Subgroups — C₅×#60344 #11983064

Order 1280.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1090 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
2	C₅×#2995	C₂	1	2	yes	maximal, complemented
3	C₅×#2995	C₂	1	2	yes	maximal, complemented
4	C₅×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2993	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2993	C₂	1	2	yes	maximal, complemented
7	C₅×#2991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2985	C₂	1	2	yes	maximal, complemented
11	C₅×#2985	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2984	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2970	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2969	C₂	1	2	yes	maximal, complemented
16	C₅×#2968	C₂	1	2	yes	maximal, complemented
17	C₅×#2967	C₂	1	2	yes	maximal, complemented
18	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2962	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2961	C₂	1	2	yes	maximal, complemented
23	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#544	C₄	1	1	yes	characteristic
25	C₅×#542	C₄	1	1	yes	characteristic
26	C₅×#542	C₄	1	1	yes	characteristic
27	C₅×#542	C₄	1	2	yes	—
28	C₅×#541	C₄	1	1	yes	characteristic
29	C₅×#541	C₄	1	1	yes	characteristic
30	C₅×#541	C₄	1	2	yes	—
31	C₅×#539	C₄	1	2	yes	—
32	C₅×#539	C₄	1	2	yes	—
33	C₅×#537	C₄	1	1	yes	characteristic
34	C₅×#536	C₄	1	1	yes	characteristic
35	C₅×#536	C₄	1	1	yes	characteristic
36	C₅×#533	C₂²	1	1	yes	characteristic
37	C₅×#533	C₂²	1	2	yes	—
38	C₅×#533	C₂²	1	1	yes	characteristic
39	C₅×#529	C₂²	1	1	yes	characteristic
40	C₅×#529	C₂²	1	2	yes	—
41	C₅×#529	C₂²	1	1	yes	characteristic
42	C₅×#529	C₂²	1	2	yes	—
43	C₅×#529	C₂²	1	2	yes	—
44	C₄×C₅×#41	C₂²	1	1	yes	characteristic
45	C₄×C₅×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
47	C₅×#446	C₂²	1	2	yes	—
48	C₅×#446	C₂²	1	1	yes	characteristic
49	C₅×#446	C₂²	1	1	yes	characteristic
50	C₅×#446	C₂²	1	2	yes	—
51	C₅×#446	C₂²	1	1	yes	characteristic
52	C₅×#446	C₂²	1	2	yes	—
53	C₅×#446	C₂²	1	1	yes	characteristic
54	C₅×#446	C₂²	1	2	yes	—
55	C₅×#446	C₂²	1	2	yes	—
56	C₅×#446	C₂²	1	1	yes	characteristic
57	C₅×#446	C₂²	1	2	yes	—
58	C₅×#446	C₂²	1	2	yes	—
59	C₅×#446	C₂²	1	2	yes	—
60	C₅×#446	C₂²	1	2	yes	—
61	C₅×#446	C₂²	1	1	yes	characteristic
62	C₅×#446	C₂²	1	1	yes	characteristic
63	C₅×#446	C₂²	1	1	yes	characteristic
64	C₅×#446	C₂²	1	2	yes	—
65	C₅×#446	C₂²	1	2	yes	—
66	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
67	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
68	C₅×C₈×Q₈	C₂²	1	2	yes	—
69	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
70	C₅×C₈×Q₈	C₂²	1	2	yes	—
71	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
72	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
73	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
74	C₅×#436	C₂²	1	2	yes	—
75	C₅×#436	C₂²	1	1	yes	characteristic
76	C₅×#436	C₂²	1	2	yes	—
77	C₅×#436	C₂²	1	1	yes	characteristic
78	C₅×#436	C₂²	1	2	yes	—
79	C₅×#436	C₂²	1	1	yes	characteristic
80	C₅×#436	C₂²	1	2	yes	—
81	C₅×#436	C₂²	1	2	yes	—
82	C₅×#436	C₂²	1	1	yes	characteristic
83	C₅×#435	C₂²	1	2	yes	—
84	C₅×#435	C₂²	1	2	yes	—
85	C₅×#435	C₂²	1	2	yes	—
86	C₅×#435	C₂²	1	2	yes	—
87	C₅×#435	C₂²	1	2	yes	—
88	C₅×#435	C₂²	1	1	yes	characteristic
89	C₅×#435	C₂²	1	1	yes	characteristic
90	C₅×#435	C₂²	1	2	yes	—
91	C₅×#435	C₂²	1	1	yes	characteristic
92	C₅×#435	C₂²	1	1	yes	characteristic
93	C₅×#435	C₂²	1	2	yes	—
94	C₅×#435	C₂²	1	2	yes	—
95	C₅×C₈×D₄	C₂²	1	2	yes	—
96	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
97	C₅×C₈×D₄	C₂²	1	2	yes	—
98	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
99	C₅×#433	C₂²	1	2	yes	—
100	C₅×#433	C₂²	1	2	yes	—
101	C₅×#433	C₂²	1	2	yes	—
102	C₅×#433	C₂²	1	2	yes	—
103	C₅×#433	C₂²	1	2	yes	—
104	C₅×#433	C₂²	1	2	yes	—
105	C₅×#433	C₂²	1	2	yes	—
106	C₅×#433	C₂²	1	2	yes	—
107	C₅×#432	C₂²	1	1	yes	characteristic
108	C₅×#432	C₂²	1	2	yes	—
109	C₅×#432	C₂²	1	1	yes	characteristic
110	C₅×#432	C₂²	1	2	yes	—
111	C₅×#431	C₂²	1	1	yes	characteristic
112	C₅×#431	C₂²	1	2	yes	—
113	C₅×#431	C₂²	1	2	yes	—
114	C₅×#431	C₂²	1	1	yes	characteristic
115	C₅×#431	C₂²	1	1	yes	characteristic
116	C₅×#431	C₂²	1	1	yes	characteristic
117	C₅×#424	C₂²	1	2	yes	—
118	C₅×#424	C₂²	1	2	yes	—
119	C₅×#424	C₂²	1	2	yes	—
120	C₅×#424	C₂²	1	2	yes	—
121	C₅×#423	C₂²	1	1	yes	characteristic
122	C₅×#423	C₂²	1	1	yes	characteristic
123	C₅×#423	C₂²	1	2	yes	—
124	C₅×#423	C₂²	1	2	yes	—
125	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₅×#405	C₂²	1	2	yes	—
127	C₅×#405	C₂²	1	2	yes	—
128	C₅×#405	C₂²	1	2	yes	—
129	C₅×#405	C₂²	1	2	yes	—
130	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
131	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
132	C₄×C₅×M₁₆	C₂²	1	2	yes	—
133	C₂×C₅×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
135	#60344	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
139	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₅×M₁₆	C₂³	1	2	yes	—
143	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₅×M₁₆	C₂³	1	2	yes	—
