Subgroups — C₅×#60601 #11983321

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3123	C₂	1	2	yes	maximal, complemented
4	C₅×#3122	C₂	1	2	yes	maximal, complemented
5	C₅×#3120	C₂	1	2	yes	maximal, complemented
6	C₅×#3119	C₂	1	2	yes	maximal, complemented
7	C₅×#3114	C₂	1	2	yes	maximal, complemented
8	C₅×#3111	C₂	1	2	yes	maximal, complemented
9	C₅×#3105	C₂	1	2	yes	maximal, complemented
10	C₅×#3102	C₂	1	2	yes	maximal, complemented
11	C₅×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#3036	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#3012	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2946	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₅×#135	C₂²	1	1	yes	characteristic
28	C₂×C₅×#135	C₂²	1	1	yes	characteristic
29	C₅×#553	—	2	2	no	—
30	C₅×#553	—	2	2	no	—
31	C₅×#553	—	2	1	no	—
32	C₅×#553	—	2	1	no	—
33	C₅×#552	—	2	1	no	—
34	C₅×#552	—	2	1	no	—
35	C₅×#541	C₂²	1	2	yes	complemented
36	C₅×#540	C₂²	1	2	yes	complemented
37	C₅×#537	C₂²	1	1	yes	characteristic
38	C₅×#537	C₂²	1	1	yes	characteristic
39	C₅×#532	C₂²	1	1	yes	characteristic, complemented
40	C₅×#529	C₂²	1	2	yes	complemented
41	C₅×#529	C₂²	1	2	yes	complemented
42	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
43	C₅×#520	—	2	1	no	—
44	C₅×#520	C₂²	1	2	yes	—
45	C₅×#520	C₂²	1	1	yes	characteristic
46	C₅×#520	C₂²	1	1	yes	characteristic
47	C₅×#520	C₂²	1	1	yes	characteristic, complemented
48	C₅×#520	C₂²	1	1	yes	characteristic, complemented
49	C₅×#518	—	2	2	no	—
50	C₅×#518	—	2	1	no	—
51	C₅×#518	C₂²	1	2	yes	—
52	C₅×#518	C₂²	1	1	yes	characteristic
53	C₄×C₅×#41	—	2	1	no	—
54	C₄×C₅×#41	C₂²	1	1	yes	characteristic
55	C₄×C₅×#41	C₂²	1	2	yes	—
56	C₄×C₅×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₅×D₄	—	2	2	no	—
58	C₂×C₄×C₅×D₄	—	2	1	no	—
59	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
61	C₅×#485	C₂²	1	2	yes	complemented
62	C₅×#485	C₂²	1	2	yes	complemented
63	C₅×#484	C₂²	1	2	yes	complemented
64	C₅×#483	C₂²	1	2	yes	complemented
65	C₅×#482	C₂²	1	2	yes	complemented
66	C₅×#482	C₂²	1	2	yes	complemented
67	C₅×#481	C₂²	1	2	yes	complemented
68	C₅×#480	C₂²	1	2	yes	complemented
69	C₅×#479	C₂²	1	2	yes	complemented
70	C₅×#479	C₂²	1	2	yes	complemented
71	C₅×#478	C₂²	1	2	yes	complemented
72	C₅×#478	C₂²	1	2	yes	complemented
73	C₅×#478	C₂²	1	2	yes	complemented
74	C₅×#478	C₂²	1	2	yes	complemented
75	C₅×#478	C₂²	1	2	yes	complemented
