Subgroups — C₅×#60300 #11983020

Order 1280.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3475	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×#2993	C₂	1	2	yes	maximal, complemented
6	C₅×#2991	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2978	C₂	1	2	yes	maximal, complemented
11	C₅×#2976	C₂	1	2	yes	maximal, complemented
12	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2974	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2969	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	1	yes	maximal, characteristic, complemented
21	C₅×#2924	C₂	1	2	yes	maximal, complemented
22	C₅×#2922	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2921	C₂	1	2	yes	maximal, complemented
24	C₅×#556	C₄	1	1	yes	characteristic
25	C₅×#555	C₄	1	1	yes	characteristic
26	C₅×#554	C₄	1	1	yes	characteristic
27	C₅×#553	C₄	1	2	yes	—
28	C₅×#552	C₄	1	2	yes	—
29	C₅×#552	C₄	1	1	yes	characteristic
30	C₅×#552	C₄	1	1	yes	characteristic
31	C₅×#551	C₄	1	2	yes	—
32	C₅×#551	C₄	1	2	yes	—
33	C₅×#547	C₄	1	1	yes	characteristic
34	C₅×#546	C₄	1	1	yes	characteristic
35	C₅×#546	C₄	1	1	yes	characteristic
36	C₅×#533	C₂²	1	1	yes	characteristic
37	C₅×#529	C₂²	1	1	yes	characteristic
38	C₅×#529	C₂²	1	2	yes	—
39	C₅×#529	C₂²	1	1	yes	characteristic
40	C₅×#529	C₂²	1	2	yes	—
41	C₅×#525	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	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×#117	C₂²	1	2	yes	—
47	C₅×#446	C₂²	1	1	yes	characteristic, complemented
48	C₅×#446	C₂²	1	1	yes	characteristic, complemented
49	C₅×#446	C₂²	1	2	yes	complemented
50	C₅×#446	C₂²	1	2	yes	complemented
51	C₅×#446	C₂²	1	1	yes	characteristic, complemented
52	C₅×#446	C₂²	1	1	yes	characteristic, complemented
53	C₅×#446	C₂²	1	2	yes	complemented
54	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
58	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
59	C₅×#436	C₂²	1	1	yes	characteristic
60	C₅×#436	C₂²	1	1	yes	characteristic
61	C₅×#436	C₂²	1	1	yes	characteristic
62	C₅×#436	C₂²	1	1	yes	characteristic
63	C₅×#436	C₂²	1	1	yes	characteristic
64	C₅×#436	C₂²	1	2	yes	—
65	C₅×#436	C₂²	1	1	yes	characteristic
66	C₅×#436	C₂²	1	2	yes	—
67	C₅×#436	C₂²	1	2	yes	complemented
68	C₅×#436	C₂²	1	2	yes	complemented
69	C₅×#436	C₂²	1	2	yes	complemented
70	C₅×#436	C₂²	1	2	yes	complemented
71	C₅×#436	C₂²	1	2	yes	complemented
72	C₅×#436	C₂²	1	2	yes	complemented
73	C₅×#435	C₂²	1	2	yes	—
74	C₅×#435	C₂²	1	2	yes	—
75	C₅×#435	C₂²	1	2	yes	complemented
76	C₅×#435	C₂²	1	2	yes	complemented
77	C₅×#435	C₂²	1	2	yes	complemented
78	C₅×#435	C₂²	1	2	yes	complemented
79	C₅×#435	C₂²	1	2	yes	complemented
80	C₅×#435	C₂²	1	2	yes	complemented
81	C₅×#435	C₂²	1	2	yes	complemented
82	C₅×#435	C₂²	1	2	yes	complemented
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	complemented
86	C₅×C₈×D₄	C₂²	1	2	yes	complemented
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	2	yes	—
91	C₅×#433	C₂²	1	1	yes	characteristic
92	C₅×#433	C₂²	1	2	yes	—
93	C₅×#433	C₂²	1	1	yes	characteristic
94	C₅×#433	C₂²	1	2	yes	complemented
95	C₅×#433	C₂²	1	2	yes	complemented
96	C₅×#433	C₂²	1	2	yes	complemented
97	C₅×#433	C₂²	1	2	yes	complemented
98	C₅×#433	C₂²	1	2	yes	complemented
99	C₅×#433	C₂²	1	1	yes	characteristic, complemented
100	C₅×#433	C₂²	1	1	yes	characteristic, complemented
101	C₅×#432	C₂²	1	1	yes	characteristic
102	C₅×#432	C₂²	1	2	yes	complemented
103	C₅×#432	C₂²	1	2	yes	complemented
104	C₅×#432	C₂²	1	1	yes	characteristic, complemented
105	C₅×#431	C₂²	1	1	yes	characteristic
106	C₅×#431	C₂²	1	1	yes	characteristic
107	C₅×#431	C₂²	1	1	yes	characteristic
108	C₅×#431	C₂²	1	1	yes	characteristic, complemented
109	C₅×#431	C₂²	1	2	yes	complemented
110	C₅×#431	C₂²	1	1	yes	characteristic, complemented
111	C₅×#431	C₂²	1	2	yes	complemented
112	C₅×#431	C₂²	1	1	yes	characteristic, complemented
113	C₅×#424	C₂²	1	1	yes	characteristic, complemented
114	C₅×#424	C₂²	1	2	yes	complemented
115	C₅×#424	C₂²	1	2	yes	complemented
116	C₅×#424	C₂²	1	1	yes	characteristic, complemented
117	C₅×#423	C₂²	1	2	yes	complemented
118	C₅×#423	C₂²	1	1	yes	characteristic, complemented
119	C₅×#423	C₂²	1	2	yes	complemented
120	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
121	C₅×#408	C₂²	1	1	yes	characteristic
122	C₅×#408	C₂²	1	1	yes	characteristic
123	C₅×#408	C₂²	1	2	yes	—
