	—	2	2	no	—
74	C₂×C₅×#41	—	4	1	no	—
75	C₂×C₅×#41	—	4	1	no	—
76	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×#41	C₂³	1	1	yes	characteristic
79	C₂×C₅×#41	C₂³	1	1	yes	characteristic
80	C₂×C₅×#41	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₅×D₄	—	2	1	no	—
83	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₅	—	2	1	no	—
85	C₂³×C₄×C₅	—	2	1	no	—
86	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₅×#135	—	2	2	no	—
88	C₅×#135	—	2	2	no	—
89	C₅×#135	—	4	1	no	—
90	C₅×#135	—	4	1	no	—
91	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
94	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
96	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
97	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
99	C₅×#131	—	2	2	no	—
100	C₅×#131	—	2	2	no	—
101	C₅×#131	—	2	2	no	—
102	C₅×#131	—	4	1	no	—
103	C₅×#131	—	4	1	no	—
104	C₅×#131	—	4	1	no	—
105	C₂×C₅×M₁₆	—	2	1	no	—
106	C₂×C₅×M₁₆	—	2	1	no	—
107	C₂×C₅×M₁₆	—	2	1	no	—
108	C₂×C₅×M₁₆	—	2	1	no	—
109	C₂×C₅×M₁₆	—	2	2	no	—
110	C₂×C₅×M₁₆	—	4	1	no	—
111	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
115	C₂²×C₅×C₈	—	2	1	no	—
116	C₂²×C₅×C₈	—	2	1	no	—
117	C₂²×C₅×C₈	—	2	1	no	—
118	C₂²×C₅×C₈	—	2	1	no	—
119	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
120	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
122	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
123	C₅×#123	—	2	1	no	—
124	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
125	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
126	C₅×#121	C₂×C₄	1	1	yes	characteristic
127	C₅×#121	C₂×C₄	1	1	yes	characteristic
128	C₅×#120	—	2	1	no	—
129	C₄×C₅×D₄	—	2	1	no	—
130	C₄×C₅×D₄	—	2	1	no	—
131	C₅×#117	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅	—	2	2	no	—
133	C₂×C₄²×C₅	—	2	1	no	—
134	C₂×C₄²×C₅	—	4	1	no	—
135	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₅×#108	—	2	2	no	—
138	C₅×#108	—	4	1	no	—
139	C₅×C₄⋊C₈	—	2	1	no	—
140	C₅×C₄⋊C₈	—	2	1	no	—
141	C₅×#104	—	2	2	no	—
142	C₅×#104	—	2	2	no	—
143	C₅×#104	—	2	2	no	—
144	C₅×#104	—	2	2	no	—
145	C₅×#104	—	4	1	no	—
146	C₅×#104	D₄	1	4	yes	complemented
147	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
148	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
149	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
150	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
151	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
152	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
153	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
154	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
155	C₅×C₂²⋊C₈	—	2	1	no	—
156	C₅×C₂²⋊C₈	—	2	1	no	—
157	C₅×C₂²⋊C₈	—	2	1	no	—
158	C₅×C₂²⋊C₈	—	2	1	no	—
159	C₅×C₂²⋊C₈	—	2	1	no	—
160	C₅×C₂²⋊C₈	—	2	1	no	—
161	C₅×C₂²⋊C₈	—	2	1	no	—
162	C₅×C₂²⋊C₈	—	2	1	no	—
163	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
164	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
165	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
166	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
