Subgroups — C₅×#60598 #11983318

Order 1280.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3512	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×#3126	C₂	1	2	yes	maximal, complemented
5	C₅×#3120	C₂	1	2	yes	maximal, complemented
6	C₅×#3119	C₂	1	2	yes	maximal, complemented
7	C₅×#3117	C₂	1	2	yes	maximal, complemented
8	C₅×#3111	C₂	1	2	yes	maximal, complemented
9	C₅×#3108	C₂	1	2	yes	maximal, complemented
10	C₅×#3102	C₂	1	2	yes	maximal, complemented
11	C₅×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#3013	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2925	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	C₂×C₅×#135	C₂²	1	1	yes	characteristic
29	C₅×#553	—	2	2	no	—
30	C₅×#553	—	2	2	no	—
31	C₅×#553	—	2	1	no	—
32	C₅×#553	—	2	1	no	—
33	C₅×#552	—	2	1	no	—
34	C₅×#552	—	2	1	no	—
35	C₅×#541	C₂²	1	2	yes	—
36	C₅×#540	C₂²	1	2	yes	—
37	C₅×#537	C₂²	1	1	yes	characteristic
38	C₅×#537	C₂²	1	1	yes	characteristic
39	C₅×#532	C₂²	1	1	yes	characteristic
40	C₅×#529	C₂²	1	2	yes	—
41	C₅×#529	C₂²	1	2	yes	—
42	C₂×C₅×#125	C₂²	1	1	yes	characteristic
43	C₅×#520	—	2	2	no	—
44	C₅×#520	—	2	1	no	—
45	C₅×#520	C₂²	1	2	yes	—
46	C₅×#520	C₂²	1	1	yes	characteristic
47	C₅×#520	C₂²	1	1	yes	characteristic
48	C₅×#520	C₂²	1	1	yes	characteristic
49	C₅×#520	C₂²	1	1	yes	characteristic
50	C₅×#519	—	2	1	no	—
51	C₅×#519	C₂²	1	2	yes	—
52	C₅×#519	C₂²	1	1	yes	characteristic
53	C₄×C₅×#41	—	2	2	no	—
54	C₄×C₅×#41	—	2	1	no	—
55	C₄×C₅×#41	C₂²	1	1	yes	characteristic
56	C₄×C₅×#41	C₂²	1	2	yes	—
57	C₄×C₅×#41	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₅×Q₈	—	2	1	no	—
59	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
61	C₅×#485	C₂²	1	2	yes	—
62	C₅×#485	C₂²	1	2	yes	—
63	C₅×#484	C₂²	1	2	yes	—
64	C₅×#483	C₂²	1	2	yes	—
65	C₅×#482	C₂²	1	2	yes	—
66	C₅×#482	C₂²	1	2	yes	—
67	C₅×#481	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×#479	C₂²	1	2	yes	—
73	C₅×#479	C₂²	1	2	yes	—
74	C₅×#479	C₂²	1	2	yes	—
75	C₅×#478	C₂²	1	2	yes	—
76	C₅×#478	C₂²	1	2	yes	—
77	C₅×#464	C₂²	1	1	yes	characteristic
78	C₅×#464	C₂²	1	1	yes	characteristic
79	C₅×#464	C₂²	1	2	yes	—
80	C₅×#464	C₂²	1	2	yes	—
81	C₅×#463	C₂²	1	1	yes	characteristic
82	C₅×#463	C₂²	1	1	yes	characteristic
83	C₅×#462	C₂²	1	1	yes	characteristic
84	C₅×#462	C₂²	1	2	yes	—
85	C₅×#461	C₂²	1	1	yes	characteristic
86	C₅×#460	C₂²	1	1	yes	characteristic
87	C₅×#460	C₂²	1	2	yes	—
88	C₅×#459	C₂²	1	1	yes	characteristic
89	C₅×#452	C₂²	1	2	yes	—
90	C₅×#452	C₂²	1	2	yes	—
91	C₅×#451	C₂²	1	2	yes	—
92	C₅×#451	C₂²	1	2	yes	—
93	C₅×#449	C₂²	1	2	yes	—
94	C₅×#449	C₂²	1	2	yes	—
95	C₅×#448	C₂²	1	2	yes	—
96	C₅×#448	C₂²	1	2	yes	—
97	C₅×#442	C₂²	1	2	yes	—
98	C₅×#441	C₂²	1	2	yes	—
99	C₅×#441	C₂²	1	2	yes	—
100	C₅×#441	C₂²	1	2	yes	—
101	C₅×#440	C₂²	1	2	yes	—
102	C₅×#440	C₂²	1	2	yes	—
103	C₅×#440	C₂²	1	2	yes	—
104	C₅×#440	C₂²	1	2	yes	—
105	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
106	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
107	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
108	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
109	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
110	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
111	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₅×D₈	C₂²	1	2	yes	—
113	C₅×#433	C₂²	1	2	yes	—
114	C₅×#433	C₂²	1	2	yes	—
115	C₅×#432	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	C₂×C₅×#107	C₂²	1	1	yes	characteristic
120	C₂×C₅×#106	C₂²	1	1	yes	characteristic
121	C₅×#423	C₂²	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	C₅×#417	C₂²	1	1	yes	characteristic