124	C₅×#407	C₂²	1	2	yes	—
125	C₅×#407	C₂²	1	2	yes	—
126	C₅×#407	C₂²	1	2	yes	—
127	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
128	C₅×#405	C₂²	1	2	yes	complemented
129	C₅×#405	C₂²	1	2	yes	complemented
130	C₅×#405	C₂²	1	2	yes	complemented
131	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
132	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
133	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
135	#60300	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	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂³	1	2	yes	—
141	C₂×C₅×M₁₆	C₂³	1	2	yes	—
142	C₂×C₅×M₁₆	C₂³	1	2	yes	—
143	C₂×C₅×M₁₆	C₂³	1	2	yes	—
144	C₂×C₅×M₁₆	C₂³	1	2	yes	—
145	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₅×M₁₆	C₂³	1	2	yes	—
148	C₂×C₅×M₁₆	C₂³	1	2	yes	—
149	C₂×C₅×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₅×#126	C₂×C₄	1	2	yes	—
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×#125	C₂×C₄	1	2	yes	—
164	C₅×#125	C₂×C₄	1	2	yes	—
165	C₅×#125	C₂×C₄	1	1	yes	characteristic
166	C₅×#125	C₂×C₄	1	1	yes	characteristic
167	C₅×#125	C₂×C₄	1	2	yes	—
168	C₅×#124	C₂×C₄	1	1	yes	characteristic
169	C₅×#124	C₂×C₄	1	1	yes	characteristic
170	C₅×#124	C₂×C₄	1	2	yes	—
171	C₅×#124	C₂×C₄	1	2	yes	—
172	C₅×#123	C₂×C₄	1	2	yes	—
173	C₅×#123	C₂×C₄	1	2	yes	—
174	C₅×#123	C₂×C₄	1	2	yes	—
175	C₅×#123	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×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₅×C₂²⋊Q₈	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×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
187	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
188	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₅×#121	C₂×C₄	1	2	yes	—
190	C₅×#121	C₂×C₄	1	2	yes	—
191	C₅×#121	C₂×C₄	1	2	yes	—
192	C₅×#121	C₂×C₄	1	2	yes	—
193	C₅×#121	C₂×C₄	1	1	yes	characteristic
194	C₅×#121	C₂×C₄	1	1	yes	characteristic
195	C₅×#120	C₂×C₄	1	2	yes	—
196	C₅×#120	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	1	yes	characteristic
200	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
201	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
202	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
203	C₄×C₅×Q₈	C₂³	1	2	yes	—
204	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
205	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
206	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
207	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
208	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
212	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
216	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
217	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
218	C₄×C₅×D₄	C₂³	1	2	yes	—
219	C₄×C₅×D₄	C₂³	1	2	yes	—
220	C₄×C₅×D₄	C₂³	1	2	yes	—
221	C₄×C₅×D₄	C₂³	1	2	yes	—
222	C₄×C₅×D₄	C₂³	1	2	yes	—
223	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
224	C₅×#117	C₂×C₄	1	2	yes	—
225	C₅×#117	C₂×C₄	1	2	yes	—
226	C₅×#117	C₂×C₄	1	2	yes	—
227	C₅×#117	C₂×C₄	1	2	yes	—
228	C₅×#117	C₂×C₄	1	2	yes	—
229	C₅×#117	C₂×C₄	1	2	yes	—
230	C₅×#117	C₂×C₄	1	1	yes	characteristic
231	C₅×#117	C₂×C₄	1	1	yes	characteristic
232	C₅×#117	C₂³	1	2	yes	—
233	C₅×#117	C₂³	1	1	yes	characteristic
234	C₅×#117	C₂³	1	2	yes	—
235	C₅×#117	C₂³	1	1	yes	characteristic
236	C₅×#117	C₂³	1	1	yes	characteristic
237	C₅×#117	C₂³	1	2	yes	—
238	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
239	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
240	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
242	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
243	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
244	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₅	C₂³	1	2	yes	—
246	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₅	C₂³	1	2	yes	—
248	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
249	C₅×C₄⋊C₈	C₂³	1	2	yes	—
250	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₅×C₄⋊C₈	C₂³	1	2	yes	—
254	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	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	2	yes	—
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	2	yes	—
278	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	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	C₅×#97	C₂³	1	2	yes	—