76	C₅×#478	C₂²	1	2	yes	complemented
77	C₅×#464	C₂²	1	1	yes	characteristic, complemented
78	C₅×#464	C₂²	1	1	yes	characteristic, complemented
79	C₅×#463	C₂²	1	1	yes	characteristic, complemented
80	C₅×#463	C₂²	1	1	yes	characteristic, complemented
81	C₅×#463	C₂²	1	2	yes	complemented
82	C₅×#463	C₂²	1	2	yes	complemented
83	C₅×#462	C₂²	1	1	yes	characteristic, complemented
84	C₅×#461	C₂²	1	1	yes	characteristic, complemented
85	C₅×#461	C₂²	1	2	yes	complemented
86	C₅×#460	C₂²	1	1	yes	characteristic, complemented
87	C₅×#459	C₂²	1	1	yes	characteristic, complemented
88	C₅×#459	C₂²	1	2	yes	complemented
89	C₅×#452	C₂²	1	2	yes	—
90	C₅×#452	C₂²	1	2	yes	—
91	C₅×#450	C₂²	1	2	yes	—
92	C₅×#450	C₂²	1	2	yes	—
93	C₅×#449	C₂²	1	2	yes	—
94	C₅×#449	C₂²	1	2	yes	—
95	C₅×#447	C₂²	1	2	yes	—
96	C₅×#447	C₂²	1	2	yes	—
97	C₅×#442	C₂²	1	2	yes	complemented
98	C₅×#442	C₂²	1	2	yes	complemented
99	C₅×#442	C₂²	1	2	yes	complemented
100	C₅×#441	C₂²	1	2	yes	complemented
101	C₅×#440	C₂²	1	2	yes	complemented
102	C₅×#440	C₂²	1	2	yes	complemented
103	C₅×#440	C₂²	1	2	yes	complemented
104	C₅×#440	C₂²	1	2	yes	complemented
105	C₄×C₅×Q₁₆	C₂²	1	2	yes	complemented
106	C₄×C₅×SD₁₆	C₂²	1	2	yes	complemented
107	C₄×C₅×SD₁₆	C₂²	1	2	yes	complemented
108	C₄×C₅×SD₁₆	C₂²	1	2	yes	complemented
109	C₄×C₅×SD₁₆	C₂²	1	2	yes	complemented
110	C₄×C₅×D₈	C₂²	1	2	yes	complemented
111	C₄×C₅×D₈	C₂²	1	2	yes	complemented
112	C₄×C₅×D₈	C₂²	1	2	yes	complemented
113	C₅×#433	C₂²	1	2	yes	complemented
114	C₅×#433	C₂²	1	2	yes	complemented
115	C₅×#432	C₂²	1	2	yes	complemented
116	C₅×#431	C₂²	1	2	yes	complemented
117	C₅×#428	C₂²	1	1	yes	characteristic, complemented
118	C₅×#428	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₅×#106	C₂²	1	1	yes	characteristic, complemented
121	C₅×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₅×#417	C₂²	1	1	yes	characteristic
124	C₅×#417	C₂²	1	1	yes	characteristic
125	C₅×#417	C₂²	1	1	yes	characteristic, complemented
126	C₅×#417	C₂²	1	1	yes	characteristic, complemented
127	C₅×#416	C₂²	1	1	yes	characteristic, complemented
128	C₅×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₅×#102	C₂²	1	1	yes	characteristic
130	C₂×C₅×#102	C₂²	1	1	yes	characteristic
131	C₅×#408	C₂²	1	1	yes	characteristic
132	C₅×#408	C₂²	1	1	yes	characteristic
133	C₅×#405	C₂²	1	1	yes	characteristic, complemented
134	C₅×#405	C₂²	1	1	yes	characteristic, complemented
