Subgroups — C₅×#17609 #11940329

Order 1280.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3495	C₂	1	1	yes	maximal, characteristic
2	C₅×#2924	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2343	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1521	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1518	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1516	C₂	1	1	yes	maximal, characteristic
7	C₅×#1515	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1512	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1511	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1509	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1506	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1504	C₂	1	1	yes	maximal, characteristic
13	C₅×#1503	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1500	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#328	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#556	—	2	1	no	—
17	C₅×#554	—	2	1	no	—
18	C₅×#552	—	2	1	no	—
19	C₅×#552	—	2	1	no	—
20	C₅×#552	—	2	1	no	—
21	C₅×#552	—	2	1	no	—
22	C₅×#551	—	2	1	no	—
23	C₅×#551	—	2	1	no	—
24	C₅×#544	C₄	1	1	yes	characteristic, complemented
25	C₅×#542	C₄	1	1	yes	characteristic, complemented
26	C₅×#542	C₄	1	1	yes	characteristic, complemented
27	C₅×#541	C₄	1	1	yes	characteristic, complemented
28	C₅×#541	C₄	1	1	yes	characteristic, complemented
29	C₅×#536	C₄	1	1	yes	characteristic, complemented
30	C₅×#533	C₂²	1	1	yes	characteristic
31	C₅×#533	C₂²	1	1	yes	characteristic
32	C₅×#529	C₂²	1	1	yes	characteristic
33	C₅×#529	C₂²	1	1	yes	characteristic
34	C₅×#525	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₅×#520	C₄	1	1	yes	characteristic, complemented
37	C₅×#519	C₄	1	1	yes	characteristic, complemented
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic
39	C₅×#433	—	2	1	no	—
40	C₅×#433	—	2	1	no	—
41	C₅×#432	C₂²	1	1	yes	characteristic
42	C₅×#432	C₂²	1	1	yes	characteristic
43	C₅×#431	C₂²	1	1	yes	characteristic
44	C₅×#431	C₂²	1	1	yes	characteristic
45	C₅×#424	—	2	1	no	—
46	C₅×#407	C₂²	1	1	yes	characteristic
47	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₅×#405	—	2	1	no	—
49	C₅×#387	—	2	1	no	—
50	C₅×#387	—	2	1	no	—
51	C₅×#385	—	2	1	no	—
52	C₅×#383	C₂²	1	1	yes	characteristic
53	C₅×#382	C₂²	1	1	yes	characteristic
54	C₅×#381	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₅×#376	C₂²	1	1	yes	characteristic
58	C₂×C₅×#95	C₂²	1	1	yes	characteristic
59	C₅×#328	C₂²	1	1	yes	characteristic
60	C₅×#328	C₂²	1	1	yes	characteristic
61	C₅×#328	C₂²	1	1	yes	characteristic
62	C₅×#328	C₂²	1	1	yes	characteristic
63	C₅×#328	C₂²	1	1	yes	characteristic
64	C₅×#328	C₂²	1	1	yes	characteristic
65	C₅×#328	C₂²	1	1	yes	characteristic
66	C₅×#328	C₂²	1	1	yes	characteristic
67	C₅×#328	C₂²	1	1	yes	characteristic
68	C₅×#328	C₂²	1	1	yes	characteristic
69	C₅×#328	C₂²	1	1	yes	characteristic
70	C₅×#328	C₂²	1	1	yes	characteristic
71	C₅×#327	C₂²	1	1	yes	characteristic
72	C₅×#327	C₂²	1	1	yes	characteristic
73	C₅×#327	C₂²	1	1	yes	characteristic
74	C₅×#327	C₂²	1	1	yes	characteristic
75	#17609	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₄×C₅	—	2	1	no	—
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