145	C₂×C₅×M₁₆	C₂³	1	2	yes	—
146	C₂×C₅×M₁₆	C₂³	1	2	yes	—
147	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₅×C₈	C₂³	1	2	yes	—
149	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₅×C₈	C₂³	1	2	yes	—
151	C₂²×C₅×C₈	C₂³	1	2	yes	—
152	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
153	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
154	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
155	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
157	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
158	C₅×#126	C₂×C₄	1	2	yes	—
159	C₅×#126	C₂×C₄	1	2	yes	—
160	C₅×#126	C₂×C₄	1	2	yes	—
161	C₅×#126	C₂×C₄	1	2	yes	—
162	C₅×#126	C₂×C₄	1	2	yes	—
163	C₅×#126	C₂×C₄	1	2	yes	—
164	C₅×#126	C₂×C₄	1	2	yes	—
165	C₅×#126	C₂×C₄	1	2	yes	—
166	C₅×#125	C₂×C₄	1	2	yes	—
167	C₅×#125	C₂×C₄	1	2	yes	—
168	C₅×#125	C₂×C₄	1	1	yes	characteristic
169	C₅×#125	C₂×C₄	1	1	yes	characteristic
170	C₅×#125	C₂×C₄	1	2	yes	—
171	C₅×#125	C₂×C₄	1	2	yes	—
172	C₅×#125	C₂×C₄	1	2	yes	—
173	C₅×#125	C₂×C₄	1	2	yes	—
174	C₅×#125	C₂×C₄	1	2	yes	—
175	C₅×#124	C₂×C₄	1	1	yes	characteristic
176	C₅×#124	C₂×C₄	1	1	yes	characteristic
177	C₅×#124	C₂×C₄	1	2	yes	—
178	C₅×#124	C₂×C₄	1	2	yes	—
179	C₅×#124	C₂×C₄	1	2	yes	—
180	C₅×#123	C₂×C₄	1	2	yes	—
181	C₅×#123	C₂×C₄	1	2	yes	—
182	C₅×#123	C₂×C₄	1	2	yes	—
183	C₅×#123	C₂×C₄	1	2	yes	—
184	C₅×#123	C₂×C₄	1	2	yes	—
185	C₅×#123	C₂×C₄	1	2	yes	—
186	C₅×#123	C₂×C₄	1	2	yes	—
187	C₅×#123	C₂×C₄	1	2	yes	—
188	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
189	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
190	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
193	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
194	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
195	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
196	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
197	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
198	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
199	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
200	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
201	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
202	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
203	C₅×#121	C₂×C₄	1	2	yes	—
204	C₅×#121	C₂×C₄	1	2	yes	—
205	C₅×#121	C₂×C₄	1	1	yes	characteristic
206	C₅×#121	C₂×C₄	1	1	yes	characteristic
207	C₅×#121	C₂×C₄	1	2	yes	—
208	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
209	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
210	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
211	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
212	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
213	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
214	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
215	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
216	C₄×C₅×Q₈	C₂³	1	2	yes	—
217	C₄×C₅×Q₈	C₂³	1	2	yes	—
218	C₄×C₅×Q₈	C₂³	1	2	yes	—
219	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
220	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
221	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
222	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
223	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
224	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
225	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
226	C₄×C₅×D₄	C₂³	1	2	yes	—
227	C₄×C₅×D₄	C₂³	1	2	yes	—
228	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
229	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
230	C₄×C₅×D₄	C₂³	1	2	yes	—
231	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
232	C₅×#117	C₂×C₄	1	1	yes	characteristic
233	C₅×#117	C₂×C₄	1	1	yes	characteristic
234	C₅×#117	C₂×C₄	1	1	yes	characteristic
235	C₅×#117	C₂×C₄	1	1	yes	characteristic
236	C₅×#117	C₂×C₄	1	2	yes	—
237	C₅×#117	C₂³	1	2	yes	—
238	C₅×#117	C₂³	1	2	yes	—
239	C₅×#117	C₂³	1	2	yes	—
240	C₅×#117	C₂³	1	2	yes	—
241	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
242	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
243	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₅	C₂³	1	2	yes	—
245	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₅	C₂³	1	2	yes	—
248	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₅×C₄⋊C₈	C₂³	1	2	yes	—
251	C₅×C₄⋊C₈	C₂³	1	2	yes	—
252	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₅×C₄⋊C₈	C₂³	1	2	yes	—
255	C₅×C₄⋊C₈	C₂³	1	2	yes	—
256	C₅×C₄⋊C₈	C₂³	1	2	yes	—
257	C₅×C₄⋊C₈	C₂³	1	2	yes	—
258	C₅×C₄⋊C₈	C₂³	1	2	yes	—
259	C₅×C₄⋊C₈	C₂³	1	2	yes	—
260	C₅×C₄⋊C₈	C₂³	1	2	yes	—
261	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₅×C₄⋊C₈	C₂³	1	2	yes	—
264	C₅×C₄⋊C₈	C₂³	1	2	yes	—
265	C₅×C₄⋊C₈	C₂³	1	2	yes	—
266	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₅×C₄⋊C₈	C₂³	1	2	yes	—
269	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₅×C₄⋊C₈	C₂³	1	2	yes	—
272	C₅×C₄⋊C₈	C₂³	1	2	yes	—
273	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₅×#97	C₂³	1	1	yes	characteristic
