Subgroups — C₅×#60302 #11983022

Order 1280.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3480	C₂	1	1	yes	maximal, characteristic
2	C₅×#2995	C₂	1	2	yes	maximal, complemented
3	C₅×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2992	C₂	1	2	yes	maximal, complemented
6	C₅×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2981	C₂	1	2	yes	maximal, complemented
11	C₅×#2981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2980	C₂	1	2	yes	maximal, complemented
13	C₅×#2979	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2969	C₂	1	1	yes	maximal, characteristic, 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×#2925	C₂	1	2	yes	maximal, complemented
21	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2923	C₂	1	2	yes	maximal, complemented
23	C₅×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#559	C₄	1	1	yes	characteristic
25	C₅×#559	C₄	1	2	yes	—
26	C₅×#557	C₄	1	1	yes	characteristic
27	C₅×#556	C₄	1	1	yes	characteristic
28	C₅×#556	C₄	1	2	yes	—
29	C₅×#553	C₄	1	1	yes	characteristic
30	C₅×#553	C₄	1	1	yes	characteristic
31	C₅×#553	C₄	1	2	yes	—
32	C₅×#553	C₄	1	2	yes	—
33	C₅×#550	C₄	1	1	yes	characteristic
34	C₅×#548	C₄	1	1	yes	characteristic
35	C₅×#548	C₄	1	1	yes	characteristic
36	C₅×#532	C₂²	1	1	yes	characteristic
37	C₅×#532	C₂²	1	2	yes	—
38	C₅×#529	C₂²	1	2	yes	—
39	C₅×#529	C₂²	1	1	yes	characteristic
40	C₅×#529	C₂²	1	1	yes	characteristic
41	C₅×#529	C₂²	1	2	yes	—
42	C₄×C₅×#41	C₂²	1	1	yes	characteristic
43	C₄×C₅×#41	C₂²	1	1	yes	characteristic
44	C₄×C₅×#41	C₂²	1	1	yes	characteristic
45	C₄×C₅×#41	C₂²	1	2	yes	—
46	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
47	C₅×#446	C₂²	1	1	yes	characteristic
48	C₅×#446	C₂²	1	1	yes	characteristic
49	C₅×#446	C₂²	1	2	yes	—
50	C₅×#446	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
55	C₅×#446	C₂²	1	2	yes	—
56	C₅×#446	C₂²	1	2	yes	—
57	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
58	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
59	C₅×#436	C₂²	1	1	yes	characteristic
60	C₅×#436	C₂²	1	1	yes	characteristic
61	C₅×#436	C₂²	1	2	yes	—
62	C₅×#436	C₂²	1	2	yes	—
63	C₅×#436	C₂²	1	1	yes	characteristic
64	C₅×#436	C₂²	1	1	yes	characteristic
65	C₅×#436	C₂²	1	2	yes	—
66	C₅×#435	C₂²	1	2	yes	—
67	C₅×#435	C₂²	1	2	yes	—
68	C₅×#435	C₂²	1	2	yes	—
69	C₅×#435	C₂²	1	2	yes	—
70	C₅×#435	C₂²	1	2	yes	—
71	C₅×#435	C₂²	1	2	yes	—
72	C₅×#435	C₂²	1	2	yes	—
73	C₅×#435	C₂²	1	2	yes	—
74	C₅×#435	C₂²	1	2	yes	—
75	C₅×#435	C₂²	1	2	yes	—
76	C₅×#435	C₂²	1	2	yes	—
77	C₅×#435	C₂²	1	2	yes	—
78	C₅×#435	C₂²	1	2	yes	—
79	C₅×#435	C₂²	1	2	yes	—
80	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
81	C₅×C₈×D₄	C₂²	1	2	yes	—
82	C₅×C₈×D₄	C₂²	1	2	yes	—
83	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
84	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
85	C₅×C₈×D₄	C₂²	1	2	yes	—
86	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
87	C₅×#433	C₂²	1	2	yes	—
88	C₅×#433	C₂²	1	2	yes	—
89	C₅×#433	C₂²	1	2	yes	—
90	C₅×#433	C₂²	1	1	yes	characteristic
91	C₅×#433	C₂²	1	1	yes	characteristic
92	C₅×#433	C₂²	1	1	yes	characteristic
93	C₅×#433	C₂²	1	1	yes	characteristic
94	C₅×#433	C₂²	1	2	yes	—
95	C₅×#433	C₂²	1	2	yes	—
96	C₅×#433	C₂²	1	2	yes	—
97	C₅×#432	C₂²	1	2	yes	—
98	C₅×#432	C₂²	1	1	yes	characteristic
99	C₅×#432	C₂²	1	2	yes	—
100	C₅×#432	C₂²	1	2	yes	—
101	C₅×#432	C₂²	1	2	yes	—
102	C₅×#432	C₂²	1	2	yes	—
103	C₅×#432	C₂²	1	1	yes	characteristic
104	C₅×#432	C₂²	1	2	yes	—
105	C₅×#431	C₂²	1	1	yes	characteristic
106	C₅×#431	C₂²	1	2	yes	—
107	C₅×#431	C₂²	1	1	yes	characteristic
108	C₅×#431	C₂²	1	1	yes	characteristic
109	C₅×#431	C₂²	1	1	yes	characteristic
110	C₅×#431	C₂²	1	1	yes	characteristic
111	C₅×#431	C₂²	1	2	yes	—
112	C₅×#431	C₂²	1	1	yes	characteristic
113	C₅×#424	C₂²	1	1	yes	characteristic
114	C₅×#424	C₂²	1	2	yes	—
115	C₅×#424	C₂²	1	2	yes	—
116	C₅×#424	C₂²	1	1	yes	characteristic
117	C₅×#423	C₂²	1	2	yes	—
118	C₅×#423	C₂²	1	1	yes	characteristic
119	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
121	C₅×#408	C₂²	1	1	yes	characteristic
122	C₅×#408	C₂²	1	2	yes	—
123	C₅×#408	C₂²	1	2	yes	—
124	C₅×#408	C₂²	1	2	yes	—
125	C₅×#408	C₂²	1	2	yes	—
126	C₅×#408	C₂²	1	1	yes	characteristic
127	C₅×#408	C₂²	1	2	yes	—
128	C₅×#405	C₂²	1	2	yes	—
129	C₅×#405	C₂²	1	2	yes	—
130	C₅×#405	C₂²	1	2	yes	—
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	#60302	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	C₂×C₅×#41	C₂³	1	1	yes	characteristic
139	C₂×C₅×#41	C₂³	1	2	yes	—
140	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₅×M₁₆	C₂³	1	2	yes	—
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	C₂×C₅×M₁₆	C₂³	1	2	yes	—
148	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₂²×C₅×C₈	C₂³	1	2	yes	—
