Subgroups — C₅×#21468 #11944188

Order 1280.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3002	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1789	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1764	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	C₅×#568	—	2	4	no	—
20	C₅×#568	—	2	4	no	—
21	C₂×C₅×#131	—	2	1	no	—
22	C₂×C₅×#131	—	2	1	no	—
23	C₂×C₅×#131	C₂²	1	1	yes	characteristic
24	C₂×C₅×#131	C₂²	1	1	yes	characteristic
25	C₂×C₅×#131	C₂²	1	1	yes	characteristic
26	C₂×C₅×#131	C₂²	1	1	yes	characteristic
27	C₂×C₅×#131	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₅×M₁₆	—	2	1	no	—
29	C₂²×C₅×M₁₆	—	2	1	no	—
30	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
31	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
32	C₅×#525	C₂²	1	1	yes	characteristic
33	C₅×#452	C₄	1	1	yes	characteristic, complemented
34	C₅×#452	C₄	1	1	yes	characteristic, complemented
35	C₅×#451	C₄	1	1	yes	characteristic, complemented
36	C₅×#450	C₄	1	1	yes	characteristic, complemented
37	C₅×#449	C₄	1	1	yes	characteristic, complemented
38	C₅×#449	C₄	1	1	yes	characteristic, complemented
39	C₅×#448	C₄	1	1	yes	characteristic, complemented
40	C₅×#447	C₄	1	1	yes	characteristic, complemented
41	C₅×#444	—	2	4	no	—
42	C₅×#443	—	2	4	no	—
43	C₅×#436	—	2	1	no	—
44	C₅×#436	—	2	1	no	—
45	C₅×#435	—	2	1	no	—
46	C₅×#435	—	2	1	no	—
47	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
49	C₅×#424	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₅×#104	C₂²	1	1	yes	characteristic
51	C₂×C₅×#104	C₂²	1	1	yes	characteristic
52	C₂×C₅×#104	C₂²	1	1	yes	characteristic
53	C₂×C₅×#104	C₂²	1	1	yes	characteristic
54	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
56	C₅×#416	C₂²	1	1	yes	characteristic
57	C₅×#416	C₂²	1	1	yes	characteristic
58	C₅×#408	C₂²	1	1	yes	characteristic, complemented
59	C₅×#407	C₂²	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×#405	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
65	C₅×#341	C₂²	1	1	yes	characteristic, complemented
66	C₅×#341	C₂²	1	1	yes	characteristic, complemented
67	C₅×#339	C₂²	1	1	yes	characteristic, complemented
68	C₅×#339	C₂²	1	1	yes	characteristic, complemented
69	C₅×#336	C₂²	1	1	yes	characteristic, complemented
70	C₅×#336	C₂²	1	1	yes	characteristic, complemented
71	#21468	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	—	2	2	no	—
73	C₂×C₅×#41	—	2	2	no	—
74	C₂×C₅×#41	—	2	2	no	—
75	C₂×C₅×#41	—	2	2	no	—
76	C₂×C₅×#41	—	2	1	no	—
77	C₂×C₅×#41	—	2	1	no	—
78	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×#41	C₂³	1	1	yes	characteristic
81	C₂×C₅×#41	C₂³	1	1	yes	characteristic
82	C₂×C₅×#41	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₅×D₄	—	2	1	no	—
85	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₅	—	2	1	no	—
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₅×#135	—	2	2	no	—
89	C₅×#135	—	2	2	no	—
90	C₅×#135	—	2	2	no	—
91	C₅×#135	—	2	2	no	—
92	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
97	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
98	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
100	C₅×#131	—	2	8	no	—
101	C₅×#131	—	2	8	no	—
102	C₅×#131	—	2	2	no	—
103	C₅×#131	—	2	2	no	—
104	C₅×#131	—	2	2	no	—
105	C₅×#131	—	2	2	no	—
