Subgroups — C₅×#22062 #11944782

Order 1280.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 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	C₅×#2930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2879	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1929	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×#1871	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1789	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	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, complemented
20	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₅×#525	C₂²	1	1	yes	characteristic
23	C₅×#452	C₄	1	1	yes	characteristic, complemented
24	C₅×#452	C₄	1	1	yes	characteristic, complemented
25	C₅×#451	C₄	1	1	yes	characteristic, complemented
26	C₅×#450	C₄	1	1	yes	characteristic, complemented
27	C₅×#449	C₄	1	1	yes	characteristic, complemented
28	C₅×#449	C₄	1	1	yes	characteristic, complemented
29	C₅×#448	C₄	1	1	yes	characteristic, complemented
30	C₅×#447	C₄	1	1	yes	characteristic, complemented
31	C₅×#436	—	2	1	no	—
32	C₅×#436	—	2	1	no	—
33	C₅×#435	—	2	1	no	—
34	C₅×#435	—	2	1	no	—
35	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
37	C₅×#424	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#104	C₂²	1	1	yes	characteristic
39	C₂×C₅×#104	C₂²	1	1	yes	characteristic
40	C₂×C₅×#104	C₂²	1	1	yes	characteristic
41	C₂×C₅×#104	C₂²	1	1	yes	characteristic
42	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
44	C₅×#416	C₂²	1	1	yes	characteristic
45	C₅×#416	C₂²	1	1	yes	characteristic
46	C₅×#408	—	2	1	no	—
47	C₅×#408	—	2	1	no	—
48	C₅×#408	C₂²	1	1	yes	characteristic
49	C₅×#408	C₂²	1	1	yes	characteristic
50	C₅×#408	C₂²	1	1	yes	characteristic
51	C₅×#408	C₂²	1	1	yes	characteristic
52	C₅×#408	C₂²	1	1	yes	characteristic, complemented
53	C₅×#407	—	2	1	no	—
54	C₅×#407	—	2	1	no	—
55	C₅×#407	C₂²	1	1	yes	characteristic
56	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×#405	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
61	C₅×#341	C₂²	1	1	yes	characteristic, complemented
62	C₅×#341	C₂²	1	1	yes	characteristic, complemented
63	C₅×#339	C₂²	1	1	yes	characteristic, complemented
64	C₅×#339	C₂²	1	1	yes	characteristic, complemented
65	C₅×#336	C₂²	1	1	yes	characteristic, complemented
66	C₅×#336	C₂²	1	1	yes	characteristic, complemented
67	#22062	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	—	2	1	no	—
70	C₂×C₅×#41	—	4	1	no	—
71	C₂×C₅×#41	—	4	1	no	—
72	C₂×C₅×#41	—	4	1	no	—
73	C₂×C₅×#41	—	4	1	no	—
74	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×#41	C₂³	1	1	yes	characteristic
77	C₂×C₅×#41	C₂³	1	1	yes	characteristic
78	C₂×C₅×#41	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₅×D₄	—	2	1	no	—
81	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₅	—	2	1	no	—
83	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₅×#135	—	4	1	no	—
85	C₅×#135	—	4	1	no	—
86	C₅×#135	—	4	1	no	—
87	C₅×#135	—	4	1	no	—
88	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