167	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
168	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₅×#97	—	2	1	no	—
172	C₅×#97	—	2	2	no	—
173	C₅×#97	—	4	1	no	—
174	C₄×C₅×C₈	—	2	1	no	—
175	#3002	C₂×C₅	1	1	yes	characteristic
176	C₂×#444	C₂×C₅	1	1	yes	characteristic, complemented
177	#2933	C₂×C₅	1	1	yes	characteristic, complemented
178	C₂²×#104	C₂×C₅	1	1	yes	characteristic, complemented
179	#2880	C₂×C₅	1	1	yes	characteristic, complemented
180	#1975	C₂×C₅	1	1	yes	characteristic, complemented
181	#1938	C₂×C₅	1	1	yes	characteristic, complemented
182	#1929	C₂×C₅	1	1	yes	characteristic, complemented
183	#1896	C₂×C₅	1	1	yes	characteristic, complemented
184	#1876	C₂×C₅	1	1	yes	characteristic, complemented
185	#1876	C₂×C₅	1	1	yes	characteristic, complemented
186	#1866	C₂×C₅	1	1	yes	characteristic, complemented
187	#1855	C₂×C₅	1	1	yes	characteristic, complemented
188	#1765	C₂×C₅	1	1	yes	characteristic, complemented
189	#1749	C₂×C₅	1	1	yes	characteristic, complemented
190	C₂⁴×C₅	—	2	1	no	—
191	C₂⁴×C₅	#41	1	1	yes	characteristic
192	C₅×#41	—	2	1	no	—
193	C₅×#41	—	2	1	no	—
194	C₅×#41	—	2	2	no	—
195	C₅×#41	—	2	2	no	—
196	C₅×#41	—	2	1	no	—
197	C₅×#41	—	2	1	no	—
198	C₅×#41	—	2	1	no	—
199	C₅×#41	—	2	1	no	—
200	C₅×#41	—	2	1	no	—
201	C₅×#41	—	2	1	no	—
202	C₅×#41	—	2	1	no	—
203	C₅×#41	—	2	1	no	—
204	C₅×#41	—	4	2	no	—
205	C₅×#41	—	4	2	no	—
206	C₅×#41	—	4	1	no	—
207	C₅×#41	—	4	1	no	—
208	C₅×#41	—	4	2	no	—
209	C₅×#41	—	4	2	no	—
210	C₅×#41	C₂×D₄	1	2	yes	—
211	C₅×#41	#41	1	2	yes	—
212	C₂×C₅×Q₈	—	2	1	no	—
213	C₂×C₅×Q₈	—	2	2	no	—
214	C₂×C₅×Q₈	—	4	1	no	—
215	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	2	2	no	—
220	C₂×C₅×D₄	—	2	1	no	—
221	C₂×C₅×D₄	—	2	1	no	—
222	C₂×C₅×D₄	—	2	1	no	—
223	C₂×C₅×D₄	—	2	1	no	—
224	C₂×C₅×D₄	—	2	1	no	—
225	C₂×C₅×D₄	—	2	1	no	—
226	C₂×C₅×D₄	—	2	1	no	—
227	C₂×C₅×D₄	—	4	1	no	—
228	C₂×C₅×D₄	—	4	2	no	—
229	C₂×C₅×D₄	—	4	2	no	—
230	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₅	—	2	1	no	—
234	C₂²×C₄×C₅	—	2	1	no	—
235	C₂²×C₄×C₅	—	2	1	no	—
236	C₂²×C₄×C₅	—	2	1	no	—
237	C₂²×C₄×C₅	—	2	1	no	—
238	C₂²×C₄×C₅	—	2	1	no	—
239	C₂²×C₄×C₅	—	2	1	no	—
240	C₂²×C₄×C₅	—	2	1	no	—
241	C₂²×C₄×C₅	—	2	1	no	—
242	C₂²×C₄×C₅	—	2	1	no	—
243	C₂²×C₄×C₅	—	2	1	no	—
244	C₂²×C₄×C₅	—	2	1	no	—
245	C₂²×C₄×C₅	—	4	2	no	—
246	C₂²×C₄×C₅	—	4	2	no	—
247	C₂²×C₄×C₅	—	4	2	no	—
248	C₂²×C₄×C₅	—	4	2	no	—
249	C₂²×C₄×C₅	—	4	2	no	—
250	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₅	#41	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
256	C₅×Q₁₆	—	2	2	no	—
257	C₅×Q₁₆	—	4	1	no	—
258	C₅×SD₁₆	—	2	2	no	—
259	C₅×SD₁₆	—	2	2	no	—
260	C₅×SD₁₆	—	4	1	no	—
261	C₅×SD₁₆	—	4	1	no	—
262	C₅×D₈	—	2	2	no	—
263	C₅×D₈	—	4	1	no	—
264	C₅×M₁₆	—	2	1	no	—
265	C₅×M₁₆	—	2	1	no	—
266	C₅×M₁₆	—	2	1	no	—
267	C₅×M₁₆	—	2	1	no	—
268	C₅×M₁₆	—	2	1	no	—
269	C₅×M₁₆	—	2	1	no	—
270	C₅×M₁₆	—	2	1	no	—
271	C₅×M₁₆	—	4	2	no	—
272	C₅×M₁₆	—	4	2	no	—
273	C₅×M₁₆	—	4	2	no	—
274	C₅×M₁₆	—	4	2	no	—
275	C₅×M₁₆	C₂×D₄	1	2	yes	—
276	C₂×C₅×C₈	—	2	1	no	—
277	C₂×C₅×C₈	—	2	1	no	—
278	C₂×C₅×C₈	—	2	1	no	—