106	C₅×#131	—	2	2	no	—
107	C₅×#131	—	2	2	no	—
108	C₅×#131	—	2	2	no	—
109	C₅×#131	—	2	2	no	—
110	C₅×#131	D₄	1	4	yes	complemented
111	C₅×#131	D₄	1	4	yes	complemented
112	C₂×C₅×M₁₆	—	2	8	no	—
113	C₂×C₅×M₁₆	—	2	8	no	—
114	C₂×C₅×M₁₆	—	2	1	no	—
115	C₂×C₅×M₁₆	—	2	2	no	—
116	C₂×C₅×M₁₆	—	2	2	no	—
117	C₂×C₅×M₁₆	—	2	1	no	—
118	C₂×C₅×M₁₆	—	2	1	no	—
119	C₂×C₅×M₁₆	—	2	1	no	—
120	C₂×C₅×M₁₆	—	2	1	no	—
121	C₂×C₅×M₁₆	—	2	2	no	—
122	C₂×C₅×M₁₆	—	2	2	no	—
123	C₂×C₅×M₁₆	—	2	1	no	—
124	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
125	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
126	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
127	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
128	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
129	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
130	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
132	C₂²×C₅×C₈	—	2	1	no	—
133	C₂²×C₅×C₈	—	2	1	no	—
134	C₂²×C₅×C₈	—	2	1	no	—
135	C₂²×C₅×C₈	—	2	1	no	—
136	C₂²×C₅×C₈	—	2	1	no	—
137	C₂²×C₅×C₈	—	2	1	no	—
138	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
142	C₅×#123	—	2	1	no	—
143	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
144	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
145	C₅×#121	C₂×C₄	1	1	yes	characteristic
146	C₅×#121	C₂×C₄	1	1	yes	characteristic
147	C₅×#120	—	2	1	no	—
148	C₄×C₅×D₄	—	2	1	no	—
149	C₄×C₅×D₄	—	2	1	no	—
150	C₅×#117	C₂³	1	1	yes	characteristic
151	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
154	C₅×#108	—	2	2	no	—
155	C₅×#108	—	2	2	no	—
156	C₅×C₄⋊C₈	—	2	1	no	—
157	C₅×C₄⋊C₈	—	2	1	no	—
158	C₅×#104	—	2	2	no	—
159	C₅×#104	—	2	2	no	—
160	C₅×#104	—	2	2	no	—
161	C₅×#104	—	2	2	no	—
162	C₅×#104	—	2	2	no	—
163	C₅×#104	—	2	2	no	—
164	C₅×#103	C₂×C₄	1	1	yes	characteristic
165	C₅×#103	C₂×C₄	1	1	yes	characteristic
166	C₅×#103	C₂×C₄	1	1	yes	characteristic
167	C₅×#103	C₂×C₄	1	1	yes	characteristic
168	C₅×#102	C₂×C₄	1	1	yes	characteristic
169	C₅×#102	C₂×C₄	1	1	yes	characteristic
170	C₅×#102	C₂×C₄	1	1	yes	characteristic
171	C₅×#102	C₂×C₄	1	1	yes	characteristic
172	C₅×C₂²⋊C₈	—	2	1	no	—
173	C₅×C₂²⋊C₈	—	2	1	no	—
174	C₅×C₂²⋊C₈	—	2	1	no	—
175	C₅×C₂²⋊C₈	—	2	1	no	—
176	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
177	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
178	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
179	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
180	C₅×#97	—	2	2	no	—
181	C₅×#97	—	2	1	no	—
182	C₄×C₅×C₈	—	2	2	no	—
183	C₄×C₅×C₈	—	2	1	no	—
184	C₅×#95	—	2	1	no	—
185	C₂×#568	C₂×C₅	1	1	yes	characteristic, complemented
186	#3002	C₂×C₅	1	1	yes	characteristic
187	C₂×#444	C₂×C₅	1	1	yes	characteristic, complemented
188	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
189	#2930	C₂×C₅	1	1	yes	characteristic, complemented
190	#1876	C₂×C₅	1	1	yes	characteristic, complemented
191	#1876	C₂×C₅	1	1	yes	characteristic, complemented
192	#1871	C₂×C₅	1	1	yes	characteristic, complemented
193	#1866	C₂×C₅	1	1	yes	characteristic, complemented
194	#1866	C₂×C₅	1	1	yes	characteristic, complemented
195	#1855	C₂×C₅	1	1	yes	characteristic, complemented
196	#1789	C₂×C₅	1	1	yes	characteristic, complemented
197	#1765	C₂×C₅	1	1	yes	characteristic, complemented