287	C₅×#97	C₂³	1	2	yes	—
288	C₅×#97	C₂³	1	2	yes	—
289	C₅×#97	C₂³	1	2	yes	—
290	C₅×#97	C₂³	1	1	yes	characteristic
291	C₅×#97	C₂³	1	2	yes	—
292	C₅×#97	C₂³	1	1	yes	characteristic
293	C₅×#97	C₂³	1	1	yes	characteristic
294	C₅×#97	C₂³	1	2	yes	—
295	C₅×#97	C₂³	1	2	yes	—
296	C₅×#97	C₂³	1	2	yes	—
297	C₅×#97	C₂³	1	2	yes	—
298	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
299	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
300	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
301	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
302	C₄×C₅×C₈	C₂³	1	2	yes	—
303	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
304	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
305	C₄×C₅×C₈	C₂³	1	2	yes	—
306	C₄×C₅×C₈	C₂³	1	2	yes	—
307	C₄×C₅×C₈	C₂³	1	2	yes	—
308	C₄×C₅×C₈	C₂³	1	2	yes	—
309	C₄×C₅×C₈	C₂³	1	2	yes	—
310	C₄×C₅×C₈	C₂³	1	2	yes	—
311	#3461	C₂×C₅	1	1	yes	characteristic
312	#2995	C₂×C₅	1	2	yes	complemented
313	#2995	C₂×C₅	1	2	yes	complemented
314	#2994	C₂×C₅	1	1	yes	characteristic, complemented
315	#2993	C₂×C₅	1	1	yes	characteristic, complemented
316	#2993	C₂×C₅	1	2	yes	complemented
317	#2991	C₂×C₅	1	1	yes	characteristic, complemented
318	#2989	C₂×C₅	1	1	yes	characteristic, complemented
319	#2986	C₂×C₅	1	1	yes	characteristic, complemented
320	#2985	C₂×C₅	1	1	yes	characteristic, complemented
321	#2985	C₂×C₅	1	2	yes	complemented
322	#2984	C₂×C₅	1	1	yes	characteristic, complemented
323	#2970	C₂×C₅	1	1	yes	characteristic, complemented
324	#2969	C₂×C₅	1	1	yes	characteristic, complemented
325	#2969	C₂×C₅	1	2	yes	complemented
326	#2968	C₂×C₅	1	2	yes	complemented
327	#2967	C₂×C₅	1	2	yes	complemented
328	#2966	C₂×C₅	1	1	yes	characteristic, complemented
329	#2965	C₂×C₅	1	1	yes	characteristic, complemented
330	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
331	#2962	C₂×C₅	1	1	yes	characteristic, complemented
332	#2961	C₂×C₅	1	2	yes	complemented
333	#2960	C₂×C₅	1	1	yes	characteristic, complemented
334	C₅×#41	—	4	2	no	—
335	C₅×#41	—	4	2	no	—
336	C₂×C₅×Q₈	—	4	2	no	—
337	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
338	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
341	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
343	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
344	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
348	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
350	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
351	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
353	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
354	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
355	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
356	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
357	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
358	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
360	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
361	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
365	C₅×M₁₆	—	2	2	no	—
366	C₅×M₁₆	—	2	2	no	—
367	C₅×M₁₆	—	4	1	no	—
368	C₅×M₁₆	—	4	2	no	—
369	C₅×M₁₆	—	4	2	no	—
370	C₅×M₁₆	—	4	1	no	—
371	C₅×M₁₆	—	4	2	no	—
372	C₅×M₁₆	—	4	2	no	—
373	C₂×C₅×C₈	—	2	2	no	—
374	C₂×C₅×C₈	—	2	4	no	—
375	C₂×C₅×C₈	—	4	2	no	—
376	C₂×C₅×C₈	—	4	2	no	—
377	C₂×C₅×C₈	—	4	1	no	—
378	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₅×C₈	C₂⁴	1	2	yes	—
380	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₅×C₈	C₂⁴	1	2	yes	—
383	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₅×C₈	C₂⁴	1	2	yes	—
385	C₂×C₅×C₈	C₂⁴	1	2	yes	—
386	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
390	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
391	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
393	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
394	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
395	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
396	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
398	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
405	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
407	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
408	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
409	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
410	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
411	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
412	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
413	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
414	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
415	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
416	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
417	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
418	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
419	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
420	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