96	C₅×#131	—	4	1	no	—
97	C₅×#131	—	4	1	no	—
98	C₂×C₅×M₁₆	—	2	1	no	—
99	C₂×C₅×M₁₆	—	2	1	no	—
100	C₂×C₅×M₁₆	—	4	1	no	—
101	C₂×C₅×M₁₆	—	4	1	no	—
102	C₂×C₅×M₁₆	—	4	1	no	—
103	C₂×C₅×M₁₆	—	4	1	no	—
104	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
105	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
106	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
107	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
108	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
112	C₂²×C₅×C₈	—	2	1	no	—
113	C₂²×C₅×C₈	—	2	1	no	—
114	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
116	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
118	C₅×#123	—	2	1	no	—
119	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
120	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
121	C₅×#121	C₂×C₄	1	1	yes	characteristic
122	C₅×#121	C₂×C₄	1	1	yes	characteristic
123	C₅×#120	—	2	1	no	—
124	C₄×C₅×D₄	—	2	1	no	—
125	C₄×C₅×D₄	—	2	1	no	—
126	C₅×#117	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₅×#108	—	4	1	no	—
131	C₅×#108	—	4	1	no	—
132	C₅×C₄⋊C₈	—	2	1	no	—
133	C₅×C₄⋊C₈	—	2	1	no	—
134	C₅×#104	—	4	1	no	—
135	C₅×#104	—	4	1	no	—
136	C₅×#104	—	4	1	no	—
137	C₅×#104	—	4	1	no	—
138	C₅×#104	—	4	1	no	—
139	C₅×#104	—	4	1	no	—
140	C₅×#103	C₂×C₄	1	1	yes	characteristic
141	C₅×#103	C₂×C₄	1	1	yes	characteristic
142	C₅×#103	C₂×C₄	1	1	yes	characteristic
143	C₅×#103	C₂×C₄	1	1	yes	characteristic
144	C₅×#102	C₂×C₄	1	1	yes	characteristic
145	C₅×#102	C₂×C₄	1	1	yes	characteristic
146	C₅×#102	C₂×C₄	1	1	yes	characteristic
147	C₅×#102	C₂×C₄	1	1	yes	characteristic
148	C₅×C₂²⋊C₈	—	2	1	no	—
149	C₅×C₂²⋊C₈	—	2	1	no	—
150	C₅×C₂²⋊C₈	—	2	1	no	—
151	C₅×C₂²⋊C₈	—	2	1	no	—
152	C₅×C₂²⋊C₈	—	2	1	no	—
153	C₅×C₂²⋊C₈	—	2	1	no	—
154	C₅×C₂²⋊C₈	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
161	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
162	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
163	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
164	C₅×#97	—	2	1	no	—
165	C₅×#97	—	4	1	no	—
166	C₄×C₅×C₈	—	2	1	no	—
167	C₄×C₅×C₈	—	4	1	no	—
168	C₅×#95	—	2	1	no	—
169	#3002	C₂×C₅	1	1	yes	characteristic
170	#2930	C₂×C₅	1	1	yes	characteristic, complemented
171	#2879	C₂×C₅	1	1	yes	characteristic, complemented
172	#1975	C₂×C₅	1	1	yes	characteristic, complemented
173	#1974	C₂×C₅	1	1	yes	characteristic, complemented
174	#1938	C₂×C₅	1	1	yes	characteristic, complemented
175	#1937	C₂×C₅	1	1	yes	characteristic, complemented
176	#1929	C₂×C₅	1	1	yes	characteristic, complemented
177	#1929	C₂×C₅	1	1	yes	characteristic, complemented
178	#1876	C₂×C₅	1	1	yes	characteristic, complemented
179	#1876	C₂×C₅	1	1	yes	characteristic, complemented
180	#1871	C₂×C₅	1	1	yes	characteristic, complemented
181	#1855	C₂×C₅	1	1	yes	characteristic, complemented
182	#1789	C₂×C₅	1	1	yes	characteristic, complemented
183	#1753	C₂×C₅	1	1	yes	characteristic, complemented
184	C₂⁴×C₅	—	2	1	no	—
185	C₂⁴×C₅	#41	1	1	yes	characteristic