279	C₂×C₅×C₈	—	2	1	no	—
280	C₂×C₅×C₈	—	2	1	no	—
281	C₂×C₅×C₈	—	2	1	no	—
282	C₂×C₅×C₈	—	2	1	no	—
283	C₂×C₅×C₈	—	2	1	no	—
284	C₂×C₅×C₈	—	2	1	no	—
285	C₂×C₅×C₈	—	2	1	no	—
286	C₂×C₅×C₈	—	2	1	no	—
287	C₂×C₅×C₈	—	2	1	no	—
288	C₂×C₅×C₈	—	4	2	no	—
289	C₂×C₅×C₈	—	4	2	no	—
290	C₂×C₅×C₈	—	4	2	no	—
291	C₂×C₅×C₈	—	4	2	no	—
292	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
293	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
294	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
295	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
296	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
297	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
298	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
299	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
303	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	—	2	1	no	—
307	C₅×C₂²⋊C₄	—	2	1	no	—
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₄²×C₅	—	2	1	no	—
310	C₄²×C₅	—	2	1	no	—
311	C₄²×C₅	—	2	1	no	—
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	4	2	no	—
314	C₄²×C₅	C₂×D₄	1	2	yes	—
315	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
316	C₂×#135	C₂²×C₅	1	1	yes	characteristic
317	C₂×#135	C₂²×C₅	1	1	yes	characteristic
318	C₂×#131	C₂²×C₅	1	1	yes	characteristic
319	C₂×#131	C₂²×C₅	1	1	yes	characteristic
320	C₂×#131	C₂²×C₅	1	1	yes	characteristic, complemented
321	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
322	#525	C₂²×C₅	1	1	yes	characteristic
323	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
324	#452	C₄×C₅	1	1	yes	characteristic, complemented
325	#452	C₄×C₅	1	1	yes	characteristic, complemented
326	#451	C₄×C₅	1	1	yes	characteristic, complemented
327	#450	C₄×C₅	1	1	yes	characteristic, complemented
328	#449	C₄×C₅	1	1	yes	characteristic, complemented
329	#449	C₄×C₅	1	1	yes	characteristic, complemented
330	#448	C₄×C₅	1	1	yes	characteristic, complemented
331	#447	C₄×C₅	1	1	yes	characteristic, complemented
332	#444	—	2	4	no	—
333	#436	—	2	1	no	—
334	#435	—	2	1	no	—
335	#435	—	2	1	no	—
336	C₈×D₄	—	2	1	no	—
337	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
338	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
339	#424	C₂²×C₅	1	1	yes	characteristic, complemented
340	C₂×#104	—	2	4	no	—
341	C₂×#104	C₂²×C₅	1	1	yes	characteristic
342	C₂×#104	C₂²×C₅	1	1	yes	characteristic
343	C₂×#104	C₂²×C₅	1	1	yes	characteristic
344	C₂×#104	C₂²×C₅	1	1	yes	characteristic
345	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
346	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
347	#416	C₂²×C₅	1	1	yes	characteristic
348	#416	C₂²×C₅	1	1	yes	characteristic
349	#408	—	2	1	no	—
350	#408	—	2	1	no	—
351	#408	C₂²×C₅	1	1	yes	characteristic
352	#408	C₂²×C₅	1	1	yes	characteristic
353	#408	C₂²×C₅	1	1	yes	characteristic, complemented
354	#407	—	2	1	no	—
355	#407	C₂²×C₅	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	—	2	1	no	—
357	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
358	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