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	1	yes	characteristic
303	C₄×C₅×C₈	C₂³	1	2	yes	—
304	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
305	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
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	#3475	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	#2993	C₂×C₅	1	2	yes	complemented
316	#2991	C₂×C₅	1	1	yes	characteristic, complemented
317	#2989	C₂×C₅	1	1	yes	characteristic, complemented
318	#2986	C₂×C₅	1	1	yes	characteristic, complemented
319	#2985	C₂×C₅	1	1	yes	characteristic, complemented
320	#2978	C₂×C₅	1	2	yes	complemented
321	#2976	C₂×C₅	1	2	yes	complemented
322	#2975	C₂×C₅	1	1	yes	characteristic, complemented
323	#2974	C₂×C₅	1	1	yes	characteristic, complemented
324	#2971	C₂×C₅	1	1	yes	characteristic, complemented
325	#2969	C₂×C₅	1	1	yes	characteristic, complemented
326	#2969	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	#2924	C₂×C₅	1	2	yes	complemented
332	#2922	C₂×C₅	1	1	yes	characteristic, complemented
333	#2921	C₂×C₅	1	2	yes	complemented
334	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
335	C₅×#41	—	4	1	no	—
336	C₅×#41	—	4	1	no	—
337	C₅×#41	—	4	2	no	—
338	C₅×#41	—	4	2	no	—
339	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
343	C₂×C₅×D₄	—	4	2	no	—
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	1	yes	characteristic
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	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
352	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
353	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
354	C₂²×C₄×C₅	—	4	2	no	—
355	C₂²×C₄×C₅	—	4	2	no	—
356	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
358	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
361	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
362	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
363	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
367	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
368	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
369	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₅×M₁₆	—	4	1	no	—
375	C₅×M₁₆	—	4	2	no	—
376	C₅×M₁₆	—	4	2	no	—
377	C₅×M₁₆	—	4	2	no	—
378	C₅×M₁₆	—	4	2	no	—
379	C₅×M₁₆	—	4	2	no	—
380	C₅×M₁₆	—	4	2	no	—
381	C₅×M₁₆	—	4	1	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	1	no	—
388	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₅×C₈	C₂⁴	1	2	yes	—
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	1	yes	characteristic
394	C₂×C₅×C₈	C₂⁴	1	2	yes	—
395	C₂×C₅×C₈	C₂⁴	1	2	yes	—
396	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₅×C₈	C₂⁴	1	2	yes	—
399	C₂×C₅×C₈	C₂⁴	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	2	yes	—
404	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
405	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
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	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	1	yes	characteristic
418	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
419	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
420	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
427	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	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	1	yes	characteristic
443	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
444	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
445	C₅×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
446	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
447	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
448	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
449	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
450	C₄²×C₅	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
458	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
464	C₄²×C₅	C₂⁴	1	2	yes	—
465	C₄²×C₅	C₂⁴	1	2	yes	—
466	#556	C₄×C₅	1	1	yes	characteristic
467	#555	C₄×C₅	1	1	yes	characteristic
468	#554	C₄×C₅	1	1	yes	characteristic
469	#553	C₄×C₅	1	2	yes	—
470	#552	C₄×C₅	1	2	yes	—
471	#552	C₄×C₅	1	1	yes	characteristic
472	#552	C₄×C₅	1	1	yes	characteristic
473	#551	C₄×C₅	1	2	yes	—
474	#551	C₄×C₅	1	2	yes	—
475	#547	C₄×C₅	1	1	yes	characteristic
476	#546	C₄×C₅	1	1	yes	characteristic
477	#546	C₄×C₅	1	1	yes	characteristic
478	#533	C₂²×C₅	1	1	yes	characteristic