124	C₅×#417	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	C₅×#405	C₂²	1	1	yes	characteristic
134	C₅×#405	C₂²	1	1	yes	characteristic
135	#60598	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	1	no	—
139	C₂×C₅×#41	—	2	2	no	—
140	C₂×C₅×#41	C₂³	1	1	yes	characteristic
141	C₂×C₅×#41	C₂³	1	1	yes	characteristic
142	C₂×C₅×#41	C₂³	1	2	yes	—
143	C₂×C₅×#41	C₂³	1	1	yes	characteristic
144	C₂×C₅×#41	C₂³	1	1	yes	characteristic
145	C₂²×C₅×Q₈	—	2	1	no	—
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	C₅×#135	—	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	1	yes	characteristic
156	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
163	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
164	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
166	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
167	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₅×#127	C₂³	1	1	yes	characteristic
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	2	no	—
176	C₅×#125	—	2	1	no	—
177	C₅×#125	—	2	1	no	—
178	C₅×#125	C₂³	1	2	yes	—
179	C₅×#125	C₂³	1	2	yes	—
180	C₅×#124	C₂³	1	1	yes	characteristic
181	C₅×#124	C₂³	1	1	yes	characteristic
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	1	no	—
188	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₅×#121	—	2	1	no	—
191	C₅×#121	—	2	1	no	—
192	C₅×#121	—	2	2	no	—
193	C₅×#121	—	2	2	no	—
194	C₅×#121	—	2	1	no	—
195	C₅×#121	—	2	1	no	—
196	C₅×#121	—	2	2	no	—
197	C₅×#121	—	2	2	no	—
198	C₅×#121	C₂³	1	2	yes	—
199	C₅×#121	C₂³	1	2	yes	—
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	2	no	—
206	C₄×C₅×Q₈	—	2	1	no	—
207	C₄×C₅×Q₈	—	2	2	no	—
208	C₄×C₅×Q₈	—	2	1	no	—
209	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
210	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
211	C₄×C₅×Q₈	C₂³	1	2	yes	—
212	C₄×C₅×Q₈	C₂³	1	2	yes	—
213	C₄×C₅×Q₈	C₂³	1	2	yes	—
214	C₄×C₅×Q₈	C₂³	1	2	yes	—
215	C₄×C₅×Q₈	C₂³	1	2	yes	—
216	C₄×C₅×Q₈	C₂³	1	2	yes	—
217	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
218	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₅×Q₈	C₂³	1	2	yes	—
220	C₄×C₅×D₄	—	2	2	no	—
221	C₄×C₅×D₄	—	2	1	no	—
222	C₄×C₅×D₄	—	2	1	no	—
223	C₄×C₅×D₄	—	2	2	no	—
224	C₄×C₅×D₄	—	2	1	no	—
225	C₄×C₅×D₄	—	2	2	no	—
226	C₄×C₅×D₄	—	2	2	no	—
227	C₄×C₅×D₄	—	2	2	no	—
228	C₄×C₅×D₄	—	2	2	no	—
229	C₄×C₅×D₄	—	2	2	no	—
230	C₄×C₅×D₄	—	2	2	no	—
231	C₄×C₅×D₄	—	2	2	no	—
232	C₄×C₅×D₄	—	2	2	no	—
233	C₄×C₅×D₄	—	2	1	no	—
234	C₄×C₅×D₄	—	2	1	no	—
235	C₄×C₅×D₄	D₄	1	2	yes	—
236	C₄×C₅×D₄	D₄	1	1	yes	characteristic
237	C₄×C₅×D₄	D₄	1	2	yes	—
238	C₄×C₅×D₄	D₄	1	1	yes	characteristic
239	C₄×C₅×D₄	C₂³	1	2	yes	—
240	C₄×C₅×D₄	C₂³	1	2	yes	—
241	C₄×C₅×D₄	C₂³	1	2	yes	—
242	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
243	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
244	C₅×#117	—	2	1	no	—
245	C₅×#117	—	2	2	no	—
246	C₅×#117	—	2	1	no	—
247	C₅×#117	—	2	1	no	—
248	C₅×#117	—	2	2	no	—
249	C₅×#117	—	2	2	no	—
250	C₅×#117	—	2	2	no	—
251	C₅×#117	—	2	2	no	—
252	C₅×#117	—	2	1	no	—
253	C₅×#117	—	2	2	no	—
254	C₅×#117	—	2	2	no	—
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	1	no	—
263	C₂×C₅×C₄⋊C₄	—	2	1	no	—
264	C₂×C₅×C₄⋊C₄	—	2	2	no	—
265	C₂×C₅×C₄⋊C₄	—	2	1	no	—
266	C₂×C₅×C₄⋊C₄	—	2	1	no	—
267	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₄²×C₅	—	2	1	no	—
272	C₂×C₄²×C₅	—	2	2	no	—
273	C₂×C₄²×C₅	—	2	2	no	—
274	C₂×C₄²×C₅	—	2	1	no	—
275	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₅	C₂³	1	2	yes	—
277	C₅×#107	C₂³	1	2	yes	—
278	C₅×#107	C₂³	1	2	yes	—
279	C₅×#107	C₂³	1	2	yes	—
280	C₅×#107	C₂³	1	2	yes	—
281	C₅×#106	C₂³	1	2	yes	—
282	C₅×#106	C₂³	1	2	yes	—
