Subgroups — C₅×#34310 #11957030

Order 1280.

3764 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#518	C₂	1	2	yes	maximal, complemented
3	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	2	yes	maximal, complemented
5	C₅×#2361	C₂	1	2	yes	maximal, complemented
6	C₅×#2358	C₂	1	4	yes	maximal, complemented
7	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₅×#2324	C₂	1	2	yes	maximal, complemented
12	C₅×#2321	C₂	1	4	yes	maximal, complemented
13	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#121	C₂	1	2	yes	maximal, complemented
15	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#390	C₂	1	2	yes	maximal, complemented
17	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×C₅×D₄	C₂²	1	2	yes	—
19	C₂³×C₅×D₄	C₂²	1	2	yes	—
20	C₅×D₄²	C₄	1	16	yes	complemented
21	C₂×C₅×#127	C₂²	1	1	yes	characteristic
22	C₂×C₅×#121	C₂²	1	2	yes	—
23	C₂×C₅×#121	C₂²	1	2	yes	—
24	C₂×C₅×#120	C₂²	1	4	yes	—
25	C₅×#518	—	2	16	no	—
26	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
33	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
36	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
37	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
38	C₂×C₅×#117	C₂²	1	2	yes	complemented
39	C₂×C₅×#117	C₂²	1	2	yes	complemented
40	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
42	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
43	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
44	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
45	C₅×#390	C₂²	1	1	yes	characteristic
46	C₅×#390	C₂²	1	2	yes	—
47	C₅×#390	C₂²	1	1	yes	characteristic
48	C₅×#390	C₂²	1	2	yes	complemented
49	C₅×#390	C₂²	1	4	yes	complemented
50	C₅×#390	C₂²	1	4	yes	complemented
51	C₅×#390	C₂²	1	2	yes	complemented
52	C₅×#390	C₂²	1	2	yes	complemented
53	C₅×#390	C₂²	1	2	yes	complemented
54	C₅×#390	C₂²	1	2	yes	complemented
55	C₅×#389	C₂²	1	1	yes	characteristic, complemented
56	C₅×#389	C₂²	1	1	yes	characteristic, complemented
57	C₅×#389	C₂²	1	2	yes	complemented
58	C₅×#388	C₂²	1	2	yes	complemented
59	C₅×#388	C₂²	1	2	yes	complemented
60	C₅×#388	C₂²	1	4	yes	complemented
61	C₅×#388	C₂²	1	4	yes	complemented
62	C₅×#388	C₂²	1	4	yes	complemented
63	C₅×#386	C₂²	1	4	yes	complemented
64	C₅×#386	C₂²	1	4	yes	complemented
65	C₅×#386	C₂²	1	4	yes	complemented
66	C₅×#386	C₂²	1	4	yes	complemented
67	C₅×#386	C₂²	1	4	yes	complemented
68	C₅×#385	C₂²	1	4	yes	complemented
69	C₅×#385	C₂²	1	4	yes	complemented
70	C₅×#384	C₂²	1	1	yes	characteristic, complemented
71	C₅×#380	C₂²	1	2	yes	complemented
72	C₅×#380	C₂²	1	2	yes	complemented
73	C₅×#379	C₂²	1	4	yes	complemented
74	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
80	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
81	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
82	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
83	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
84	C₄³×C₅	C₂²	1	1	yes	characteristic, complemented
85	#34310	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁵×C₅	C₂³	1	4	yes	—
87	C₂²×C₅×D₄	—	2	8	no	—
88	C₂²×C₅×D₄	—	2	8	no	—
89	C₂²×C₅×D₄	—	4	4	no	—
90	C₂²×C₅×D₄	—	4	4	no	—
91	C₂²×C₅×D₄	C₂×C₄	1	16	yes	complemented
92	C₂²×C₅×D₄	C₂×C₄	1	16	yes	complemented
93	C₂²×C₅×D₄	C₂³	1	4	yes	—
94	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₅×D₄	C₂³	1	2	yes	—
96	C₂²×C₅×D₄	C₂³	1	2	yes	—
97	C₂²×C₅×D₄	C₂³	1	4	yes	—
98	C₂²×C₅×D₄	C₂³	1	2	yes	—
99	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅	C₂³	1	2	yes	—