479	#529	C₂²×C₅	1	1	yes	characteristic
480	#529	C₂²×C₅	1	2	yes	—
481	#529	C₂²×C₅	1	1	yes	characteristic
482	#529	C₂²×C₅	1	2	yes	—
483	#525	C₂²×C₅	1	2	yes	—
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	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
488	C₂×#117	C₂²×C₅	1	2	yes	—
489	#446	C₂²×C₅	1	1	yes	characteristic, complemented
490	#446	C₂²×C₅	1	1	yes	characteristic, complemented
491	#446	C₂²×C₅	1	1	yes	characteristic, complemented
492	#446	C₂²×C₅	1	2	yes	complemented
493	#446	C₂²×C₅	1	2	yes	complemented
494	#446	C₂²×C₅	1	2	yes	complemented
495	#446	C₂²×C₅	1	1	yes	characteristic, complemented
496	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
497	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
498	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
499	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
500	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
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	1	yes	characteristic
506	#436	C₂²×C₅	1	2	yes	—
507	#436	C₂²×C₅	1	1	yes	characteristic
508	#436	C₂²×C₅	1	1	yes	characteristic
509	#436	C₂²×C₅	1	2	yes	complemented
510	#436	C₂²×C₅	1	2	yes	complemented
511	#436	C₂²×C₅	1	2	yes	complemented
512	#436	C₂²×C₅	1	2	yes	complemented
513	#436	C₂²×C₅	1	2	yes	complemented
514	#436	C₂²×C₅	1	2	yes	complemented
515	#435	C₂²×C₅	1	2	yes	—
516	#435	C₂²×C₅	1	2	yes	—
517	#435	C₂²×C₅	1	2	yes	complemented
518	#435	C₂²×C₅	1	2	yes	complemented
519	#435	C₂²×C₅	1	2	yes	complemented
520	#435	C₂²×C₅	1	2	yes	complemented
521	#435	C₂²×C₅	1	2	yes	complemented
522	#435	C₂²×C₅	1	2	yes	complemented
523	#435	C₂²×C₅	1	2	yes	complemented
524	#435	C₂²×C₅	1	2	yes	complemented
525	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
526	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
527	C₈×D₄	C₂²×C₅	1	2	yes	complemented
528	C₈×D₄	C₂²×C₅	1	2	yes	complemented
529	#433	C₂²×C₅	1	1	yes	characteristic
530	#433	C₂²×C₅	1	2	yes	—
531	#433	C₂²×C₅	1	2	yes	—
532	#433	C₂²×C₅	1	2	yes	—
533	#433	C₂²×C₅	1	1	yes	characteristic
534	#433	C₂²×C₅	1	2	yes	—
535	#433	C₂²×C₅	1	2	yes	—
536	#433	C₂²×C₅	1	2	yes	complemented
537	#433	C₂²×C₅	1	2	yes	complemented
538	#433	C₂²×C₅	1	2	yes	complemented
539	#433	C₂²×C₅	1	2	yes	complemented
540	#433	C₂²×C₅	1	1	yes	characteristic, complemented
541	#433	C₂²×C₅	1	1	yes	characteristic, complemented
542	#433	C₂²×C₅	1	2	yes	complemented
543	#432	C₂²×C₅	1	1	yes	characteristic
544	#432	C₂²×C₅	1	2	yes	complemented
545	#432	C₂²×C₅	1	2	yes	complemented
546	#432	C₂²×C₅	1	1	yes	characteristic, complemented
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, complemented
551	#431	C₂²×C₅	1	1	yes	characteristic, complemented
552	#431	C₂²×C₅	1	2	yes	complemented
553	#431	C₂²×C₅	1	2	yes	complemented
554	#431	C₂²×C₅	1	1	yes	characteristic, complemented
555	#424	C₂²×C₅	1	1	yes	characteristic, complemented
556	#424	C₂²×C₅	1	1	yes	characteristic, complemented
557	#424	C₂²×C₅	1	2	yes	complemented
558	#424	C₂²×C₅	1	2	yes	complemented
559	#423	C₂²×C₅	1	2	yes	complemented
560	#423	C₂²×C₅	1	2	yes	complemented
561	#423	C₂²×C₅	1	1	yes	characteristic, complemented
562	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
563	#408	C₂²×C₅	1	1	yes	characteristic
564	#408	C₂²×C₅	1	1	yes	characteristic
565	#408	C₂²×C₅	1	2	yes	—
566	#407	C₂²×C₅	1	2	yes	—
567	#407	C₂²×C₅	1	2	yes	—
568	#407	C₂²×C₅	1	2	yes	—
569	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
570	#405	C₂²×C₅	1	2	yes	complemented
571	#405	C₂²×C₅	1	2	yes	complemented
572	#405	C₂²×C₅	1	2	yes	complemented
573	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
574	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
575	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
576	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
577	C₂³×C₅	—	4	2	no	—
578	C₂³×C₅	—	4	2	no	—
579	C₂³×C₅	—	4	2	no	—
580	C₂³×C₅	C₂³×C₄	1	2	yes	—
581	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
582	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
583	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
584	C₂³×C₅	C₂³×C₄	1	2	yes	—
585	C₅×Q₈	—	2	2	no	—
586	C₅×Q₈	—	2	2	no	—
587	C₅×Q₈	—	4	2	no	—
588	C₅×Q₈	—	4	1	no	—
589	C₅×D₄	—	2	2	no	—
590	C₅×D₄	—	2	2	no	—
591	C₅×D₄	—	4	2	no	—
592	C₅×D₄	—	4	2	no	—