283	C₅×#106	C₂³	1	2	yes	—
284	C₅×#106	C₂³	1	2	yes	—
285	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₅×C₄⋊C₈	C₂³	1	2	yes	—
290	C₅×C₄⋊C₈	C₂³	1	2	yes	—
291	C₅×#103	C₂³	1	2	yes	—
292	C₅×#103	C₂³	1	2	yes	—
293	C₅×#103	C₂³	1	2	yes	—
294	C₅×#103	C₂³	1	2	yes	—
295	C₅×#103	C₂³	1	1	yes	characteristic
296	C₅×#103	C₂³	1	1	yes	characteristic
297	C₅×#103	C₂³	1	1	yes	characteristic
298	C₅×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
310	C₅×#102	C₂³	1	2	yes	—
311	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₅×#97	C₂³	1	2	yes	—
316	C₅×#97	C₂³	1	2	yes	—
317	C₄×C₅×C₈	C₂³	1	2	yes	—
318	C₄×C₅×C₈	C₂³	1	2	yes	—
319	#3512	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	#3126	C₂×C₅	1	2	yes	complemented
323	#3120	C₂×C₅	1	2	yes	complemented
324	#3119	C₂×C₅	1	2	yes	complemented
325	#3117	C₂×C₅	1	2	yes	complemented
326	#3111	C₂×C₅	1	2	yes	complemented
327	#3108	C₂×C₅	1	2	yes	complemented
328	#3102	C₂×C₅	1	2	yes	complemented
329	#3099	C₂×C₅	1	1	yes	characteristic, complemented
330	#3098	C₂×C₅	1	1	yes	characteristic, complemented
331	#3080	C₂×C₅	1	1	yes	characteristic, complemented
332	C₂×#479	C₂×C₅	1	1	yes	characteristic, complemented
333	#3037	C₂×C₅	1	1	yes	characteristic, complemented
334	#3035	C₂×C₅	1	1	yes	characteristic, complemented
335	#3013	C₂×C₅	1	1	yes	characteristic, complemented
336	#3013	C₂×C₅	1	1	yes	characteristic, complemented
337	#2952	C₂×C₅	1	1	yes	characteristic, complemented
338	#2951	C₂×C₅	1	1	yes	characteristic, complemented
339	#2947	C₂×C₅	1	1	yes	characteristic, complemented
340	#2947	C₂×C₅	1	1	yes	characteristic, complemented
341	#2925	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	—	2	2	no	—
352	C₅×#41	—	2	2	no	—
353	C₅×#41	#41	1	4	yes	—
354	C₂×C₅×Q₈	—	2	8	no	—
355	C₂×C₅×Q₈	—	2	4	no	—
356	C₂×C₅×Q₈	—	2	4	no	—
357	C₂×C₅×Q₈	—	2	2	no	—
358	C₂×C₅×Q₈	—	2	1	no	—
359	C₂×C₅×Q₈	—	2	2	no	—
360	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
361	C₂×C₅×Q₈	#41	1	4	yes	—
362	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
365	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
366	C₂×C₅×D₄	—	2	2	no	—
367	C₂×C₅×D₄	—	2	1	no	—
368	C₂×C₅×D₄	—	2	1	no	—
369	C₂×C₅×D₄	—	2	1	no	—
370	C₂×C₅×D₄	—	2	2	no	—
371	C₂×C₅×D₄	—	2	2	no	—
372	C₂×C₅×D₄	—	2	1	no	—
373	C₂×C₅×D₄	—	2	1	no	—
374	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
375	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅	—	2	2	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	2	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	1	no	—
389	C₂²×C₄×C₅	—	2	1	no	—
390	C₂²×C₄×C₅	—	2	2	no	—
391	C₂²×C₄×C₅	—	2	1	no	—
392	C₂²×C₄×C₅	—	2	2	no	—
393	C₂²×C₄×C₅	—	2	2	no	—
394	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
396	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
398	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₅×Q₁₆	—	2	2	no	—
401	C₅×Q₁₆	—	2	2	no	—
402	C₅×Q₁₆	—	2	4	no	—
403	C₅×Q₁₆	—	2	4	no	—
404	C₅×SD₁₆	—	2	2	no	—
405	C₅×SD₁₆	—	2	2	no	—
406	C₅×SD₁₆	—	2	4	no	—
407	C₅×SD₁₆	—	2	4	no	—
408	C₅×SD₁₆	—	2	2	no	—
409	C₅×SD₁₆	—	2	2	no	—
410	C₅×D₈	—	2	2	no	—
411	C₅×D₈	—	2	2	no	—
412	C₅×M₁₆	—	2	2	no	—
413	C₅×M₁₆	—	2	2	no	—
414	C₂×C₅×C₈	—	2	2	no	—
415	C₂×C₅×C₈	—	2	2	no	—
416	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
419	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₅×C₈	C₂⁴	1	2	yes	—
421	C₂×C₅×C₈	C₂⁴	1	2	yes	—
422	C₅×C₄⋊C₄	—	2	2	no	—
423	C₅×C₄⋊C₄	—	2	2	no	—
424	C₅×C₄⋊C₄	—	2	2	no	—
425	C₅×C₄⋊C₄	—	2	2	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	1	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	—	2	1	no	—