421	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
422	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
423	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
424	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
426	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
427	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
428	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
429	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
430	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
431	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
433	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
434	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
435	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
436	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
437	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
438	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
439	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
441	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
442	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
443	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
444	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₅	C₂²×C₄	1	2	yes	—
447	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
448	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₅	C₂²×C₄	1	2	yes	—
451	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₅	C₂²×C₄	1	2	yes	—
453	C₄²×C₅	C₂²×C₄	1	2	yes	—
454	C₄²×C₅	C₂⁴	1	1	yes	characteristic
455	C₄²×C₅	C₂⁴	1	1	yes	characteristic
456	C₄²×C₅	C₂⁴	1	1	yes	characteristic
457	C₄²×C₅	C₂⁴	1	2	yes	—
458	C₄²×C₅	C₂⁴	1	1	yes	characteristic
459	C₄²×C₅	C₂⁴	1	2	yes	—
460	C₄²×C₅	C₂⁴	1	2	yes	—
461	#544	C₄×C₅	1	1	yes	characteristic
462	#542	C₄×C₅	1	1	yes	characteristic
463	#542	C₄×C₅	1	1	yes	characteristic
464	#542	C₄×C₅	1	2	yes	—
465	#541	C₄×C₅	1	1	yes	characteristic
466	#541	C₄×C₅	1	1	yes	characteristic
467	#541	C₄×C₅	1	2	yes	—
468	#539	C₄×C₅	1	2	yes	—
469	#539	C₄×C₅	1	2	yes	—
470	#537	C₄×C₅	1	1	yes	characteristic
471	#536	C₄×C₅	1	1	yes	characteristic
472	#536	C₄×C₅	1	1	yes	characteristic
473	#533	C₂²×C₅	1	1	yes	characteristic
474	#533	C₂²×C₅	1	2	yes	—
475	#533	C₂²×C₅	1	1	yes	characteristic
476	#529	C₂²×C₅	1	1	yes	characteristic
477	#529	C₂²×C₅	1	2	yes	—
478	#529	C₂²×C₅	1	2	yes	—
479	#529	C₂²×C₅	1	1	yes	characteristic
480	#529	C₂²×C₅	1	2	yes	—
481	C₄×#41	C₂²×C₅	1	1	yes	characteristic
482	C₄×#41	C₂²×C₅	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
484	#446	C₂²×C₅	1	2	yes	—
485	#446	C₂²×C₅	1	1	yes	characteristic
486	#446	C₂²×C₅	1	1	yes	characteristic
487	#446	C₂²×C₅	1	1	yes	characteristic
488	#446	C₂²×C₅	1	2	yes	—
489	#446	C₂²×C₅	1	2	yes	—
490	#446	C₂²×C₅	1	2	yes	—
491	#446	C₂²×C₅	1	2	yes	—
492	#446	C₂²×C₅	1	2	yes	—
493	#446	C₂²×C₅	1	2	yes	—
494	#446	C₂²×C₅	1	1	yes	characteristic
495	#446	C₂²×C₅	1	2	yes	—
496	#446	C₂²×C₅	1	1	yes	characteristic
497	#446	C₂²×C₅	1	2	yes	—
498	#446	C₂²×C₅	1	1	yes	characteristic
499	#446	C₂²×C₅	1	1	yes	characteristic
500	#446	C₂²×C₅	1	2	yes	—
501	#446	C₂²×C₅	1	2	yes	—
502	#446	C₂²×C₅	1	1	yes	characteristic
503	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
504	C₈×Q₈	C₂²×C₅	1	2	yes	—
505	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
506	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
507	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
508	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
509	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
510	C₈×Q₈	C₂²×C₅	1	2	yes	—
511	#436	C₂²×C₅	1	1	yes	characteristic
512	#436	C₂²×C₅	1	1	yes	characteristic
513	#436	C₂²×C₅	1	1	yes	characteristic
514	#436	C₂²×C₅	1	2	yes	—
515	#436	C₂²×C₅	1	2	yes	—
516	#436	C₂²×C₅	1	1	yes	characteristic
517	#436	C₂²×C₅	1	2	yes	—
518	#436	C₂²×C₅	1	2	yes	—
519	#436	C₂²×C₅	1	2	yes	—
520	#435	C₂²×C₅	1	1	yes	characteristic
521	#435	C₂²×C₅	1	1	yes	characteristic
522	#435	C₂²×C₅	1	1	yes	characteristic
523	#435	C₂²×C₅	1	1	yes	characteristic
524	#435	C₂²×C₅	1	2	yes	—
525	#435	C₂²×C₅	1	2	yes	—
526	#435	C₂²×C₅	1	2	yes	—
527	#435	C₂²×C₅	1	2	yes	—
528	#435	C₂²×C₅	1	2	yes	—
529	#435	C₂²×C₅	1	2	yes	—
530	#435	C₂²×C₅	1	2	yes	—
531	#435	C₂²×C₅	1	2	yes	—
532	C₈×D₄	C₂²×C₅	1	2	yes	—
533	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
534	C₈×D₄	C₂²×C₅	1	2	yes	—
535	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
536	#433	C₂²×C₅	1	2	yes	—
537	#433	C₂²×C₅	1	2	yes	—
538	#433	C₂²×C₅	1	2	yes	—
539	#433	C₂²×C₅	1	2	yes	—
540	#433	C₂²×C₅	1	2	yes	—
541	#433	C₂²×C₅	1	2	yes	—
542	#433	C₂²×C₅	1	2	yes	—
543	#433	C₂²×C₅	1	2	yes	—
544	#432	C₂²×C₅	1	1	yes	characteristic
545	#432	C₂²×C₅	1	2	yes	—
546	#432	C₂²×C₅	1	1	yes	characteristic
547	#432	C₂²×C₅	1	2	yes	—
548	#431	C₂²×C₅	1	1	yes	characteristic
549	#431	C₂²×C₅	1	1	yes	characteristic
550	#431	C₂²×C₅	1	1	yes	characteristic
551	#431	C₂²×C₅	1	2	yes	—
552	#431	C₂²×C₅	1	2	yes	—
553	#431	C₂²×C₅	1	1	yes	characteristic
