Subgroups — C₅×#60573 #11983293

Order 1280.

2004 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3127	C₂	1	2	yes	maximal, complemented
4	C₅×#3124	C₂	1	2	yes	maximal, complemented
5	C₅×#3121	C₂	1	2	yes	maximal, complemented
6	C₅×#3120	C₂	1	2	yes	maximal, complemented
7	C₅×#3108	C₂	1	2	yes	maximal, complemented
8	C₅×#3107	C₂	1	2	yes	maximal, complemented
9	C₅×#3104	C₂	1	2	yes	maximal, complemented
10	C₅×#3102	C₂	1	2	yes	maximal, complemented
11	C₅×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3044	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#3013	C₂	1	1	yes	maximal, characteristic
18	C₅×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₅×#137	C₂²	1	1	yes	characteristic
26	C₂×C₅×#137	C₂²	1	1	yes	characteristic
27	C₂×C₅×#135	C₂²	1	1	yes	characteristic
28	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
29	C₅×#544	C₂²	1	1	yes	characteristic
30	C₅×#542	—	2	1	no	—
31	C₅×#542	C₂²	1	2	yes	—
32	C₅×#541	—	2	1	no	—
33	C₅×#541	C₂²	1	2	yes	—
34	C₅×#539	—	2	2	no	—
35	C₅×#537	C₂²	1	1	yes	characteristic
36	C₅×#536	C₂²	1	1	yes	characteristic
37	C₅×#536	C₂²	1	1	yes	characteristic
38	C₅×#533	—	2	1	no	—
39	C₅×#533	C₂²	1	2	yes	—
40	C₅×#529	—	2	2	no	—
41	C₅×#529	—	2	1	no	—
42	C₅×#529	C₂²	1	2	yes	—
43	C₅×#520	—	2	2	no	—
44	C₅×#520	—	2	1	no	—
45	C₅×#520	C₂²	1	1	yes	characteristic
46	C₅×#520	C₂²	1	2	yes	—
47	C₅×#520	C₂²	1	1	yes	characteristic
48	C₅×#519	—	2	1	no	—
49	C₅×#519	C₂²	1	1	yes	characteristic
50	C₅×#519	C₂²	1	2	yes	—
51	C₄×C₅×#41	—	2	2	no	—
52	C₄×C₅×#41	—	2	1	no	—
53	C₄×C₅×#41	C₂²	1	2	yes	—
54	C₄×C₅×#41	C₂²	1	1	yes	characteristic
55	C₄×C₅×#41	C₂²	1	1	yes	characteristic
56	C₄×C₅×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₅×Q₈	—	2	1	no	—
58	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
59	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
61	C₅×#485	C₂²	1	2	yes	—
62	C₅×#485	C₂²	1	2	yes	—
63	C₅×#485	C₂²	1	2	yes	—
64	C₅×#484	C₂²	1	2	yes	—
65	C₅×#484	C₂²	1	2	yes	—
66	C₅×#483	C₂²	1	2	yes	—
67	C₅×#482	C₂²	1	2	yes	—
68	C₅×#480	C₂²	1	2	yes	—
69	C₅×#479	C₂²	1	2	yes	—
70	C₅×#479	C₂²	1	2	yes	—
71	C₅×#479	C₂²	1	2	yes	—
72	C₅×#478	C₂²	1	2	yes	—
73	C₅×#477	C₂²	1	2	yes	—
74	C₅×#477	C₂²	1	2	yes	—
75	C₅×#475	C₂²	1	2	yes	—
76	C₅×#474	C₂²	1	2	yes	—
77	C₅×#464	C₂²	1	2	yes	—
78	C₅×#464	C₂²	1	2	yes	—
79	C₅×#464	C₂²	1	2	yes	—
80	C₅×#463	C₂²	1	2	yes	—
81	C₅×#462	C₂²	1	2	yes	—
82	C₅×#462	C₂²	1	2	yes	—
83	C₅×#462	C₂²	1	2	yes	—
84	C₅×#461	C₂²	1	2	yes	—
85	C₅×#452	C₂²	1	2	yes	—
86	C₅×#452	C₂²	1	2	yes	—
87	C₅×#452	C₂²	1	2	yes	—
88	C₅×#451	C₂²	1	2	yes	—
89	C₅×#451	C₂²	1	2	yes	—
90	C₅×#451	C₂²	1	2	yes	—
91	C₅×#449	C₂²	1	2	yes	—
92	C₅×#448	C₂²	1	2	yes	—
93	C₅×#441	C₂²	1	2	yes	—
94	C₅×#441	C₂²	1	2	yes	—
95	C₅×#440	C₂²	1	2	yes	—
96	C₅×#440	C₂²	1	2	yes	—
97	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
98	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
99	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
100	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
101	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
102	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
103	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
104	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
105	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
106	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
107	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
108	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
109	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
111	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
112	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
113	C₅×#433	C₂²	1	2	yes	—
114	C₅×#433	C₂²	1	2	yes	—
115	C₅×#431	C₂²	1	2	yes	—
116	C₅×#431	C₂²	1	2	yes	—
117	C₅×#428	C₂²	1	1	yes	characteristic
118	C₅×#428	C₂²	1	1	yes	characteristic
119	C₅×#427	C₂²	1	1	yes	characteristic