593	C₅×D₄	—	4	2	no	—
594	C₅×D₄	—	4	1	no	—
595	C₅×D₄	—	4	1	no	—
596	C₅×D₄	—	4	1	no	—
597	C₅×D₄	—	4	2	no	—
598	C₅×D₄	—	4	2	no	—
599	C₂×C₄×C₅	—	2	2	no	—
600	C₂×C₄×C₅	—	2	2	no	—
601	C₂×C₄×C₅	—	2	2	no	—
602	C₂×C₄×C₅	—	2	1	no	—
603	C₂×C₄×C₅	—	2	2	no	—
604	C₂×C₄×C₅	—	2	2	no	—
605	C₂×C₄×C₅	—	2	1	no	—
606	C₂×C₄×C₅	—	2	1	no	—
607	C₂×C₄×C₅	—	2	2	no	—
608	C₂×C₄×C₅	—	2	2	no	—
609	C₂×C₄×C₅	—	2	1	no	—
610	C₂×C₄×C₅	—	2	1	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	4	2	no	—
613	C₂×C₄×C₅	—	4	2	no	—
614	C₂×C₄×C₅	—	4	2	no	—
615	C₂×C₄×C₅	—	4	1	no	—
616	C₂×C₄×C₅	—	4	1	no	—
617	C₂×C₄×C₅	—	4	2	no	—
618	C₂×C₄×C₅	—	4	2	no	—
619	C₂×C₄×C₅	—	4	1	no	—
620	C₂×C₄×C₅	—	4	2	no	—
621	C₂×C₄×C₅	—	4	2	no	—
622	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
630	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
631	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
632	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
633	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
634	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
635	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
636	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
637	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
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	2	no	—
645	C₅×C₈	—	2	2	no	—
646	C₅×C₈	—	2	1	no	—
647	C₅×C₈	—	2	1	no	—
648	C₅×C₈	—	2	1	no	—
649	C₅×C₈	—	2	1	no	—
650	C₅×C₈	—	2	1	no	—
651	C₅×C₈	—	2	2	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	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₅	1	2	yes	—
657	C₂×M₁₆	C₂³×C₅	1	2	yes	—
658	C₂×M₁₆	C₂³×C₅	1	2	yes	—
659	C₂×M₁₆	C₂³×C₅	1	2	yes	—
660	C₂×M₁₆	C₂³×C₅	1	2	yes	—
661	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
662	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
663	C₂×M₁₆	C₂³×C₅	1	2	yes	—
664	C₂×M₁₆	C₂³×C₅	1	2	yes	—
665	C₂×M₁₆	C₂³×C₅	1	2	yes	—
666	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
667	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
673	#126	C₂×C₄×C₅	1	2	yes	—
674	#126	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	#125	C₂×C₄×C₅	1	2	yes	—
680	#125	C₂×C₄×C₅	1	2	yes	—
681	#125	C₂×C₄×C₅	1	1	yes	characteristic
682	#125	C₂×C₄×C₅	1	1	yes	characteristic
683	#125	C₂×C₄×C₅	1	2	yes	—
684	#124	C₂×C₄×C₅	1	1	yes	characteristic
685	#124	C₂×C₄×C₅	1	1	yes	characteristic
686	#124	C₂×C₄×C₅	1	2	yes	—
687	#124	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	#123	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	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
697	C₂²⋊Q₈	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	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
703	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
704	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
705	#121	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	2	yes	—
709	#121	C₂×C₄×C₅	1	1	yes	characteristic
710	#121	C₂×C₄×C₅	1	1	yes	characteristic
711	#120	C₂×C₄×C₅	1	2	yes	—
712	#120	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	1	yes	characteristic
716	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
717	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₅	1	2	yes	—
720	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
721	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
722	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
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	1	yes	characteristic
726	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
727	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
728	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
732	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
733	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₅	1	2	yes	—
736	C₄×D₄	C₂³×C₅	1	2	yes	—
737	C₄×D₄	C₂³×C₅	1	2	yes	—
738	C₄×D₄	C₂³×C₅	1	2	yes	—
739	C₄×D₄	C₂³×C₅	1	2	yes	—
740	#117	C₂×C₄×C₅	1	2	yes	—
741	#117	C₂×C₄×C₅	1	2	yes	—
742	#117	C₂×C₄×C₅	1	2	yes	—
743	#117	C₂×C₄×C₅	1	2	yes	—
744	#117	C₂×C₄×C₅	1	2	yes	—
745	#117	C₂×C₄×C₅	1	2	yes	—
746	#117	C₂×C₄×C₅	1	1	yes	characteristic
747	#117	C₂×C₄×C₅	1	1	yes	characteristic
748	#117	C₂³×C₅	1	1	yes	characteristic
749	#117	C₂³×C₅	1	2	yes	—
750	#117	C₂³×C₅	1	2	yes	—
751	#117	C₂³×C₅	1	2	yes	—
752	#117	C₂³×C₅	1	1	yes	characteristic