84	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
85	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
86	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
87	C₅×#126	—	2	1	no	—
88	C₅×#126	—	2	1	no	—
89	C₅×#126	—	2	1	no	—
90	C₅×#126	—	2	1	no	—
91	C₅×#126	—	2	1	no	—
92	C₅×#126	—	2	1	no	—
93	C₅×#126	—	2	1	no	—
94	C₅×#126	—	2	1	no	—
95	C₅×#125	—	2	1	no	—
96	C₅×#125	—	2	1	no	—
97	C₅×#125	—	2	1	no	—
98	C₅×#125	—	2	1	no	—
99	C₅×#125	—	2	1	no	—
100	C₅×#125	—	2	1	no	—
101	C₅×#125	—	2	1	no	—
102	C₅×#125	C₂×C₄	1	1	yes	characteristic, complemented
103	C₅×#125	C₂×C₄	1	1	yes	characteristic, complemented
104	C₅×#124	—	2	1	no	—
105	C₅×#124	—	2	1	no	—
106	C₅×#124	C₂×C₄	1	1	yes	characteristic, complemented
107	C₅×#124	C₂×C₄	1	1	yes	characteristic, complemented
108	C₅×#123	—	2	1	no	—
109	C₅×#123	—	2	1	no	—
110	C₅×#123	—	2	1	no	—
111	C₅×#123	—	2	1	no	—
112	C₅×#123	—	2	1	no	—
113	C₅×#123	—	2	1	no	—
114	C₅×#123	—	2	1	no	—
115	C₅×C₂²⋊Q₈	—	2	1	no	—
116	C₅×C₂²⋊Q₈	—	2	1	no	—
117	C₅×C₂²⋊Q₈	—	2	1	no	—
118	C₅×C₂²⋊Q₈	—	2	1	no	—
119	C₅×C₂²⋊Q₈	—	2	1	no	—
120	C₅×C₂²⋊Q₈	—	2	1	no	—
121	C₅×C₂²⋊Q₈	—	2	1	no	—
122	C₅×C₂²⋊Q₈	—	2	1	no	—
123	C₅×C₂²⋊Q₈	—	2	1	no	—
124	C₅×C₂²⋊Q₈	—	2	1	no	—
125	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
126	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
127	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
128	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
129	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
130	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
131	C₅×#121	C₂×C₄	1	1	yes	characteristic
132	C₅×#121	C₂³	1	1	yes	characteristic
133	C₅×#120	—	2	1	no	—
134	C₄×C₅×Q₈	—	2	1	no	—
135	C₄×C₅×Q₈	—	2	1	no	—
136	C₄×C₅×Q₈	—	2	1	no	—
137	C₄×C₅×Q₈	—	2	1	no	—
138	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
139	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
140	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
141	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
142	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
143	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
144	C₄×C₅×D₄	—	2	1	no	—
145	C₄×C₅×D₄	—	2	1	no	—
146	C₄×C₅×D₄	—	2	1	no	—
147	C₄×C₅×D₄	—	2	1	no	—
148	C₄×C₅×D₄	—	2	1	no	—
149	C₄×C₅×D₄	—	2	1	no	—
150	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
151	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
152	C₅×#117	—	2	1	no	—
153	C₅×#117	—	2	1	no	—
154	C₅×#117	—	2	1	no	—
155	C₅×#117	—	2	1	no	—
156	C₅×#117	—	2	1	no	—
157	C₅×#117	—	2	1	no	—
158	C₅×#117	—	2	1	no	—
159	C₅×#117	C₂×C₄	1	1	yes	characteristic
160	C₅×#117	C₂×C₄	1	1	yes	characteristic
161	C₅×#117	C₂×C₄	1	1	yes	characteristic
162	C₅×#117	C₂×C₄	1	1	yes	characteristic
163	C₅×#117	C₂×C₄	1	1	yes	characteristic
164	C₅×#117	D₄	1	1	yes	characteristic
165	C₅×#117	D₄	1	1	yes	characteristic
166	C₅×#117	D₄	1	1	yes	characteristic
167	C₅×#117	D₄	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	—	2	1	no	—
169	C₂×C₅×C₄⋊C₄	—	2	1	no	—
170	C₂×C₅×C₄⋊C₄	—	2	1	no	—
171	C₂×C₅×C₄⋊C₄	—	2	1	no	—
172	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
173	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