153	C₂²×C₅×C₈	C₂³	1	2	yes	—
154	C₂²×C₅×C₈	C₂³	1	2	yes	—
155	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
157	C₅×#127	C₂×C₄	1	1	yes	characteristic
158	C₅×#127	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×#125	C₂×C₄	1	2	yes	—
166	C₅×#125	C₂×C₄	1	1	yes	characteristic
167	C₅×#125	C₂×C₄	1	1	yes	characteristic
168	C₅×#125	C₂×C₄	1	2	yes	—
169	C₅×#124	C₂×C₄	1	1	yes	characteristic
170	C₅×#124	C₂×C₄	1	1	yes	characteristic
171	C₅×#124	C₂×C₄	1	2	yes	—
172	C₅×#124	C₂×C₄	1	2	yes	—
173	C₅×#124	C₂×C₄	1	2	yes	—
174	C₅×#124	C₂×C₄	1	2	yes	—
175	C₅×#124	C₂×C₄	1	2	yes	—
176	C₅×#123	C₂×C₄	1	2	yes	—
177	C₅×#123	C₂×C₄	1	2	yes	—
178	C₅×#123	C₂×C₄	1	2	yes	—
179	C₅×#123	C₂×C₄	1	2	yes	—
180	C₅×#123	C₂×C₄	1	2	yes	—
181	C₅×#123	C₂×C₄	1	2	yes	—
182	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
184	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₅×#121	C₂×C₄	1	1	yes	characteristic
187	C₅×#121	C₂×C₄	1	1	yes	characteristic
188	C₅×#121	C₂×C₄	1	2	yes	—
189	C₅×#121	C₂×C₄	1	2	yes	—
190	C₅×#121	C₂×C₄	1	1	yes	characteristic
191	C₅×#121	C₂×C₄	1	1	yes	characteristic
192	C₅×#121	C₂×C₄	1	2	yes	—
193	C₅×#121	C₂×C₄	1	2	yes	—
194	C₅×#121	C₂×C₄	1	2	yes	—
195	C₅×#121	C₂×C₄	1	2	yes	—
196	C₅×#121	C₂×C₄	1	2	yes	—
197	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
198	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
199	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
200	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
201	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
202	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
203	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
204	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
205	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
206	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
207	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
208	C₄×C₅×Q₈	C₂³	1	2	yes	—
209	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
210	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
211	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
212	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
213	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
214	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
215	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
216	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
217	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
218	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
219	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
220	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
221	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
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	2	yes	—
225	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
226	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
227	C₄×C₅×D₄	C₂³	1	2	yes	—
228	C₄×C₅×D₄	C₂³	1	2	yes	—
229	C₄×C₅×D₄	C₂³	1	2	yes	—
230	C₄×C₅×D₄	C₂³	1	2	yes	—
231	C₄×C₅×D₄	C₂³	1	2	yes	—
232	C₅×#117	C₂×C₄	1	1	yes	characteristic
233	C₅×#117	C₂×C₄	1	1	yes	characteristic
234	C₅×#117	C₂×C₄	1	2	yes	—
235	C₅×#117	C₂×C₄	1	2	yes	—
236	C₅×#117	C₂³	1	2	yes	—
237	C₅×#117	C₂³	1	1	yes	characteristic
238	C₅×#117	C₂³	1	1	yes	characteristic
239	C₅×#117	C₂³	1	2	yes	—
240	C₅×#117	C₂³	1	1	yes	characteristic
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	2	yes	—
247	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
248	C₂×C₄²×C₅	C₂³	1	2	yes	—
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	2	yes	—
253	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₅×C₄⋊C₈	C₂³	1	2	yes	—
256	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
264	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₅×C₄⋊C₈	C₂³	1	2	yes	—
268	C₅×C₄⋊C₈	C₂³	1	2	yes	—
269	C₅×C₄⋊C₈	C₂³	1	2	yes	—
270	C₅×C₄⋊C₈	C₂³	1	2	yes	—
271	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
278	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
289	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
290	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
291	C₅×#97	C₂³	1	1	yes	characteristic
292	C₅×#97	C₂³	1	2	yes	—
293	C₅×#97	C₂³	1	2	yes	—
294	C₅×#97	C₂³	1	2	yes	—
295	C₅×#97	C₂³	1	1	yes	characteristic
296	C₅×#97	C₂³	1	2	yes	—
297	C₅×#97	C₂³	1	2	yes	—
298	C₅×#97	C₂³	1	2	yes	—
299	C₅×#97	C₂³	1	2	yes	—
300	C₅×#97	C₂³	1	2	yes	—
301	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
302	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
307	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
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	#3480	C₂×C₅	1	1	yes	characteristic