120	C₂×C₅×#107	C₂²	1	1	yes	characteristic
121	C₅×#424	C₂²	1	1	yes	characteristic
122	C₅×#424	C₂²	1	1	yes	characteristic
123	C₅×#419	C₂²	1	1	yes	characteristic
124	C₅×#419	C₂²	1	1	yes	characteristic
125	C₅×#417	C₂²	1	1	yes	characteristic
126	C₅×#417	C₂²	1	1	yes	characteristic
127	C₅×#416	C₂²	1	1	yes	characteristic
128	C₅×#416	C₂²	1	1	yes	characteristic
129	C₂×C₅×#103	C₂²	1	1	yes	characteristic
130	C₂×C₅×#103	C₂²	1	1	yes	characteristic
131	C₅×#408	C₂²	1	1	yes	characteristic
132	C₅×#408	C₂²	1	1	yes	characteristic
133	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
135	#60573	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₅×2₋¹⁺⁴	—	2	4	no	—
137	C₅×2₋¹⁺⁴	—	2	4	no	—
138	C₂×C₅×#41	—	2	2	no	—
139	C₂×C₅×#41	—	2	1	no	—
140	C₂×C₅×#41	C₂³	1	1	yes	characteristic
141	C₂×C₅×#41	C₂³	1	2	yes	—
142	C₂×C₅×#41	C₂³	1	1	yes	characteristic
143	C₂×C₅×#41	C₂³	1	1	yes	characteristic
144	C₂²×C₅×Q₈	—	2	1	no	—
145	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
146	C₂²×C₅×Q₈	C₂³	1	2	yes	—
147	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
148	C₅×#137	—	2	4	no	—
149	C₅×#137	—	2	4	no	—
150	C₅×#135	—	2	4	no	—
151	C₂×C₅×Q₁₆	—	2	4	no	—
152	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
154	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
155	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
156	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
157	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
162	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
164	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
165	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
166	C₅×C₄⋊Q₈	—	2	1	no	—
167	C₅×C₄⋊Q₈	—	2	1	no	—
168	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₅×#126	—	2	2	no	—
171	C₅×#126	—	2	2	no	—
172	C₅×#126	—	2	2	no	—
173	C₅×#126	—	2	2	no	—
174	C₅×#125	—	2	2	no	—
175	C₅×#125	—	2	1	no	—
176	C₅×#125	—	2	2	no	—
177	C₅×#125	—	2	2	no	—
178	C₅×#125	C₂³	1	2	yes	—
179	C₅×#124	—	2	1	no	—
180	C₅×#124	—	2	2	no	—
181	C₅×#124	C₂³	1	2	yes	—
182	C₅×#123	—	2	2	no	—
183	C₅×#123	—	2	2	no	—
184	C₅×#123	—	2	2	no	—
185	C₅×#123	—	2	2	no	—
186	C₅×C₂²⋊Q₈	—	2	1	no	—
187	C₅×C₂²⋊Q₈	—	2	2	no	—
188	C₅×C₂²⋊Q₈	—	2	1	no	—
189	C₅×C₂²⋊Q₈	—	2	1	no	—
190	C₅×C₂²⋊Q₈	—	2	2	no	—
191	C₅×C₂²⋊Q₈	—	2	2	no	—
192	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₅×#121	—	2	2	no	—
196	C₅×#121	—	2	1	no	—
197	C₅×#121	C₂³	1	2	yes	—
198	C₄×C₅×Q₈	—	2	1	no	—
199	C₄×C₅×Q₈	—	2	2	no	—
200	C₄×C₅×Q₈	—	2	1	no	—
201	C₄×C₅×Q₈	—	2	1	no	—
202	C₄×C₅×Q₈	—	2	2	no	—
203	C₄×C₅×Q₈	—	2	1	no	—
204	C₄×C₅×Q₈	—	2	2	no	—
205	C₄×C₅×Q₈	—	2	1	no	—
206	C₄×C₅×Q₈	—	2	2	no	—
207	C₄×C₅×Q₈	—	2	1	no	—
208	C₄×C₅×Q₈	—	2	1	no	—
209	C₄×C₅×Q₈	—	2	2	no	—
210	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
211	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
212	C₄×C₅×Q₈	C₂³	1	2	yes	—
213	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
214	C₄×C₅×Q₈	C₂³	1	2	yes	—
215	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
216	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
217	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
218	C₄×C₅×Q₈	C₂³	1	2	yes	—
219	C₄×C₅×Q₈	C₂³	1	2	yes	—
220	C₄×C₅×Q₈	C₂³	1	2	yes	—
221	C₄×C₅×Q₈	C₂³	1	2	yes	—
222	C₄×C₅×Q₈	C₂³	1	2	yes	—
223	C₄×C₅×D₄	—	2	2	no	—
224	C₄×C₅×D₄	—	2	1	no	—
225	C₄×C₅×D₄	—	2	1	no	—
226	C₄×C₅×D₄	—	2	2	no	—
227	C₄×C₅×D₄	—	2	1	no	—
228	C₄×C₅×D₄	—	2	2	no	—
229	C₄×C₅×D₄	—	2	1	no	—
230	C₄×C₅×D₄	—	2	1	no	—
231	C₄×C₅×D₄	—	2	2	no	—
232	C₄×C₅×D₄	—	2	2	no	—
233	C₄×C₅×D₄	—	2	2	no	—
234	C₄×C₅×D₄	—	2	2	no	—
235	C₄×C₅×D₄	D₄	1	1	yes	characteristic
236	C₄×C₅×D₄	D₄	1	2	yes	—
237	C₄×C₅×D₄	D₄	1	2	yes	—
238	C₄×C₅×D₄	D₄	1	1	yes	characteristic
239	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
240	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
241	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