198	#1764	C₂×C₅	1	1	yes	characteristic, complemented
199	#1753	C₂×C₅	1	1	yes	characteristic, complemented
200	C₂⁴×C₅	—	2	1	no	—
201	C₂⁴×C₅	#41	1	1	yes	characteristic
202	C₅×#41	—	2	4	no	—
203	C₅×#41	—	2	4	no	—
204	C₅×#41	—	2	4	no	—
205	C₅×#41	—	2	4	no	—
206	C₅×#41	—	2	2	no	—
207	C₅×#41	—	2	2	no	—
208	C₅×#41	—	2	2	no	—
209	C₅×#41	—	2	2	no	—
210	C₅×#41	—	2	1	no	—
211	C₅×#41	—	2	1	no	—
212	C₅×#41	—	2	1	no	—
213	C₅×#41	—	2	1	no	—
214	C₅×#41	—	2	1	no	—
215	C₅×#41	—	2	1	no	—
216	C₅×#41	—	2	1	no	—
217	C₅×#41	—	2	1	no	—
218	C₅×#41	C₂×D₄	1	2	yes	—
219	C₅×#41	C₂×D₄	1	2	yes	—
220	C₅×#41	#41	1	2	yes	—
221	C₅×#41	#41	1	2	yes	—
222	C₂×C₅×Q₈	—	2	2	no	—
223	C₂×C₅×Q₈	—	2	2	no	—
224	C₂×C₅×Q₈	—	2	1	no	—
225	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₅×D₄	—	2	4	no	—
229	C₂×C₅×D₄	—	2	4	no	—
230	C₂×C₅×D₄	—	2	1	no	—
231	C₂×C₅×D₄	—	2	1	no	—
232	C₂×C₅×D₄	—	2	1	no	—
233	C₂×C₅×D₄	—	2	1	no	—
234	C₂×C₅×D₄	—	2	2	no	—
235	C₂×C₅×D₄	—	2	2	no	—
236	C₂×C₅×D₄	—	2	1	no	—
237	C₂×C₅×D₄	—	2	1	no	—
238	C₂×C₅×D₄	—	2	1	no	—
239	C₂×C₅×D₄	—	2	1	no	—
240	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
242	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₅	—	2	4	no	—
244	C₂²×C₄×C₅	—	2	4	no	—
245	C₂²×C₄×C₅	—	2	1	no	—
246	C₂²×C₄×C₅	—	2	1	no	—
247	C₂²×C₄×C₅	—	2	1	no	—
248	C₂²×C₄×C₅	—	2	1	no	—
249	C₂²×C₄×C₅	—	2	1	no	—
250	C₂²×C₄×C₅	—	2	1	no	—
251	C₂²×C₄×C₅	—	2	1	no	—
252	C₂²×C₄×C₅	—	2	1	no	—
253	C₂²×C₄×C₅	—	2	1	no	—
254	C₂²×C₄×C₅	—	2	1	no	—
255	C₂²×C₄×C₅	—	2	1	no	—
256	C₂²×C₄×C₅	—	2	1	no	—
257	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₅	#41	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₅×Q₁₆	—	2	2	no	—
264	C₅×Q₁₆	—	2	2	no	—
265	C₅×SD₁₆	—	2	2	no	—
266	C₅×SD₁₆	—	2	2	no	—
267	C₅×SD₁₆	—	2	2	no	—
268	C₅×SD₁₆	—	2	2	no	—
269	C₅×D₈	—	2	2	no	—
270	C₅×D₈	—	2	2	no	—
271	C₅×M₁₆	—	2	4	no	—
272	C₅×M₁₆	—	2	4	no	—
273	C₅×M₁₆	—	2	4	no	—
274	C₅×M₁₆	—	2	1	no	—
275	C₅×M₁₆	—	2	1	no	—
276	C₅×M₁₆	—	2	2	no	—
277	C₅×M₁₆	—	2	2	no	—
278	C₅×M₁₆	—	2	4	no	—
279	C₅×M₁₆	—	2	4	no	—
280	C₅×M₁₆	—	2	2	no	—
281	C₅×M₁₆	—	2	2	no	—
282	C₅×M₁₆	—	2	1	no	—
283	C₅×M₁₆	—	2	1	no	—
284	C₅×M₁₆	—	2	1	no	—
285	C₅×M₁₆	—	2	1	no	—
286	C₅×M₁₆	—	4	2	no	—
287	C₅×M₁₆	C₂×D₄	1	2	yes	—
288	C₅×M₁₆	C₂×D₄	1	2	yes	—
289	C₂×C₅×C₈	—	2	4	no	—
290	C₂×C₅×C₈	—	2	4	no	—
291	C₂×C₅×C₈	—	2	4	no	—
292	C₂×C₅×C₈	—	2	1	no	—
293	C₂×C₅×C₈	—	2	1	no	—
294	C₂×C₅×C₈	—	2	1	no	—
295	C₂×C₅×C₈	—	2	1	no	—
296	C₂×C₅×C₈	—	2	1	no	—
297	C₂×C₅×C₈	—	2	1	no	—
298	C₂×C₅×C₈	—	2	1	no	—
299	C₂×C₅×C₈	—	2	1	no	—
300	C₂×C₅×C₈	—	2	4	no	—
301	C₂×C₅×C₈	—	2	4	no	—
302	C₂×C₅×C₈	—	2	1	no	—
303	C₂×C₅×C₈	—	2	1	no	—
304	C₂×C₅×C₈	—	4	2	no	—
305	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
306	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
307	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
308	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
309	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
310	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
311	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
312	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
313	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
314	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
315	C₅×C₄⋊C₄	—	2	1	no	—