312	#2995	C₂×C₅	1	2	yes	complemented
313	#2994	C₂×C₅	1	1	yes	characteristic, complemented
314	#2993	C₂×C₅	1	1	yes	characteristic, complemented
315	#2992	C₂×C₅	1	2	yes	complemented
316	#2990	C₂×C₅	1	1	yes	characteristic, complemented
317	#2989	C₂×C₅	1	1	yes	characteristic, complemented
318	#2984	C₂×C₅	1	1	yes	characteristic, complemented
319	#2983	C₂×C₅	1	1	yes	characteristic, complemented
320	#2981	C₂×C₅	1	1	yes	characteristic, complemented
321	#2981	C₂×C₅	1	2	yes	complemented
322	#2980	C₂×C₅	1	2	yes	complemented
323	#2979	C₂×C₅	1	1	yes	characteristic, complemented
324	#2970	C₂×C₅	1	1	yes	characteristic, complemented
325	#2969	C₂×C₅	1	1	yes	characteristic, 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	#2925	C₂×C₅	1	1	yes	characteristic, complemented
331	#2925	C₂×C₅	1	2	yes	complemented
332	#2923	C₂×C₅	1	2	yes	complemented
333	#2922	C₂×C₅	1	1	yes	characteristic, complemented
334	C₅×#41	—	4	1	no	—
335	C₅×#41	—	4	2	no	—
336	C₅×#41	—	4	1	no	—
337	C₅×#41	—	4	2	no	—
338	C₅×#41	—	4	2	no	—
339	C₅×#41	—	4	2	no	—
340	C₂×C₅×Q₈	—	4	2	no	—
341	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
345	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
346	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
351	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
352	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
354	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
355	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
356	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
357	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
358	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
359	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
361	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
362	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
365	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
366	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
367	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
368	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
369	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
370	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
371	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
376	C₅×M₁₆	—	4	1	no	—
377	C₅×M₁₆	—	4	2	no	—
378	C₅×M₁₆	—	4	2	no	—
379	C₅×M₁₆	—	4	1	no	—
380	C₅×M₁₆	—	4	2	no	—
381	C₅×M₁₆	—	4	2	no	—
382	C₅×M₁₆	—	4	2	no	—
383	C₂×C₅×C₈	—	4	2	no	—
384	C₂×C₅×C₈	—	4	1	no	—
385	C₂×C₅×C₈	—	4	2	no	—
386	C₂×C₅×C₈	—	4	2	no	—
387	C₂×C₅×C₈	—	4	2	no	—
388	C₂×C₅×C₈	—	4	2	no	—
389	C₂×C₅×C₈	—	4	1	no	—
390	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₅×C₈	C₂⁴	1	2	yes	—
394	C₂×C₅×C₈	C₂⁴	1	2	yes	—
395	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
396	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₅×C₈	C₂⁴	1	2	yes	—
400	C₂×C₅×C₈	C₂⁴	1	2	yes	—
401	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
402	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
403	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
412	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
417	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
421	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
422	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
423	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
424	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
425	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
426	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
427	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
428	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
429	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
430	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
431	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
433	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
434	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
436	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
437	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
438	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
439	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
445	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
446	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
447	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
448	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₅	C₂²×C₄	1	2	yes	—
450	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₅	C₂²×C₄	1	2	yes	—
452	C₄²×C₅	C₂²×C₄	1	2	yes	—
453	C₄²×C₅	C₂²×C₄	1	2	yes	—
454	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
455	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