242	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
243	C₄×C₅×D₄	C₂³	1	2	yes	—
244	C₅×#117	—	2	2	no	—
245	C₅×#117	—	2	1	no	—
246	C₅×#117	—	2	2	no	—
247	C₅×#117	—	2	2	no	—
248	C₅×#117	—	2	2	no	—
249	C₅×#117	—	2	2	no	—
250	C₅×#117	—	2	1	no	—
251	C₅×#117	—	2	2	no	—
252	C₅×#117	—	2	1	no	—
253	C₅×#117	—	2	2	no	—
254	C₅×#117	C₂³	1	1	yes	characteristic
255	C₅×#117	C₂³	1	1	yes	characteristic
256	C₅×#117	C₂³	1	2	yes	—
257	C₅×#117	C₂³	1	1	yes	characteristic
258	C₅×#117	C₂³	1	2	yes	—
259	C₂×C₅×C₄⋊C₄	—	2	1	no	—
260	C₂×C₅×C₄⋊C₄	—	2	2	no	—
261	C₂×C₅×C₄⋊C₄	—	2	1	no	—
262	C₂×C₅×C₄⋊C₄	—	2	2	no	—
263	C₂×C₅×C₄⋊C₄	—	2	1	no	—
264	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₄²×C₅	—	2	1	no	—
268	C₂×C₄²×C₅	—	2	2	no	—
269	C₂×C₄²×C₅	—	2	1	no	—
270	C₂×C₄²×C₅	—	2	1	no	—
271	C₂×C₄²×C₅	—	2	2	no	—
272	C₂×C₄²×C₅	—	2	1	no	—
273	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₅	C₂³	1	2	yes	—
275	C₅×#107	C₂³	1	2	yes	—
276	C₅×#107	C₂³	1	2	yes	—
277	C₅×#107	C₂³	1	1	yes	characteristic
278	C₅×#107	C₂³	1	1	yes	characteristic
279	C₅×#107	C₂³	1	2	yes	—
280	C₅×#107	C₂³	1	2	yes	—
281	C₅×#106	C₂³	1	1	yes	characteristic
282	C₅×#106	C₂³	1	1	yes	characteristic
283	C₅×#106	C₂³	1	2	yes	—
284	C₅×#106	C₂³	1	2	yes	—
285	C₅×C₄⋊C₈	C₂³	1	2	yes	—
286	C₅×C₄⋊C₈	C₂³	1	2	yes	—
287	C₅×C₄⋊C₈	C₂³	1	2	yes	—
288	C₅×C₄⋊C₈	C₂³	1	2	yes	—
289	C₅×#103	C₂³	1	2	yes	—
290	C₅×#103	C₂³	1	2	yes	—
291	C₅×#103	C₂³	1	2	yes	—
292	C₅×#103	C₂³	1	2	yes	—
293	C₅×#103	C₂³	1	1	yes	characteristic
294	C₅×#103	C₂³	1	1	yes	characteristic
295	C₅×#103	C₂³	1	1	yes	characteristic
296	C₅×#103	C₂³	1	1	yes	characteristic
297	C₅×#103	C₂³	1	2	yes	—
298	C₅×#103	C₂³	1	2	yes	—
299	C₅×#103	C₂³	1	2	yes	—
300	C₅×#103	C₂³	1	2	yes	—
301	C₅×#103	C₂³	1	2	yes	—
302	C₅×#103	C₂³	1	2	yes	—
303	C₅×#102	C₂³	1	1	yes	characteristic
304	C₅×#102	C₂³	1	1	yes	characteristic
305	C₅×#102	C₂³	1	1	yes	characteristic
306	C₅×#102	C₂³	1	1	yes	characteristic
307	C₅×#102	C₂³	1	2	yes	—
308	C₅×#102	C₂³	1	2	yes	—
309	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₅×#97	C₂³	1	2	yes	—
314	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
316	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
317	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
318	C₄×C₅×C₈	C₂³	1	2	yes	—
319	#3461	C₂×C₅	1	1	yes	characteristic, complemented
320	C₄×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic, complemented
321	#3127	C₂×C₅	1	2	yes	complemented
322	#3124	C₂×C₅	1	2	yes	complemented
323	#3121	C₂×C₅	1	2	yes	complemented
324	#3120	C₂×C₅	1	2	yes	complemented
325	#3108	C₂×C₅	1	2	yes	complemented
326	#3107	C₂×C₅	1	2	yes	complemented
327	#3104	C₂×C₅	1	2	yes	complemented
328	#3102	C₂×C₅	1	2	yes	complemented
329	#3098	C₂×C₅	1	1	yes	characteristic, complemented
330	#3097	C₂×C₅	1	1	yes	characteristic, complemented
331	#3083	C₂×C₅	1	1	yes	characteristic, complemented
332	#3082	C₂×C₅	1	1	yes	characteristic, complemented
333	#3046	C₂×C₅	1	1	yes	characteristic, complemented
334	#3044	C₂×C₅	1	1	yes	characteristic, complemented
335	#3013	C₂×C₅	1	1	yes	characteristic
336	#3011	C₂×C₅	1	1	yes	characteristic, complemented
337	C₄×#137	C₂×C₅	1	1	yes	characteristic, complemented
338	C₄×#137	C₂×C₅	1	1	yes	characteristic, complemented
339	C₄×#135	C₂×C₅	1	1	yes	characteristic, complemented
340	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
341	#2922	C₂×C₅	1	1	yes	characteristic, complemented
342	C₅×#41	—	2	16	no	—
343	C₅×#41	—	2	8	no	—
344	C₅×#41	—	2	4	no	—
345	C₅×#41	—	2	4	no	—
346	C₅×#41	—	2	2	no	—
347	C₅×#41	—	2	2	no	—
348	C₅×#41	—	2	2	no	—
349	C₅×#41	—	2	2	no	—
350	C₅×#41	—	2	2	no	—
351	C₅×#41	#41	1	4	yes	—
352	C₂×C₅×Q₈	—	2	8	no	—
353	C₂×C₅×Q₈	—	2	4	no	—
354	C₂×C₅×Q₈	—	2	4	no	—
355	C₂×C₅×Q₈	—	2	2	no	—
356	C₂×C₅×Q₈	—	2	1	no	—
357	C₂×C₅×Q₈	—	2	1	no	—
358	C₂×C₅×Q₈	—	2	2	no	—
359	C₂×C₅×Q₈	—	2	2	no	—
360	C₂×C₅×Q₈	—	2	2	no	—
361	C₂×C₅×Q₈	—	2	2	no	—
362	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