554	#424	C₂²×C₅	1	2	yes	—
555	#424	C₂²×C₅	1	2	yes	—
556	#424	C₂²×C₅	1	2	yes	—
557	#424	C₂²×C₅	1	2	yes	—
558	#423	C₂²×C₅	1	1	yes	characteristic
559	#423	C₂²×C₅	1	2	yes	—
560	#423	C₂²×C₅	1	1	yes	characteristic
561	#423	C₂²×C₅	1	2	yes	—
562	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
563	#405	C₂²×C₅	1	2	yes	—
564	#405	C₂²×C₅	1	2	yes	—
565	#405	C₂²×C₅	1	2	yes	—
566	#405	C₂²×C₅	1	2	yes	—
567	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
568	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
569	C₄×M₁₆	C₂²×C₅	1	2	yes	—
570	C₂×#97	C₂²×C₅	1	2	yes	—
571	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
572	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
573	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
574	C₂³×C₅	C₂³×C₄	1	2	yes	—
575	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
576	C₅×Q₈	—	2	2	no	—
577	C₅×Q₈	—	2	2	no	—
578	C₅×Q₈	—	2	2	no	—
579	C₅×Q₈	—	4	2	no	—
580	C₅×Q₈	—	4	2	no	—
581	C₅×Q₈	—	4	2	no	—
582	C₅×Q₈	—	4	1	no	—
583	C₅×D₄	—	2	2	no	—
584	C₅×D₄	—	4	2	no	—
585	C₅×D₄	—	4	2	no	—
586	C₅×D₄	—	4	1	no	—
587	C₅×D₄	—	4	1	no	—
588	C₅×D₄	—	4	1	no	—
589	C₅×D₄	—	4	2	no	—
590	C₂×C₄×C₅	—	2	2	no	—
591	C₂×C₄×C₅	—	2	2	no	—
592	C₂×C₄×C₅	—	2	2	no	—
593	C₂×C₄×C₅	—	2	1	no	—
594	C₂×C₄×C₅	—	2	2	no	—
595	C₂×C₄×C₅	—	2	1	no	—
596	C₂×C₄×C₅	—	2	1	no	—
597	C₂×C₄×C₅	—	2	1	no	—
598	C₂×C₄×C₅	—	2	2	no	—
599	C₂×C₄×C₅	—	2	1	no	—
600	C₂×C₄×C₅	—	2	1	no	—
601	C₂×C₄×C₅	—	4	1	no	—
602	C₂×C₄×C₅	—	4	1	no	—
603	C₂×C₄×C₅	—	4	2	no	—
604	C₂×C₄×C₅	—	4	1	no	—
605	C₂×C₄×C₅	—	4	2	no	—
606	C₂×C₄×C₅	—	4	2	no	—
607	C₂×C₄×C₅	—	4	2	no	—
608	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
609	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
610	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
611	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
612	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
613	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
614	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
615	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
617	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
618	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
619	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
620	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
621	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
622	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
624	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
626	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
627	C₅×C₈	—	2	1	no	—
628	C₅×C₈	—	2	2	no	—
629	C₅×C₈	—	2	1	no	—
630	C₅×C₈	—	2	1	no	—
631	C₅×C₈	—	2	1	no	—
632	C₅×C₈	—	2	2	no	—
633	C₅×C₈	—	2	2	no	—
634	C₅×C₈	—	2	1	no	—
635	C₅×C₈	—	2	1	no	—
636	C₅×C₈	—	2	2	no	—
637	C₅×C₈	—	2	1	no	—
638	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
639	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
640	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
641	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
642	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
643	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
644	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
645	C₂×M₁₆	C₂³×C₅	1	2	yes	—
646	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
647	C₂×M₁₆	C₂³×C₅	1	2	yes	—
648	C₂×M₁₆	C₂³×C₅	1	2	yes	—
649	C₂×M₁₆	C₂³×C₅	1	2	yes	—
650	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
651	C₂²×C₈	C₂³×C₅	1	2	yes	—
652	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
653	C₂²×C₈	C₂³×C₅	1	2	yes	—
654	C₂²×C₈	C₂³×C₅	1	2	yes	—
655	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
656	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
657	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
658	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
659	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
660	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
661	#126	C₂×C₄×C₅	1	2	yes	—
662	#126	C₂×C₄×C₅	1	2	yes	—
663	#126	C₂×C₄×C₅	1	2	yes	—
664	#126	C₂×C₄×C₅	1	2	yes	—
665	#126	C₂×C₄×C₅	1	2	yes	—
666	#126	C₂×C₄×C₅	1	2	yes	—
667	#126	C₂×C₄×C₅	1	2	yes	—
668	#126	C₂×C₄×C₅	1	2	yes	—
669	#125	C₂×C₄×C₅	1	2	yes	—
670	#125	C₂×C₄×C₅	1	2	yes	—
671	#125	C₂×C₄×C₅	1	1	yes	characteristic
672	#125	C₂×C₄×C₅	1	2	yes	—
673	#125	C₂×C₄×C₅	1	1	yes	characteristic
674	#125	C₂×C₄×C₅	1	2	yes	—
675	#125	C₂×C₄×C₅	1	2	yes	—
676	#125	C₂×C₄×C₅	1	2	yes	—
677	#125	C₂×C₄×C₅	1	2	yes	—
678	#124	C₂×C₄×C₅	1	1	yes	characteristic
679	#124	C₂×C₄×C₅	1	1	yes	characteristic
680	#124	C₂×C₄×C₅	1	2	yes	—
681	#124	C₂×C₄×C₅	1	2	yes	—
682	#124	C₂×C₄×C₅	1	2	yes	—
683	#123	C₂×C₄×C₅	1	2	yes	—
684	#123	C₂×C₄×C₅	1	2	yes	—
685	#123	C₂×C₄×C₅	1	2	yes	—
686	#123	C₂×C₄×C₅	1	2	yes	—
687	#123	C₂×C₄×C₅	1	2	yes	—
688	#123	C₂×C₄×C₅	1	2	yes	—
689	#123	C₂×C₄×C₅	1	2	yes	—
690	#123	C₂×C₄×C₅	1	2	yes	—
691	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
694	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