456	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
457	C₄²×C₅	C₂²×C₄	1	2	yes	—
458	C₄²×C₅	C₂²×C₄	1	2	yes	—
459	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
460	C₄²×C₅	C₂⁴	1	1	yes	characteristic
461	C₄²×C₅	C₂⁴	1	1	yes	characteristic
462	C₄²×C₅	C₂⁴	1	1	yes	characteristic
463	C₄²×C₅	C₂⁴	1	2	yes	—
464	C₄²×C₅	C₂⁴	1	1	yes	characteristic
465	C₄²×C₅	C₂⁴	1	2	yes	—
466	#559	C₄×C₅	1	1	yes	characteristic
467	#559	C₄×C₅	1	2	yes	—
468	#557	C₄×C₅	1	1	yes	characteristic
469	#556	C₄×C₅	1	1	yes	characteristic
470	#556	C₄×C₅	1	2	yes	—
471	#553	C₄×C₅	1	1	yes	characteristic
472	#553	C₄×C₅	1	1	yes	characteristic
473	#553	C₄×C₅	1	2	yes	—
474	#553	C₄×C₅	1	2	yes	—
475	#550	C₄×C₅	1	1	yes	characteristic
476	#548	C₄×C₅	1	1	yes	characteristic
477	#548	C₄×C₅	1	1	yes	characteristic
478	#532	C₂²×C₅	1	1	yes	characteristic
479	#532	C₂²×C₅	1	2	yes	—
480	#529	C₂²×C₅	1	1	yes	characteristic
481	#529	C₂²×C₅	1	2	yes	—
482	#529	C₂²×C₅	1	2	yes	—
483	#529	C₂²×C₅	1	1	yes	characteristic
484	C₄×#41	C₂²×C₅	1	1	yes	characteristic
485	C₄×#41	C₂²×C₅	1	1	yes	characteristic
486	C₄×#41	C₂²×C₅	1	1	yes	characteristic
487	C₄×#41	C₂²×C₅	1	2	yes	—
488	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
489	#446	C₂²×C₅	1	1	yes	characteristic
490	#446	C₂²×C₅	1	1	yes	characteristic
491	#446	C₂²×C₅	1	1	yes	characteristic
492	#446	C₂²×C₅	1	2	yes	—
493	#446	C₂²×C₅	1	2	yes	—
494	#446	C₂²×C₅	1	2	yes	—
495	#446	C₂²×C₅	1	2	yes	—
496	#446	C₂²×C₅	1	1	yes	characteristic
497	#446	C₂²×C₅	1	1	yes	characteristic
498	#446	C₂²×C₅	1	1	yes	characteristic
499	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
500	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
501	#436	C₂²×C₅	1	1	yes	characteristic
502	#436	C₂²×C₅	1	1	yes	characteristic
503	#436	C₂²×C₅	1	1	yes	characteristic
504	#436	C₂²×C₅	1	2	yes	—
505	#436	C₂²×C₅	1	2	yes	—
506	#436	C₂²×C₅	1	1	yes	characteristic
507	#436	C₂²×C₅	1	2	yes	—
508	#435	C₂²×C₅	1	2	yes	—
509	#435	C₂²×C₅	1	2	yes	—
510	#435	C₂²×C₅	1	2	yes	—
511	#435	C₂²×C₅	1	2	yes	—
512	#435	C₂²×C₅	1	2	yes	—
513	#435	C₂²×C₅	1	2	yes	—
514	#435	C₂²×C₅	1	2	yes	—
515	#435	C₂²×C₅	1	2	yes	—
516	#435	C₂²×C₅	1	2	yes	—
517	#435	C₂²×C₅	1	2	yes	—
518	#435	C₂²×C₅	1	2	yes	—
519	#435	C₂²×C₅	1	2	yes	—
520	#435	C₂²×C₅	1	2	yes	—
521	#435	C₂²×C₅	1	2	yes	—
522	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
523	C₈×D₄	C₂²×C₅	1	2	yes	—
524	C₈×D₄	C₂²×C₅	1	2	yes	—
525	C₈×D₄	C₂²×C₅	1	2	yes	—
526	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
527	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
528	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
529	#433	C₂²×C₅	1	1	yes	characteristic
530	#433	C₂²×C₅	1	1	yes	characteristic
531	#433	C₂²×C₅	1	1	yes	characteristic
532	#433	C₂²×C₅	1	1	yes	characteristic
533	#433	C₂²×C₅	1	2	yes	—
534	#433	C₂²×C₅	1	2	yes	—
535	#433	C₂²×C₅	1	2	yes	—
536	#433	C₂²×C₅	1	2	yes	—
537	#433	C₂²×C₅	1	2	yes	—
538	#433	C₂²×C₅	1	2	yes	—
539	#432	C₂²×C₅	1	2	yes	—
540	#432	C₂²×C₅	1	2	yes	—
541	#432	C₂²×C₅	1	2	yes	—
542	#432	C₂²×C₅	1	2	yes	—
543	#432	C₂²×C₅	1	1	yes	characteristic
544	#432	C₂²×C₅	1	2	yes	—
545	#432	C₂²×C₅	1	2	yes	—
546	#432	C₂²×C₅	1	1	yes	characteristic
547	#431	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
553	#431	C₂²×C₅	1	1	yes	characteristic
554	#431	C₂²×C₅	1	2	yes	—
555	#424	C₂²×C₅	1	1	yes	characteristic
556	#424	C₂²×C₅	1	1	yes	characteristic
557	#424	C₂²×C₅	1	2	yes	—
558	#424	C₂²×C₅	1	2	yes	—
559	#423	C₂²×C₅	1	2	yes	—
560	#423	C₂²×C₅	1	1	yes	characteristic
561	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
562	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
563	#408	C₂²×C₅	1	1	yes	characteristic
564	#408	C₂²×C₅	1	1	yes	characteristic
565	#408	C₂²×C₅	1	2	yes	—
566	#408	C₂²×C₅	1	2	yes	—
567	#408	C₂²×C₅	1	2	yes	—
568	#408	C₂²×C₅	1	2	yes	—
569	#408	C₂²×C₅	1	2	yes	—
570	#405	C₂²×C₅	1	2	yes	—
571	#405	C₂²×C₅	1	2	yes	—
572	#405	C₂²×C₅	1	2	yes	—
573	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
574	C₄×M₁₆	C₂²×C₅	1	2	yes	—
575	C₂×#97	C₂²×C₅	1	2	yes	—
576	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
577	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
578	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
579	C₂³×C₅	C₂³×C₄	1	2	yes	—
580	C₂³×C₅	C₂³×C₄	1	2	yes	—
581	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
582	C₅×Q₈	—	2	2	no	—
583	C₅×Q₈	—	2	2	no	—
584	C₅×Q₈	—	4	2	no	—
585	C₅×Q₈	—	4	1	no	—
586	C₅×Q₈	—	4	2	no	—
587	C₅×D₄	—	2	2	no	—
588	C₅×D₄	—	2	2	no	—
589	C₅×D₄	—	4	2	no	—
590	C₅×D₄	—	4	2	no	—
591	C₅×D₄	—	4	2	no	—
592	C₅×D₄	—	4	1	no	—
593	C₅×D₄	—	4	2	no	—
594	C₅×D₄	—	4	1	no	—
595	C₅×D₄	—	4	2	no	—
596	C₅×D₄	—	4	1	no	—
597	C₅×D₄	—	4	2	no	—