178	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
179	C₂×C₄²×C₅	—	2	1	no	—
180	C₂×C₄²×C₅	—	2	1	no	—
181	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
183	C₅×C₄⋊C₈	—	2	1	no	—
184	C₅×C₄⋊C₈	—	2	1	no	—
185	C₅×C₄⋊C₈	—	2	1	no	—
186	C₅×C₄⋊C₈	—	2	1	no	—
187	C₅×C₂²⋊C₈	—	2	1	no	—
188	C₅×C₂²⋊C₈	—	2	1	no	—
189	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
190	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
191	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
192	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
193	C₅×#97	—	2	1	no	—
194	C₅×#97	—	2	1	no	—
195	C₄×C₅×C₈	—	2	1	no	—
196	C₄×C₅×C₈	—	2	1	no	—
197	C₅×#95	—	2	1	no	—
198	C₅×#95	—	2	1	no	—
199	C₅×#95	—	2	1	no	—
200	C₅×#95	—	2	1	no	—
201	C₅×#95	—	2	1	no	—
202	C₅×#95	—	2	1	no	—
203	C₅×#95	C₂³	1	1	yes	characteristic
204	C₅×#95	C₂³	1	1	yes	characteristic
205	C₅×#95	C₂³	1	1	yes	characteristic
206	C₅×#95	C₂³	1	1	yes	characteristic
207	#3495	C₂×C₅	1	1	yes	characteristic
208	#2924	C₂×C₅	1	1	yes	characteristic, complemented
209	#2343	C₂×C₅	1	1	yes	characteristic, complemented
210	#1521	C₂×C₅	1	1	yes	characteristic, complemented
211	#1518	C₂×C₅	1	1	yes	characteristic, complemented
212	#1516	C₂×C₅	1	1	yes	characteristic
213	#1515	C₂×C₅	1	1	yes	characteristic, complemented
214	#1512	C₂×C₅	1	1	yes	characteristic, complemented
215	#1511	C₂×C₅	1	1	yes	characteristic, complemented
216	#1509	C₂×C₅	1	1	yes	characteristic, complemented
217	#1506	C₂×C₅	1	1	yes	characteristic, complemented
218	#1504	C₂×C₅	1	1	yes	characteristic
219	#1503	C₂×C₅	1	1	yes	characteristic, complemented
220	#1500	C₂×C₅	1	1	yes	characteristic, complemented
221	C₂×#328	C₂×C₅	1	1	yes	characteristic, complemented
222	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
223	C₅×#41	—	4	2	no	—
224	C₂×C₅×Q₈	—	2	1	no	—
225	C₂×C₅×Q₈	—	2	1	no	—
226	C₂×C₅×Q₈	—	2	1	no	—
227	C₂×C₅×Q₈	—	4	2	no	—
228	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
229	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
230	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
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	—	4	2	no	—
245	C₂²×C₄×C₅	—	4	2	no	—
246	C₂²×C₄×C₅	—	4	2	no	—
247	C₂²×C₄×C₅	—	8	1	no	—
248	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₅×M₁₆	—	4	2	no	—
259	C₂×C₅×C₈	—	2	1	no	—
260	C₂×C₅×C₈	—	2	1	no	—
261	C₂×C₅×C₈	—	2	1	no	—
262	C₂×C₅×C₈	—	2	1	no	—
263	C₂×C₅×C₈	—	4	2	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	—	2	1	no	—
266	C₅×C₄⋊C₄	—	2	1	no	—
267	C₅×C₄⋊C₄	—	2	1	no	—
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	2	1	no	—
271	C₅×C₄⋊C₄	—	2	1	no	—
272	C₅×C₄⋊C₄	—	2	1	no	—
273	C₅×C₄⋊C₄	—	2	1	no	—
274	C₅×C₄⋊C₄	—	2	1	no	—
275	C₅×C₄⋊C₄	—	2	1	no	—
276	C₅×C₄⋊C₄	—	2	1	no	—
277	C₅×C₄⋊C₄	—	2	1	no	—
278	C₅×C₄⋊C₄	—	2	1	no	—
279	C₅×C₄⋊C₄	—	2	1	no	—
280	C₅×C₄⋊C₄	—	2	1	no	—
281	C₅×C₄⋊C₄	—	2	1	no	—
282	C₅×C₄⋊C₄	—	2	1	no	—
283	C₅×C₄⋊C₄	—	2	1	no	—
284	C₅×C₄⋊C₄	—	2	1	no	—
285	C₅×C₄⋊C₄	—	2	1	no	—
286	C₅×C₄⋊C₄	—	2	1	no	—
287	C₅×C₄⋊C₄	—	4	2	no	—
288	C₅×C₄⋊C₄	—	8	1	no	—
289	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
290	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