696	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
699	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
702	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
703	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
704	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
705	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
706	#121	C₂×C₄×C₅	1	2	yes	—
707	#121	C₂×C₄×C₅	1	2	yes	—
708	#121	C₂×C₄×C₅	1	1	yes	characteristic
709	#121	C₂×C₄×C₅	1	1	yes	characteristic
710	#121	C₂×C₄×C₅	1	2	yes	—
711	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
712	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
713	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
714	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
715	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
716	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
717	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₅	1	2	yes	—
719	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
721	C₄×Q₈	C₂³×C₅	1	2	yes	—
722	C₄×Q₈	C₂³×C₅	1	2	yes	—
723	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
724	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
725	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
726	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
727	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
728	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₅	1	2	yes	—
733	C₄×D₄	C₂³×C₅	1	2	yes	—
734	C₄×D₄	C₂³×C₅	1	2	yes	—
735	#117	C₂×C₄×C₅	1	1	yes	characteristic
736	#117	C₂×C₄×C₅	1	1	yes	characteristic
737	#117	C₂×C₄×C₅	1	1	yes	characteristic
738	#117	C₂×C₄×C₅	1	1	yes	characteristic
739	#117	C₂×C₄×C₅	1	2	yes	—
740	#117	C₂³×C₅	1	2	yes	—
741	#117	C₂³×C₅	1	2	yes	—
742	#117	C₂³×C₅	1	2	yes	—
743	#117	C₂³×C₅	1	2	yes	—
744	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
746	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₅	1	2	yes	—
748	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₅	1	2	yes	—
750	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
752	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
753	C₄⋊C₈	C₂³×C₅	1	2	yes	—
754	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
755	C₄⋊C₈	C₂³×C₅	1	2	yes	—
756	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
757	C₄⋊C₈	C₂³×C₅	1	2	yes	—
758	C₄⋊C₈	C₂³×C₅	1	2	yes	—
759	C₄⋊C₈	C₂³×C₅	1	2	yes	—
760	C₄⋊C₈	C₂³×C₅	1	2	yes	—
761	C₄⋊C₈	C₂³×C₅	1	2	yes	—
762	C₄⋊C₈	C₂³×C₅	1	2	yes	—
763	C₄⋊C₈	C₂³×C₅	1	2	yes	—
764	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
765	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
766	C₄⋊C₈	C₂³×C₅	1	2	yes	—
767	C₄⋊C₈	C₂³×C₅	1	2	yes	—
768	C₄⋊C₈	C₂³×C₅	1	2	yes	—
769	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
770	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₅	1	2	yes	—
772	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
773	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
774	C₄⋊C₈	C₂³×C₅	1	2	yes	—
775	C₄⋊C₈	C₂³×C₅	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
777	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
779	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
780	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
782	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
783	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
789	#97	C₂³×C₅	1	1	yes	characteristic
790	#97	C₂³×C₅	1	2	yes	—
791	#97	C₂³×C₅	1	2	yes	—
792	#97	C₂³×C₅	1	2	yes	—
793	#97	C₂³×C₅	1	1	yes	characteristic
794	#97	C₂³×C₅	1	2	yes	—
795	#97	C₂³×C₅	1	1	yes	characteristic
796	#97	C₂³×C₅	1	1	yes	characteristic
797	#97	C₂³×C₅	1	2	yes	—
798	#97	C₂³×C₅	1	2	yes	—
799	#97	C₂³×C₅	1	2	yes	—
800	#97	C₂³×C₅	1	2	yes	—
801	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
802	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
803	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
804	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
805	C₄×C₈	C₂³×C₅	1	2	yes	—
806	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
807	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
808	C₄×C₈	C₂³×C₅	1	2	yes	—
809	C₄×C₈	C₂³×C₅	1	2	yes	—
810	C₄×C₈	C₂³×C₅	1	2	yes	—
811	C₄×C₈	C₂³×C₅	1	2	yes	—
812	C₄×C₈	C₂³×C₅	1	2	yes	—
813	C₄×C₈	C₂³×C₅	1	2	yes	—
814	C₂²×C₅	—	2	1	no	—
815	C₂²×C₅	—	2	2	no	—
816	C₂²×C₅	—	2	1	no	—
817	C₂²×C₅	—	2	1	no	—
818	C₂²×C₅	—	2	1	no	—
819	C₂²×C₅	—	2	1	no	—
820	C₂²×C₅	—	2	1	no	—
821	C₂²×C₅	—	2	2	no	—
822	C₂²×C₅	—	2	1	no	—
823	C₂²×C₅	—	2	1	no	—
824	C₂²×C₅	—	2	1	no	—
825	C₂²×C₅	—	2	2	no	—
826	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
827	C₄×C₅	—	2	1	no	—
828	C₄×C₅	—	2	2	no	—
829	C₄×C₅	—	2	1	no	—
830	C₄×C₅	—	2	1	no	—
831	C₄×C₅	—	2	1	no	—
832	C₄×C₅	—	2	1	no	—
833	C₄×C₅	—	2	1	no	—
834	C₄×C₅	—	2	2	no	—
835	C₄×C₅	—	2	2	no	—
836	C₄×C₅	—	2	2	no	—
837	C₄×C₅	—	2	1	no	—
838	C₄×C₅	—	2	1	no	—
839	C₄×C₅	—	2	2	no	—
840	C₄×C₅	—	2	2	no	—
841	C₄×C₅	—	2	1	no	—
842	C₄×C₅	—	2	2	no	—
843	C₄×C₅	—	2	1	no	—
844	C₄×C₅	#568	1	2	yes	—