186	C₅×#41	—	2	1	no	—
187	C₅×#41	—	2	1	no	—
188	C₅×#41	—	2	1	no	—
189	C₅×#41	—	2	1	no	—
190	C₅×#41	—	2	1	no	—
191	C₅×#41	—	2	1	no	—
192	C₅×#41	—	2	1	no	—
193	C₅×#41	—	2	1	no	—
194	C₅×#41	—	2	1	no	—
195	C₅×#41	—	2	1	no	—
196	C₅×#41	—	2	1	no	—
197	C₅×#41	—	2	1	no	—
198	C₅×#41	—	4	1	no	—
199	C₅×#41	—	4	1	no	—
200	C₅×#41	—	4	1	no	—
201	C₅×#41	—	4	1	no	—
202	C₅×#41	—	4	2	no	—
203	C₅×#41	—	4	2	no	—
204	C₅×#41	—	4	2	no	—
205	C₅×#41	—	4	2	no	—
206	C₂×C₅×Q₈	—	2	1	no	—
207	C₂×C₅×Q₈	—	4	1	no	—
208	C₂×C₅×Q₈	—	4	1	no	—
209	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	2	1	no	—
214	C₂×C₅×D₄	—	2	1	no	—
215	C₂×C₅×D₄	—	2	1	no	—
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	1	no	—
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	—	4	1	no	—
221	C₂×C₅×D₄	—	4	1	no	—
222	C₂×C₅×D₄	—	4	2	no	—
223	C₂×C₅×D₄	—	4	2	no	—
224	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₅	—	2	1	no	—
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	—	2	1	no	—
230	C₂²×C₄×C₅	—	2	1	no	—
231	C₂²×C₄×C₅	—	2	1	no	—
232	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
240	C₂²×C₄×C₅	—	4	2	no	—
241	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₅	#41	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₅×Q₁₆	—	4	1	no	—
248	C₅×Q₁₆	—	4	1	no	—
249	C₅×SD₁₆	—	4	1	no	—
250	C₅×SD₁₆	—	4	1	no	—
251	C₅×SD₁₆	—	4	1	no	—
252	C₅×SD₁₆	—	4	1	no	—
253	C₅×D₈	—	4	1	no	—
254	C₅×D₈	—	4	1	no	—
255	C₅×M₁₆	—	2	1	no	—
256	C₅×M₁₆	—	2	1	no	—
257	C₅×M₁₆	—	2	1	no	—
258	C₅×M₁₆	—	2	1	no	—
259	C₅×M₁₆	—	2	1	no	—
260	C₅×M₁₆	—	2	1	no	—
261	C₅×M₁₆	—	2	1	no	—
262	C₅×M₁₆	—	2	1	no	—
263	C₅×M₁₆	—	4	1	no	—
264	C₅×M₁₆	—	4	1	no	—
265	C₅×M₁₆	—	4	1	no	—
266	C₅×M₁₆	—	4	1	no	—
267	C₅×M₁₆	—	4	2	no	—
268	C₅×M₁₆	—	4	2	no	—
269	C₂×C₅×C₈	—	2	1	no	—
270	C₂×C₅×C₈	—	2	1	no	—
271	C₂×C₅×C₈	—	2	1	no	—
272	C₂×C₅×C₈	—	2	1	no	—
273	C₂×C₅×C₈	—	2	1	no	—
274	C₂×C₅×C₈	—	2	1	no	—
275	C₂×C₅×C₈	—	2	1	no	—
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	—	4	2	no	—
282	C₂×C₅×C₈	—	4	2	no	—
283	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
284	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
285	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
286	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
287	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
288	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
289	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	—	2	1	no	—
293	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
295	C₅×C₂²⋊C₄	—	2	1	no	—
296	C₅×C₂²⋊C₄	—	2	1	no	—
297	C₅×C₂²⋊C₄	—	2	1	no	—
298	C₅×C₂²⋊C₄	—	2	1	no	—
299	C₅×C₂²⋊C₄	—	2	1	no	—
300	C₅×C₂²⋊C₄	—	4	2	no	—
301	C₄²×C₅	—	2	1	no	—
302	C₄²×C₅	—	2	1	no	—
303	C₄²×C₅	—	2	1	no	—
304	C₄²×C₅	—	2	1	no	—
305	C₄²×C₅	—	2	1	no	—
306	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
307	C₂×#135	C₂²×C₅	1	1	yes	characteristic
308	C₂×#135	C₂²×C₅	1	1	yes	characteristic
309	C₂×#131	C₂²×C₅	1	1	yes	characteristic, complemented
310	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