363	C₂×C₅×Q₈	#41	1	4	yes	—
364	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
365	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
366	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
368	C₂×C₅×D₄	—	2	2	no	—
369	C₂×C₅×D₄	—	2	1	no	—
370	C₂×C₅×D₄	—	2	1	no	—
371	C₂×C₅×D₄	—	2	2	no	—
372	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
373	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
374	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅	—	2	2	no	—
377	C₂²×C₄×C₅	—	2	1	no	—
378	C₂²×C₄×C₅	—	2	2	no	—
379	C₂²×C₄×C₅	—	2	1	no	—
380	C₂²×C₄×C₅	—	2	1	no	—
381	C₂²×C₄×C₅	—	2	2	no	—
382	C₂²×C₄×C₅	—	2	1	no	—
383	C₂²×C₄×C₅	—	2	1	no	—
384	C₂²×C₄×C₅	—	2	1	no	—
385	C₂²×C₄×C₅	—	2	1	no	—
386	C₂²×C₄×C₅	—	2	1	no	—
387	C₂²×C₄×C₅	—	2	1	no	—
388	C₂²×C₄×C₅	—	2	2	no	—
389	C₂²×C₄×C₅	—	2	1	no	—
390	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
392	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
394	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₅×Q₁₆	—	2	4	no	—
397	C₅×Q₁₆	—	2	4	no	—
398	C₅×Q₁₆	—	2	2	no	—
399	C₅×Q₁₆	—	2	4	no	—
400	C₅×Q₁₆	—	2	4	no	—
401	C₅×SD₁₆	—	2	2	no	—
402	C₅×SD₁₆	—	2	4	no	—
403	C₅×SD₁₆	—	2	2	no	—
404	C₅×SD₁₆	—	2	4	no	—
405	C₅×D₈	—	2	2	no	—
406	C₅×M₁₆	—	2	2	no	—
407	C₅×M₁₆	—	2	2	no	—
408	C₂×C₅×C₈	—	2	2	no	—
409	C₂×C₅×C₈	—	2	2	no	—
410	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₅×C₈	C₂⁴	1	2	yes	—
415	C₂×C₅×C₈	C₂⁴	1	2	yes	—
416	C₅×C₄⋊C₄	—	2	2	no	—
417	C₅×C₄⋊C₄	—	2	2	no	—
418	C₅×C₄⋊C₄	—	2	2	no	—
419	C₅×C₄⋊C₄	—	2	2	no	—
420	C₅×C₄⋊C₄	—	2	1	no	—
421	C₅×C₄⋊C₄	—	2	2	no	—
422	C₅×C₄⋊C₄	—	2	1	no	—
423	C₅×C₄⋊C₄	—	2	2	no	—
424	C₅×C₄⋊C₄	—	2	2	no	—
425	C₅×C₄⋊C₄	—	2	1	no	—
426	C₅×C₄⋊C₄	—	2	1	no	—
427	C₅×C₄⋊C₄	—	2	2	no	—
428	C₅×C₄⋊C₄	—	2	1	no	—
429	C₅×C₄⋊C₄	—	2	1	no	—
430	C₅×C₄⋊C₄	—	2	2	no	—
431	C₅×C₄⋊C₄	—	2	2	no	—
432	C₅×C₄⋊C₄	—	2	2	no	—
433	C₅×C₄⋊C₄	—	2	2	no	—
434	C₅×C₄⋊C₄	—	2	2	no	—
435	C₅×C₄⋊C₄	—	2	2	no	—
436	C₅×C₄⋊C₄	—	2	2	no	—
437	C₅×C₄⋊C₄	—	2	2	no	—
438	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
439	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
442	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₅×C₂²⋊C₄	—	2	2	no	—
449	C₅×C₂²⋊C₄	—	2	1	no	—
450	C₅×C₂²⋊C₄	—	2	2	no	—
451	C₅×C₂²⋊C₄	—	2	2	no	—
452	C₅×C₂²⋊C₄	—	2	1	no	—
453	C₅×C₂²⋊C₄	—	2	2	no	—
454	C₅×C₂²⋊C₄	—	2	1	no	—
455	C₅×C₂²⋊C₄	—	2	1	no	—
456	C₅×C₂²⋊C₄	—	2	2	no	—
457	C₅×C₂²⋊C₄	—	2	1	no	—
458	C₅×C₂²⋊C₄	—	2	1	no	—
459	C₅×C₂²⋊C₄	—	2	2	no	—
460	C₅×C₂²⋊C₄	—	2	2	no	—
461	C₅×C₂²⋊C₄	—	2	2	no	—
462	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₄²×C₅	—	2	1	no	—
466	C₄²×C₅	—	2	2	no	—
467	C₄²×C₅	—	2	2	no	—
468	C₄²×C₅	—	2	2	no	—
469	C₄²×C₅	—	2	2	no	—
470	C₄²×C₅	—	2	2	no	—
471	C₄²×C₅	—	2	1	no	—
472	C₄²×C₅	—	2	1	no	—
473	C₄²×C₅	—	2	1	no	—
474	C₄²×C₅	—	2	2	no	—
475	C₄²×C₅	—	2	2	no	—
476	C₄²×C₅	—	2	1	no	—
477	C₄²×C₅	—	2	2	no	—
478	C₄²×C₅	—	2	1	no	—
479	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
480	C₄²×C₅	C₂×D₄	1	2	yes	—
481	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₅	C₂×D₄	1	2	yes	—
483	C₄²×C₅	C₂⁴	1	1	yes	characteristic
484	C₄²×C₅	C₂⁴	1	2	yes	—
485	C₄²×C₅	C₂⁴	1	1	yes	characteristic
486	C₂×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic
487	C₂×#137	C₂²×C₅	1	1	yes	characteristic
488	C₂×#137	C₂²×C₅	1	1	yes	characteristic
489	C₂×#135	C₂²×C₅	1	1	yes	characteristic
490	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
491	#544	C₂²×C₅	1	1	yes	characteristic
492	#542	—	2	1	no	—
493	#542	C₂²×C₅	1	2	yes	—
494	#541	—	2	1	no	—
495	#541	C₂²×C₅	1	2	yes	—
496	#539	—	2	2	no	—
497	#537	C₂²×C₅	1	1	yes	characteristic
498	#536	C₂²×C₅	1	1	yes	characteristic
499	#536	C₂²×C₅	1	1	yes	characteristic
500	#533	—	2	1	no	—
501	#533	C₂²×C₅	1	2	yes	—
502	#529	—	2	2	no	—
503	#529	—	2	1	no	—
504	#529	C₂²×C₅	1	2	yes	—
505	#520	—	2	2	no	—
506	#520	—	2	1	no	—
507	#520	C₂²×C₅	1	1	yes	characteristic