598	C₅×D₄	—	4	2	no	—
599	C₅×D₄	—	4	2	no	—
600	C₂×C₄×C₅	—	2	2	no	—
601	C₂×C₄×C₅	—	2	2	no	—
602	C₂×C₄×C₅	—	2	2	no	—
603	C₂×C₄×C₅	—	2	2	no	—
604	C₂×C₄×C₅	—	2	1	no	—
605	C₂×C₄×C₅	—	2	1	no	—
606	C₂×C₄×C₅	—	2	2	no	—
607	C₂×C₄×C₅	—	2	2	no	—
608	C₂×C₄×C₅	—	2	1	no	—
609	C₂×C₄×C₅	—	2	1	no	—
610	C₂×C₄×C₅	—	2	2	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	2	1	no	—
613	C₂×C₄×C₅	—	4	1	no	—
614	C₂×C₄×C₅	—	4	2	no	—
615	C₂×C₄×C₅	—	4	1	no	—
616	C₂×C₄×C₅	—	4	2	no	—
617	C₂×C₄×C₅	—	4	1	no	—
618	C₂×C₄×C₅	—	4	2	no	—
619	C₂×C₄×C₅	—	4	2	no	—
620	C₂×C₄×C₅	—	4	2	no	—
621	C₂×C₄×C₅	—	4	2	no	—
622	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
623	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
624	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
625	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
626	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
627	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
628	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
629	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
630	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
631	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
632	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
633	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
634	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
635	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
636	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
637	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
638	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
639	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
640	C₅×C₈	—	2	1	no	—
641	C₅×C₈	—	2	2	no	—
642	C₅×C₈	—	2	1	no	—
643	C₅×C₈	—	2	1	no	—
644	C₅×C₈	—	2	1	no	—
645	C₅×C₈	—	2	2	no	—
646	C₅×C₈	—	2	1	no	—
647	C₅×C₈	—	2	2	no	—
648	C₅×C₈	—	2	2	no	—
649	C₅×C₈	—	2	1	no	—
650	C₅×C₈	—	2	1	no	—
651	C₅×C₈	—	2	1	no	—
652	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
653	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
654	C₂×#41	C₂³×C₅	1	1	yes	characteristic
655	C₂×#41	C₂³×C₅	1	2	yes	—
656	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
657	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
658	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
659	C₂×M₁₆	C₂³×C₅	1	2	yes	—
660	C₂×M₁₆	C₂³×C₅	1	2	yes	—
661	C₂×M₁₆	C₂³×C₅	1	2	yes	—
662	C₂×M₁₆	C₂³×C₅	1	2	yes	—
663	C₂×M₁₆	C₂³×C₅	1	2	yes	—
664	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
665	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
666	C₂²×C₈	C₂³×C₅	1	2	yes	—
667	C₂²×C₈	C₂³×C₅	1	2	yes	—
668	C₂²×C₈	C₂³×C₅	1	2	yes	—
669	C₂²×C₈	C₂³×C₅	1	2	yes	—
670	C₂²×C₈	C₂³×C₅	1	2	yes	—
671	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
672	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
673	#127	C₂×C₄×C₅	1	1	yes	characteristic
674	#127	C₂×C₄×C₅	1	2	yes	—
675	#126	C₂×C₄×C₅	1	2	yes	—
676	#126	C₂×C₄×C₅	1	2	yes	—
677	#126	C₂×C₄×C₅	1	2	yes	—
678	#126	C₂×C₄×C₅	1	2	yes	—
679	#126	C₂×C₄×C₅	1	2	yes	—
680	#126	C₂×C₄×C₅	1	2	yes	—
681	#125	C₂×C₄×C₅	1	1	yes	characteristic
682	#125	C₂×C₄×C₅	1	2	yes	—
683	#125	C₂×C₄×C₅	1	2	yes	—
684	#125	C₂×C₄×C₅	1	1	yes	characteristic
685	#124	C₂×C₄×C₅	1	1	yes	characteristic
686	#124	C₂×C₄×C₅	1	1	yes	characteristic
687	#124	C₂×C₄×C₅	1	2	yes	—
688	#124	C₂×C₄×C₅	1	2	yes	—
689	#124	C₂×C₄×C₅	1	2	yes	—
690	#124	C₂×C₄×C₅	1	2	yes	—
691	#124	C₂×C₄×C₅	1	2	yes	—
692	#123	C₂×C₄×C₅	1	2	yes	—
693	#123	C₂×C₄×C₅	1	2	yes	—
694	#123	C₂×C₄×C₅	1	2	yes	—
695	#123	C₂×C₄×C₅	1	2	yes	—
696	#123	C₂×C₄×C₅	1	2	yes	—
697	#123	C₂×C₄×C₅	1	2	yes	—
698	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
701	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
702	#121	C₂×C₄×C₅	1	1	yes	characteristic
703	#121	C₂×C₄×C₅	1	1	yes	characteristic
704	#121	C₂×C₄×C₅	1	2	yes	—
705	#121	C₂×C₄×C₅	1	2	yes	—
706	#121	C₂×C₄×C₅	1	1	yes	characteristic
707	#121	C₂×C₄×C₅	1	1	yes	characteristic
708	#121	C₂×C₄×C₅	1	2	yes	—
709	#121	C₂×C₄×C₅	1	2	yes	—
710	#121	C₂×C₄×C₅	1	2	yes	—
711	#121	C₂×C₄×C₅	1	2	yes	—
712	#121	C₂×C₄×C₅	1	2	yes	—
713	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
714	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
715	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
716	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
717	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
718	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
719	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
720	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
721	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
722	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