135	#60601	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₅×H(5,𝔽₂)	—	2	4	no	—
137	C₅×H(5,𝔽₂)	—	2	4	no	—
138	C₂×C₅×#41	—	2	1	no	—
139	C₂×C₅×#41	C₂³	1	1	yes	characteristic
140	C₂×C₅×#41	C₂³	1	1	yes	characteristic
141	C₂×C₅×#41	C₂³	1	2	yes	—
142	C₂×C₅×#41	C₂³	1	1	yes	characteristic
143	C₂×C₅×#41	C₂³	1	1	yes	characteristic
144	C₂²×C₅×D₄	—	2	2	no	—
145	C₂²×C₅×D₄	—	2	1	no	—
146	C₂²×C₅×D₄	C₂³	1	2	yes	—
147	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₅	—	2	1	no	—
149	C₂³×C₄×C₅	—	2	2	no	—
150	C₅×AGL(1,ℤ/8)	—	2	4	no	—
151	C₅×AGL(1,ℤ/8)	—	2	4	no	—
152	C₅×#135	—	2	4	no	—
153	C₅×#135	—	2	4	no	—
154	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₅×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
163	C₂×C₅×D₈	C₂³	1	2	yes	—
164	C₂×C₅×D₈	C₂³	1	2	yes	—
165	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
166	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
168	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
169	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₅×#127	C₂³	1	1	yes	characteristic
172	C₅×#126	—	2	2	no	—
173	C₅×#126	—	2	2	no	—
174	C₅×#126	—	2	2	no	—
175	C₅×#126	—	2	2	no	—
176	C₅×#125	—	2	2	no	—
177	C₅×#125	—	2	2	no	—
178	C₅×#125	—	2	1	no	—
179	C₅×#125	—	2	1	no	—
180	C₅×#125	C₂³	1	2	yes	—
181	C₅×#125	C₂³	1	2	yes	—
182	C₅×#124	C₂³	1	1	yes	characteristic
183	C₅×#124	C₂³	1	1	yes	characteristic
184	C₅×#123	—	2	2	no	—
185	C₅×#123	—	2	2	no	—
186	C₅×#123	—	2	2	no	—
187	C₅×#123	—	2	2	no	—
188	C₅×C₂²⋊Q₈	—	2	1	no	—
189	C₅×C₂²⋊Q₈	—	2	1	no	—
190	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₅×#121	—	2	1	no	—
193	C₅×#121	—	2	1	no	—
194	C₅×#121	—	2	2	no	—
195	C₅×#121	—	2	2	no	—
196	C₅×#121	—	2	1	no	—
197	C₅×#121	—	2	1	no	—
198	C₅×#121	—	2	2	no	—
199	C₅×#121	—	2	2	no	—
200	C₅×#121	C₂³	1	2	yes	—
201	C₅×#121	C₂³	1	2	yes	—
202	C₄×C₅×Q₈	—	2	1	no	—
203	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
204	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
205	C₄×C₅×Q₈	C₂³	1	2	yes	—
206	C₄×C₅×Q₈	C₂³	1	2	yes	—
207	C₄×C₅×Q₈	C₂³	1	2	yes	—
208	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
209	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
210	C₄×C₅×D₄	—	2	2	no	—
211	C₄×C₅×D₄	—	2	1	no	—
212	C₄×C₅×D₄	—	2	1	no	—
213	C₄×C₅×D₄	—	2	2	no	—
214	C₄×C₅×D₄	—	2	1	no	—
215	C₄×C₅×D₄	—	2	2	no	—
216	C₄×C₅×D₄	—	2	2	no	—
217	C₄×C₅×D₄	—	2	2	no	—
218	C₄×C₅×D₄	—	2	1	no	—
219	C₄×C₅×D₄	—	2	2	no	—
220	C₄×C₅×D₄	—	2	1	no	—