439	C₅×C₄⋊C₄	—	2	2	no	—
440	C₅×C₄⋊C₄	—	2	2	no	—
441	C₅×C₄⋊C₄	—	2	1	no	—
442	C₅×C₄⋊C₄	—	2	1	no	—
443	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
446	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
447	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
451	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₅×C₂²⋊C₄	—	2	2	no	—
453	C₅×C₂²⋊C₄	—	2	1	no	—
454	C₅×C₂²⋊C₄	—	2	2	no	—
455	C₅×C₂²⋊C₄	—	2	2	no	—
456	C₅×C₂²⋊C₄	—	2	1	no	—
457	C₅×C₂²⋊C₄	—	2	2	no	—
458	C₅×C₂²⋊C₄	—	2	1	no	—
459	C₅×C₂²⋊C₄	—	2	1	no	—
460	C₅×C₂²⋊C₄	—	2	1	no	—
461	C₅×C₂²⋊C₄	—	2	2	no	—
462	C₅×C₂²⋊C₄	—	2	2	no	—
463	C₅×C₂²⋊C₄	—	2	2	no	—
464	C₅×C₂²⋊C₄	—	2	2	no	—
465	C₅×C₂²⋊C₄	—	2	1	no	—
466	C₅×C₂²⋊C₄	—	2	1	no	—
467	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₄²×C₅	—	2	2	no	—
471	C₄²×C₅	—	2	1	no	—
472	C₄²×C₅	—	2	2	no	—
473	C₄²×C₅	—	2	1	no	—
474	C₄²×C₅	—	2	2	no	—
475	C₄²×C₅	—	2	2	no	—
476	C₄²×C₅	—	2	2	no	—
477	C₄²×C₅	—	2	2	no	—
478	C₄²×C₅	—	2	1	no	—
479	C₄²×C₅	—	2	2	no	—
480	C₄²×C₅	—	2	2	no	—
481	C₄²×C₅	C₂×D₄	1	2	yes	—
482	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₅	C₂×D₄	1	2	yes	—
484	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₅	C₂⁴	1	1	yes	characteristic
486	C₄²×C₅	C₂⁴	1	2	yes	—
487	C₄²×C₅	C₂⁴	1	1	yes	characteristic
488	C₂×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic
489	C₂×#137	C₂²×C₅	1	1	yes	characteristic
490	C₂×#137	C₂²×C₅	1	1	yes	characteristic
491	C₂×#135	C₂²×C₅	1	1	yes	characteristic
492	C₂×#135	C₂²×C₅	1	1	yes	characteristic
493	#553	—	2	2	no	—
494	#553	—	2	2	no	—
495	#553	—	2	1	no	—
496	#553	—	2	1	no	—
497	#552	—	2	1	no	—
498	#552	—	2	1	no	—
499	#541	C₂²×C₅	1	2	yes	—
500	#540	C₂²×C₅	1	2	yes	—
501	#537	C₂²×C₅	1	1	yes	characteristic
502	#537	C₂²×C₅	1	1	yes	characteristic
503	#532	C₂²×C₅	1	1	yes	characteristic
504	#529	C₂²×C₅	1	2	yes	—
505	#529	C₂²×C₅	1	2	yes	—
506	C₂×#125	C₂²×C₅	1	1	yes	characteristic
507	#520	—	2	2	no	—
508	#520	—	2	1	no	—
509	#520	C₂²×C₅	1	2	yes	—
510	#520	C₂²×C₅	1	1	yes	characteristic
511	#520	C₂²×C₅	1	1	yes	characteristic
512	#520	C₂²×C₅	1	1	yes	characteristic
513	#520	C₂²×C₅	1	1	yes	characteristic
514	#519	—	2	1	no	—
515	#519	C₂²×C₅	1	2	yes	—
516	#519	C₂²×C₅	1	1	yes	characteristic
517	C₄×#41	—	2	2	no	—
518	C₄×#41	—	2	1	no	—
519	C₄×#41	C₂²×C₅	1	1	yes	characteristic
520	C₄×#41	C₂²×C₅	1	2	yes	—
521	C₄×#41	C₂²×C₅	1	1	yes	characteristic
522	C₂×C₄×Q₈	—	2	1	no	—
523	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
524	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
525	#485	C₂²×C₅	1	2	yes	—
526	#485	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	#482	C₂²×C₅	1	2	yes	—
531	#481	C₂²×C₅	1	2	yes	—
532	#480	C₂²×C₅	1	2	yes	—
533	#479	C₂²×C₅	1	2	yes	—
534	#479	C₂²×C₅	1	2	yes	—
535	#479	C₂²×C₅	1	2	yes	—
536	#479	C₂²×C₅	1	2	yes	—
537	#479	C₂²×C₅	1	2	yes	—
538	#479	C₂²×C₅	1	2	yes	—
539	#478	C₂²×C₅	1	2	yes	—
540	#478	C₂²×C₅	1	2	yes	—
541	#464	C₂²×C₅	1	2	yes	—
542	#464	C₂²×C₅	1	1	yes	characteristic
543	#464	C₂²×C₅	1	2	yes	—
544	#464	C₂²×C₅	1	1	yes	characteristic
545	#463	C₂²×C₅	1	1	yes	characteristic
546	#463	C₂²×C₅	1	1	yes	characteristic
547	#462	C₂²×C₅	1	2	yes	—
548	#462	C₂²×C₅	1	1	yes	characteristic
549	#461	C₂²×C₅	1	1	yes	characteristic
550	#460	C₂²×C₅	1	2	yes	—
551	#460	C₂²×C₅	1	1	yes	characteristic
552	#459	C₂²×C₅	1	1	yes	characteristic
553	#452	C₂²×C₅	1	2	yes	—
554	#452	C₂²×C₅	1	2	yes	—
555	#451	C₂²×C₅	1	2	yes	—
556	#451	C₂²×C₅	1	2	yes	—
557	#449	C₂²×C₅	1	2	yes	—
558	#449	C₂²×C₅	1	2	yes	—
559	#448	C₂²×C₅	1	2	yes	—
560	#448	C₂²×C₅	1	2	yes	—
561	#442	C₂²×C₅	1	2	yes	—
562	#441	C₂²×C₅	1	2	yes	—
563	#441	C₂²×C₅	1	2	yes	—