101	C₂³×C₄×C₅	C₂³	1	2	yes	—
102	C₂³×C₄×C₅	C₂³	1	2	yes	—
103	C₂³×C₄×C₅	C₂³	1	4	yes	—
104	C₂³×C₄×C₅	C₂³	1	4	yes	—
105	C₂³×C₄×C₅	C₂³	1	4	yes	—
106	C₂³×C₄×C₅	C₂³	1	2	yes	—
107	C₅×#127	C₂×C₄	1	8	yes	complemented
108	C₅×#121	C₂×C₄	1	16	yes	complemented
109	C₅×#121	C₂×C₄	1	16	yes	complemented
110	C₅×#120	C₂×C₄	1	32	yes	complemented
111	C₄×C₅×D₄	—	2	8	no	—
112	C₄×C₅×D₄	—	2	4	no	—
113	C₄×C₅×D₄	—	2	16	no	—
114	C₄×C₅×D₄	—	2	8	no	—
115	C₄×C₅×D₄	—	2	16	no	—
116	C₄×C₅×D₄	—	2	8	no	—
117	C₄×C₅×D₄	—	4	4	no	—
118	C₄×C₅×D₄	—	4	4	no	—
119	C₄×C₅×D₄	—	4	4	no	—
120	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
121	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
122	C₄×C₅×D₄	D₄	1	8	yes	complemented
123	C₅×#117	—	2	8	no	—
124	C₅×#117	—	2	8	no	—
125	C₂×C₅×C₄⋊C₄	—	4	4	no	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
139	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
140	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
141	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₄²×C₅	—	4	4	no	—
160	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂³	1	2	yes	—
165	C₂×C₄²×C₅	C₂³	1	4	yes	—
166	C₂×C₄²×C₅	C₂³	1	2	yes	—
167	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₅	C₂³	1	2	yes	—
169	C₂×C₄²×C₅	C₂³	1	2	yes	—
170	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
172	C₅×#95	C₂³	1	2	yes	—
173	C₅×#95	C₂³	1	2	yes	—
174	C₅×#95	C₂³	1	2	yes	—
175	C₅×#95	C₂³	1	2	yes	—
176	C₅×#95	C₂³	1	4	yes	—
177	C₅×#95	C₂³	1	2	yes	—
178	C₅×#95	C₂³	1	4	yes	—
179	C₅×#95	C₂³	1	2	yes	—
180	C₂×D₄²	C₂×C₅	1	1	yes	characteristic
181	C₂×#518	C₂×C₅	1	2	yes	complemented
182	#2366	C₂×C₅	1	1	yes	characteristic, complemented
183	#2363	C₂×C₅	1	2	yes	complemented
184	#2361	C₂×C₅	1	2	yes	complemented
185	#2358	C₂×C₅	1	4	yes	complemented
186	#2354	C₂×C₅	1	1	yes	characteristic, complemented
187	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
188	D₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
189	D₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
190	#2324	C₂×C₅	1	2	yes	complemented
191	#2321	C₂×C₅	1	4	yes	complemented
192	C₄×#127	C₂×C₅	1	1	yes	characteristic, complemented
193	C₄×#121	C₂×C₅	1	2	yes	complemented
194	#2293	C₂×C₅	1	1	yes	characteristic, complemented
195	C₂×#390	C₂×C₅	1	2	yes	complemented
196	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
197	C₂⁴×C₅	—	2	8	no	—
198	C₂⁴×C₅	—	2	8	no	—
199	C₂⁴×C₅	—	4	4	no	—
200	C₂⁴×C₅	—	4	4	no	—
201	C₂⁴×C₅	—	4	4	no	—
202	C₂⁴×C₅	—	4	4	no	—
203	C₂⁴×C₅	C₂²×C₄	1	16	yes	—
204	C₂⁴×C₅	C₂⁴	1	2	yes	—
205	C₂⁴×C₅	C₂⁴	1	4	yes	—
206	C₂⁴×C₅	C₂⁴	1	2	yes	—
207	C₂×C₅×D₄	—	2	8	no	—
208	C₂×C₅×D₄	—	2	8	no	—
209	C₂×C₅×D₄	—	2	64	no	—
210	C₂×C₅×D₄	—	2	4	no	—
211	C₂×C₅×D₄	—	2	4	no	—
212	C₂×C₅×D₄	—	2	4	no	—
213	C₂×C₅×D₄	—	2	4	no	—
214	C₂×C₅×D₄	—	2	2	no	—
215	C₂×C₅×D₄	—	2	2	no	—
216	C₂×C₅×D₄	—	4	32	no	—
217	C₂×C₅×D₄	—	4	2	no	—
218	C₂×C₅×D₄	—	4	4	no	—
219	C₂×C₅×D₄	—	4	4	no	—
220	C₂×C₅×D₄	—	4	2	no	—
221	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
222	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
223	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
224	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
225	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
226	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
227	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
228	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
229	C₂×C₅×D₄	#41	1	4	yes	—
230	C₂²×C₄×C₅	—	2	4	no	—
231	C₂²×C₄×C₅	—	2	4	no	—