316	C₅×C₄⋊C₄	—	2	1	no	—
317	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
318	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
319	C₅×C₂²⋊C₄	—	2	1	no	—
320	C₅×C₂²⋊C₄	—	2	1	no	—
321	C₅×C₂²⋊C₄	—	2	1	no	—
322	C₅×C₂²⋊C₄	—	2	1	no	—
323	C₅×C₂²⋊C₄	—	2	1	no	—
324	C₅×C₂²⋊C₄	—	4	2	no	—
325	C₄²×C₅	—	2	1	no	—
326	C₄²×C₅	—	2	1	no	—
327	C₄²×C₅	—	2	1	no	—
328	C₄²×C₅	—	2	1	no	—
329	C₄²×C₅	—	2	1	no	—
330	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
331	C₂×#135	C₂²×C₅	1	1	yes	characteristic
332	C₂×#135	C₂²×C₅	1	1	yes	characteristic
333	#568	—	2	4	no	—
334	#568	—	2	4	no	—
335	C₂×#131	—	2	1	no	—
336	C₂×#131	—	2	1	no	—
337	C₂×#131	C₂²×C₅	1	1	yes	characteristic
338	C₂×#131	C₂²×C₅	1	1	yes	characteristic
339	C₂×#131	C₂²×C₅	1	1	yes	characteristic
340	C₂×#131	C₂²×C₅	1	1	yes	characteristic
341	C₂×#131	C₂²×C₅	1	1	yes	characteristic, complemented
342	C₂²×M₁₆	—	2	1	no	—
343	C₂²×M₁₆	—	2	1	no	—
344	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
346	#525	C₂²×C₅	1	1	yes	characteristic
347	#452	C₄×C₅	1	1	yes	characteristic, complemented
348	#452	C₄×C₅	1	1	yes	characteristic, complemented
349	#451	C₄×C₅	1	1	yes	characteristic, complemented
350	#450	C₄×C₅	1	1	yes	characteristic, complemented
351	#449	C₄×C₅	1	1	yes	characteristic, complemented
352	#449	C₄×C₅	1	1	yes	characteristic, complemented
353	#448	C₄×C₅	1	1	yes	characteristic, complemented
354	#447	C₄×C₅	1	1	yes	characteristic, complemented
355	#444	—	2	4	no	—
356	#443	—	2	4	no	—
357	#436	—	2	1	no	—
358	#436	—	2	1	no	—
359	#435	—	2	1	no	—
360	#435	—	2	1	no	—
361	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
362	C₂×#108	C₂²×C₅	1	1	yes	characteristic, complemented
363	#424	C₂²×C₅	1	1	yes	characteristic, complemented
364	C₂×#104	C₂²×C₅	1	1	yes	characteristic
365	C₂×#104	C₂²×C₅	1	1	yes	characteristic
366	C₂×#104	C₂²×C₅	1	1	yes	characteristic
367	C₂×#104	C₂²×C₅	1	1	yes	characteristic
368	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
369	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
370	#416	C₂²×C₅	1	1	yes	characteristic
371	#416	C₂²×C₅	1	1	yes	characteristic
372	#408	C₂²×C₅	1	1	yes	characteristic, complemented
373	#407	C₂²×C₅	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
375	#405	C₂²×C₅	1	1	yes	characteristic, complemented
376	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
377	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
378	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
379	#341	C₂²×C₅	1	1	yes	characteristic, complemented
380	#341	C₂²×C₅	1	1	yes	characteristic, complemented
381	#339	C₂²×C₅	1	1	yes	characteristic, complemented
382	#339	C₂²×C₅	1	1	yes	characteristic, complemented
383	#336	C₂²×C₅	1	1	yes	characteristic, complemented
384	#336	C₂²×C₅	1	1	yes	characteristic, complemented
385	C₂³×C₅	—	2	4	no	—
386	C₂³×C₅	—	2	1	no	—
387	C₂³×C₅	—	2	1	no	—
388	C₂³×C₅	—	2	1	no	—
389	C₂³×C₅	—	2	1	no	—
390	C₂³×C₅	—	2	1	no	—
391	C₂³×C₅	—	4	1	no	—
392	C₂³×C₅	—	4	1	no	—
393	C₂³×C₅	—	8	1	no	—
394	C₂³×C₅	—	8	1	no	—
395	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
396	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
397	C₂³×C₅	C₂×#41	1	1	yes	characteristic
398	C₅×Q₈	—	2	4	no	—
399	C₅×Q₈	—	2	1	no	—