291	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
293	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
298	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
300	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	2	1	no	—
303	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	4	2	no	—
317	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
318	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
319	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
320	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
322	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
324	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₅	—	2	1	no	—
331	C₄²×C₅	—	2	1	no	—
332	C₄²×C₅	—	4	2	no	—
333	C₄²×C₅	—	8	1	no	—
334	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
335	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
336	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
337	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
338	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
342	#556	—	2	1	no	—
343	#554	—	2	1	no	—
344	#552	—	2	1	no	—
345	#552	—	2	1	no	—
346	#552	—	2	1	no	—
347	#552	—	2	1	no	—
348	#551	—	2	1	no	—
349	#551	—	2	1	no	—
350	#544	C₄×C₅	1	1	yes	characteristic, complemented
351	#542	C₄×C₅	1	1	yes	characteristic, complemented
352	#542	C₄×C₅	1	1	yes	characteristic, complemented
353	#541	C₄×C₅	1	1	yes	characteristic, complemented
354	#541	C₄×C₅	1	1	yes	characteristic, complemented
355	#536	C₄×C₅	1	1	yes	characteristic, complemented
356	#533	C₂²×C₅	1	1	yes	characteristic
357	#533	C₂²×C₅	1	1	yes	characteristic
358	#529	C₂²×C₅	1	1	yes	characteristic
359	#529	C₂²×C₅	1	1	yes	characteristic
360	#525	C₂²×C₅	1	1	yes	characteristic
361	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
362	#520	C₄×C₅	1	1	yes	characteristic, complemented
363	#519	C₄×C₅	1	1	yes	characteristic, complemented
364	C₂×#117	C₂²×C₅	1	1	yes	characteristic
365	#433	—	2	1	no	—
366	#433	—	2	1	no	—
367	#432	C₂²×C₅	1	1	yes	characteristic
368	#432	C₂²×C₅	1	1	yes	characteristic
369	#431	C₂²×C₅	1	1	yes	characteristic
370	#431	C₂²×C₅	1	1	yes	characteristic
371	#424	—	2	1	no	—
372	#407	C₂²×C₅	1	1	yes	characteristic
373	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
374	#405	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#385	—	2	1	no	—
378	#383	C₂²×C₅	1	1	yes	characteristic
379	#382	C₂²×C₅	1	1	yes	characteristic
380	#381	C₂²×C₅	1	1	yes	characteristic
381	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
382	C₄×C₂²⋊C₄	—	2	1	no	—
383	#376	C₂²×C₅	1	1	yes	characteristic
384	C₂×#95	C₂²×C₅	1	1	yes	characteristic
385	#328	C₂²×C₅	1	1	yes	characteristic
386	#328	C₂²×C₅	1	1	yes	characteristic
387	#328	C₂²×C₅	1	1	yes	characteristic
388	#328	C₂²×C₅	1	1	yes	characteristic
389	#328	C₂²×C₅	1	1	yes	characteristic
390	#328	C₂²×C₅	1	1	yes	characteristic
391	#328	C₂²×C₅	1	1	yes	characteristic
392	#328	C₂²×C₅	1	1	yes	characteristic
393	#328	C₂²×C₅	1	1	yes	characteristic
394	#328	C₂²×C₅	1	1	yes	characteristic
395	#328	C₂²×C₅	1	1	yes	characteristic
396	#328	C₂²×C₅	1	1	yes	characteristic
397	#327	C₂²×C₅	1	1	yes	characteristic
398	#327	C₂²×C₅	1	1	yes	characteristic
399	#327	C₂²×C₅	1	1	yes	characteristic