232	C₂²×C₄×C₅	—	2	4	no	—
233	C₂²×C₄×C₅	—	2	4	no	—
234	C₂²×C₄×C₅	—	2	4	no	—
235	C₂²×C₄×C₅	—	2	8	no	—
236	C₂²×C₄×C₅	—	2	4	no	—
237	C₂²×C₄×C₅	—	2	8	no	—
238	C₂²×C₄×C₅	—	2	8	no	—
239	C₂²×C₄×C₅	—	4	2	no	—
240	C₂²×C₄×C₅	—	4	2	no	—
241	C₂²×C₄×C₅	—	4	2	no	—
242	C₂²×C₄×C₅	—	4	4	no	—
243	C₂²×C₄×C₅	—	4	4	no	—
244	C₂²×C₄×C₅	—	4	4	no	—
245	C₂²×C₄×C₅	—	4	4	no	—
246	C₂²×C₄×C₅	—	4	4	no	—
247	C₂²×C₄×C₅	—	4	4	no	—
248	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
249	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
250	C₂²×C₄×C₅	C₂×D₄	1	8	yes	complemented
251	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₅×C₄⋊C₄	—	2	4	no	—
266	C₅×C₄⋊C₄	—	2	4	no	—
267	C₅×C₄⋊C₄	—	2	4	no	—
268	C₅×C₄⋊C₄	—	2	2	no	—
269	C₅×C₄⋊C₄	—	2	2	no	—
270	C₅×C₄⋊C₄	—	2	4	no	—
271	C₅×C₄⋊C₄	—	2	2	no	—
272	C₅×C₄⋊C₄	—	4	4	no	—
273	C₅×C₄⋊C₄	—	4	2	no	—
274	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
275	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
276	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
277	C₅×C₂²⋊C₄	—	2	8	no	—
278	C₅×C₂²⋊C₄	—	2	4	no	—
279	C₅×C₂²⋊C₄	—	2	8	no	—
280	C₅×C₂²⋊C₄	—	2	4	no	—
281	C₅×C₂²⋊C₄	—	2	4	no	—
282	C₅×C₂²⋊C₄	—	2	8	no	—
283	C₅×C₂²⋊C₄	—	2	8	no	—
284	C₅×C₂²⋊C₄	—	2	4	no	—
285	C₅×C₂²⋊C₄	—	2	8	no	—
286	C₅×C₂²⋊C₄	—	4	4	no	—
287	C₅×C₂²⋊C₄	—	4	4	no	—
288	C₅×C₂²⋊C₄	—	4	2	no	—
289	C₅×C₂²⋊C₄	—	4	4	no	—
290	C₅×C₂²⋊C₄	—	4	4	no	—
291	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
292	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
293	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
294	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
295	C₄²×C₅	—	2	8	no	—
296	C₄²×C₅	—	2	4	no	—
297	C₄²×C₅	—	2	2	no	—
298	C₄²×C₅	—	2	2	no	—
299	C₄²×C₅	—	2	4	no	—
300	C₄²×C₅	—	2	2	no	—
301	C₄²×C₅	—	2	2	no	—
302	C₄²×C₅	—	4	2	no	—
303	C₄²×C₅	—	4	2	no	—
304	C₄²×C₅	—	4	1	no	—
305	C₄²×C₅	C₂²×C₄	1	4	yes	—
306	C₄²×C₅	C₂×D₄	1	4	yes	complemented
307	C₂³×D₄	C₂²×C₅	1	2	yes	—
308	C₂³×D₄	C₂²×C₅	1	2	yes	—
309	D₄²	C₄×C₅	1	16	yes	complemented
310	C₂×#127	C₂²×C₅	1	1	yes	characteristic
311	C₂×#121	C₂²×C₅	1	2	yes	—
312	C₂×#121	C₂²×C₅	1	2	yes	—
313	C₂×#120	C₂²×C₅	1	4	yes	—
314	#518	—	2	16	no	—
315	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
317	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
321	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
322	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
323	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
324	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
325	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
326	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
327	C₂×#117	C₂²×C₅	1	2	yes	complemented
328	C₂×#117	C₂²×C₅	1	2	yes	complemented
329	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
330	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
331	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
332	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
333	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
334	#390	C₂²×C₅	1	1	yes	characteristic
335	#390	C₂²×C₅	1	2	yes	—
336	#390	C₂²×C₅	1	1	yes	characteristic
337	#390	C₂²×C₅	1	2	yes	complemented
338	#390	C₂²×C₅	1	2	yes	complemented
339	#390	C₂²×C₅	1	2	yes	complemented
340	#390	C₂²×C₅	1	4	yes	complemented
341	#390	C₂²×C₅	1	2	yes	complemented
342	#390	C₂²×C₅	1	4	yes	complemented
343	#390	C₂²×C₅	1	2	yes	complemented
344	#389	C₂²×C₅	1	2	yes	complemented
345	#389	C₂²×C₅	1	1	yes	characteristic, complemented