753	#117	C₂³×C₅	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
755	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
756	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
760	C₂×C₄²	C₂³×C₅	1	2	yes	—
761	C₂×C₄²	C₂³×C₅	1	2	yes	—
762	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
765	C₄⋊C₈	C₂³×C₅	1	2	yes	—
766	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
767	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
768	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
769	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
770	C₄⋊C₈	C₂³×C₅	1	2	yes	—
771	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
772	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
773	C₄⋊C₈	C₂³×C₅	1	2	yes	—
774	C₄⋊C₈	C₂³×C₅	1	2	yes	—
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	2	yes	—
789	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
792	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
793	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
794	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
795	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
796	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
798	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
799	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
800	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
801	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
802	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
803	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
805	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
810	#97	C₂³×C₅	1	2	yes	—
811	#97	C₂³×C₅	1	2	yes	—
812	#97	C₂³×C₅	1	2	yes	—
813	#97	C₂³×C₅	1	2	yes	—
814	#97	C₂³×C₅	1	2	yes	—
815	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
816	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
817	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
818	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
819	C₄×C₈	C₂³×C₅	1	2	yes	—
820	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
821	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
822	C₄×C₈	C₂³×C₅	1	2	yes	—
823	C₄×C₈	C₂³×C₅	1	2	yes	—
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	2	no	—
829	C₂²×C₅	—	2	2	no	—
830	C₂²×C₅	—	2	1	no	—
831	C₂²×C₅	—	2	1	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	2	no	—
838	C₂²×C₅	—	2	1	no	—
839	C₂²×C₅	—	2	1	no	—
840	C₂²×C₅	—	2	1	no	—
841	C₂²×C₅	—	2	2	no	—
842	C₂²×C₅	—	8	4	no	—
843	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
844	C₄×C₅	—	2	1	no	—
845	C₄×C₅	—	2	2	no	—
846	C₄×C₅	—	2	2	no	—
847	C₄×C₅	—	2	1	no	—
848	C₄×C₅	—	2	1	no	—
849	C₄×C₅	—	2	1	no	—
850	C₄×C₅	—	2	1	no	—
851	C₄×C₅	—	2	1	no	—
852	C₄×C₅	—	2	2	no	—
853	C₄×C₅	—	2	2	no	—
854	C₄×C₅	—	2	1	no	—
855	C₄×C₅	—	2	1	no	—
856	C₄×C₅	—	2	1	no	—
857	C₄×C₅	—	2	2	no	—
858	C₄×C₅	—	2	2	no	—
859	C₄×C₅	—	2	1	no	—
860	C₄×C₅	#568	1	2	yes	—
861	C₄×C₅	#585	1	1	yes	characteristic
862	C₄×C₅	#585	1	1	yes	characteristic
863	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
864	#41	—	4	1	no	—
865	#41	—	4	1	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
881	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
882	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
886	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
890	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
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	1	yes	characteristic
894	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
895	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
896	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
897	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
900	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
903	M₁₆	—	4	1	no	—
904	M₁₆	—	4	2	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	M₁₆	—	4	2	no	—
908	M₁₆	—	4	2	no	—
909	M₁₆	—	4	2	no	—
910	M₁₆	—	4	1	no	—
911	M₁₆	—	4	2	no	—
912	C₂×C₈	—	4	2	no	—
913	C₂×C₈	—	4	1	no	—
914	C₂×C₈	—	4	2	no	—
915	C₂×C₈	—	4	2	no	—
916	C₂×C₈	—	4	1	no	—
917	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
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	2	yes	—
922	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₅	1	2	yes	—
926	C₂×C₈	C₂⁴×C₅	1	2	yes	—
927	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₅	1	2	yes	—