400	#327	C₂²×C₅	1	1	yes	characteristic
401	C₂³×C₅	—	2	1	no	—
402	C₂³×C₅	—	2	1	no	—
403	C₂³×C₅	—	2	2	no	—
404	C₂³×C₅	—	2	1	no	—
405	C₂³×C₅	—	4	1	no	—
406	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
408	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
409	C₅×Q₈	—	4	1	no	—
410	C₅×Q₈	—	4	1	no	—
411	C₅×Q₈	—	4	1	no	—
412	C₅×Q₈	—	4	2	no	—
413	C₅×Q₈	—	8	1	no	—
414	C₅×Q₈	—	8	1	no	—
415	C₅×D₄	—	4	1	no	—
416	C₅×D₄	—	4	1	no	—
417	C₅×D₄	—	4	1	no	—
418	C₅×D₄	—	4	2	no	—
419	C₅×D₄	—	8	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	1	no	—
424	C₂×C₄×C₅	—	2	2	no	—
425	C₂×C₄×C₅	—	2	2	no	—
426	C₂×C₄×C₅	—	2	2	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	1	no	—
434	C₂×C₄×C₅	—	4	1	no	—
435	C₂×C₄×C₅	—	4	1	no	—
436	C₂×C₄×C₅	—	4	1	no	—
437	C₂×C₄×C₅	—	4	1	no	—
438	C₂×C₄×C₅	—	4	1	no	—
439	C₂×C₄×C₅	—	4	1	no	—
440	C₂×C₄×C₅	—	4	2	no	—
441	C₂×C₄×C₅	—	4	1	no	—
442	C₂×C₄×C₅	—	4	1	no	—
443	C₂×C₄×C₅	—	4	2	no	—
444	C₂×C₄×C₅	—	4	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	—	4	1	no	—
453	C₂×C₄×C₅	—	8	1	no	—
454	C₂×C₄×C₅	—	8	1	no	—
455	C₂×C₄×C₅	—	8	1	no	—
456	C₂×C₄×C₅	—	8	4	no	—
457	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
468	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
469	C₅×C₈	—	4	1	no	—
470	C₅×C₈	—	4	1	no	—
471	C₅×C₈	—	4	1	no	—
472	C₅×C₈	—	4	1	no	—
473	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
474	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
477	C₂×M₁₆	—	2	1	no	—
478	C₂²×C₈	—	2	1	no	—
479	C₄⋊Q₈	—	2	1	no	—
480	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
481	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
482	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
483	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
484	#126	—	2	1	no	—
485	#126	—	2	1	no	—
486	#126	—	2	1	no	—
487	#126	—	2	1	no	—
488	#126	—	2	1	no	—
489	#126	—	2	1	no	—
490	#126	—	2	1	no	—
491	#126	—	2	1	no	—
492	#125	—	2	1	no	—
493	#125	—	2	1	no	—
494	#125	—	2	1	no	—
495	#125	—	2	1	no	—
496	#125	—	2	1	no	—
497	#125	—	2	1	no	—
498	#125	—	2	1	no	—
499	#125	C₂×C₄×C₅	1	1	yes	characteristic, complemented
500	#125	C₂×C₄×C₅	1	1	yes	characteristic, complemented
501	#124	—	2	1	no	—
502	#124	—	2	1	no	—
503	#124	C₂×C₄×C₅	1	1	yes	characteristic, complemented
504	#124	C₂×C₄×C₅	1	1	yes	characteristic, complemented
505	#123	—	2	1	no	—
506	#123	—	2	1	no	—
507	#123	—	2	1	no	—
508	#123	—	2	1	no	—
509	#123	—	2	1	no	—
510	#123	—	2	1	no	—
511	#123	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	1	no	—
515	C₂²⋊Q₈	—	2	1	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	—	2	1	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
523	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
524	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
525	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
526	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
527	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
528	#121	C₂×C₄×C₅	1	1	yes	characteristic
529	#121	C₂³×C₅	1	1	yes	characteristic
530	#120	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×Q₈	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