400	C₅×Q₈	—	2	1	no	—
401	C₅×Q₈	—	2	1	no	—
402	C₅×Q₈	—	2	1	no	—
403	C₅×Q₈	C₄×D₄	1	2	yes	—
404	C₅×Q₈	C₄×D₄	1	2	yes	—
405	C₅×D₄	—	2	4	no	—
406	C₅×D₄	—	2	4	no	—
407	C₅×D₄	—	2	4	no	—
408	C₅×D₄	—	2	2	no	—
409	C₅×D₄	—	2	2	no	—
410	C₅×D₄	—	2	2	no	—
411	C₅×D₄	—	2	2	no	—
412	C₅×D₄	—	2	1	no	—
413	C₅×D₄	—	2	1	no	—
414	C₅×D₄	—	2	1	no	—
415	C₅×D₄	—	2	1	no	—
416	C₅×D₄	—	4	1	no	—
417	C₅×D₄	—	4	1	no	—
418	C₅×D₄	—	8	1	no	—
419	C₅×D₄	—	8	1	no	—
420	C₅×D₄	C₄×D₄	1	2	yes	—
421	C₅×D₄	C₄×D₄	1	2	yes	—
422	C₂×C₄×C₅	—	2	4	no	—
423	C₂×C₄×C₅	—	2	4	no	—
424	C₂×C₄×C₅	—	2	4	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	2	no	—
434	C₂×C₄×C₅	—	2	2	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	2	no	—
439	C₂×C₄×C₅	—	2	2	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	2	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	4	1	no	—
446	C₂×C₄×C₅	—	4	1	no	—
447	C₂×C₄×C₅	—	4	1	no	—
448	C₂×C₄×C₅	—	4	1	no	—
449	C₂×C₄×C₅	—	4	1	no	—
450	C₂×C₄×C₅	—	4	1	no	—
451	C₂×C₄×C₅	—	4	1	no	—
452	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
454	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
455	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
459	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
460	C₅×C₈	—	2	1	no	—
461	C₅×C₈	—	2	1	no	—
462	C₅×C₈	—	2	1	no	—
463	C₅×C₈	—	2	1	no	—
464	C₅×C₈	—	2	2	no	—
465	C₅×C₈	—	2	2	no	—
466	C₅×C₈	—	2	1	no	—
467	C₅×C₈	—	2	1	no	—
468	C₅×C₈	—	4	1	no	—
469	C₅×C₈	—	4	1	no	—
470	C₅×C₈	#120	1	2	yes	—
471	C₅×C₈	#120	1	2	yes	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	2	no	—
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
479	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
480	C₂×#41	C₂³×C₅	1	1	yes	characteristic
481	C₂×#41	C₂³×C₅	1	1	yes	characteristic
482	C₂×#41	C₂³×C₅	1	1	yes	characteristic
483	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
488	#135	—	2	2	no	—
489	#135	—	2	2	no	—
490	#135	—	2	2	no	—
491	#135	—	2	2	no	—
492	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
493	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
494	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
495	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
496	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
497	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
498	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
499	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
500	#131	—	2	8	no	—
501	#131	—	2	8	no	—
502	#131	—	2	2	no	—
503	#131	—	2	2	no	—
504	#131	—	2	2	no	—
505	#131	—	2	2	no	—
506	#131	—	2	2	no	—
507	#131	—	2	2	no	—
508	#131	—	2	2	no	—
509	#131	—	2	2	no	—
510	#131	C₅×D₄	1	4	yes	complemented
511	#131	C₅×D₄	1	4	yes	complemented
512	C₂×M₁₆	—	2	8	no	—
513	C₂×M₁₆	—	2	8	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	2	1	no	—
518	C₂×M₁₆	—	2	1	no	—
519	C₂×M₁₆	—	2	1	no	—
520	C₂×M₁₆	—	2	1	no	—
521	C₂×M₁₆	—	2	2	no	—
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	2	1	no	—
524	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
525	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
526	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
527	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
528	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