346	#389	C₂²×C₅	1	1	yes	characteristic, complemented
347	#388	C₂²×C₅	1	2	yes	complemented
348	#388	C₂²×C₅	1	4	yes	complemented
349	#388	C₂²×C₅	1	4	yes	complemented
350	#388	C₂²×C₅	1	4	yes	complemented
351	#388	C₂²×C₅	1	2	yes	complemented
352	#386	C₂²×C₅	1	4	yes	complemented
353	#386	C₂²×C₅	1	4	yes	complemented
354	#386	C₂²×C₅	1	4	yes	complemented
355	#386	C₂²×C₅	1	4	yes	complemented
356	#386	C₂²×C₅	1	4	yes	complemented
357	#385	C₂²×C₅	1	4	yes	complemented
358	#385	C₂²×C₅	1	4	yes	complemented
359	#384	C₂²×C₅	1	1	yes	characteristic, complemented
360	#380	C₂²×C₅	1	2	yes	complemented
361	#380	C₂²×C₅	1	2	yes	complemented
362	#379	C₂²×C₅	1	4	yes	complemented
363	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
364	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
365	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
366	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
367	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
368	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
369	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
370	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
371	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
372	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
373	C₄³	C₂²×C₅	1	1	yes	characteristic, complemented
374	C₂³×C₅	—	2	2	no	—
375	C₂³×C₅	—	2	2	no	—
376	C₂³×C₅	—	2	2	no	—
377	C₂³×C₅	—	2	2	no	—
378	C₂³×C₅	—	2	2	no	—
379	C₂³×C₅	—	2	4	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	—	2	4	no	—
382	C₂³×C₅	—	2	2	no	—
383	C₂³×C₅	—	2	4	no	—
384	C₂³×C₅	—	2	4	no	—
385	C₂³×C₅	—	2	4	no	—
386	C₂³×C₅	—	2	2	no	—
387	C₂³×C₅	—	2	2	no	—
388	C₂³×C₅	—	2	2	no	—
389	C₂³×C₅	—	2	4	no	—
390	C₂³×C₅	—	2	32	no	—
391	C₂³×C₅	—	4	16	no	—
392	C₂³×C₅	—	4	16	no	—
393	C₂³×C₅	—	8	8	no	—
394	C₂³×C₅	—	8	8	no	—
395	C₂³×C₅	—	8	8	no	—
396	C₂³×C₅	—	8	8	no	—
397	C₂³×C₅	C₂³×C₄	1	4	yes	—
398	C₂³×C₅	C₂³×C₄	1	8	yes	—
399	C₂³×C₅	C₂³×C₄	1	4	yes	—
400	C₂³×C₅	C₂²×D₄	1	4	yes	—
401	C₂³×C₅	C₂×#41	1	4	yes	—
402	C₂³×C₅	C₂⁵	1	1	yes	characteristic
403	C₅×D₄	—	2	32	no	—
404	C₅×D₄	—	2	16	no	—
405	C₅×D₄	—	2	8	no	—
406	C₅×D₄	—	2	16	no	—
407	C₅×D₄	—	4	16	no	—
408	C₅×D₄	—	4	8	no	—
409	C₅×D₄	C₄×D₄	1	16	yes	complemented
410	C₂×C₄×C₅	—	2	2	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	—	2	1	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	1	no	—
419	C₂×C₄×C₅	—	2	2	no	—
420	C₂×C₄×C₅	—	2	2	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	—	2	16	no	—
425	C₂×C₄×C₅	—	2	16	no	—
426	C₂×C₄×C₅	—	2	2	no	—
427	C₂×C₄×C₅	—	2	4	no	—
428	C₂×C₄×C₅	—	2	2	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	2	no	—
431	C₂×C₄×C₅	—	2	2	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	2	no	—
434	C₂×C₄×C₅	—	2	4	no	—
435	C₂×C₄×C₅	—	2	2	no	—
436	C₂×C₄×C₅	—	2	2	no	—
437	C₂×C₄×C₅	—	2	4	no	—
438	C₂×C₄×C₅	—	2	2	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	2	no	—
441	C₂×C₄×C₅	—	4	8	no	—
442	C₂×C₄×C₅	—	4	8	no	—
443	C₂×C₄×C₅	—	8	8	no	—
444	C₂×C₄×C₅	—	8	8	no	—
445	C₂×C₄×C₅	—	8	8	no	—
446	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
448	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
449	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
450	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
451	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
452	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₅	C₂×#41	1	2	yes	—
456	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
457	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