536	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
537	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
538	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
539	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
540	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
548	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
549	#117	—	2	1	no	—
550	#117	—	2	1	no	—
551	#117	—	2	1	no	—
552	#117	—	2	1	no	—
553	#117	—	2	1	no	—
554	#117	—	2	1	no	—
555	#117	—	2	1	no	—
556	#117	C₂×C₄×C₅	1	1	yes	characteristic
557	#117	C₂×C₄×C₅	1	1	yes	characteristic
558	#117	C₂×C₄×C₅	1	1	yes	characteristic
559	#117	C₂×C₄×C₅	1	1	yes	characteristic
560	#117	C₂×C₄×C₅	1	1	yes	characteristic
561	#117	C₅×D₄	1	1	yes	characteristic
562	#117	C₅×D₄	1	1	yes	characteristic
563	#117	C₅×D₄	1	1	yes	characteristic
564	#117	C₅×D₄	1	1	yes	characteristic
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
576	C₂×C₄²	—	2	1	no	—
577	C₂×C₄²	—	2	1	no	—
578	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
580	C₄⋊C₈	—	2	1	no	—
581	C₄⋊C₈	—	2	1	no	—
582	C₄⋊C₈	—	2	1	no	—
583	C₄⋊C₈	—	2	1	no	—
584	C₂²⋊C₈	—	2	1	no	—
585	C₂²⋊C₈	—	2	1	no	—
586	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
587	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
588	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
589	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
590	#97	—	2	1	no	—
591	#97	—	2	1	no	—
592	C₄×C₈	—	2	1	no	—
593	C₄×C₈	—	2	1	no	—
594	#95	—	2	1	no	—
595	#95	—	2	1	no	—
596	#95	—	2	1	no	—
597	#95	—	2	1	no	—
598	#95	—	2	1	no	—
599	#95	—	2	1	no	—
600	#95	C₂³×C₅	1	1	yes	characteristic
601	#95	C₂³×C₅	1	1	yes	characteristic
602	#95	C₂³×C₅	1	1	yes	characteristic
603	#95	C₂³×C₅	1	1	yes	characteristic
604	C₂²×C₅	—	2	1	no	—
605	C₂²×C₅	—	2	1	no	—
606	C₂²×C₅	—	2	1	no	—
607	C₂²×C₅	—	2	1	no	—
608	C₂²×C₅	—	2	1	no	—
609	C₂²×C₅	—	2	1	no	—
610	C₂²×C₅	—	2	1	no	—
611	C₂²×C₅	—	4	2	no	—
612	C₂²×C₅	—	4	2	no	—
613	C₂²×C₅	—	4	1	no	—
614	C₂²×C₅	—	4	1	no	—
615	C₂²×C₅	—	4	1	no	—
616	C₂²×C₅	#410	1	2	yes	—
617	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
618	C₂²×C₅	#577	1	1	yes	characteristic
619	C₂²×C₅	#578	1	1	yes	characteristic
620	C₄×C₅	—	2	1	no	—
621	C₄×C₅	—	2	1	no	—
622	C₄×C₅	—	2	1	no	—
623	C₄×C₅	—	2	1	no	—
624	C₄×C₅	—	2	1	no	—
625	C₄×C₅	—	2	1	no	—
626	C₄×C₅	—	2	1	no	—
627	C₄×C₅	—	2	1	no	—
628	C₄×C₅	—	2	1	no	—
629	C₄×C₅	—	2	1	no	—
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	2	1	no	—
632	C₄×C₅	—	4	2	no	—
633	C₄×C₅	—	4	1	no	—
634	C₄×C₅	—	4	1	no	—
635	C₄×C₅	—	4	1	no	—
636	C₄×C₅	—	4	1	no	—
637	C₄×C₅	—	4	1	no	—
638	C₄×C₅	—	4	1	no	—
639	C₄×C₅	—	4	1	no	—
640	C₄×C₅	—	8	1	no	—
641	C₄×C₅	—	8	1	no	—
642	C₄×C₅	—	8	1	no	—
643	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
644	#41	—	4	2	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
650	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
651	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	8	1	no	—
669	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
670	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
673	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
674	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