508	#520	C₂²×C₅	1	2	yes	—
509	#520	C₂²×C₅	1	1	yes	characteristic
510	#519	—	2	1	no	—
511	#519	C₂²×C₅	1	1	yes	characteristic
512	#519	C₂²×C₅	1	2	yes	—
513	C₄×#41	—	2	2	no	—
514	C₄×#41	—	2	1	no	—
515	C₄×#41	C₂²×C₅	1	2	yes	—
516	C₄×#41	C₂²×C₅	1	1	yes	characteristic
517	C₄×#41	C₂²×C₅	1	1	yes	characteristic
518	C₄×#41	C₂²×C₅	1	1	yes	characteristic
519	C₂×C₄×Q₈	—	2	1	no	—
520	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
521	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
522	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
523	#485	C₂²×C₅	1	2	yes	—
524	#485	C₂²×C₅	1	2	yes	—
525	#485	C₂²×C₅	1	2	yes	—
526	#484	C₂²×C₅	1	2	yes	—
527	#484	C₂²×C₅	1	2	yes	—
528	#483	C₂²×C₅	1	2	yes	—
529	#482	C₂²×C₅	1	2	yes	—
530	#480	C₂²×C₅	1	2	yes	—
531	#479	C₂²×C₅	1	2	yes	—
532	#479	C₂²×C₅	1	2	yes	—
533	#479	C₂²×C₅	1	2	yes	—
534	#478	C₂²×C₅	1	2	yes	—
535	#477	C₂²×C₅	1	2	yes	—
536	#477	C₂²×C₅	1	2	yes	—
537	#475	C₂²×C₅	1	2	yes	—
538	#474	C₂²×C₅	1	2	yes	—
539	#464	C₂²×C₅	1	2	yes	—
540	#464	C₂²×C₅	1	2	yes	—
541	#464	C₂²×C₅	1	2	yes	—
542	#463	C₂²×C₅	1	2	yes	—
543	#462	C₂²×C₅	1	2	yes	—
544	#462	C₂²×C₅	1	2	yes	—
545	#462	C₂²×C₅	1	2	yes	—
546	#461	C₂²×C₅	1	2	yes	—
547	#452	C₂²×C₅	1	2	yes	—
548	#452	C₂²×C₅	1	2	yes	—
549	#452	C₂²×C₅	1	2	yes	—
550	#451	C₂²×C₅	1	2	yes	—
551	#451	C₂²×C₅	1	2	yes	—
552	#451	C₂²×C₅	1	2	yes	—
553	#449	C₂²×C₅	1	2	yes	—
554	#448	C₂²×C₅	1	2	yes	—
555	#441	C₂²×C₅	1	2	yes	—
556	#441	C₂²×C₅	1	2	yes	—
557	#440	C₂²×C₅	1	2	yes	—
558	#440	C₂²×C₅	1	2	yes	—
559	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
561	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
562	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
563	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
564	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
565	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
566	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
567	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
568	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
569	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
570	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
571	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
572	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
573	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
574	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
575	#433	C₂²×C₅	1	2	yes	—
576	#433	C₂²×C₅	1	2	yes	—
577	#431	C₂²×C₅	1	2	yes	—
578	#431	C₂²×C₅	1	2	yes	—
579	#428	C₂²×C₅	1	1	yes	characteristic
580	#428	C₂²×C₅	1	1	yes	characteristic
581	#427	C₂²×C₅	1	1	yes	characteristic
582	C₂×#107	C₂²×C₅	1	1	yes	characteristic
583	#424	C₂²×C₅	1	1	yes	characteristic
584	#424	C₂²×C₅	1	1	yes	characteristic
585	#419	C₂²×C₅	1	1	yes	characteristic
586	#419	C₂²×C₅	1	1	yes	characteristic
587	#417	C₂²×C₅	1	1	yes	characteristic
588	#417	C₂²×C₅	1	1	yes	characteristic
589	#416	C₂²×C₅	1	1	yes	characteristic
590	#416	C₂²×C₅	1	1	yes	characteristic
591	C₂×#103	C₂²×C₅	1	1	yes	characteristic
592	C₂×#103	C₂²×C₅	1	1	yes	characteristic
593	#408	C₂²×C₅	1	1	yes	characteristic
594	#408	C₂²×C₅	1	1	yes	characteristic
595	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
596	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
597	C₂³×C₅	—	2	1	no	—
598	C₂³×C₅	—	2	1	no	—
599	C₂³×C₅	C₂²×D₄	1	2	yes	—
600	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
601	C₅×Q₈	—	2	8	no	—
602	C₅×Q₈	—	2	2	no	—
603	C₅×Q₈	—	2	4	no	—
604	C₅×Q₈	—	2	1	no	—
605	C₅×Q₈	—	2	2	no	—
606	C₅×Q₈	—	2	2	no	—
607	C₅×Q₈	—	2	1	no	—
608	C₅×Q₈	—	2	2	no	—
609	C₅×Q₈	—	2	1	no	—
610	C₅×Q₈	—	4	2	no	—
611	C₅×Q₈	—	8	2	no	—
612	C₅×Q₈	C₂×#41	1	2	yes	—
613	C₅×Q₈	C₂×#41	1	4	yes	—
614	C₅×D₄	—	2	8	no	—
615	C₅×D₄	—	2	4	no	—
616	C₅×D₄	—	2	4	no	—
617	C₅×D₄	—	2	2	no	—
618	C₅×D₄	—	2	1	no	—
619	C₅×D₄	—	2	1	no	—
620	C₅×D₄	—	2	1	no	—
621	C₅×D₄	—	4	2	no	—
622	C₅×D₄	—	8	2	no	—