723	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
724	C₄×Q₈	C₂³×C₅	1	2	yes	—
725	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
726	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
727	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
728	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
729	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
730	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
731	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
732	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
733	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
734	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
735	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
736	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
737	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
738	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
739	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
740	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
741	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
742	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
743	C₄×D₄	C₂³×C₅	1	2	yes	—
744	C₄×D₄	C₂³×C₅	1	2	yes	—
745	C₄×D₄	C₂³×C₅	1	2	yes	—
746	C₄×D₄	C₂³×C₅	1	2	yes	—
747	C₄×D₄	C₂³×C₅	1	2	yes	—
748	#117	C₂×C₄×C₅	1	1	yes	characteristic
749	#117	C₂×C₄×C₅	1	1	yes	characteristic
750	#117	C₂×C₄×C₅	1	2	yes	—
751	#117	C₂×C₄×C₅	1	2	yes	—
752	#117	C₂³×C₅	1	1	yes	characteristic
753	#117	C₂³×C₅	1	1	yes	characteristic
754	#117	C₂³×C₅	1	2	yes	—
755	#117	C₂³×C₅	1	1	yes	characteristic
756	#117	C₂³×C₅	1	2	yes	—
757	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
759	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₅	1	2	yes	—
761	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₅	1	2	yes	—
763	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
775	C₄⋊C₈	C₂³×C₅	1	2	yes	—
776	C₄⋊C₈	C₂³×C₅	1	2	yes	—
777	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
778	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
779	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
780	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
781	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
782	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
783	C₄⋊C₈	C₂³×C₅	1	2	yes	—
784	C₄⋊C₈	C₂³×C₅	1	2	yes	—
785	C₄⋊C₈	C₂³×C₅	1	2	yes	—
786	C₄⋊C₈	C₂³×C₅	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
788	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
789	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
790	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
791	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
793	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
794	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
795	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
796	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
797	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
799	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
800	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
801	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
802	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
805	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
806	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
807	#97	C₂³×C₅	1	1	yes	characteristic
808	#97	C₂³×C₅	1	2	yes	—
809	#97	C₂³×C₅	1	2	yes	—
810	#97	C₂³×C₅	1	2	yes	—
811	#97	C₂³×C₅	1	1	yes	characteristic
812	#97	C₂³×C₅	1	2	yes	—
813	#97	C₂³×C₅	1	2	yes	—
814	#97	C₂³×C₅	1	2	yes	—
815	#97	C₂³×C₅	1	2	yes	—
816	#97	C₂³×C₅	1	2	yes	—
817	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
818	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
819	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
820	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
821	C₄×C₈	C₂³×C₅	1	2	yes	—
822	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
823	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
824	C₄×C₈	C₂³×C₅	1	2	yes	—
825	C₄×C₈	C₂³×C₅	1	2	yes	—
826	C₄×C₈	C₂³×C₅	1	2	yes	—
827	C₂²×C₅	—	2	1	no	—
828	C₂²×C₅	—	2	1	no	—
829	C₂²×C₅	—	2	2	no	—
830	C₂²×C₅	—	2	1	no	—
831	C₂²×C₅	—	2	2	no	—
832	C₂²×C₅	—	2	1	no	—
833	C₂²×C₅	—	2	1	no	—
834	C₂²×C₅	—	2	1	no	—
835	C₂²×C₅	—	2	2	no	—
836	C₂²×C₅	—	2	2	no	—
837	C₂²×C₅	—	2	1	no	—
838	C₂²×C₅	—	2	1	no	—
839	C₂²×C₅	—	2	1	no	—
840	C₂²×C₅	—	2	2	no	—
841	C₂²×C₅	—	2	2	no	—
842	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
843	C₄×C₅	—	2	1	no	—
844	C₄×C₅	—	2	2	no	—
845	C₄×C₅	—	2	1	no	—
846	C₄×C₅	—	2	1	no	—
847	C₄×C₅	—	2	2	no	—
848	C₄×C₅	—	2	1	no	—
849	C₄×C₅	—	2	1	no	—
850	C₄×C₅	—	2	1	no	—
851	C₄×C₅	—	2	2	no	—