359	#405	C₂²×C₅	1	1	yes	characteristic, complemented
360	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
361	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
362	#341	C₂²×C₅	1	1	yes	characteristic, complemented
363	#341	C₂²×C₅	1	1	yes	characteristic, complemented
364	#339	C₂²×C₅	1	1	yes	characteristic, complemented
365	#339	C₂²×C₅	1	1	yes	characteristic, complemented
366	#336	C₂²×C₅	1	1	yes	characteristic, complemented
367	#336	C₂²×C₅	1	1	yes	characteristic, complemented
368	C₂³×C₅	—	2	1	no	—
369	C₂³×C₅	—	2	1	no	—
370	C₂³×C₅	—	2	1	no	—
371	C₂³×C₅	—	2	2	no	—
372	C₂³×C₅	—	2	1	no	—
373	C₂³×C₅	—	2	1	no	—
374	C₂³×C₅	—	4	1	no	—
375	C₂³×C₅	—	4	2	no	—
376	C₂³×C₅	—	4	2	no	—
377	C₂³×C₅	—	8	1	no	—
378	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
379	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
380	C₂³×C₅	C₂×#41	1	1	yes	characteristic
381	C₅×Q₈	—	2	1	no	—
382	C₅×Q₈	—	2	1	no	—
383	C₅×Q₈	—	2	1	no	—
384	C₅×Q₈	—	2	1	no	—
385	C₅×Q₈	—	2	1	no	—
386	C₅×Q₈	—	4	2	no	—
387	C₅×Q₈	C₄×D₄	1	2	yes	—
388	C₅×D₄	—	2	2	no	—
389	C₅×D₄	—	2	2	no	—
390	C₅×D₄	—	2	1	no	—
391	C₅×D₄	—	2	1	no	—
392	C₅×D₄	—	2	1	no	—
393	C₅×D₄	—	2	1	no	—
394	C₅×D₄	—	2	1	no	—
395	C₅×D₄	—	4	2	no	—
396	C₅×D₄	—	4	2	no	—
397	C₅×D₄	—	4	2	no	—
398	C₅×D₄	—	4	1	no	—
399	C₅×D₄	—	4	1	no	—
400	C₅×D₄	—	4	1	no	—
401	C₅×D₄	—	4	1	no	—
402	C₅×D₄	—	4	2	no	—
403	C₅×D₄	—	8	1	no	—
404	C₅×D₄	C₄×D₄	1	2	yes	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	2	2	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	2	no	—
416	C₂×C₄×C₅	—	2	1	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	2	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	2	2	no	—
424	C₂×C₄×C₅	—	4	2	no	—
425	C₂×C₄×C₅	—	4	2	no	—
426	C₂×C₄×C₅	—	4	2	no	—
427	C₂×C₄×C₅	—	4	1	no	—
428	C₂×C₄×C₅	—	4	1	no	—
429	C₂×C₄×C₅	—	4	1	no	—
430	C₂×C₄×C₅	—	4	8	no	—
431	C₂×C₄×C₅	—	4	1	no	—
432	C₂×C₄×C₅	—	4	1	no	—
433	C₂×C₄×C₅	—	4	1	no	—
434	C₂×C₄×C₅	—	4	1	no	—
435	C₂×C₄×C₅	—	4	1	no	—
436	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
437	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
439	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
442	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
443	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
444	C₅×C₈	—	2	1	no	—
445	C₅×C₈	—	2	1	no	—
446	C₅×C₈	—	2	1	no	—
447	C₅×C₈	—	2	1	no	—
448	C₅×C₈	—	2	1	no	—
449	C₅×C₈	—	2	1	no	—
450	C₅×C₈	—	2	2	no	—
451	C₅×C₈	—	2	1	no	—
452	C₅×C₈	—	2	1	no	—
453	C₅×C₈	—	4	1	no	—
454	C₅×C₈	—	4	1	no	—
455	C₅×C₈	—	4	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	2	no	—
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	4	1	no	—
461	C₂×#41	—	4	1	no	—
462	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
463	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
464	C₂×#41	C₂³×C₅	1	1	yes	characteristic
465	C₂×#41	C₂³×C₅	1	1	yes	characteristic
466	C₂×#41	C₂³×C₅	1	1	yes	characteristic
467	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
473	#135	—	2	2	no	—
474	#135	—	2	2	no	—
475	#135	—	4	1	no	—
476	#135	—	4	1	no	—