311	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
312	#525	C₂²×C₅	1	1	yes	characteristic
313	#452	C₄×C₅	1	1	yes	characteristic, complemented
314	#452	C₄×C₅	1	1	yes	characteristic, complemented
315	#451	C₄×C₅	1	1	yes	characteristic, complemented
316	#450	C₄×C₅	1	1	yes	characteristic, complemented
317	#449	C₄×C₅	1	1	yes	characteristic, complemented
318	#449	C₄×C₅	1	1	yes	characteristic, complemented
319	#448	C₄×C₅	1	1	yes	characteristic, complemented
320	#447	C₄×C₅	1	1	yes	characteristic, complemented
321	#436	—	2	1	no	—
322	#436	—	2	1	no	—
323	#435	—	2	1	no	—
324	#435	—	2	1	no	—
325	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
326	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
327	#424	C₂²×C₅	1	1	yes	characteristic, complemented
328	C₂×#104	C₂²×C₅	1	1	yes	characteristic
329	C₂×#104	C₂²×C₅	1	1	yes	characteristic
330	C₂×#104	C₂²×C₅	1	1	yes	characteristic
331	C₂×#104	C₂²×C₅	1	1	yes	characteristic
332	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
333	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
334	#416	C₂²×C₅	1	1	yes	characteristic
335	#416	C₂²×C₅	1	1	yes	characteristic
336	#408	—	2	1	no	—
337	#408	—	2	1	no	—
338	#408	C₂²×C₅	1	1	yes	characteristic
339	#408	C₂²×C₅	1	1	yes	characteristic
340	#408	C₂²×C₅	1	1	yes	characteristic
341	#408	C₂²×C₅	1	1	yes	characteristic
342	#408	C₂²×C₅	1	1	yes	characteristic, complemented
343	#407	—	2	1	no	—
344	#407	—	2	1	no	—
345	#407	C₂²×C₅	1	1	yes	characteristic
346	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
347	#405	C₂²×C₅	1	1	yes	characteristic, complemented
348	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
349	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
350	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
351	#341	C₂²×C₅	1	1	yes	characteristic, complemented
352	#341	C₂²×C₅	1	1	yes	characteristic, complemented
353	#339	C₂²×C₅	1	1	yes	characteristic, complemented
354	#339	C₂²×C₅	1	1	yes	characteristic, complemented
355	#336	C₂²×C₅	1	1	yes	characteristic, complemented
356	#336	C₂²×C₅	1	1	yes	characteristic, complemented
357	C₂³×C₅	—	2	1	no	—
358	C₂³×C₅	—	2	1	no	—
359	C₂³×C₅	—	2	1	no	—
360	C₂³×C₅	—	2	1	no	—
361	C₂³×C₅	—	2	1	no	—
362	C₂³×C₅	—	4	1	no	—
363	C₂³×C₅	—	4	1	no	—
364	C₂³×C₅	—	4	2	no	—
365	C₂³×C₅	—	8	1	no	—
366	C₂³×C₅	—	8	1	no	—
367	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
368	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
369	C₂³×C₅	C₂×#41	1	1	yes	characteristic
370	C₅×Q₈	—	2	1	no	—
371	C₅×Q₈	—	2	1	no	—
372	C₅×Q₈	—	2	1	no	—
373	C₅×Q₈	—	2	1	no	—
374	C₅×Q₈	—	2	1	no	—
375	C₅×Q₈	—	2	1	no	—
376	C₅×Q₈	—	4	2	no	—
377	C₅×D₄	—	2	1	no	—
378	C₅×D₄	—	2	1	no	—
379	C₅×D₄	—	2	1	no	—
380	C₅×D₄	—	2	1	no	—
381	C₅×D₄	—	2	1	no	—
382	C₅×D₄	—	2	1	no	—
383	C₅×D₄	—	4	2	no	—
384	C₅×D₄	—	4	2	no	—
385	C₅×D₄	—	4	2	no	—
386	C₅×D₄	—	4	1	no	—
387	C₅×D₄	—	4	1	no	—
388	C₅×D₄	—	4	1	no	—
389	C₅×D₄	—	4	1	no	—
390	C₅×D₄	—	4	1	no	—
391	C₅×D₄	—	4	1	no	—