221	C₄×C₅×D₄	—	2	2	no	—
222	C₄×C₅×D₄	—	2	2	no	—
223	C₄×C₅×D₄	—	2	2	no	—
224	C₄×C₅×D₄	—	2	2	no	—
225	C₄×C₅×D₄	—	2	2	no	—
226	C₄×C₅×D₄	—	2	2	no	—
227	C₄×C₅×D₄	—	2	2	no	—
228	C₄×C₅×D₄	—	2	1	no	—
229	C₄×C₅×D₄	—	2	2	no	—
230	C₄×C₅×D₄	—	2	1	no	—
231	C₄×C₅×D₄	—	2	1	no	—
232	C₄×C₅×D₄	—	2	1	no	—
233	C₄×C₅×D₄	D₄	1	2	yes	—
234	C₄×C₅×D₄	D₄	1	1	yes	characteristic
235	C₄×C₅×D₄	D₄	1	2	yes	—
236	C₄×C₅×D₄	D₄	1	1	yes	characteristic
237	C₄×C₅×D₄	C₂³	1	2	yes	—
238	C₄×C₅×D₄	C₂³	1	2	yes	—
239	C₄×C₅×D₄	C₂³	1	2	yes	—
240	C₄×C₅×D₄	C₂³	1	2	yes	—
241	C₄×C₅×D₄	C₂³	1	2	yes	—
242	C₄×C₅×D₄	C₂³	1	2	yes	—
243	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
244	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₅×D₄	C₂³	1	2	yes	—
246	C₅×#117	—	2	1	no	—
247	C₅×#117	—	2	2	no	—
248	C₅×#117	—	2	1	no	—
249	C₅×#117	—	2	1	no	—
250	C₅×#117	—	2	2	no	—
251	C₅×#117	—	2	1	no	—
252	C₅×#117	—	2	2	no	—
253	C₅×#117	—	2	2	no	—
254	C₅×#117	C₂³	1	1	yes	characteristic
255	C₅×#117	C₂³	1	2	yes	—
256	C₅×#117	C₂³	1	1	yes	characteristic
257	C₅×#117	C₂³	1	2	yes	—
258	C₂×C₅×C₄⋊C₄	—	2	1	no	—
259	C₂×C₅×C₄⋊C₄	—	2	1	no	—
260	C₂×C₅×C₄⋊C₄	—	2	1	no	—
261	C₂×C₅×C₄⋊C₄	—	2	2	no	—
262	C₂×C₅×C₄⋊C₄	—	2	1	no	—
263	C₂×C₅×C₄⋊C₄	—	2	1	no	—
264	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₅	—	2	2	no	—
274	C₂×C₄²×C₅	—	2	1	no	—
275	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₅	C₂³	1	2	yes	—
277	C₅×#107	C₂³	1	2	yes	—
278	C₅×#107	C₂³	1	2	yes	—
279	C₅×#107	C₂³	1	2	yes	—
280	C₅×#107	C₂³	1	2	yes	—
281	C₅×#106	C₂³	1	2	yes	—
282	C₅×#106	C₂³	1	2	yes	—
283	C₅×#106	C₂³	1	2	yes	—
284	C₅×#106	C₂³	1	2	yes	—
285	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₅×C₄⋊C₈	C₂³	1	2	yes	—
290	C₅×C₄⋊C₈	C₂³	1	2	yes	—
291	C₅×#103	C₂³	1	1	yes	characteristic
292	C₅×#103	C₂³	1	1	yes	characteristic
293	C₅×#103	C₂³	1	1	yes	characteristic
294	C₅×#103	C₂³	1	1	yes	characteristic
295	C₅×#103	C₂³	1	2	yes	—
296	C₅×#103	C₂³	1	2	yes	—
297	C₅×#103	C₂³	1	2	yes	—
298	C₅×#103	C₂³	1	2	yes	—
299	C₅×#102	C₂³	1	2	yes	—
300	C₅×#102	C₂³	1	2	yes	—
301	C₅×#102	C₂³	1	2	yes	—
302	C₅×#102	C₂³	1	2	yes	—
303	C₅×#102	C₂³	1	1	yes	characteristic
304	C₅×#102	C₂³	1	1	yes	characteristic
305	C₅×#102	C₂³	1	1	yes	characteristic
306	C₅×#102	C₂³	1	1	yes	characteristic
307	C₅×#102	C₂³	1	2	yes	—
308	C₅×#102	C₂³	1	2	yes	—
309	C₅×#102	C₂³	1	2	yes	—
310	C₅×#102	C₂³	1	2	yes	—