477	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
478	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
479	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
480	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
481	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
482	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
483	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
484	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
485	#131	—	2	2	no	—
486	#131	—	2	2	no	—
487	#131	—	2	2	no	—
488	#131	—	4	1	no	—
489	#131	—	4	1	no	—
490	#131	—	4	1	no	—
491	C₂×M₁₆	—	2	1	no	—
492	C₂×M₁₆	—	2	1	no	—
493	C₂×M₁₆	—	2	1	no	—
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	2	no	—
496	C₂×M₁₆	—	4	1	no	—
497	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
498	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
499	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
500	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
501	C₂²×C₈	—	2	1	no	—
502	C₂²×C₈	—	2	1	no	—
503	C₂²×C₈	—	2	1	no	—
504	C₂²×C₈	—	2	1	no	—
505	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
509	#123	—	2	1	no	—
510	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
511	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
512	#121	C₂×C₄×C₅	1	1	yes	characteristic
513	#121	C₂×C₄×C₅	1	1	yes	characteristic
514	#120	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	#117	C₂³×C₅	1	1	yes	characteristic
518	C₂×C₄²	—	2	2	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	—	4	1	no	—
521	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
523	#108	—	2	2	no	—
524	#108	—	4	1	no	—
525	C₄⋊C₈	—	2	1	no	—
526	C₄⋊C₈	—	2	1	no	—
527	#104	—	2	2	no	—
528	#104	—	2	2	no	—
529	#104	—	2	2	no	—
530	#104	—	2	2	no	—
531	#104	—	4	1	no	—
532	#104	C₅×D₄	1	4	yes	complemented
533	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
534	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
535	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
536	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
537	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
538	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
539	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
540	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
541	C₂²⋊C₈	—	2	1	no	—
542	C₂²⋊C₈	—	2	1	no	—
543	C₂²⋊C₈	—	2	1	no	—
544	C₂²⋊C₈	—	2	1	no	—
545	C₂²⋊C₈	—	2	1	no	—
546	C₂²⋊C₈	—	2	1	no	—
547	C₂²⋊C₈	—	2	1	no	—
548	C₂²⋊C₈	—	2	1	no	—
549	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
550	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
551	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
552	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
553	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
554	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
555	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
556	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
557	#97	—	2	1	no	—
558	#97	—	2	2	no	—
559	#97	—	4	1	no	—
560	C₄×C₈	—	2	1	no	—