392	C₅×D₄	—	8	1	no	—
393	C₅×D₄	—	8	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	2	no	—
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	—	4	2	no	—
411	C₂×C₄×C₅	—	4	2	no	—
412	C₂×C₄×C₅	—	4	1	no	—
413	C₂×C₄×C₅	—	4	2	no	—
414	C₂×C₄×C₅	—	4	1	no	—
415	C₂×C₄×C₅	—	4	1	no	—
416	C₂×C₄×C₅	—	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	—	4	1	no	—
422	C₂×C₄×C₅	—	4	1	no	—
423	C₂×C₄×C₅	—	4	1	no	—
424	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
425	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
426	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
427	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
432	C₅×C₈	—	2	1	no	—
433	C₅×C₈	—	2	1	no	—
434	C₅×C₈	—	2	1	no	—
435	C₅×C₈	—	2	1	no	—
436	C₅×C₈	—	2	1	no	—
437	C₅×C₈	—	2	1	no	—
438	C₅×C₈	—	2	1	no	—
439	C₅×C₈	—	2	1	no	—
440	C₅×C₈	—	4	1	no	—
441	C₅×C₈	—	4	1	no	—
442	C₅×C₈	—	4	1	no	—
443	C₅×C₈	—	4	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	4	1	no	—
447	C₂×#41	—	4	1	no	—
448	C₂×#41	—	4	1	no	—
449	C₂×#41	—	4	1	no	—
450	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
451	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
452	C₂×#41	C₂³×C₅	1	1	yes	characteristic
453	C₂×#41	C₂³×C₅	1	1	yes	characteristic
454	C₂×#41	C₂³×C₅	1	1	yes	characteristic
455	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
460	#135	—	4	1	no	—
461	#135	—	4	1	no	—
462	#135	—	4	1	no	—
463	#135	—	4	1	no	—
464	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
465	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
466	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
467	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
468	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
469	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
470	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
471	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
472	#131	—	4	1	no	—
473	#131	—	4	1	no	—
474	C₂×M₁₆	—	2	1	no	—
475	C₂×M₁₆	—	2	1	no	—
476	C₂×M₁₆	—	4	1	no	—
477	C₂×M₁₆	—	4	1	no	—
478	C₂×M₁₆	—	4	1	no	—
479	C₂×M₁₆	—	4	1	no	—
480	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
481	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
482	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
483	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
484	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
485	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
486	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
488	C₂²×C₈	—	2	1	no	—
489	C₂²×C₈	—	2	1	no	—
490	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
494	#123	—	2	1	no	—
495	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
496	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
497	#121	C₂×C₄×C₅	1	1	yes	characteristic
498	#121	C₂×C₄×C₅	1	1	yes	characteristic
499	#120	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	#117	C₂³×C₅	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
506	#108	—	4	1	no	—