679	M₁₆	—	4	2	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	4	2	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	8	1	no	—
710	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
711	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
712	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
713	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
714	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
715	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
716	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
717	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
739	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
740	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
741	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
742	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
743	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
744	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
745	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
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	C₄²	—	2	1	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	4	2	no	—
754	C₄²	—	8	1	no	—
755	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
756	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
757	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
758	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
759	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
760	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
761	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
762	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
763	C₂×C₅	—	2	1	no	—
764	C₂×C₅	—	2	1	no	—
765	C₂×C₅	—	2	2	no	—
766	C₂×C₅	—	4	1	no	—
767	C₂×C₅	—	8	1	no	—
768	C₂×C₅	C₂×#410	1	1	yes	characteristic
769	C₂×C₅	#2898	1	1	yes	characteristic
770	C₂×C₅	#2901	1	1	yes	characteristic
771	C₂³	—	2	2	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	4	1	no	—
776	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
777	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
778	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
779	Q₈	—	4	1	no	—
780	Q₈	—	4	1	no	—
781	Q₈	—	4	1	no	—
782	Q₈	—	4	2	no	—
783	Q₈	—	8	1	no	—
784	Q₈	—	8	1	no	—
785	D₄	—	4	1	no	—
786	D₄	—	4	2	no	—
787	D₄	—	4	1	no	—
788	D₄	—	4	1	no	—
789	D₄	—	8	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	8	1	no	—
824	C₂×C₄	—	8	1	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	4	no	—
827	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
828	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
829	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
830	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
831	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
832	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
833	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
834	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
835	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
836	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
837	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
838	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