459	C₂⁵	C₂³×C₅	1	4	yes	—
460	C₂²×D₄	—	2	8	no	—
461	C₂²×D₄	—	2	8	no	—
462	C₂²×D₄	—	4	4	no	—
463	C₂²×D₄	—	4	4	no	—
464	C₂²×D₄	C₂×C₄×C₅	1	16	yes	complemented
465	C₂²×D₄	C₂×C₄×C₅	1	16	yes	complemented
466	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₅	1	4	yes	—
468	C₂²×D₄	C₂³×C₅	1	2	yes	—
469	C₂²×D₄	C₂³×C₅	1	2	yes	—
470	C₂²×D₄	C₂³×C₅	1	2	yes	—
471	C₂²×D₄	C₂³×C₅	1	4	yes	—
472	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₅	1	2	yes	—
474	C₂³×C₄	C₂³×C₅	1	2	yes	—
475	C₂³×C₄	C₂³×C₅	1	2	yes	—
476	C₂³×C₄	C₂³×C₅	1	4	yes	—
477	C₂³×C₄	C₂³×C₅	1	4	yes	—
478	C₂³×C₄	C₂³×C₅	1	4	yes	—
479	C₂³×C₄	C₂³×C₅	1	2	yes	—
480	#127	C₂×C₄×C₅	1	8	yes	complemented
481	#121	C₂×C₄×C₅	1	16	yes	complemented
482	#121	C₂×C₄×C₅	1	16	yes	complemented
483	#120	C₂×C₄×C₅	1	32	yes	complemented
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	4	no	—
486	C₄×D₄	—	2	16	no	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	2	16	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	4	4	no	—
491	C₄×D₄	—	4	4	no	—
492	C₄×D₄	—	4	4	no	—
493	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
494	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
495	C₄×D₄	C₅×D₄	1	8	yes	complemented
496	#117	—	2	8	no	—
497	#117	—	2	8	no	—
498	C₂×C₄⋊C₄	—	4	4	no	—
499	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	—	2	16	no	—
512	C₂×C₂²⋊C₄	—	2	16	no	—
513	C₂×C₂²⋊C₄	—	4	8	no	—
514	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
532	C₂×C₄²	—	4	4	no	—
533	C₂×C₄²	C₂³×C₅	1	2	yes	—
534	C₂×C₄²	C₂³×C₅	1	4	yes	—
535	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₅	1	2	yes	—
539	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₅	1	2	yes	—
542	C₂×C₄²	C₂³×C₅	1	2	yes	—
543	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
545	#95	C₂³×C₅	1	2	yes	—
546	#95	C₂³×C₅	1	2	yes	—
547	#95	C₂³×C₅	1	2	yes	—
548	#95	C₂³×C₅	1	2	yes	—
549	#95	C₂³×C₅	1	4	yes	—
550	#95	C₂³×C₅	1	2	yes	—
551	#95	C₂³×C₅	1	4	yes	—
552	#95	C₂³×C₅	1	2	yes	—
553	C₂²×C₅	—	2	4	no	—
554	C₂²×C₅	—	2	4	no	—
555	C₂²×C₅	—	2	4	no	—
556	C₂²×C₅	—	2	4	no	—
557	C₂²×C₅	—	2	4	no	—
558	C₂²×C₅	—	2	4	no	—
559	C₂²×C₅	—	2	4	no	—
560	C₂²×C₅	—	2	8	no	—
561	C₂²×C₅	—	2	4	no	—
562	C₂²×C₅	—	2	8	no	—
563	C₂²×C₅	—	2	8	no	—
564	C₂²×C₅	—	2	4	no	—
565	C₂²×C₅	—	4	4	no	—
566	C₂²×C₅	—	4	2	no	—
567	C₂²×C₅	—	4	4	no	—
568	C₂²×C₅	—	4	2	no	—
569	C₂²×C₅	—	4	4	no	—
570	C₂²×C₅	—	4	2	no	—
571	C₂²×C₅	—	4	4	no	—
572	C₂²×C₅	—	4	2	no	—
573	C₂²×C₅	—	8	32	no	—
574	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
575	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
576	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
577	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
578	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₅	#585	1	1	yes	characteristic
582	C₄×C₅	—	2	4	no	—
583	C₄×C₅	—	2	4	no	—
584	C₄×C₅	—	2	2	no	—
585	C₄×C₅	—	2	2	no	—
586	C₄×C₅	—	2	4	no	—
587	C₄×C₅	—	2	2	no	—
588	C₄×C₅	—	2	2	no	—
589	C₄×C₅	—	4	2	no	—
590	C₄×C₅	—	4	2	no	—
591	C₄×C₅	—	4	4	no	—
592	C₄×C₅	—	4	1	no	—
593	C₄×C₅	—	4	2	no	—
594	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
595	C₄×C₅	#518	1	4	yes	complemented
596	C₂⁴	—	2	8	no	—
597	C₂⁴	—	2	8	no	—
598	C₂⁴	—	4	4	no	—
599	C₂⁴	—	4	4	no	—
600	C₂⁴	—	4	4	no	—
601	C₂⁴	—	4	4	no	—
602	C₂⁴	C₂²×C₄×C₅	1	16	yes	—
603	C₂⁴	C₂⁴×C₅	1	2	yes	—
604	C₂⁴	C₂⁴×C₅	1	4	yes	—
605	C₂⁴	C₂⁴×C₅	1	2	yes	—
606	C₂×D₄	—	2	8	no	—
607	C₂×D₄	—	2	8	no	—
608	C₂×D₄	—	2	64	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	4	32	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