929	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
930	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
939	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
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	2	yes	—
943	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
944	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
946	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
947	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
948	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
956	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
961	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
962	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
963	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
965	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
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	1	yes	characteristic
972	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
973	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
974	C₂²⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
975	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
976	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
977	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
978	C₂²⋊C₄	C₂²×C₄×C₅	1	2	yes	—
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	2	yes	—
983	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
984	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
985	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
986	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
987	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
988	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
989	C₄²	C₂⁴×C₅	1	1	yes	characteristic
990	C₄²	C₂⁴×C₅	1	1	yes	characteristic
991	C₄²	C₂⁴×C₅	1	1	yes	characteristic
992	C₄²	C₂⁴×C₅	1	2	yes	—
993	C₄²	C₂⁴×C₅	1	2	yes	—
994	C₄²	C₂⁴×C₅	1	1	yes	characteristic
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	—	4	1	no	—
1000	C₂×C₅	#3428	1	1	yes	characteristic
1001	C₂×C₅	C₂×#568	1	1	yes	characteristic
1002	C₂×C₅	#3573	1	1	yes	characteristic
1003	C₂³	—	4	2	no	—
1004	C₂³	—	4	2	no	—
1005	C₂³	—	4	2	no	—
1006	C₂³	C₂³×C₄×C₅	1	2	yes	—
1007	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
1008	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
1009	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
1010	C₂³	C₂³×C₄×C₅	1	2	yes	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	4	1	no	—
1014	Q₈	—	4	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	1	no	—
1019	D₄	—	4	1	no	—
1020	D₄	—	4	1	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	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	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	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
1055	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1056	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
1064	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1065	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	2	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₅	#60300	1	1	yes	characteristic, direct product factor, Sylow
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	8	4	no	—
1095	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	C₅×#568	1	2	yes	—
1113	C₄	C₅×#585	1	1	yes	characteristic
1114	C₄	C₅×#585	1	1	yes	characteristic
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	1	no	—
1120	C₂	C₅×#3428	1	1	yes	characteristic
1121	C₂	C₂×C₅×#568	1	1	yes	characteristic
1122	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×#3475	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×#2993	C₂	semidirect
6. C₅×#2991	C₂	semidirect
7. C₅×#2989	C₂	semidirect
8. C₅×#2986	C₂	semidirect
9. C₅×#2985	C₂	semidirect
10. C₅×#2978	C₂	semidirect
11. C₅×#2976	C₂	semidirect
12. C₅×#2975	C₂	semidirect
13. C₅×#2974	C₂	semidirect
14. C₅×#2971	C₂	semidirect
15. C₅×#2969	C₂	semidirect
16. C₅×#2969	C₂	semidirect
17. C₅×#2967	C₂	semidirect
18. C₅×#2966	C₂	semidirect
19. C₅×#2965	C₂	semidirect
20. C₅×#2925	C₂	semidirect
21. C₅×#2924	C₂	semidirect
22. C₅×#2922	C₂	semidirect
23. C₅×#2921	C₂	semidirect
47. C₅×#446	C₂²	semidirect
48. C₅×#446	C₂²	semidirect
49. C₅×#446	C₂²	semidirect
50. C₅×#446	C₂²	semidirect