839	C₈	—	4	1	no	—
840	C₈	—	4	1	no	—
841	C₈	—	4	1	no	—
842	C₈	—	4	1	no	—
843	C₅	#17609	1	1	yes	characteristic, direct product factor, Sylow
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	C₅×#410	1	2	yes	—
857	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
858	C₂²	C₅×#577	1	1	yes	characteristic
859	C₂²	C₅×#578	1	1	yes	characteristic
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	8	1	no	—
881	C₄	—	8	1	no	—
882	C₄	—	8	1	no	—
883	C₂	—	2	1	no	—
884	C₂	—	2	1	no	—
885	C₂	—	2	2	no	—
886	C₂	—	4	1	no	—
887	C₂	—	8	1	no	—
888	C₂	C₂×C₅×#410	1	1	yes	characteristic
889	C₂	C₅×#2898	1	1	yes	characteristic
890	C₂	C₅×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2924	C₂	semidirect
3. C₅×#2343	C₂	semidirect
4. C₅×#1521	C₂	semidirect
5. C₅×#1518	C₂	semidirect
7. C₅×#1515	C₂	semidirect
8. C₅×#1512	C₂	semidirect
9. C₅×#1511	C₂	semidirect
10. C₅×#1509	C₂	semidirect
11. C₅×#1506	C₂	semidirect
13. C₅×#1503	C₂	semidirect
14. C₅×#1500	C₂	semidirect
15. C₂×C₅×#328	C₂	semidirect
24. C₅×#544	C₄	semidirect
25. C₅×#542	C₄	semidirect
26. C₅×#542	C₄	semidirect
27. C₅×#541	C₄	semidirect
28. C₅×#541	C₄	semidirect
29. C₅×#536	C₄	semidirect
36. C₅×#520	C₄	semidirect
37. C₅×#519	C₄	semidirect
75. #17609	C₅	direct (N × H)
83. C₅×C₄⋊Q₈	C₂×C₄	semidirect
84. C₅×C₄⋊Q₈	C₂×C₄	semidirect
85. C₅×C₄⋊Q₈	C₂×C₄	semidirect
86. C₅×C₄⋊Q₈	C₂×C₄	semidirect
102. C₅×#125	C₂×C₄	semidirect
103. C₅×#125	C₂×C₄	semidirect
106. C₅×#124	C₂×C₄	semidirect
107. C₅×#124	C₂×C₄	semidirect
138. C₄×C₅×Q₈	C₂×C₄	semidirect
139. C₄×C₅×Q₈	C₂×C₄	semidirect
140. C₄×C₅×Q₈	C₂×C₄	semidirect
141. C₄×C₅×Q₈	C₂×C₄	semidirect
142. C₄×C₅×Q₈	C₂×C₄	semidirect
143. C₄×C₅×Q₈	C₂×C₄	semidirect
150. C₄×C₅×D₄	C₂×C₄	semidirect
151. C₄×C₅×D₄	C₂×C₄	semidirect
208. #2924	C₂×C₅	semidirect
209. #2343	C₂×C₅	semidirect
210. #1521	C₂×C₅	semidirect
211. #1518	C₂×C₅	semidirect
213. #1515	C₂×C₅	semidirect
214. #1512	C₂×C₅	semidirect
215. #1511	C₂×C₅	semidirect
216. #1509	C₂×C₅	semidirect
217. #1506	C₂×C₅	semidirect
219. #1503	C₂×C₅	semidirect
220. #1500	C₂×C₅	semidirect
221. C₂×#328	C₂×C₅	semidirect
350. #544	C₄×C₅	semidirect
351. #542	C₄×C₅	semidirect
352. #542	C₄×C₅	semidirect
353. #541	C₄×C₅	semidirect
354. #541	C₄×C₅	semidirect
355. #536	C₄×C₅	semidirect
362. #520	C₄×C₅	semidirect
363. #519	C₄×C₅	semidirect
480. C₄⋊Q₈	C₂×C₄×C₅	semidirect
481. C₄⋊Q₈	C₂×C₄×C₅	semidirect
482. C₄⋊Q₈	C₂×C₄×C₅	semidirect
483. C₄⋊Q₈	C₂×C₄×C₅	semidirect
499. #125	C₂×C₄×C₅	semidirect
500. #125	C₂×C₄×C₅	semidirect
503. #124	C₂×C₄×C₅	semidirect
504. #124	C₂×C₄×C₅	semidirect
535. C₄×Q₈	C₂×C₄×C₅	semidirect
536. C₄×Q₈	C₂×C₄×C₅	semidirect
537. C₄×Q₈	C₂×C₄×C₅	semidirect
538. C₄×Q₈	C₂×C₄×C₅	semidirect
539. C₄×Q₈	C₂×C₄×C₅	semidirect
540. C₄×Q₈	C₂×C₄×C₅	semidirect
547. C₄×D₄	C₂×C₄×C₅	semidirect
548. C₄×D₄	C₂×C₄×C₅	semidirect
843. C₅	#17609	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×#3495	2
C₅×#2924	2
C₅×#2343	2
C₅×#1521	2
C₅×#1518	2
C₅×#1516	2
C₅×#1515	2
C₅×#1512	2
C₅×#1511	2
C₅×#1509	2
C₅×#1506	2
C₅×#1504	2
C₅×#1503	2
C₅×#1500	2
C₂×C₅×#328	2
#17609	5

Subgroups — C5×#17609 #11940329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17609 #11940329