621	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
622	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
623	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
624	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
625	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
626	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
627	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
628	C₂×D₄	C₅×#41	1	4	yes	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	8	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	8	no	—
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
648	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
649	C₂²×C₄	C₂×C₅×D₄	1	8	yes	complemented
650	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	4	4	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
674	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
675	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	complemented
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
691	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
692	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
693	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	complemented
694	C₄²	—	2	8	no	—
695	C₄²	—	2	4	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	4	2	no	—
702	C₄²	—	4	2	no	—
703	C₄²	—	4	1	no	—
704	C₄²	C₂²×C₄×C₅	1	4	yes	—
705	C₄²	C₂×C₅×D₄	1	4	yes	complemented
706	C₂×C₅	—	2	8	no	—
707	C₂×C₅	—	4	8	no	—
708	C₂×C₅	—	4	4	no	—
709	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
710	C₂×C₅	C₂×#518	1	1	yes	characteristic
711	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
712	C₂×C₅	#3496	1	1	yes	characteristic
713	C₂×C₅	#3498	1	1	yes	characteristic
714	C₂×C₅	#3514	1	1	yes	characteristic
715	C₂×C₅	#3519	1	1	yes	characteristic
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	32	no	—
733	C₂³	—	4	16	no	—
734	C₂³	—	4	16	no	—
735	C₂³	—	8	8	no	—
736	C₂³	—	8	8	no	—
737	C₂³	—	8	8	no	—
738	C₂³	—	8	8	no	—
739	C₂³	C₂³×C₄×C₅	1	4	yes	—
740	C₂³	C₂³×C₄×C₅	1	8	yes	—
741	C₂³	C₂³×C₄×C₅	1	4	yes	—
742	C₂³	C₂²×C₅×D₄	1	4	yes	—
743	C₂³	C₂×C₅×#41	1	4	yes	—
744	C₂³	C₂⁵×C₅	1	1	yes	characteristic
745	D₄	—	2	32	no	—
746	D₄	—	2	16	no	—
747	D₄	—	2	8	no	—
748	D₄	—	2	16	no	—
749	D₄	—	4	16	no	—
750	D₄	—	4	8	no	—
751	D₄	C₄×C₅×D₄	1	16	yes	complemented
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	16	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	8	8	no	—
786	C₂×C₄	—	8	8	no	—
787	C₂×C₄	—	8	8	no	—
788	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
789	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
790	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
791	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
792	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
793	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
794	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
795	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
796	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
797	C₂×C₄	C₂×C₅×#41	1	2	yes	—
798	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
799	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
800	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
801	C₅	#34310	1	1	yes	characteristic, direct product factor, Sylow
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	8	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	2	8	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	4	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	8	32	no	—