561	C₂²×C₅	—	2	1	no	—
562	C₂²×C₅	—	2	1	no	—
563	C₂²×C₅	—	2	1	no	—
564	C₂²×C₅	—	2	1	no	—
565	C₂²×C₅	—	2	1	no	—
566	C₂²×C₅	—	2	2	no	—
567	C₂²×C₅	—	2	1	no	—
568	C₂²×C₅	—	2	1	no	—
569	C₂²×C₅	—	4	2	no	—
570	C₂²×C₅	—	4	2	no	—
571	C₂²×C₅	—	4	1	no	—
572	C₂²×C₅	—	4	1	no	—
573	C₂²×C₅	—	4	1	no	—
574	C₂²×C₅	—	4	1	no	—
575	C₂²×C₅	—	4	1	no	—
576	C₂²×C₅	—	4	1	no	—
577	C₂²×C₅	—	4	1	no	—
578	C₂²×C₅	—	4	1	no	—
579	C₂²×C₅	—	8	4	no	—
580	C₂²×C₅	#444	1	2	yes	complemented
581	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
582	C₂²×C₅	#546	1	1	yes	characteristic
583	C₂²×C₅	#551	1	1	yes	characteristic
584	C₄×C₅	—	2	1	no	—
585	C₄×C₅	—	2	1	no	—
586	C₄×C₅	—	2	2	no	—
587	C₄×C₅	—	4	2	no	—
588	C₄×C₅	—	4	2	no	—
589	C₄×C₅	—	4	1	no	—
590	C₄×C₅	—	4	1	no	—
591	C₄×C₅	—	4	1	no	—
592	C₄×C₅	—	4	1	no	—
593	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
594	C₄×C₅	#518	1	1	yes	characteristic
595	C₄×C₅	D₄²	1	1	yes	characteristic
596	C₄×C₅	#546	1	1	yes	characteristic
597	C₂⁴	—	2	1	no	—
598	C₂⁴	C₅×#41	1	1	yes	characteristic
599	#41	—	2	1	no	—
600	#41	—	2	1	no	—
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	#41	—	2	1	no	—
604	#41	—	2	1	no	—
605	#41	—	2	1	no	—
606	#41	—	2	1	no	—
607	#41	—	2	1	no	—
608	#41	—	2	1	no	—
609	#41	—	2	1	no	—
610	#41	—	2	1	no	—
611	#41	—	4	2	no	—
612	#41	—	4	2	no	—
613	#41	—	4	1	no	—
614	#41	—	4	1	no	—
615	#41	—	4	2	no	—
616	#41	—	4	2	no	—
617	#41	C₂×C₅×D₄	1	2	yes	—
618	#41	C₅×#41	1	2	yes	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	4	1	no	—
622	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
623	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
624	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
638	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
639	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
658	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
659	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
660	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
661	C₂²×C₄	C₅×#41	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
663	Q₁₆	—	2	2	no	—
664	Q₁₆	—	4	1	no	—
665	SD₁₆	—	2	2	no	—
666	SD₁₆	—	2	2	no	—
667	SD₁₆	—	4	1	no	—
668	SD₁₆	—	4	1	no	—
669	D₈	—	2	2	no	—
670	D₈	—	4	1	no	—
671	M₁₆	—	2	1	no	—
672	M₁₆	—	2	1	no	—
673	M₁₆	—	2	1	no	—
674	M₁₆	—	2	1	no	—
675	M₁₆	—	2	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	2	1	no	—
678	M₁₆	—	4	2	no	—
679	M₁₆	—	4	2	no	—
680	M₁₆	—	4	2	no	—
681	M₁₆	—	4	2	no	—
682	M₁₆	C₂×C₅×D₄	1	2	yes	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	4	2	no	—
696	C₂×C₈	—	4	2	no	—
697	C₂×C₈	—	4	2	no	—
698	C₂×C₈	—	4	2	no	—
699	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
700	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
701	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
702	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
703	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
704	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
705	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