564	#441	C₂²×C₅	1	2	yes	—
565	#440	C₂²×C₅	1	2	yes	—
566	#440	C₂²×C₅	1	2	yes	—
567	#440	C₂²×C₅	1	2	yes	—
568	#440	C₂²×C₅	1	2	yes	—
569	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
570	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
571	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
572	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
573	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
574	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
575	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
576	C₄×D₈	C₂²×C₅	1	2	yes	—
577	#433	C₂²×C₅	1	2	yes	—
578	#433	C₂²×C₅	1	2	yes	—
579	#432	C₂²×C₅	1	2	yes	—
580	#431	C₂²×C₅	1	2	yes	—
581	#428	C₂²×C₅	1	1	yes	characteristic
582	#428	C₂²×C₅	1	1	yes	characteristic
583	C₂×#107	C₂²×C₅	1	1	yes	characteristic
584	C₂×#106	C₂²×C₅	1	1	yes	characteristic
585	#423	C₂²×C₅	1	1	yes	characteristic
586	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
587	#417	C₂²×C₅	1	1	yes	characteristic
588	#417	C₂²×C₅	1	1	yes	characteristic
589	#417	C₂²×C₅	1	1	yes	characteristic
590	#417	C₂²×C₅	1	1	yes	characteristic
591	#416	C₂²×C₅	1	1	yes	characteristic
592	#416	C₂²×C₅	1	1	yes	characteristic
593	C₂×#103	C₂²×C₅	1	1	yes	characteristic
594	C₂×#103	C₂²×C₅	1	1	yes	characteristic
595	#408	C₂²×C₅	1	1	yes	characteristic
596	#408	C₂²×C₅	1	1	yes	characteristic
597	#405	C₂²×C₅	1	1	yes	characteristic
598	#405	C₂²×C₅	1	1	yes	characteristic
599	C₂³×C₅	—	2	1	no	—
600	C₂³×C₅	—	2	1	no	—
601	C₂³×C₅	—	2	1	no	—
602	C₂³×C₅	C₂²×D₄	1	2	yes	—
603	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
604	C₅×Q₈	—	2	8	no	—
605	C₅×Q₈	—	2	2	no	—
606	C₅×Q₈	—	2	4	no	—
607	C₅×Q₈	—	2	1	no	—
608	C₅×Q₈	—	2	2	no	—
609	C₅×Q₈	—	2	1	no	—
610	C₅×Q₈	—	2	1	no	—
611	C₅×Q₈	—	2	1	no	—
612	C₅×Q₈	—	2	1	no	—
613	C₅×Q₈	C₂×#41	1	2	yes	—
614	C₅×Q₈	C₂×#41	1	4	yes	—
615	C₅×D₄	—	2	8	no	—
616	C₅×D₄	—	2	4	no	—
617	C₅×D₄	—	2	4	no	—
618	C₅×D₄	—	2	2	no	—
619	C₅×D₄	—	2	1	no	—
620	C₅×D₄	—	2	1	no	—
621	C₅×D₄	—	2	1	no	—
622	C₅×D₄	—	2	1	no	—
623	C₅×D₄	—	2	1	no	—
624	C₅×D₄	—	4	2	no	—
625	C₅×D₄	—	4	2	no	—
626	C₅×D₄	—	8	1	no	—
627	C₅×D₄	—	8	1	no	—
628	C₅×D₄	—	8	2	no	—
629	C₅×D₄	—	8	2	no	—
630	C₅×D₄	C₂×#41	1	2	yes	—
631	C₂×C₄×C₅	—	2	8	no	—
632	C₂×C₄×C₅	—	2	8	no	—
633	C₂×C₄×C₅	—	2	4	no	—
634	C₂×C₄×C₅	—	2	2	no	—
635	C₂×C₄×C₅	—	2	1	no	—
636	C₂×C₄×C₅	—	2	4	no	—
637	C₂×C₄×C₅	—	2	2	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	—	2	1	no	—
643	C₂×C₄×C₅	—	2	1	no	—
644	C₂×C₄×C₅	—	2	2	no	—
645	C₂×C₄×C₅	—	2	2	no	—
646	C₂×C₄×C₅	—	4	2	no	—
647	C₂×C₄×C₅	—	4	1	no	—
648	C₂×C₄×C₅	—	4	2	no	—
649	C₂×C₄×C₅	—	4	1	no	—
650	C₂×C₄×C₅	—	4	2	no	—
651	C₂×C₄×C₅	—	4	2	no	—
652	C₂×C₄×C₅	—	4	2	no	—
653	C₂×C₄×C₅	—	8	2	no	—
654	C₂×C₄×C₅	—	8	2	no	—
655	C₂×C₄×C₅	—	8	1	no	—
656	C₂×C₄×C₅	—	8	2	no	—
657	C₂×C₄×C₅	—	8	1	no	—
658	C₂×C₄×C₅	—	8	2	no	—
659	C₂×C₄×C₅	—	8	1	no	—
660	C₂×C₄×C₅	—	8	1	no	—
661	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
663	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
664	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
665	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
666	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
667	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
668	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
669	C₂×C₄×C₅	C₂×#41	1	2	yes	—
670	C₂×C₄×C₅	C₂×#41	1	2	yes	—
671	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
672	C₅×C₈	—	2	1	no	—
673	C₅×C₈	—	2	1	no	—
674	C₅×C₈	—	2	1	no	—
675	C₅×C₈	—	2	1	no	—
676	C₅×C₈	—	2	2	no	—
677	C₅×C₈	—	2	2	no	—
678	2₋¹⁺⁴	—	2	4	no	—
679	2₋¹⁺⁴	—	2	4	no	—
680	C₂×#41	—	2	1	no	—