623	C₅×D₄	C₂×#41	1	2	yes	—
624	C₂×C₄×C₅	—	2	8	no	—
625	C₂×C₄×C₅	—	2	8	no	—
626	C₂×C₄×C₅	—	2	4	no	—
627	C₂×C₄×C₅	—	2	2	no	—
628	C₂×C₄×C₅	—	2	1	no	—
629	C₂×C₄×C₅	—	2	4	no	—
630	C₂×C₄×C₅	—	2	2	no	—
631	C₂×C₄×C₅	—	2	4	no	—
632	C₂×C₄×C₅	—	2	2	no	—
633	C₂×C₄×C₅	—	2	2	no	—
634	C₂×C₄×C₅	—	2	1	no	—
635	C₂×C₄×C₅	—	2	2	no	—
636	C₂×C₄×C₅	—	2	1	no	—
637	C₂×C₄×C₅	—	2	1	no	—
638	C₂×C₄×C₅	—	2	2	no	—
639	C₂×C₄×C₅	—	2	1	no	—
640	C₂×C₄×C₅	—	2	1	no	—
641	C₂×C₄×C₅	—	2	2	no	—
642	C₂×C₄×C₅	—	4	1	no	—
643	C₂×C₄×C₅	—	4	2	no	—
644	C₂×C₄×C₅	—	4	2	no	—
645	C₂×C₄×C₅	—	4	2	no	—
646	C₂×C₄×C₅	—	4	2	no	—
647	C₂×C₄×C₅	—	4	2	no	—
648	C₂×C₄×C₅	—	8	1	no	—
649	C₂×C₄×C₅	—	8	1	no	—
650	C₂×C₄×C₅	—	8	2	no	—
651	C₂×C₄×C₅	—	8	1	no	—
652	C₂×C₄×C₅	—	8	2	no	—
653	C₂×C₄×C₅	—	8	1	no	—
654	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
655	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
656	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
657	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
658	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
659	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
660	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₅	C₂×#41	1	2	yes	—
663	C₂×C₄×C₅	C₂×#41	1	2	yes	—
664	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
665	C₅×C₈	—	2	1	no	—
666	C₅×C₈	—	2	1	no	—
667	C₅×C₈	—	2	1	no	—
668	C₅×C₈	—	2	1	no	—
669	C₅×C₈	—	2	2	no	—
670	C₅×C₈	—	2	2	no	—
671	2₋¹⁺⁴	—	2	4	no	—
672	2₋¹⁺⁴	—	2	4	no	—
673	C₂×#41	—	2	2	no	—
674	C₂×#41	—	2	1	no	—
675	C₂×#41	C₂³×C₅	1	2	yes	—
676	C₂×#41	C₂³×C₅	1	1	yes	characteristic
677	C₂×#41	C₂³×C₅	1	1	yes	characteristic
678	C₂×#41	C₂³×C₅	1	1	yes	characteristic
679	C₂²×Q₈	—	2	1	no	—
680	C₂²×Q₈	C₂³×C₅	1	2	yes	—
681	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
683	#137	—	2	4	no	—
684	#137	—	2	4	no	—
685	#135	—	2	4	no	—
686	C₂×Q₁₆	—	2	4	no	—
687	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
688	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
689	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
691	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
693	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
695	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
696	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
698	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
699	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
700	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	1	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	C₂³×C₅	1	2	yes	—
714	#124	—	2	1	no	—
715	#124	—	2	2	no	—
716	#124	C₂³×C₅	1	2	yes	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
728	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
730	#121	—	2	2	no	—
731	#121	—	2	1	no	—
732	#121	C₂³×C₅	1	2	yes	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	2	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	2	no	—
745	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
746	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
747	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
748	C₄×Q₈	C₂³×C₅	1	2	yes	—
749	C₄×Q₈	C₂³×C₅	1	2	yes	—
750	C₄×Q₈	C₂³×C₅	1	2	yes	—
751	C₄×Q₈	C₂³×C₅	1	2	yes	—
752	C₄×Q₈	C₂³×C₅	1	2	yes	—
753	C₄×Q₈	C₂³×C₅	1	2	yes	—
754	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₅	1	2	yes	—
756	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	C₅×D₄	1	1	yes	characteristic
771	C₄×D₄	C₅×D₄	1	2	yes	—
772	C₄×D₄	C₅×D₄	1	2	yes	—
773	C₄×D₄	C₅×D₄	1	1	yes	characteristic
774	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
775	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₅	1	2	yes	—
777	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
779	#117	—	2	2	no	—
780	#117	—	2	1	no	—
781	#117	—	2	2	no	—
782	#117	—	2	2	no	—
783	#117	—	2	2	no	—
784	#117	—	2	2	no	—
785	#117	—	2	1	no	—
786	#117	—	2	2	no	—
787	#117	—	2	1	no	—
788	#117	—	2	2	no	—