51. C₅×#446	C₂²	semidirect
52. C₅×#446	C₂²	semidirect
53. C₅×#446	C₂²	semidirect
54. C₅×C₈×Q₈	C₂²	semidirect
55. C₅×C₈×Q₈	C₂²	semidirect
56. C₅×C₈×Q₈	C₂²	semidirect
57. C₅×C₈×Q₈	C₂²	semidirect
58. C₅×C₈×Q₈	C₂²	semidirect
67. C₅×#436	C₂²	semidirect
68. C₅×#436	C₂²	semidirect
69. C₅×#436	C₂²	semidirect
70. C₅×#436	C₂²	semidirect
71. C₅×#436	C₂²	semidirect
72. C₅×#436	C₂²	semidirect
75. C₅×#435	C₂²	semidirect
76. C₅×#435	C₂²	semidirect
77. C₅×#435	C₂²	semidirect
78. C₅×#435	C₂²	semidirect
79. C₅×#435	C₂²	semidirect
80. C₅×#435	C₂²	semidirect
81. C₅×#435	C₂²	semidirect
82. C₅×#435	C₂²	semidirect
85. C₅×C₈×D₄	C₂²	semidirect
86. C₅×C₈×D₄	C₂²	semidirect
94. C₅×#433	C₂²	semidirect
95. C₅×#433	C₂²	semidirect
96. C₅×#433	C₂²	semidirect
97. C₅×#433	C₂²	semidirect
98. C₅×#433	C₂²	semidirect
99. C₅×#433	C₂²	semidirect
100. C₅×#433	C₂²	semidirect
102. C₅×#432	C₂²	semidirect
103. C₅×#432	C₂²	semidirect
104. C₅×#432	C₂²	semidirect
108. C₅×#431	C₂²	semidirect
109. C₅×#431	C₂²	semidirect
110. C₅×#431	C₂²	semidirect
111. C₅×#431	C₂²	semidirect
112. C₅×#431	C₂²	semidirect
113. C₅×#424	C₂²	semidirect
114. C₅×#424	C₂²	semidirect
115. C₅×#424	C₂²	semidirect
116. C₅×#424	C₂²	semidirect
117. C₅×#423	C₂²	semidirect
118. C₅×#423	C₂²	semidirect
119. C₅×#423	C₂²	semidirect
120. C₂×C₅×C₄⋊C₈	C₂²	semidirect
128. C₅×#405	C₂²	semidirect
129. C₅×#405	C₂²	semidirect
130. C₅×#405	C₂²	semidirect
131. C₄×C₅×M₁₆	C₂²	semidirect
132. C₄×C₅×M₁₆	C₂²	semidirect
133. C₄×C₅×M₁₆	C₂²	semidirect
134. C₂×C₄×C₅×C₈	C₂²	semidirect
135. #60300	C₅	direct (N × H)
312. #2995	C₂×C₅	semidirect
313. #2994	C₂×C₅	semidirect
314. #2993	C₂×C₅	semidirect
315. #2993	C₂×C₅	semidirect
316. #2991	C₂×C₅	semidirect
317. #2989	C₂×C₅	semidirect
318. #2986	C₂×C₅	semidirect
319. #2985	C₂×C₅	semidirect
320. #2978	C₂×C₅	semidirect
321. #2976	C₂×C₅	semidirect
322. #2975	C₂×C₅	semidirect
323. #2974	C₂×C₅	semidirect
324. #2971	C₂×C₅	semidirect
325. #2969	C₂×C₅	semidirect
326. #2969	C₂×C₅	semidirect
327. #2967	C₂×C₅	semidirect
328. #2966	C₂×C₅	semidirect
329. #2965	C₂×C₅	semidirect
330. #2925	C₂×C₅	semidirect
331. #2924	C₂×C₅	semidirect
332. #2922	C₂×C₅	semidirect
333. #2921	C₂×C₅	semidirect
489. #446	C₂²×C₅	semidirect
490. #446	C₂²×C₅	semidirect
491. #446	C₂²×C₅	semidirect
492. #446	C₂²×C₅	semidirect
493. #446	C₂²×C₅	semidirect
494. #446	C₂²×C₅	semidirect
495. #446	C₂²×C₅	semidirect
496. C₈×Q₈	C₂²×C₅	semidirect
497. C₈×Q₈	C₂²×C₅	semidirect
498. C₈×Q₈	C₂²×C₅	semidirect
499. C₈×Q₈	C₂²×C₅	semidirect
500. C₈×Q₈	C₂²×C₅	semidirect
509. #436	C₂²×C₅	semidirect
510. #436	C₂²×C₅	semidirect
511. #436	C₂²×C₅	semidirect
512. #436	C₂²×C₅	semidirect
513. #436	C₂²×C₅	semidirect
514. #436	C₂²×C₅	semidirect
517. #435	C₂²×C₅	semidirect
518. #435	C₂²×C₅	semidirect
519. #435	C₂²×C₅	semidirect
520. #435	C₂²×C₅	semidirect
521. #435	C₂²×C₅	semidirect
522. #435	C₂²×C₅	semidirect
523. #435	C₂²×C₅	semidirect
524. #435	C₂²×C₅	semidirect
527. C₈×D₄	C₂²×C₅	semidirect
528. C₈×D₄	C₂²×C₅	semidirect
536. #433	C₂²×C₅	semidirect
537. #433	C₂²×C₅	semidirect
538. #433	C₂²×C₅	semidirect
539. #433	C₂²×C₅	semidirect
540. #433	C₂²×C₅	semidirect
541. #433	C₂²×C₅	semidirect
542. #433	C₂²×C₅	semidirect
544. #432	C₂²×C₅	semidirect
545. #432	C₂²×C₅	semidirect
546. #432	C₂²×C₅	semidirect
550. #431	C₂²×C₅	semidirect
551. #431	C₂²×C₅	semidirect
552. #431	C₂²×C₅	semidirect
553. #431	C₂²×C₅	semidirect
554. #431	C₂²×C₅	semidirect
555. #424	C₂²×C₅	semidirect
556. #424	C₂²×C₅	semidirect
557. #424	C₂²×C₅	semidirect
558. #424	C₂²×C₅	semidirect
559. #423	C₂²×C₅	semidirect
560. #423	C₂²×C₅	semidirect
561. #423	C₂²×C₅	semidirect
562. C₂×C₄⋊C₈	C₂²×C₅	semidirect
570. #405	C₂²×C₅	semidirect
571. #405	C₂²×C₅	semidirect
572. #405	C₂²×C₅	semidirect
573. C₄×M₁₆	C₂²×C₅	semidirect
574. C₄×M₁₆	C₂²×C₅	semidirect
575. C₄×M₁₆	C₂²×C₅	semidirect
576. C₂×C₄×C₈	C₂²×C₅	semidirect
1078. C₅	#60300	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×#3475	2
C₅×#2995	2
C₅×#2994	2
C₅×#2993	2
C₅×#2991	2
C₅×#2989	2
C₅×#2986	2
C₅×#2985	2
C₅×#2978	2
C₅×#2976	2
C₅×#2975	2
C₅×#2974	2
C₅×#2971	2
C₅×#2969	2
C₅×#2967	2
C₅×#2966	2
C₅×#2965	2
C₅×#2925	2
C₅×#2924	2
C₅×#2922	2
C₅×#2921	2
#60300	5

Subgroups — C5×#60300 #11983020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60300 #11983020