507	#108	—	4	1	no	—
508	C₄⋊C₈	—	2	1	no	—
509	C₄⋊C₈	—	2	1	no	—
510	#104	—	4	1	no	—
511	#104	—	4	1	no	—
512	#104	—	4	1	no	—
513	#104	—	4	1	no	—
514	#104	—	4	1	no	—
515	#104	—	4	1	no	—
516	#103	C₂×C₄×C₅	1	1	yes	characteristic
517	#103	C₂×C₄×C₅	1	1	yes	characteristic
518	#103	C₂×C₄×C₅	1	1	yes	characteristic
519	#103	C₂×C₄×C₅	1	1	yes	characteristic
520	#102	C₂×C₄×C₅	1	1	yes	characteristic
521	#102	C₂×C₄×C₅	1	1	yes	characteristic
522	#102	C₂×C₄×C₅	1	1	yes	characteristic
523	#102	C₂×C₄×C₅	1	1	yes	characteristic
524	C₂²⋊C₈	—	2	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	C₂²⋊C₈	—	2	1	no	—
528	C₂²⋊C₈	—	2	1	no	—
529	C₂²⋊C₈	—	2	1	no	—
530	C₂²⋊C₈	—	2	1	no	—
531	C₂²⋊C₈	—	2	1	no	—
532	C₂²⋊C₈	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	C₂²⋊C₈	—	2	1	no	—
535	C₂²⋊C₈	—	2	1	no	—
536	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
537	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
538	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
539	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
540	#97	—	2	1	no	—
541	#97	—	4	1	no	—
542	C₄×C₈	—	2	1	no	—
543	C₄×C₈	—	4	1	no	—
544	#95	—	2	1	no	—
545	C₂²×C₅	—	2	1	no	—
546	C₂²×C₅	—	2	1	no	—
547	C₂²×C₅	—	2	1	no	—
548	C₂²×C₅	—	2	1	no	—
549	C₂²×C₅	—	2	1	no	—
550	C₂²×C₅	—	2	1	no	—
551	C₂²×C₅	—	2	1	no	—
552	C₂²×C₅	—	2	1	no	—
553	C₂²×C₅	—	4	1	no	—
554	C₂²×C₅	—	4	1	no	—
555	C₂²×C₅	—	4	1	no	—
556	C₂²×C₅	—	4	1	no	—
557	C₂²×C₅	—	4	1	no	—
558	C₂²×C₅	—	4	1	no	—
559	C₂²×C₅	—	4	1	no	—
560	C₂²×C₅	—	4	1	no	—
561	C₂²×C₅	—	4	1	no	—
562	C₂²×C₅	—	8	1	no	—
563	C₂²×C₅	—	8	1	no	—
564	C₂²×C₅	—	8	4	no	—
565	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
566	C₂²×C₅	#538	1	1	yes	characteristic
567	C₂²×C₅	#538	1	1	yes	characteristic
568	C₄×C₅	—	2	1	no	—
569	C₄×C₅	—	2	1	no	—
570	C₄×C₅	—	4	2	no	—
571	C₄×C₅	—	4	1	no	—
572	C₄×C₅	—	4	1	no	—
573	C₄×C₅	—	4	1	no	—
574	C₄×C₅	—	4	1	no	—
575	C₄×C₅	—	4	1	no	—
576	C₄×C₅	—	8	1	no	—
577	C₄×C₅	#518	1	1	yes	characteristic
578	C₄×C₅	#518	1	1	yes	characteristic
579	C₄×C₅	#534	1	1	yes	characteristic
580	C₄×C₅	#535	1	1	yes	characteristic
581	C₂⁴	—	2	1	no	—
582	C₂⁴	C₅×#41	1	1	yes	characteristic
583	#41	—	2	1	no	—
584	#41	—	2	1	no	—
585	#41	—	2	1	no	—
586	#41	—	2	1	no	—
587	#41	—	2	1	no	—
588	#41	—	2	1	no	—
589	#41	—	2	1	no	—
590	#41	—	2	1	no	—
591	#41	—	2	1	no	—
592	#41	—	2	1	no	—
593	#41	—	2	1	no	—
594	#41	—	2	1	no	—
595	#41	—	4	1	no	—
596	#41	—	4	1	no	—
597	#41	—	4	1	no	—
598	#41	—	4	1	no	—
599	#41	—	4	2	no	—
600	#41	—	4	2	no	—
601	#41	—	4	2	no	—
602	#41	—	4	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	4	1	no	—
605	C₂×Q₈	—	4	1	no	—
606	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
607	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
608	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	4	1	no	—
618	C₂×D₄	—	4	1	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
622	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
623	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