845	C₄×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
846	C₄×C₅	#585	1	1	yes	characteristic
847	#41	—	4	2	no	—
848	#41	—	4	2	no	—
849	C₂×Q₈	—	4	2	no	—
850	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
851	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
852	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
853	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
854	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
855	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
856	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
857	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
858	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
859	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
860	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
861	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
862	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
863	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
864	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
865	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
866	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
867	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
868	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
869	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
870	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
871	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
872	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
873	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
878	M₁₆	—	2	2	no	—
879	M₁₆	—	2	2	no	—
880	M₁₆	—	4	1	no	—
881	M₁₆	—	4	2	no	—
882	M₁₆	—	4	2	no	—
883	M₁₆	—	4	1	no	—
884	M₁₆	—	4	2	no	—
885	M₁₆	—	4	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	2	4	no	—
888	C₂×C₈	—	4	2	no	—
889	C₂×C₈	—	4	2	no	—
890	C₂×C₈	—	4	1	no	—
891	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₅	1	2	yes	—
896	C₂×C₈	C₂⁴×C₅	1	2	yes	—
897	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₅	1	2	yes	—
900	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₅	1	2	yes	—
902	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
903	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
904	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
905	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
906	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
907	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
908	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
909	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
910	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
911	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
912	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
914	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
915	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
916	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
917	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
918	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
919	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
920	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
921	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
922	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
923	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
924	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
925	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
926	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
927	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
928	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
929	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
930	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
931	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
932	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
933	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
934	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
935	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
936	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
937	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
938	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
939	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
940	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
941	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
942	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
943	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
944	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
945	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
946	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
947	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
948	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
949	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
950	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
951	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