311	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₅×#97	C₂³	1	2	yes	—
316	C₅×#97	C₂³	1	2	yes	—
317	C₄×C₅×C₈	C₂³	1	2	yes	—
318	C₄×C₅×C₈	C₂³	1	2	yes	—
319	#3512	C₂×C₅	1	1	yes	characteristic, complemented
320	C₄×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
321	#3123	C₂×C₅	1	2	yes	complemented
322	#3122	C₂×C₅	1	2	yes	complemented
323	#3120	C₂×C₅	1	2	yes	complemented
324	#3119	C₂×C₅	1	2	yes	complemented
325	#3114	C₂×C₅	1	2	yes	complemented
326	#3111	C₂×C₅	1	2	yes	complemented
327	#3105	C₂×C₅	1	2	yes	complemented
328	#3102	C₂×C₅	1	2	yes	complemented
329	#3099	C₂×C₅	1	1	yes	characteristic, complemented
330	#3098	C₂×C₅	1	1	yes	characteristic, complemented
331	#3080	C₂×C₅	1	1	yes	characteristic, complemented
332	C₂×#478	C₂×C₅	1	1	yes	characteristic, complemented
333	#3036	C₂×C₅	1	1	yes	characteristic, complemented
334	#3035	C₂×C₅	1	1	yes	characteristic, complemented
335	#3012	C₂×C₅	1	1	yes	characteristic, complemented
336	#3012	C₂×C₅	1	1	yes	characteristic, complemented
337	#2952	C₂×C₅	1	1	yes	characteristic, complemented
338	#2951	C₂×C₅	1	1	yes	characteristic, complemented
339	#2946	C₂×C₅	1	1	yes	characteristic, complemented
340	#2946	C₂×C₅	1	1	yes	characteristic, complemented
341	#2925	C₂×C₅	1	1	yes	characteristic, complemented
342	C₂⁴×C₅	—	2	2	no	—
343	C₂⁴×C₅	—	2	1	no	—
344	C₅×#41	—	2	8	no	—
345	C₅×#41	—	2	4	no	—
346	C₅×#41	—	2	4	no	—
347	C₅×#41	—	2	2	no	—
348	C₅×#41	—	2	2	no	—
349	C₅×#41	—	2	2	no	—
350	C₅×#41	—	2	2	no	—
351	C₅×#41	—	2	2	no	—
352	C₅×#41	—	2	2	no	—
353	C₅×#41	—	2	2	no	—
354	C₅×#41	#41	1	4	yes	—
355	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
356	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₅×D₄	—	2	16	no	—
360	C₂×C₅×D₄	—	2	8	no	—
361	C₂×C₅×D₄	—	2	2	no	—
362	C₂×C₅×D₄	—	2	1	no	—
363	C₂×C₅×D₄	—	2	4	no	—
364	C₂×C₅×D₄	—	2	4	no	—
365	C₂×C₅×D₄	—	2	1	no	—
366	C₂×C₅×D₄	—	2	1	no	—
367	C₂×C₅×D₄	—	2	2	no	—
368	C₂×C₅×D₄	—	2	2	no	—
369	C₂×C₅×D₄	—	2	2	no	—
370	C₂×C₅×D₄	—	2	1	no	—
371	C₂×C₅×D₄	—	2	1	no	—
372	C₂×C₅×D₄	—	2	1	no	—
373	C₂×C₅×D₄	—	2	2	no	—
374	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
375	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂×C₅×D₄	#41	1	4	yes	—
377	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₅×D₄	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₅	—	2	2	no	—
382	C₂²×C₄×C₅	—	2	1	no	—
383	C₂²×C₄×C₅	—	2	2	no	—
384	C₂²×C₄×C₅	—	2	1	no	—
385	C₂²×C₄×C₅	—	2	1	no	—