852	C₄×C₅	—	2	2	no	—
853	C₄×C₅	—	2	1	no	—
854	C₄×C₅	—	2	1	no	—
855	C₄×C₅	—	2	1	no	—
856	C₄×C₅	—	2	2	no	—
857	C₄×C₅	—	2	1	no	—
858	C₄×C₅	—	2	2	no	—
859	C₄×C₅	#568	1	2	yes	—
860	C₄×C₅	#585	1	1	yes	characteristic
861	C₄×C₅	#585	1	1	yes	characteristic
862	#41	—	4	1	no	—
863	#41	—	4	2	no	—
864	#41	—	4	1	no	—
865	#41	—	4	2	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	C₂×Q₈	—	4	2	no	—
869	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
870	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
871	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
872	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
873	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
874	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
875	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
876	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
877	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
878	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
879	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
880	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
881	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
882	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
883	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
884	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
885	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
886	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
887	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
888	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
889	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
890	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
891	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
892	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
893	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
894	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
895	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
896	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
897	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
898	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
904	M₁₆	—	4	1	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	M₁₆	—	4	1	no	—
908	M₁₆	—	4	2	no	—
909	M₁₆	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	2	no	—
912	C₂×C₈	—	4	1	no	—
913	C₂×C₈	—	4	2	no	—
914	C₂×C₈	—	4	2	no	—
915	C₂×C₈	—	4	2	no	—
916	C₂×C₈	—	4	2	no	—
917	C₂×C₈	—	4	1	no	—
918	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₅	1	2	yes	—
924	C₂×C₈	C₂⁴×C₅	1	2	yes	—
925	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
927	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₅	1	2	yes	—
929	C₂×C₈	C₂⁴×C₅	1	2	yes	—
930	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
931	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
932	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
933	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
934	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
935	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
936	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
937	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
940	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
942	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
944	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
946	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
947	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
948	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
949	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
950	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
951	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
952	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
953	C₄⋊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	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
958	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
959	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
960	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
961	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
962	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
963	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
965	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
967	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
969	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
970	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
971	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
972	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