789	#117	C₂³×C₅	1	1	yes	characteristic
790	#117	C₂³×C₅	1	2	yes	—
791	#117	C₂³×C₅	1	1	yes	characteristic
792	#117	C₂³×C₅	1	1	yes	characteristic
793	#117	C₂³×C₅	1	2	yes	—
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
802	C₂×C₄²	—	2	1	no	—
803	C₂×C₄²	—	2	2	no	—
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	—	2	1	no	—
806	C₂×C₄²	—	2	2	no	—
807	C₂×C₄²	—	2	1	no	—
808	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
809	C₂×C₄²	C₂³×C₅	1	2	yes	—
810	#107	C₂³×C₅	1	2	yes	—
811	#107	C₂³×C₅	1	2	yes	—
812	#107	C₂³×C₅	1	1	yes	characteristic
813	#107	C₂³×C₅	1	1	yes	characteristic
814	#107	C₂³×C₅	1	2	yes	—
815	#107	C₂³×C₅	1	2	yes	—
816	#106	C₂³×C₅	1	1	yes	characteristic
817	#106	C₂³×C₅	1	1	yes	characteristic
818	#106	C₂³×C₅	1	2	yes	—
819	#106	C₂³×C₅	1	2	yes	—
820	C₄⋊C₈	C₂³×C₅	1	2	yes	—
821	C₄⋊C₈	C₂³×C₅	1	2	yes	—
822	C₄⋊C₈	C₂³×C₅	1	2	yes	—
823	C₄⋊C₈	C₂³×C₅	1	2	yes	—
824	#103	C₂³×C₅	1	2	yes	—
825	#103	C₂³×C₅	1	2	yes	—
826	#103	C₂³×C₅	1	2	yes	—
827	#103	C₂³×C₅	1	2	yes	—
828	#103	C₂³×C₅	1	1	yes	characteristic
829	#103	C₂³×C₅	1	1	yes	characteristic
830	#103	C₂³×C₅	1	1	yes	characteristic
831	#103	C₂³×C₅	1	1	yes	characteristic
832	#103	C₂³×C₅	1	2	yes	—
833	#103	C₂³×C₅	1	2	yes	—
834	#103	C₂³×C₅	1	2	yes	—
835	#103	C₂³×C₅	1	2	yes	—
836	#103	C₂³×C₅	1	2	yes	—
837	#103	C₂³×C₅	1	2	yes	—
838	#102	C₂³×C₅	1	1	yes	characteristic
839	#102	C₂³×C₅	1	1	yes	characteristic
840	#102	C₂³×C₅	1	1	yes	characteristic
841	#102	C₂³×C₅	1	1	yes	characteristic
842	#102	C₂³×C₅	1	2	yes	—
843	#102	C₂³×C₅	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
848	#97	C₂³×C₅	1	2	yes	—
849	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₅	1	2	yes	—
854	C₂²×C₅	—	2	1	no	—
855	C₂²×C₅	—	2	1	no	—
856	C₂²×C₅	—	2	2	no	—
857	C₂²×C₅	—	2	2	no	—
858	C₂²×C₅	—	2	2	no	—
859	C₂²×C₅	—	2	2	no	—
860	C₂²×C₅	—	4	1	no	—
861	C₂²×C₅	—	4	1	no	—
862	C₂²×C₅	—	4	1	no	—
863	C₂²×C₅	—	4	1	no	—
864	C₂²×C₅	—	4	1	no	—
865	C₂²×C₅	#525	1	2	yes	—
866	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
867	C₄×C₅	—	2	1	no	—
868	C₄×C₅	—	2	1	no	—
869	C₄×C₅	—	2	2	no	—
870	C₄×C₅	—	2	4	no	—
871	C₄×C₅	—	2	2	no	—
872	C₄×C₅	—	2	2	no	—
873	C₄×C₅	—	2	1	no	—
874	C₄×C₅	—	2	2	no	—
875	C₄×C₅	—	4	1	no	—
876	C₄×C₅	—	4	2	no	—
877	C₄×C₅	—	4	2	no	—
878	C₄×C₅	—	4	1	no	—
879	C₄×C₅	—	4	1	no	—
880	C₄×C₅	—	4	2	no	—
881	C₄×C₅	—	4	1	no	—
882	C₄×C₅	—	4	1	no	—
883	C₄×C₅	#525	1	2	yes	—
884	C₄×C₅	#578	1	2	yes	—
885	C₄×C₅	C₂²×#41	1	1	yes	characteristic
886	C₄×C₅	C₂²×#41	1	1	yes	characteristic
887	#41	—	2	16	no	—
888	#41	—	2	8	no	—
889	#41	—	2	4	no	—
890	#41	—	2	4	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	C₅×#41	1	4	yes	—
897	C₂×Q₈	—	2	8	no	—
898	C₂×Q₈	—	2	4	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
908	C₂×Q₈	C₅×#41	1	4	yes	—
909	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
918	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
936	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
937	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
938	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
939	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
940	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
941	Q₁₆	—	2	4	no	—
942	Q₁₆	—	2	4	no	—
943	Q₁₆	—	2	2	no	—
944	Q₁₆	—	2	4	no	—
945	Q₁₆	—	2	4	no	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	2	4	no	—
950	D₈	—	2	2	no	—
951	M₁₆	—	2	2	no	—
952	M₁₆	—	2	2	no	—
953	C₂×C₈	—	2	2	no	—
954	C₂×C₈	—	2	2	no	—
955	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₅	1	2	yes	—
960	C₂×C₈	C₂⁴×C₅	1	2	yes	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
984	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1008	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1025	C₄²	C₂×C₅×D₄	1	2	yes	—
1026	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1027	C₄²	C₂×C₅×D₄	1	2	yes	—