640	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
641	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₅×#41	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
644	Q₁₆	—	4	1	no	—
645	Q₁₆	—	4	1	no	—
646	SD₁₆	—	4	1	no	—
647	SD₁₆	—	4	1	no	—
648	SD₁₆	—	4	1	no	—
649	SD₁₆	—	4	1	no	—
650	D₈	—	4	1	no	—
651	D₈	—	4	1	no	—
652	M₁₆	—	2	1	no	—
653	M₁₆	—	2	1	no	—
654	M₁₆	—	2	1	no	—
655	M₁₆	—	2	1	no	—
656	M₁₆	—	2	1	no	—
657	M₁₆	—	2	1	no	—
658	M₁₆	—	2	1	no	—
659	M₁₆	—	2	1	no	—
660	M₁₆	—	4	1	no	—
661	M₁₆	—	4	1	no	—
662	M₁₆	—	4	1	no	—
663	M₁₆	—	4	1	no	—
664	M₁₆	—	4	2	no	—
665	M₁₆	—	4	2	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	4	2	no	—
679	C₂×C₈	—	4	2	no	—
680	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
681	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
682	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
683	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
684	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
685	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
686	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
687	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
691	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	1	no	—
703	C₂×C₅	—	2	1	no	—
704	C₂×C₅	—	2	1	no	—
705	C₂×C₅	—	4	1	no	—
706	C₂×C₅	—	4	1	no	—
707	C₂×C₅	—	8	1	no	—
708	C₂×C₅	—	8	1	no	—
709	C₂×C₅	—	8	1	no	—
710	C₂×C₅	#2321	1	1	yes	characteristic
711	C₂×C₅	#2956	1	1	yes	characteristic
712	C₂×C₅	#2957	1	1	yes	characteristic
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	2	no	—
721	C₂³	—	8	1	no	—
722	C₂³	—	8	1	no	—
723	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
724	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
725	C₂³	C₂×C₅×#41	1	1	yes	characteristic
726	Q₈	—	2	1	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	4	2	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	2	1	no	—
737	D₄	—	2	1	no	—
738	D₄	—	2	1	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	8	1	no	—
749	D₄	—	8	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
781	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
783	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
784	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
785	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
786	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
787	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
788	C₈	—	2	1	no	—
789	C₈	—	2	1	no	—
790	C₈	—	2	1	no	—
791	C₈	—	2	1	no	—
792	C₈	—	2	1	no	—
793	C₈	—	2	1	no	—
794	C₈	—	2	1	no	—
795	C₈	—	2	1	no	—
796	C₈	—	4	1	no	—
797	C₈	—	4	1	no	—
798	C₈	—	4	1	no	—
799	C₈	—	4	1	no	—
800	C₅	#22062	1	1	yes	characteristic, direct product factor, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	4	no	—
821	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
822	C₂²	C₅×#538	1	1	yes	characteristic
823	C₂²	C₅×#538	1	1	yes	characteristic
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	8	1	no	—