529	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
530	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
531	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
537	C₂²×C₈	—	2	1	no	—
538	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
540	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
542	#123	—	2	1	no	—
543	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
544	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
545	#121	C₂×C₄×C₅	1	1	yes	characteristic
546	#121	C₂×C₄×C₅	1	1	yes	characteristic
547	#120	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	#117	C₂³×C₅	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
554	#108	—	2	2	no	—
555	#108	—	2	2	no	—
556	C₄⋊C₈	—	2	1	no	—
557	C₄⋊C₈	—	2	1	no	—
558	#104	—	2	2	no	—
559	#104	—	2	2	no	—
560	#104	—	2	2	no	—
561	#104	—	2	2	no	—
562	#104	—	2	2	no	—
563	#104	—	2	2	no	—
564	#103	C₂×C₄×C₅	1	1	yes	characteristic
565	#103	C₂×C₄×C₅	1	1	yes	characteristic
566	#103	C₂×C₄×C₅	1	1	yes	characteristic
567	#103	C₂×C₄×C₅	1	1	yes	characteristic
568	#102	C₂×C₄×C₅	1	1	yes	characteristic
569	#102	C₂×C₄×C₅	1	1	yes	characteristic
570	#102	C₂×C₄×C₅	1	1	yes	characteristic
571	#102	C₂×C₄×C₅	1	1	yes	characteristic
572	C₂²⋊C₈	—	2	1	no	—
573	C₂²⋊C₈	—	2	1	no	—
574	C₂²⋊C₈	—	2	1	no	—
575	C₂²⋊C₈	—	2	1	no	—
576	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
577	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
578	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
579	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
580	#97	—	2	2	no	—
581	#97	—	2	1	no	—
582	C₄×C₈	—	2	2	no	—
583	C₄×C₈	—	2	1	no	—
584	#95	—	2	1	no	—
585	C₂²×C₅	—	2	1	no	—
586	C₂²×C₅	—	2	1	no	—
587	C₂²×C₅	—	2	1	no	—
588	C₂²×C₅	—	2	1	no	—
589	C₂²×C₅	—	2	1	no	—
590	C₂²×C₅	—	2	1	no	—
591	C₂²×C₅	—	2	1	no	—
592	C₂²×C₅	—	2	1	no	—
593	C₂²×C₅	—	2	2	no	—
594	C₂²×C₅	—	2	2	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	—	4	1	no	—
597	C₂²×C₅	—	4	1	no	—
598	C₂²×C₅	—	4	1	no	—
599	C₂²×C₅	—	4	1	no	—
600	C₂²×C₅	—	4	1	no	—
601	C₂²×C₅	—	4	1	no	—
602	C₂²×C₅	—	8	1	no	—
603	C₂²×C₅	—	8	1	no	—
604	C₂²×C₅	—	8	4	no	—
605	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
606	C₂²×C₅	#525	1	1	yes	characteristic
607	C₂²×C₅	#525	1	1	yes	characteristic
608	C₄×C₅	—	2	1	no	—
609	C₄×C₅	—	2	2	no	—
610	C₄×C₅	—	2	2	no	—
611	C₄×C₅	—	2	1	no	—
612	C₄×C₅	—	4	2	no	—
613	C₄×C₅	—	4	1	no	—
614	C₄×C₅	—	4	1	no	—
615	C₄×C₅	—	4	1	no	—
616	C₄×C₅	—	8	1	no	—
617	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
618	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
619	C₄×C₅	C₂×#120	1	1	yes	characteristic
620	C₄×C₅	#525	1	1	yes	characteristic
621	C₂⁴	—	2	1	no	—
622	C₂⁴	C₅×#41	1	1	yes	characteristic
623	#41	—	2	4	no	—
624	#41	—	2	4	no	—
625	#41	—	2	4	no	—
626	#41	—	2	4	no	—
627	#41	—	2	2	no	—
628	#41	—	2	2	no	—
629	#41	—	2	2	no	—
630	#41	—	2	2	no	—
631	#41	—	2	1	no	—
632	#41	—	2	1	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	2	1	no	—
637	#41	—	2	1	no	—
638	#41	—	2	1	no	—
639	#41	C₂×C₅×D₄	1	2	yes	—
640	#41	C₂×C₅×D₄	1	2	yes	—
641	#41	C₅×#41	1	2	yes	—
642	#41	C₅×#41	1	2	yes	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
647	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