823	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
824	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
825	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
826	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
827	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
828	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
829	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂²	C₅×#585	1	1	yes	characteristic
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	4	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
844	C₄	C₅×#518	1	4	yes	complemented
845	C₂	—	2	8	no	—
846	C₂	—	4	4	no	—
847	C₂	—	4	8	no	—
848	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
849	C₂	C₂×C₅×#518	1	1	yes	characteristic
850	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
851	C₂	C₅×#3496	1	1	yes	characteristic
852	C₂	C₅×#3498	1	1	yes	characteristic
853	C₂	C₅×#3514	1	1	yes	characteristic
854	C₂	C₅×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×D₄²	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#518	C₂	semidirect
3. C₅×#2366	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2361	C₂	semidirect
6. C₅×#2358	C₂	semidirect
7. C₅×#2354	C₂	semidirect
8. C₅×D₄×C₄⋊C₄	C₂	semidirect
9. C₅×D₄×C₂²⋊C₄	C₂	semidirect
10. C₅×D₄×C₂²⋊C₄	C₂	semidirect
11. C₅×#2324	C₂	semidirect
12. C₅×#2321	C₂	semidirect
13. C₄×C₅×#127	C₂	semidirect
14. C₄×C₅×#121	C₂	semidirect
15. C₅×#2293	C₂	semidirect
16. C₂×C₅×#390	C₂	semidirect
17. C₄²×C₅×D₄	C₂	semidirect
20. C₅×D₄²	C₄	semidirect
31. C₂×C₄×C₅×D₄	C₂²	semidirect
32. C₂×C₄×C₅×D₄	C₂²	semidirect
33. C₂×C₄×C₅×D₄	C₂²	semidirect
34. C₂×C₄×C₅×D₄	C₂²	semidirect
35. C₂×C₄×C₅×D₄	C₂²	semidirect
36. C₂×C₄×C₅×D₄	C₂²	semidirect
37. C₂×C₄×C₅×D₄	C₂²	semidirect
38. C₂×C₅×#117	C₂²	semidirect
39. C₂×C₅×#117	C₂²	semidirect
40. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
41. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
42. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
43. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
44. C₂²×C₄²×C₅	C₂²	semidirect
48. C₅×#390	C₂²	semidirect
49. C₅×#390	C₂²	semidirect
50. C₅×#390	C₂²	semidirect
51. C₅×#390	C₂²	semidirect
52. C₅×#390	C₂²	semidirect
53. C₅×#390	C₂²	semidirect
54. C₅×#390	C₂²	semidirect
55. C₅×#389	C₂²	semidirect
56. C₅×#389	C₂²	semidirect
57. C₅×#389	C₂²	semidirect
58. C₅×#388	C₂²	semidirect
59. C₅×#388	C₂²	semidirect
60. C₅×#388	C₂²	semidirect
61. C₅×#388	C₂²	semidirect
62. C₅×#388	C₂²	semidirect
63. C₅×#386	C₂²	semidirect
64. C₅×#386	C₂²	semidirect
65. C₅×#386	C₂²	semidirect
66. C₅×#386	C₂²	semidirect
67. C₅×#386	C₂²	semidirect
68. C₅×#385	C₂²	semidirect
69. C₅×#385	C₂²	semidirect
70. C₅×#384	C₂²	semidirect
71. C₅×#380	C₂²	semidirect
72. C₅×#380	C₂²	semidirect
73. C₅×#379	C₂²	semidirect
74. C₄×C₅×C₄⋊C₄	C₂²	semidirect
75. C₄×C₅×C₄⋊C₄	C₂²	semidirect
76. C₄×C₅×C₄⋊C₄	C₂²	semidirect
77. C₄×C₅×C₄⋊C₄	C₂²	semidirect
78. C₄×C₅×C₄⋊C₄	C₂²	semidirect
79. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
80. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
81. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
82. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
83. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
84. C₄³×C₅	C₂²	semidirect
85. #34310	C₅	direct (N × H)
91. C₂²×C₅×D₄	C₂×C₄	semidirect
92. C₂²×C₅×D₄	C₂×C₄	semidirect
107. C₅×#127	C₂×C₄	semidirect