681	C₂×#41	—	2	2	no	—
682	C₂×#41	C₂³×C₅	1	2	yes	—
683	C₂×#41	C₂³×C₅	1	1	yes	characteristic
684	C₂×#41	C₂³×C₅	1	1	yes	characteristic
685	C₂×#41	C₂³×C₅	1	1	yes	characteristic
686	C₂×#41	C₂³×C₅	1	1	yes	characteristic
687	C₂²×Q₈	—	2	1	no	—
688	C₂²×Q₈	C₂³×C₅	1	2	yes	—
689	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
690	#137	—	2	4	no	—
691	#137	—	2	4	no	—
692	#135	—	2	4	no	—
693	#135	—	2	4	no	—
694	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
695	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
696	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
697	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
702	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
704	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
705	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
706	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
707	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
708	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
711	#127	C₂³×C₅	1	1	yes	characteristic
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	—	2	1	no	—
720	#125	C₂³×C₅	1	2	yes	—
721	#125	C₂³×C₅	1	2	yes	—
722	#124	C₂³×C₅	1	1	yes	characteristic
723	#124	C₂³×C₅	1	1	yes	characteristic
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
732	#121	—	2	1	no	—
733	#121	—	2	1	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	1	no	—
737	#121	—	2	1	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	C₂³×C₅	1	2	yes	—
741	#121	C₂³×C₅	1	2	yes	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	2	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
752	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
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	2	yes	—
757	C₄×Q₈	C₂³×C₅	1	2	yes	—
758	C₄×Q₈	C₂³×C₅	1	2	yes	—
759	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
760	C₄×Q₈	C₂³×C₅	1	2	yes	—
761	C₄×Q₈	C₂³×C₅	1	2	yes	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	C₅×D₄	1	2	yes	—
778	C₄×D₄	C₅×D₄	1	1	yes	characteristic
779	C₄×D₄	C₅×D₄	1	2	yes	—
780	C₄×D₄	C₅×D₄	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₅	1	2	yes	—
783	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₅	1	2	yes	—
785	C₄×D₄	C₂³×C₅	1	2	yes	—
786	#117	—	2	1	no	—
787	#117	—	2	2	no	—
788	#117	—	2	1	no	—
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	2	no	—
793	#117	—	2	2	no	—
794	#117	—	2	1	no	—
795	#117	—	2	2	no	—
796	#117	—	2	2	no	—
797	#117	C₂³×C₅	1	1	yes	characteristic
798	#117	C₂³×C₅	1	2	yes	—
799	#117	C₂³×C₅	1	1	yes	characteristic
800	#117	C₂³×C₅	1	2	yes	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	—	2	2	no	—
803	C₂×C₄⋊C₄	—	2	1	no	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
810	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
811	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
812	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
813	C₂×C₄²	—	2	1	no	—
814	C₂×C₄²	—	2	2	no	—
815	C₂×C₄²	—	2	2	no	—
816	C₂×C₄²	—	2	1	no	—
817	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₅	1	2	yes	—
819	#107	C₂³×C₅	1	2	yes	—
820	#107	C₂³×C₅	1	2	yes	—
821	#107	C₂³×C₅	1	2	yes	—
822	#107	C₂³×C₅	1	2	yes	—
823	#106	C₂³×C₅	1	2	yes	—
824	#106	C₂³×C₅	1	2	yes	—
825	#106	C₂³×C₅	1	2	yes	—
826	#106	C₂³×C₅	1	2	yes	—
827	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₅	1	2	yes	—
832	C₄⋊C₈	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	1	yes	characteristic
838	#103	C₂³×C₅	1	1	yes	characteristic
839	#103	C₂³×C₅	1	1	yes	characteristic
840	#103	C₂³×C₅	1	1	yes	characteristic
841	#103	C₂³×C₅	1	2	yes	—
842	#103	C₂³×C₅	1	2	yes	—