648	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
662	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
663	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
679	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
680	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
681	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
682	C₂²×C₄	C₅×#41	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
684	Q₁₆	—	2	2	no	—
685	Q₁₆	—	2	2	no	—
686	SD₁₆	—	2	2	no	—
687	SD₁₆	—	2	2	no	—
688	SD₁₆	—	2	2	no	—
689	SD₁₆	—	2	2	no	—
690	D₈	—	2	2	no	—
691	D₈	—	2	2	no	—
692	M₁₆	—	2	4	no	—
693	M₁₆	—	2	4	no	—
694	M₁₆	—	2	4	no	—
695	M₁₆	—	2	1	no	—
696	M₁₆	—	2	1	no	—
697	M₁₆	—	2	2	no	—
698	M₁₆	—	2	2	no	—
699	M₁₆	—	2	4	no	—
700	M₁₆	—	2	4	no	—
701	M₁₆	—	2	2	no	—
702	M₁₆	—	2	2	no	—
703	M₁₆	—	2	1	no	—
704	M₁₆	—	2	1	no	—
705	M₁₆	—	2	1	no	—
706	M₁₆	—	2	1	no	—
707	M₁₆	—	4	2	no	—
708	M₁₆	C₂×C₅×D₄	1	2	yes	—
709	M₁₆	C₂×C₅×D₄	1	2	yes	—
710	C₂×C₈	—	2	4	no	—
711	C₂×C₈	—	2	4	no	—
712	C₂×C₈	—	2	4	no	—
713	C₂×C₈	—	2	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	4	2	no	—
726	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
727	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
728	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
729	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
730	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
731	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
732	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
733	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
734	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
735	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	1	no	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	1	no	—
751	C₂×C₅	—	2	1	no	—
752	C₂×C₅	—	2	1	no	—
753	C₂×C₅	—	4	1	no	—
754	C₂×C₅	—	4	1	no	—
755	C₂×C₅	—	4	2	no	—
756	C₂×C₅	—	4	2	no	—
757	C₂×C₅	—	8	1	no	—
758	C₂×C₅	C₄×#120	1	1	yes	characteristic
759	C₂×C₅	#2956	1	1	yes	characteristic
760	C₂×C₅	#2957	1	1	yes	characteristic
761	C₂³	—	2	4	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
772	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
773	C₂³	C₂×C₅×#41	1	1	yes	characteristic
774	Q₈	—	2	4	no	—
775	Q₈	—	2	1	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	1	no	—
779	Q₈	C₄×C₅×D₄	1	2	yes	—
780	Q₈	C₄×C₅×D₄	1	2	yes	—
781	D₄	—	2	4	no	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	4	1	no	—
793	D₄	—	4	1	no	—
794	D₄	—	8	1	no	—
795	D₄	—	8	1	no	—
796	D₄	C₄×C₅×D₄	1	2	yes	—
797	D₄	C₄×C₅×D₄	1	2	yes	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
829	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
830	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
832	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
833	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
835	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	2	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	1	no	—
843	C₈	—	2	1	no	—
844	C₈	—	4	1	no	—
845	C₈	—	4	1	no	—
846	C₈	C₅×#120	1	2	yes	—
847	C₈	C₅×#120	1	2	yes	—
848	C₅	#21468	1	1	yes	characteristic, direct product factor, Sylow
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	4	no	—