973	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
974	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
975	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
976	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
977	C₄²	C₂²×C₄×C₅	1	2	yes	—
978	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
979	C₄²	C₂²×C₄×C₅	1	2	yes	—
980	C₄²	C₂²×C₄×C₅	1	2	yes	—
981	C₄²	C₂²×C₄×C₅	1	2	yes	—
982	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
983	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
984	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
985	C₄²	C₂²×C₄×C₅	1	2	yes	—
986	C₄²	C₂²×C₄×C₅	1	2	yes	—
987	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
988	C₄²	C₂⁴×C₅	1	1	yes	characteristic
989	C₄²	C₂⁴×C₅	1	1	yes	characteristic
990	C₄²	C₂⁴×C₅	1	2	yes	—
991	C₄²	C₂⁴×C₅	1	1	yes	characteristic
992	C₄²	C₂⁴×C₅	1	2	yes	—
993	C₄²	C₂⁴×C₅	1	1	yes	characteristic
994	C₂×C₅	—	4	1	no	—
995	C₂×C₅	—	4	1	no	—
996	C₂×C₅	—	4	1	no	—
997	C₂×C₅	—	4	2	no	—
998	C₂×C₅	—	4	2	no	—
999	C₂×C₅	#3428	1	1	yes	characteristic
1000	C₂×C₅	C₂×#568	1	1	yes	characteristic
1001	C₂×C₅	#3573	1	1	yes	characteristic
1002	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
1003	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
1004	C₂³	C₂³×C₄×C₅	1	2	yes	—
1005	C₂³	C₂³×C₄×C₅	1	2	yes	—
1006	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	1	no	—
1011	Q₈	—	4	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	4	1	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	1	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	1	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1048	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1049	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1050	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1051	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1052	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1053	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1054	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1055	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1056	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1057	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1058	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1059	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1060	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1061	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1062	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1063	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	1	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	2	no	—
1071	C₈	—	2	1	no	—
1072	C₈	—	2	2	no	—
1073	C₈	—	2	2	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₅	#60302	1	1	yes	characteristic, direct product factor, Sylow
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	C₅×#568	1	2	yes	—
1111	C₄	C₅×#585	1	1	yes	characteristic
1112	C₄	C₅×#585	1	1	yes	characteristic
1113	C₂	—	4	1	no	—
1114	C₂	—	4	1	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₅×#3428	1	1	yes	characteristic
1119	C₂	C₂×C₅×#568	1	1	yes	characteristic
1120	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×#3480	C₂
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×#2994	C₂	semidirect
4. C₅×#2993	C₂	semidirect
5. C₅×#2992	C₂	semidirect
6. C₅×#2990	C₂	semidirect
7. C₅×#2989	C₂	semidirect
8. C₅×#2984	C₂	semidirect
9. C₅×#2983	C₂	semidirect
10. C₅×#2981	C₂	semidirect
11. C₅×#2981	C₂	semidirect
12. C₅×#2980	C₂	semidirect
13. C₅×#2979	C₂	semidirect
14. C₅×#2970	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×#2925	C₂	semidirect
21. C₅×#2925	C₂	semidirect
22. C₅×#2923	C₂	semidirect
23. C₅×#2922	C₂	semidirect
135. #60302	C₅	direct (N × H)
312. #2995	C₂×C₅	semidirect
313. #2994	C₂×C₅	semidirect
314. #2993	C₂×C₅	semidirect
315. #2992	C₂×C₅	semidirect
316. #2990	C₂×C₅	semidirect
317. #2989	C₂×C₅	semidirect
318. #2984	C₂×C₅	semidirect
319. #2983	C₂×C₅	semidirect
320. #2981	C₂×C₅	semidirect
321. #2981	C₂×C₅	semidirect
322. #2980	C₂×C₅	semidirect
323. #2979	C₂×C₅	semidirect
324. #2970	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. #2925	C₂×C₅	semidirect
331. #2925	C₂×C₅	semidirect
332. #2923	C₂×C₅	semidirect
333. #2922	C₂×C₅	semidirect
1077. C₅	#60302	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×#3480	2
C₅×#2995	2
C₅×#2994	2
C₅×#2993	2
C₅×#2992	2
C₅×#2990	2
C₅×#2989	2
C₅×#2984	2
C₅×#2983	2
C₅×#2981	2
C₅×#2980	2
C₅×#2979	2
C₅×#2970	2
C₅×#2969	2
C₅×#2968	2
C₅×#2967	2
C₅×#2966	2
C₅×#2965	2
C₅×#2925	2
C₅×#2923	2
C₅×#2922	2
#60302	5

Subgroups — C5×#60302 #11983022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60302 #11983022