833	C₄	C₅×#518	1	1	yes	characteristic
834	C₄	C₅×#518	1	1	yes	characteristic
835	C₄	C₅×#534	1	1	yes	characteristic
836	C₄	C₅×#535	1	1	yes	characteristic
837	C₂	—	2	1	no	—
838	C₂	—	2	1	no	—
839	C₂	—	4	1	no	—
840	C₂	—	4	1	no	—
841	C₂	—	8	1	no	—
842	C₂	—	8	1	no	—
843	C₂	—	8	1	no	—
844	C₂	C₅×#2321	1	1	yes	characteristic
845	C₂	C₅×#2956	1	1	yes	characteristic
846	C₂	C₅×#2957	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 ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2930	C₂	semidirect
3. C₅×#2879	C₂	semidirect
4. C₅×#1975	C₂	semidirect
5. C₅×#1974	C₂	semidirect
6. C₅×#1938	C₂	semidirect
7. C₅×#1937	C₂	semidirect
8. C₅×#1929	C₂	semidirect
9. C₅×#1929	C₂	semidirect
10. C₅×#1876	C₂	semidirect
11. C₅×#1876	C₂	semidirect
12. C₅×#1871	C₂	semidirect
13. C₅×#1855	C₂	semidirect
14. C₅×#1789	C₂	semidirect
15. C₅×#1753	C₂	semidirect
19. C₂×C₅×#131	C₂²	semidirect
23. C₅×#452	C₄	semidirect
24. C₅×#452	C₄	semidirect
25. C₅×#451	C₄	semidirect
26. C₅×#450	C₄	semidirect
27. C₅×#449	C₄	semidirect
28. C₅×#449	C₄	semidirect
29. C₅×#448	C₄	semidirect
30. C₅×#447	C₄	semidirect
35. C₂×C₅×#108	C₂²	semidirect
36. C₂×C₅×#108	C₂²	semidirect
37. C₅×#424	C₂²	semidirect
42. C₂×C₅×#104	C₂²	semidirect
43. C₂×C₅×#104	C₂²	semidirect
52. C₅×#408	C₂²	semidirect
57. C₅×#405	C₂²	semidirect
58. C₂×C₅×#97	C₂²	semidirect
59. C₂×C₄×C₅×C₈	C₂²	semidirect
61. C₅×#341	C₂²	semidirect
62. C₅×#341	C₂²	semidirect
63. C₅×#339	C₂²	semidirect
64. C₅×#339	C₂²	semidirect
65. C₅×#336	C₂²	semidirect
66. C₅×#336	C₂²	semidirect
67. #22062	C₅	direct (N × H)
170. #2930	C₂×C₅	semidirect
171. #2879	C₂×C₅	semidirect
172. #1975	C₂×C₅	semidirect
173. #1974	C₂×C₅	semidirect
174. #1938	C₂×C₅	semidirect
175. #1937	C₂×C₅	semidirect
176. #1929	C₂×C₅	semidirect
177. #1929	C₂×C₅	semidirect
178. #1876	C₂×C₅	semidirect
179. #1876	C₂×C₅	semidirect
180. #1871	C₂×C₅	semidirect
181. #1855	C₂×C₅	semidirect
182. #1789	C₂×C₅	semidirect
183. #1753	C₂×C₅	semidirect
309. C₂×#131	C₂²×C₅	semidirect
313. #452	C₄×C₅	semidirect
314. #452	C₄×C₅	semidirect
315. #451	C₄×C₅	semidirect
316. #450	C₄×C₅	semidirect
317. #449	C₄×C₅	semidirect
318. #449	C₄×C₅	semidirect
319. #448	C₄×C₅	semidirect
320. #447	C₄×C₅	semidirect
325. C₂×#108	C₂²×C₅	semidirect
326. C₂×#108	C₂²×C₅	semidirect
327. #424	C₂²×C₅	semidirect
332. C₂×#104	C₂²×C₅	semidirect
333. C₂×#104	C₂²×C₅	semidirect
342. #408	C₂²×C₅	semidirect
347. #405	C₂²×C₅	semidirect
348. C₂×#97	C₂²×C₅	semidirect
349. C₂×C₄×C₈	C₂²×C₅	semidirect
351. #341	C₂²×C₅	semidirect
352. #341	C₂²×C₅	semidirect
353. #339	C₂²×C₅	semidirect
354. #339	C₂²×C₅	semidirect
355. #336	C₂²×C₅	semidirect
356. #336	C₂²×C₅	semidirect
800. C₅	#22062	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3002	2
C₅×#2930	2
C₅×#2879	2
C₅×#1975	2
C₅×#1974	2
C₅×#1938	2
C₅×#1937	2
C₅×#1929	2
C₅×#1876	2
C₅×#1871	2
C₅×#1855	2
C₅×#1789	2
C₅×#1753	2
#22062	5

Subgroups — C5×#22062 #11944782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22062 #11944782