869	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
870	C₂²	C₅×#525	1	1	yes	characteristic
871	C₂²	C₅×#525	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	8	1	no	—
881	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
882	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
883	C₄	C₂×C₅×#120	1	1	yes	characteristic
884	C₄	C₅×#525	1	1	yes	characteristic
885	C₂	—	2	1	no	—
886	C₂	—	2	1	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	8	1	no	—
892	C₂	C₄×C₅×#120	1	1	yes	characteristic
893	C₂	C₅×#2956	1	1	yes	characteristic
894	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
1. C₂×C₅×#568	C₂	semidirect
3. C₂×C₅×#444	C₂	semidirect
4. C₂×C₅×#443	C₂	semidirect
5. C₅×#2930	C₂	semidirect
6. C₅×#1876	C₂	semidirect
7. C₅×#1876	C₂	semidirect
8. C₅×#1871	C₂	semidirect
9. C₅×#1866	C₂	semidirect
10. C₅×#1866	C₂	semidirect
11. C₅×#1855	C₂	semidirect
12. C₅×#1789	C₂	semidirect
13. C₅×#1765	C₂	semidirect
14. C₅×#1764	C₂	semidirect
15. C₅×#1753	C₂	semidirect
27. C₂×C₅×#131	C₂²	semidirect
33. C₅×#452	C₄	semidirect
34. C₅×#452	C₄	semidirect
35. C₅×#451	C₄	semidirect
36. C₅×#450	C₄	semidirect
37. C₅×#449	C₄	semidirect
38. C₅×#449	C₄	semidirect
39. C₅×#448	C₄	semidirect
40. C₅×#447	C₄	semidirect
47. C₂×C₅×#108	C₂²	semidirect
48. C₂×C₅×#108	C₂²	semidirect
49. C₅×#424	C₂²	semidirect
54. C₂×C₅×#104	C₂²	semidirect
55. C₂×C₅×#104	C₂²	semidirect
58. C₅×#408	C₂²	semidirect
61. C₅×#405	C₂²	semidirect
62. C₂×C₅×#97	C₂²	semidirect
63. C₂×C₄×C₅×C₈	C₂²	semidirect
65. C₅×#341	C₂²	semidirect
66. C₅×#341	C₂²	semidirect
67. C₅×#339	C₂²	semidirect
68. C₅×#339	C₂²	semidirect
69. C₅×#336	C₂²	semidirect
70. C₅×#336	C₂²	semidirect
71. #21468	C₅	direct (N × H)
110. C₅×#131	D₄	semidirect
111. C₅×#131	D₄	semidirect
185. C₂×#568	C₂×C₅	semidirect
187. C₂×#444	C₂×C₅	semidirect
188. C₂×#443	C₂×C₅	semidirect
189. #2930	C₂×C₅	semidirect
190. #1876	C₂×C₅	semidirect
191. #1876	C₂×C₅	semidirect
192. #1871	C₂×C₅	semidirect
193. #1866	C₂×C₅	semidirect
194. #1866	C₂×C₅	semidirect
195. #1855	C₂×C₅	semidirect
196. #1789	C₂×C₅	semidirect
197. #1765	C₂×C₅	semidirect
198. #1764	C₂×C₅	semidirect
199. #1753	C₂×C₅	semidirect
341. C₂×#131	C₂²×C₅	semidirect
347. #452	C₄×C₅	semidirect
348. #452	C₄×C₅	semidirect
349. #451	C₄×C₅	semidirect
350. #450	C₄×C₅	semidirect
351. #449	C₄×C₅	semidirect
352. #449	C₄×C₅	semidirect
353. #448	C₄×C₅	semidirect
354. #447	C₄×C₅	semidirect
361. C₂×#108	C₂²×C₅	semidirect
362. C₂×#108	C₂²×C₅	semidirect
363. #424	C₂²×C₅	semidirect
368. C₂×#104	C₂²×C₅	semidirect
369. C₂×#104	C₂²×C₅	semidirect
372. #408	C₂²×C₅	semidirect
375. #405	C₂²×C₅	semidirect
376. C₂×#97	C₂²×C₅	semidirect
377. C₂×C₄×C₈	C₂²×C₅	semidirect
379. #341	C₂²×C₅	semidirect
380. #341	C₂²×C₅	semidirect
381. #339	C₂²×C₅	semidirect
382. #339	C₂²×C₅	semidirect
383. #336	C₂²×C₅	semidirect
384. #336	C₂²×C₅	semidirect
510. #131	C₅×D₄	semidirect
511. #131	C₅×D₄	semidirect
848. C₅	#21468	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#568	2
C₅×#3002	2
C₂×C₅×#444	2
C₂×C₅×#443	2
C₅×#2930	2
C₅×#1876	2
C₅×#1871	2
C₅×#1866	2
C₅×#1855	2
C₅×#1789	2
C₅×#1765	2
C₅×#1764	2
C₅×#1753	2
#21468	5

Subgroups — C5×#21468 #11944188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21468 #11944188