1028	C₄²	C₂⁴×C₅	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₅	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₅	1	2	yes	—
1031	C₂×C₅	—	2	2	no	—
1032	C₂×C₅	—	4	2	no	—
1033	C₂×C₅	—	4	2	no	—
1034	C₂×C₅	—	8	1	no	—
1035	C₂×C₅	C₂×#525	1	1	yes	characteristic
1036	C₂×C₅	C₂×#578	1	1	yes	characteristic
1037	C₂×C₅	#3584	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	C₂²×C₅×D₄	1	2	yes	—
1041	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
1042	Q₈	—	2	8	no	—
1043	Q₈	—	2	2	no	—
1044	Q₈	—	2	4	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	8	2	no	—
1053	Q₈	C₂×C₅×#41	1	2	yes	—
1054	Q₈	C₂×C₅×#41	1	4	yes	—
1055	D₄	—	2	8	no	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	4	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	C₂×C₅×#41	1	2	yes	—
1065	C₂×C₄	—	2	8	no	—
1066	C₂×C₄	—	2	8	no	—
1067	C₂×C₄	—	2	4	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	4	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	4	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	8	1	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1096	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1097	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1098	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1099	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1100	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1103	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1104	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1105	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₅	#60573	1	1	yes	characteristic, direct product factor, Sylow
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	C₅×#525	1	2	yes	—
1125	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1126	C₄	—	2	4	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	C₅×#525	1	2	yes	—
1143	C₄	C₅×#578	1	2	yes	—
1144	C₄	C₂²×C₅×#41	1	1	yes	characteristic
1145	C₄	C₂²×C₅×#41	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	1	no	—
1150	C₂	C₂×C₅×#525	1	1	yes	characteristic
1151	C₂	C₂×C₅×#578	1	1	yes	characteristic
1152	C₂	C₅×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
prime radical	C₅×#3013	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3461	C₂	semidirect
2. C₄×C₅×2₋¹⁺⁴	C₂	semidirect
3. C₅×#3127	C₂	semidirect
4. C₅×#3124	C₂	semidirect
5. C₅×#3121	C₂	semidirect
6. C₅×#3120	C₂	semidirect
7. C₅×#3108	C₂	semidirect
8. C₅×#3107	C₂	semidirect
9. C₅×#3104	C₂	semidirect
10. C₅×#3102	C₂	semidirect
11. C₅×#3098	C₂	semidirect
12. C₅×#3097	C₂	semidirect
13. C₅×#3083	C₂	semidirect
14. C₅×#3082	C₂	semidirect
15. C₅×#3046	C₂	semidirect
16. C₅×#3044	C₂	semidirect
18. C₅×#3011	C₂	semidirect
19. C₄×C₅×#137	C₂	semidirect
20. C₄×C₅×#137	C₂	semidirect
21. C₄×C₅×#135	C₂	semidirect
22. C₂×C₄×C₅×Q₁₆	C₂	semidirect
23. C₅×#2922	C₂	semidirect
135. #60573	C₅	direct (N × H)
319. #3461	C₂×C₅	semidirect
320. C₄×2₋¹⁺⁴	C₂×C₅	semidirect
321. #3127	C₂×C₅	semidirect
322. #3124	C₂×C₅	semidirect
323. #3121	C₂×C₅	semidirect
324. #3120	C₂×C₅	semidirect
325. #3108	C₂×C₅	semidirect
326. #3107	C₂×C₅	semidirect
327. #3104	C₂×C₅	semidirect
328. #3102	C₂×C₅	semidirect
329. #3098	C₂×C₅	semidirect
330. #3097	C₂×C₅	semidirect
331. #3083	C₂×C₅	semidirect
332. #3082	C₂×C₅	semidirect
333. #3046	C₂×C₅	semidirect
334. #3044	C₂×C₅	semidirect
336. #3011	C₂×C₅	semidirect
337. C₄×#137	C₂×C₅	semidirect
338. C₄×#137	C₂×C₅	semidirect
339. C₄×#135	C₂×C₅	semidirect
340. C₂×C₄×Q₁₆	C₂×C₅	semidirect
341. #2922	C₂×C₅	semidirect
1112. C₅	#60573	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×#3461	2
C₄×C₅×2₋¹⁺⁴	2
C₅×#3127	2
C₅×#3124	2
C₅×#3121	2
C₅×#3120	2
C₅×#3108	2
C₅×#3107	2
C₅×#3104	2
C₅×#3102	2
C₅×#3098	2
C₅×#3097	2
C₅×#3083	2
C₅×#3082	2
C₅×#3046	2
C₅×#3044	2
C₅×#3013	2
C₅×#3011	2
C₄×C₅×#137	2
C₄×C₅×#135	2
C₂×C₄×C₅×Q₁₆	2
C₅×#2922	2
#60573	5

Subgroups — C5×#60573 #11983293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60573 #11983293