108. C₅×#121	C₂×C₄	semidirect
109. C₅×#121	C₂×C₄	semidirect
110. C₅×#120	C₂×C₄	semidirect
120. C₄×C₅×D₄	C₂×C₄	semidirect
121. C₄×C₅×D₄	C₂×C₄	semidirect
122. C₄×C₅×D₄	D₄	semidirect
181. C₂×#518	C₂×C₅	semidirect
182. #2366	C₂×C₅	semidirect
183. #2363	C₂×C₅	semidirect
184. #2361	C₂×C₅	semidirect
185. #2358	C₂×C₅	semidirect
186. #2354	C₂×C₅	semidirect
187. D₄×C₄⋊C₄	C₂×C₅	semidirect
188. D₄×C₂²⋊C₄	C₂×C₅	semidirect
189. D₄×C₂²⋊C₄	C₂×C₅	semidirect
190. #2324	C₂×C₅	semidirect
191. #2321	C₂×C₅	semidirect
192. C₄×#127	C₂×C₅	semidirect
193. C₄×#121	C₂×C₅	semidirect
194. #2293	C₂×C₅	semidirect
195. C₂×#390	C₂×C₅	semidirect
196. C₄²×D₄	C₂×C₅	semidirect
250. C₂²×C₄×C₅	C₂×D₄	semidirect
276. C₅×C₄⋊C₄	C₂×D₄	semidirect
294. C₅×C₂²⋊C₄	C₂×D₄	semidirect
306. C₄²×C₅	C₂×D₄	semidirect
309. D₄²	C₄×C₅	semidirect
320. C₂×C₄×D₄	C₂²×C₅	semidirect
321. C₂×C₄×D₄	C₂²×C₅	semidirect
322. C₂×C₄×D₄	C₂²×C₅	semidirect
323. C₂×C₄×D₄	C₂²×C₅	semidirect
324. C₂×C₄×D₄	C₂²×C₅	semidirect
325. C₂×C₄×D₄	C₂²×C₅	semidirect
326. C₂×C₄×D₄	C₂²×C₅	semidirect
327. C₂×#117	C₂²×C₅	semidirect
328. C₂×#117	C₂²×C₅	semidirect
329. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
330. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
331. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
332. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
333. C₂²×C₄²	C₂²×C₅	semidirect
337. #390	C₂²×C₅	semidirect
338. #390	C₂²×C₅	semidirect
339. #390	C₂²×C₅	semidirect
340. #390	C₂²×C₅	semidirect
341. #390	C₂²×C₅	semidirect
342. #390	C₂²×C₅	semidirect
343. #390	C₂²×C₅	semidirect
344. #389	C₂²×C₅	semidirect
345. #389	C₂²×C₅	semidirect
346. #389	C₂²×C₅	semidirect
347. #388	C₂²×C₅	semidirect
348. #388	C₂²×C₅	semidirect
349. #388	C₂²×C₅	semidirect
350. #388	C₂²×C₅	semidirect
351. #388	C₂²×C₅	semidirect
352. #386	C₂²×C₅	semidirect
353. #386	C₂²×C₅	semidirect
354. #386	C₂²×C₅	semidirect
355. #386	C₂²×C₅	semidirect
356. #386	C₂²×C₅	semidirect
357. #385	C₂²×C₅	semidirect
358. #385	C₂²×C₅	semidirect
359. #384	C₂²×C₅	semidirect
360. #380	C₂²×C₅	semidirect
361. #380	C₂²×C₅	semidirect
362. #379	C₂²×C₅	semidirect
363. C₄×C₄⋊C₄	C₂²×C₅	semidirect
364. C₄×C₄⋊C₄	C₂²×C₅	semidirect
365. C₄×C₄⋊C₄	C₂²×C₅	semidirect
366. C₄×C₄⋊C₄	C₂²×C₅	semidirect
367. C₄×C₄⋊C₄	C₂²×C₅	semidirect
368. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
369. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
370. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
371. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
373. C₄³	C₂²×C₅	semidirect
409. C₅×D₄	C₄×D₄	semidirect
464. C₂²×D₄	C₂×C₄×C₅	semidirect
465. C₂²×D₄	C₂×C₄×C₅	semidirect
480. #127	C₂×C₄×C₅	semidirect
481. #121	C₂×C₄×C₅	semidirect
482. #121	C₂×C₄×C₅	semidirect
483. #120	C₂×C₄×C₅	semidirect
493. C₄×D₄	C₂×C₄×C₅	semidirect
494. C₄×D₄	C₂×C₄×C₅	semidirect
495. C₄×D₄	C₅×D₄	semidirect
595. C₄×C₅	#518	semidirect
649. C₂²×C₄	C₂×C₅×D₄	semidirect
675. C₄⋊C₄	C₂×C₅×D₄	semidirect
693. C₂²⋊C₄	C₂×C₅×D₄	semidirect
705. C₄²	C₂×C₅×D₄	semidirect
751. D₄	C₄×C₅×D₄	semidirect
801. C₅	#34310	direct (N × H)
844. C₄	C₅×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₄²	2
C₂×C₅×#518	2
C₅×#2366	2
C₅×#2363	2
C₅×#2361	2
C₅×#2358	2
C₅×#2354	2
C₅×D₄×C₄⋊C₄	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2324	2
C₅×#2321	2
C₄×C₅×#127	2
C₄×C₅×#121	2
C₅×#2293	2
C₂×C₅×#390	2
C₄²×C₅×D₄	2
#34310	5

Subgroups — C5×#34310 #11957030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34310 #11957030