843	#103	C₂³×C₅	1	2	yes	—
844	#103	C₂³×C₅	1	2	yes	—
845	#102	C₂³×C₅	1	1	yes	characteristic
846	#102	C₂³×C₅	1	1	yes	characteristic
847	#102	C₂³×C₅	1	1	yes	characteristic
848	#102	C₂³×C₅	1	1	yes	characteristic
849	#102	C₂³×C₅	1	2	yes	—
850	#102	C₂³×C₅	1	2	yes	—
851	#102	C₂³×C₅	1	2	yes	—
852	#102	C₂³×C₅	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
857	#97	C₂³×C₅	1	2	yes	—
858	#97	C₂³×C₅	1	2	yes	—
859	C₄×C₈	C₂³×C₅	1	2	yes	—
860	C₄×C₈	C₂³×C₅	1	2	yes	—
861	C₂²×C₅	—	2	1	no	—
862	C₂²×C₅	—	2	1	no	—
863	C₂²×C₅	—	2	2	no	—
864	C₂²×C₅	—	2	2	no	—
865	C₂²×C₅	—	2	2	no	—
866	C₂²×C₅	—	2	2	no	—
867	C₂²×C₅	—	4	1	no	—
868	C₂²×C₅	—	4	1	no	—
869	C₂²×C₅	—	4	1	no	—
870	C₂²×C₅	—	4	1	no	—
871	C₂²×C₅	—	4	1	no	—
872	C₂²×C₅	—	4	1	no	—
873	C₂²×C₅	—	4	1	no	—
874	C₂²×C₅	—	4	1	no	—
875	C₂²×C₅	#525	1	2	yes	—
876	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
877	C₄×C₅	—	2	1	no	—
878	C₄×C₅	—	2	2	no	—
879	C₄×C₅	—	2	1	no	—
880	C₄×C₅	—	2	1	no	—
881	C₄×C₅	—	2	2	no	—
882	C₄×C₅	—	2	1	no	—
883	C₄×C₅	—	2	4	no	—
884	C₄×C₅	—	2	2	no	—
885	C₄×C₅	—	2	2	no	—
886	C₄×C₅	—	4	2	no	—
887	C₄×C₅	—	4	1	no	—
888	C₄×C₅	—	4	2	no	—
889	C₄×C₅	—	4	1	no	—
890	C₄×C₅	—	4	2	no	—
891	C₄×C₅	—	4	1	no	—
892	C₄×C₅	—	4	1	no	—
893	C₄×C₅	#525	1	2	yes	—
894	C₄×C₅	C₂²×#41	1	1	yes	characteristic
895	C₄×C₅	C₂²×#41	1	1	yes	characteristic
896	#41	—	2	16	no	—
897	#41	—	2	8	no	—
898	#41	—	2	4	no	—
899	#41	—	2	4	no	—
900	#41	—	2	2	no	—
901	#41	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	2	2	no	—
904	#41	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	C₅×#41	1	4	yes	—
908	C₂×Q₈	—	2	8	no	—
909	C₂×Q₈	—	2	4	no	—
910	C₂×Q₈	—	2	4	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
915	C₂×Q₈	C₅×#41	1	4	yes	—
916	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
919	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
929	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
930	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
949	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
950	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
951	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
954	Q₁₆	—	2	2	no	—
955	Q₁₆	—	2	2	no	—
956	Q₁₆	—	2	4	no	—
957	Q₁₆	—	2	4	no	—
958	SD₁₆	—	2	2	no	—
959	SD₁₆	—	2	2	no	—
960	SD₁₆	—	2	4	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	2	no	—
963	SD₁₆	—	2	2	no	—
964	D₈	—	2	2	no	—
965	D₈	—	2	2	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	2	2	no	—
968	C₂×C₈	—	2	2	no	—
969	C₂×C₈	—	2	2	no	—
970	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₅	1	2	yes	—
973	C₂×C₈	C₂⁴×C₅	1	2	yes	—
974	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
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	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
998	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
999	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
1000	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1022	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1023	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×C₅×D₄	1	2	yes	—
1036	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1037	C₄²	C₂×C₅×D₄	1	2	yes	—
1038	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₅	1	2	yes	—
1040	C₄²	C₂⁴×C₅	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₅	1	1	yes	characteristic
1042	C₂×C₅	—	2	2	no	—
1043	C₂×C₅	—	4	2	no	—
1044	C₂×C₅	—	4	2	no	—
1045	C₂×C₅	—	8	1	no	—
1046	C₂×C₅	—	8	1	no	—
1047	C₂×C₅	C₂×#525	1	1	yes	characteristic
1048	C₂×C₅	#3584	1	1	yes	characteristic
1049	C₂×C₅	#3586	1	1	yes	characteristic