706	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
710	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	4	2	no	—
721	C₄²	C₂×C₅×D₄	1	2	yes	—
722	C₂×C₅	—	2	1	no	—
723	C₂×C₅	—	2	2	no	—
724	C₂×C₅	—	2	1	no	—
725	C₂×C₅	—	4	1	no	—
726	C₂×C₅	—	4	2	no	—
727	C₂×C₅	—	8	1	no	—
728	C₂×C₅	—	8	1	no	—
729	C₂×C₅	#2358	1	1	yes	characteristic
730	C₂×C₅	C₂×#444	1	1	yes	characteristic
731	C₂×C₅	#2956	1	1	yes	characteristic
732	C₂³	—	2	2	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	8	1	no	—
742	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
743	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
744	C₂³	C₂×C₅×#41	1	1	yes	characteristic
745	Q₈	—	2	1	no	—
746	Q₈	—	2	1	no	—
747	Q₈	—	2	1	no	—
748	Q₈	—	2	1	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	4	2	no	—
751	Q₈	C₄×C₅×D₄	1	2	yes	—
752	D₄	—	2	2	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	1	no	—
755	D₄	—	2	1	no	—
756	D₄	—	2	1	no	—
757	D₄	—	2	1	no	—
758	D₄	—	2	1	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	8	1	no	—
768	D₄	C₄×C₅×D₄	1	2	yes	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	8	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
801	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
803	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
805	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
806	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
807	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
808	C₈	—	2	1	no	—
809	C₈	—	2	1	no	—
810	C₈	—	2	1	no	—
811	C₈	—	2	1	no	—
812	C₈	—	2	1	no	—
813	C₈	—	2	1	no	—
814	C₈	—	2	2	no	—
815	C₈	—	2	1	no	—
816	C₈	—	2	1	no	—
817	C₈	—	4	1	no	—
818	C₈	—	4	1	no	—
819	C₈	—	4	1	no	—
820	C₅	#22886	1	1	yes	characteristic, direct product factor, Sylow
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	8	4	no	—
840	C₂²	C₅×#444	1	2	yes	complemented
841	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
842	C₂²	C₅×#546	1	1	yes	characteristic
843	C₂²	C₅×#551	1	1	yes	characteristic
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
854	C₄	C₅×#518	1	1	yes	characteristic
855	C₄	C₅×D₄²	1	1	yes	characteristic
856	C₄	C₅×#546	1	1	yes	characteristic
857	C₂	—	2	1	no	—
858	C₂	—	2	2	no	—
859	C₂	—	2	1	no	—
860	C₂	—	4	1	no	—
861	C₂	—	4	2	no	—
862	C₂	—	8	1	no	—
863	C₂	—	8	1	no	—
864	C₂	C₅×#2358	1	1	yes	characteristic
865	C₂	C₂×C₅×#444	1	1	yes	characteristic
866	C₂	C₅×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#444	C₂	semidirect
3. C₅×#2933	C₂	semidirect
4. C₂²×C₅×#104	C₂	semidirect
5. C₅×#2880	C₂	semidirect
6. C₅×#1975	C₂	semidirect
7. C₅×#1938	C₂	semidirect
8. C₅×#1929	C₂	semidirect
9. C₅×#1896	C₂	semidirect
10. C₅×#1876	C₂	semidirect
11. C₅×#1876	C₂	semidirect
12. C₅×#1866	C₂	semidirect
13. C₅×#1855	C₂	semidirect
14. C₅×#1765	C₂	semidirect
15. C₅×#1749	C₂	semidirect
21. C₂×C₅×#131	C₂²	semidirect
25. C₅×#452	C₄	semidirect
26. C₅×#452	C₄	semidirect
27. C₅×#451	C₄	semidirect
28. C₅×#450	C₄	semidirect
29. C₅×#449	C₄	semidirect
30. C₅×#449	C₄	semidirect
31. C₅×#448	C₄	semidirect
32. C₅×#447	C₄	semidirect