952	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
957	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
958	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
959	C₄²	C₂²×C₄×C₅	1	2	yes	—
960	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
961	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
962	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
963	C₄²	C₂²×C₄×C₅	1	2	yes	—
964	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
965	C₄²	C₂²×C₄×C₅	1	2	yes	—
966	C₄²	C₂²×C₄×C₅	1	2	yes	—
967	C₄²	C₂⁴×C₅	1	1	yes	characteristic
968	C₄²	C₂⁴×C₅	1	1	yes	characteristic
969	C₄²	C₂⁴×C₅	1	2	yes	—
970	C₄²	C₂⁴×C₅	1	2	yes	—
971	C₄²	C₂⁴×C₅	1	2	yes	—
972	C₄²	C₂⁴×C₅	1	1	yes	characteristic
973	C₄²	C₂⁴×C₅	1	1	yes	characteristic
974	C₂×C₅	—	4	1	no	—
975	C₂×C₅	—	4	1	no	—
976	C₂×C₅	—	4	1	no	—
977	C₂×C₅	—	4	2	no	—
978	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
979	C₂×C₅	C₂×#568	1	1	yes	characteristic
980	C₂×C₅	#3573	1	1	yes	characteristic
981	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
982	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
983	C₂³	C₂³×C₄×C₅	1	2	yes	—
984	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	2	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	1	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	4	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	4	1	no	—
994	D₄	—	4	1	no	—
995	D₄	—	4	1	no	—
996	D₄	—	4	2	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	4	1	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1018	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1019	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1020	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1021	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1022	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1023	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1024	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1025	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1026	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1027	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1028	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1029	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1030	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1031	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1032	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1033	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1034	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1035	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
1036	C₈	—	2	1	no	—
1037	C₈	—	2	2	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	2	no	—
1042	C₈	—	2	2	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	2	no	—
1047	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
1048	C₅	#60344	1	1	yes	characteristic, direct product factor, Sylow
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	C₅×#568	1	2	yes	—
1080	C₄	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₄	C₅×#585	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1087	C₂	C₂×C₅×#568	1	1	yes	characteristic
1088	C₂	C₅×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂⁴×C₄
prime radical	C₅×#537	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2995	C₂	semidirect
3. C₅×#2995	C₂	semidirect
4. C₅×#2994	C₂	semidirect
5. C₅×#2993	C₂	semidirect
6. C₅×#2993	C₂	semidirect
7. C₅×#2991	C₂	semidirect
8. C₅×#2989	C₂	semidirect
9. C₅×#2986	C₂	semidirect
10. C₅×#2985	C₂	semidirect
11. C₅×#2985	C₂	semidirect
12. C₅×#2984	C₂	semidirect
13. C₅×#2970	C₂	semidirect
14. C₅×#2969	C₂	semidirect
15. C₅×#2969	C₂	semidirect
16. C₅×#2968	C₂	semidirect
17. C₅×#2967	C₂	semidirect
18. C₅×#2966	C₂	semidirect
19. C₅×#2965	C₂	semidirect
20. C₅×Q₈×M₁₆	C₂	semidirect
21. C₅×#2962	C₂	semidirect
22. C₅×#2961	C₂	semidirect
23. C₅×#2960	C₂	semidirect
135. #60344	C₅	direct (N × H)
312. #2995	C₂×C₅	semidirect
313. #2995	C₂×C₅	semidirect
314. #2994	C₂×C₅	semidirect
315. #2993	C₂×C₅	semidirect
316. #2993	C₂×C₅	semidirect
317. #2991	C₂×C₅	semidirect
318. #2989	C₂×C₅	semidirect
319. #2986	C₂×C₅	semidirect
320. #2985	C₂×C₅	semidirect
321. #2985	C₂×C₅	semidirect
322. #2984	C₂×C₅	semidirect
323. #2970	C₂×C₅	semidirect
324. #2969	C₂×C₅	semidirect
325. #2969	C₂×C₅	semidirect
326. #2968	C₂×C₅	semidirect
327. #2967	C₂×C₅	semidirect
328. #2966	C₂×C₅	semidirect
329. #2965	C₂×C₅	semidirect
330. Q₈×M₁₆	C₂×C₅	semidirect
331. #2962	C₂×C₅	semidirect
332. #2961	C₂×C₅	semidirect
333. #2960	C₂×C₅	semidirect
1048. C₅	#60344	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
C₅×#2995	2
C₅×#2994	2
C₅×#2993	2
C₅×#2991	2
C₅×#2989	2
C₅×#2986	2
C₅×#2985	2
C₅×#2984	2
C₅×#2970	2
C₅×#2969	2
C₅×#2968	2
C₅×#2967	2
C₅×#2966	2
C₅×#2965	2
C₅×Q₈×M₁₆	2
C₅×#2962	2
C₅×#2961	2
C₅×#2960	2
#60344	5

Subgroups — C5×#60344 #11983064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60344 #11983064