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	C₂²×C₅×D₄	1	2	yes	—
1054	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
1055	Q₈	—	2	8	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	4	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	C₂×C₅×#41	1	2	yes	—
1065	Q₈	C₂×C₅×#41	1	4	yes	—
1066	D₄	—	2	8	no	—
1067	D₄	—	2	4	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	C₂×C₅×#41	1	2	yes	—
1082	C₂×C₄	—	2	8	no	—
1083	C₂×C₄	—	2	8	no	—
1084	C₂×C₄	—	2	4	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	4	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	1	no	—
1111	C₂×C₄	—	8	1	no	—
1112	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1113	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1114	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1115	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1116	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1117	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1118	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1119	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1120	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1121	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1122	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₅	#60598	1	1	yes	characteristic, direct product factor, Sylow
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	C₅×#525	1	2	yes	—
1145	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1146	C₄	—	2	4	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	C₅×#525	1	2	yes	—
1163	C₄	C₂²×C₅×#41	1	1	yes	characteristic
1164	C₄	C₂²×C₅×#41	1	1	yes	characteristic
1165	C₂	—	2	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	1	no	—
1170	C₂	C₂×C₅×#525	1	1	yes	characteristic
1171	C₂	C₅×#3584	1	1	yes	characteristic
1172	C₂	C₅×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅×#3512	C₂	semidirect
2. C₄×C₅×2₋¹⁺⁴	C₂	semidirect
3. C₅×#3127	C₂	semidirect
4. C₅×#3126	C₂	semidirect
5. C₅×#3120	C₂	semidirect
6. C₅×#3119	C₂	semidirect
7. C₅×#3117	C₂	semidirect
8. C₅×#3111	C₂	semidirect
9. C₅×#3108	C₂	semidirect
10. C₅×#3102	C₂	semidirect
11. C₅×#3099	C₂	semidirect
12. C₅×#3098	C₂	semidirect
13. C₅×#3080	C₂	semidirect
14. C₂×C₅×#479	C₂	semidirect
15. C₅×#3037	C₂	semidirect
16. C₅×#3035	C₂	semidirect
17. C₅×#3013	C₂	semidirect
18. C₅×#3013	C₂	semidirect
19. C₅×#2952	C₂	semidirect
20. C₅×#2951	C₂	semidirect
21. C₅×#2947	C₂	semidirect
22. C₅×#2947	C₂	semidirect
23. C₅×#2925	C₂	semidirect
135. #60598	C₅	direct (N × H)
319. #3512	C₂×C₅	semidirect
320. C₄×2₋¹⁺⁴	C₂×C₅	semidirect
321. #3127	C₂×C₅	semidirect
322. #3126	C₂×C₅	semidirect
323. #3120	C₂×C₅	semidirect
324. #3119	C₂×C₅	semidirect
325. #3117	C₂×C₅	semidirect
326. #3111	C₂×C₅	semidirect
327. #3108	C₂×C₅	semidirect
328. #3102	C₂×C₅	semidirect
329. #3099	C₂×C₅	semidirect
330. #3098	C₂×C₅	semidirect
331. #3080	C₂×C₅	semidirect
332. C₂×#479	C₂×C₅	semidirect
333. #3037	C₂×C₅	semidirect
334. #3035	C₂×C₅	semidirect
335. #3013	C₂×C₅	semidirect
336. #3013	C₂×C₅	semidirect
337. #2952	C₂×C₅	semidirect
338. #2951	C₂×C₅	semidirect
339. #2947	C₂×C₅	semidirect
340. #2947	C₂×C₅	semidirect
341. #2925	C₂×C₅	semidirect
1129. C₅	#60598	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×#3512	2
C₄×C₅×2₋¹⁺⁴	2
C₅×#3127	2
C₅×#3126	2
C₅×#3120	2
C₅×#3119	2
C₅×#3117	2
C₅×#3111	2
C₅×#3108	2
C₅×#3102	2
C₅×#3099	2
C₅×#3098	2
C₅×#3080	2
C₂×C₅×#479	2
C₅×#3037	2
C₅×#3035	2
C₅×#3013	2
C₅×#2952	2
C₅×#2951	2
C₅×#2947	2
C₅×#2925	2
#60598	5

Subgroups — C5×#60598 #11983318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60598 #11983318