38. C₂×C₅×#108	C₂²	semidirect
39. C₂×C₅×#108	C₂²	semidirect
40. C₅×#424	C₂²	semidirect
46. C₂×C₅×#104	C₂²	semidirect
47. C₂×C₅×#104	C₂²	semidirect
54. C₅×#408	C₂²	semidirect
60. C₅×#405	C₂²	semidirect
61. C₂×C₅×#97	C₂²	semidirect
62. C₂×C₅×#97	C₂²	semidirect
63. C₅×#341	C₂²	semidirect
64. C₅×#341	C₂²	semidirect
65. C₅×#339	C₂²	semidirect
66. C₅×#339	C₂²	semidirect
67. C₅×#336	C₂²	semidirect
68. C₅×#336	C₂²	semidirect
69. #22886	C₅	direct (N × H)
91. C₂×C₅×Q₁₆	C₂×C₄	semidirect
92. C₂×C₅×Q₁₆	C₂×C₄	semidirect
93. C₂×C₅×SD₁₆	C₂×C₄	semidirect
94. C₂×C₅×SD₁₆	C₂×C₄	semidirect
95. C₂×C₅×SD₁₆	C₂×C₄	semidirect
96. C₂×C₅×SD₁₆	C₂×C₄	semidirect
97. C₂×C₅×D₈	C₂×C₄	semidirect
98. C₂×C₅×D₈	C₂×C₄	semidirect
146. C₅×#104	D₄	semidirect
147. C₅×#103	C₂×C₄	semidirect
148. C₅×#103	C₂×C₄	semidirect
149. C₅×#103	C₂×C₄	semidirect
150. C₅×#103	C₂×C₄	semidirect
151. C₅×#102	C₂×C₄	semidirect
152. C₅×#102	C₂×C₄	semidirect
153. C₅×#102	C₂×C₄	semidirect
154. C₅×#102	C₂×C₄	semidirect
176. C₂×#444	C₂×C₅	semidirect
177. #2933	C₂×C₅	semidirect
178. C₂²×#104	C₂×C₅	semidirect
179. #2880	C₂×C₅	semidirect
180. #1975	C₂×C₅	semidirect
181. #1938	C₂×C₅	semidirect
182. #1929	C₂×C₅	semidirect
183. #1896	C₂×C₅	semidirect
184. #1876	C₂×C₅	semidirect
185. #1876	C₂×C₅	semidirect
186. #1866	C₂×C₅	semidirect
187. #1855	C₂×C₅	semidirect
188. #1765	C₂×C₅	semidirect
189. #1749	C₂×C₅	semidirect
320. C₂×#131	C₂²×C₅	semidirect
324. #452	C₄×C₅	semidirect
325. #452	C₄×C₅	semidirect
326. #451	C₄×C₅	semidirect
327. #450	C₄×C₅	semidirect
328. #449	C₄×C₅	semidirect
329. #449	C₄×C₅	semidirect
330. #448	C₄×C₅	semidirect
331. #447	C₄×C₅	semidirect
337. C₂×#108	C₂²×C₅	semidirect
338. C₂×#108	C₂²×C₅	semidirect
339. #424	C₂²×C₅	semidirect
345. C₂×#104	C₂²×C₅	semidirect
346. C₂×#104	C₂²×C₅	semidirect
353. #408	C₂²×C₅	semidirect
359. #405	C₂²×C₅	semidirect
360. C₂×#97	C₂²×C₅	semidirect
361. C₂×#97	C₂²×C₅	semidirect
362. #341	C₂²×C₅	semidirect
363. #341	C₂²×C₅	semidirect
364. #339	C₂²×C₅	semidirect
365. #339	C₂²×C₅	semidirect
366. #336	C₂²×C₅	semidirect
367. #336	C₂²×C₅	semidirect
477. C₂×Q₁₆	C₂×C₄×C₅	semidirect
478. C₂×Q₁₆	C₂×C₄×C₅	semidirect
479. C₂×SD₁₆	C₂×C₄×C₅	semidirect
480. C₂×SD₁₆	C₂×C₄×C₅	semidirect
481. C₂×SD₁₆	C₂×C₄×C₅	semidirect
482. C₂×SD₁₆	C₂×C₄×C₅	semidirect
483. C₂×D₈	C₂×C₄×C₅	semidirect
484. C₂×D₈	C₂×C₄×C₅	semidirect
532. #104	C₅×D₄	semidirect
533. #103	C₂×C₄×C₅	semidirect
534. #103	C₂×C₄×C₅	semidirect
535. #103	C₂×C₄×C₅	semidirect
536. #103	C₂×C₄×C₅	semidirect
537. #102	C₂×C₄×C₅	semidirect
538. #102	C₂×C₄×C₅	semidirect
539. #102	C₂×C₄×C₅	semidirect
540. #102	C₂×C₄×C₅	semidirect
580. C₂²×C₅	#444	semidirect
820. C₅	#22886	direct (N × H)
840. C₂²	C₅×#444	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3002	2
C₂×C₅×#444	2
C₅×#2933	2
C₂²×C₅×#104	2
C₅×#2880	2
C₅×#1975	2
C₅×#1938	2
C₅×#1929	2
C₅×#1896	2
C₅×#1876	2
C₅×#1866	2
C₅×#1855	2
C₅×#1765	2
C₅×#1749	2
#22886	5

Subgroups — C5×#22886 #11945606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22886 #11945606