386	C₂²×C₄×C₅	—	2	1	no	—
387	C₂²×C₄×C₅	—	2	2	no	—
388	C₂²×C₄×C₅	—	2	1	no	—
389	C₂²×C₄×C₅	—	2	1	no	—
390	C₂²×C₄×C₅	—	2	1	no	—
391	C₂²×C₄×C₅	—	2	2	no	—
392	C₂²×C₄×C₅	—	2	1	no	—
393	C₂²×C₄×C₅	—	2	2	no	—
394	C₂²×C₄×C₅	—	2	2	no	—
395	C₂²×C₄×C₅	—	2	2	no	—
396	C₂²×C₄×C₅	—	2	2	no	—
397	C₂²×C₄×C₅	—	2	2	no	—
398	C₂²×C₄×C₅	—	8	4	no	—
399	C₂²×C₄×C₅	—	8	2	no	—
400	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
402	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
404	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
406	C₅×Q₁₆	—	2	2	no	—
407	C₅×Q₁₆	—	2	2	no	—
408	C₅×SD₁₆	—	2	2	no	—
409	C₅×SD₁₆	—	2	2	no	—
410	C₅×SD₁₆	—	2	2	no	—
411	C₅×SD₁₆	—	2	2	no	—
412	C₅×SD₁₆	—	2	4	no	—
413	C₅×SD₁₆	—	2	4	no	—
414	C₅×D₈	—	2	2	no	—
415	C₅×D₈	—	2	2	no	—
416	C₅×D₈	—	2	4	no	—
417	C₅×D₈	—	2	4	no	—
418	C₅×M₁₆	—	2	2	no	—
419	C₅×M₁₆	—	2	2	no	—
420	C₂×C₅×C₈	—	2	2	no	—
421	C₂×C₅×C₈	—	2	2	no	—
422	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
426	C₂×C₅×C₈	C₂⁴	1	2	yes	—
427	C₂×C₅×C₈	C₂⁴	1	2	yes	—
428	C₅×C₄⋊C₄	—	2	2	no	—
429	C₅×C₄⋊C₄	—	2	1	no	—
430	C₅×C₄⋊C₄	—	2	2	no	—
431	C₅×C₄⋊C₄	—	2	1	no	—
432	C₅×C₄⋊C₄	—	2	1	no	—
433	C₅×C₄⋊C₄	—	2	1	no	—
434	C₅×C₄⋊C₄	—	2	2	no	—
435	C₅×C₄⋊C₄	—	2	2	no	—
436	C₅×C₄⋊C₄	—	2	2	no	—
437	C₅×C₄⋊C₄	—	2	2	no	—
438	C₅×C₄⋊C₄	—	2	2	no	—
439	C₅×C₄⋊C₄	—	2	2	no	—
440	C₅×C₄⋊C₄	—	2	1	no	—
441	C₅×C₄⋊C₄	—	2	2	no	—
442	C₅×C₄⋊C₄	—	2	2	no	—
443	C₅×C₄⋊C₄	—	2	1	no	—
444	C₅×C₄⋊C₄	—	2	1	no	—
445	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
448	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
449	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
452	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
453	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₅×C₂²⋊C₄	—	2	2	no	—
455	C₅×C₂²⋊C₄	—	2	1	no	—
456	C₅×C₂²⋊C₄	—	2	2	no	—
457	C₅×C₂²⋊C₄	—	2	2	no	—
458	C₅×C₂²⋊C₄	—	2	2	no	—
459	C₅×C₂²⋊C₄	—	2	1	no	—
460	C₅×C₂²⋊C₄	—	2	2	no	—
461	C₅×C₂²⋊C₄	—	2	2	no	—
462	C₅×C₂²⋊C₄	—	2	2	no	—
463	C₅×C₂²⋊C₄	—	2	2	no	—
464	C₅×C₂²⋊C₄	—	2	1	no	—
465	C₅×C₂²⋊C₄	—	2	1	no	—
466	C₅×C₂²⋊C₄	—	2	1	no	—
467	C₅×C₂²⋊C₄	—	2	2	no	—
468	C₅×C₂²⋊C₄	—	2	2	no	—
469	C₅×C₂²⋊C₄	—	2	2	no	—
470	C₅×C₂²⋊C₄	—	2	2	no	—
471	C₅×C₂²⋊C₄	—	2	1	no	—
472	C₅×C₂²⋊C₄	—	2	1	no	—
473	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
474	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₄²×C₅	—	2	1	no	—
477	C₄²×C₅	—	2	2	no	—
478	C₄²×C₅	—	2	1	no	—
479	C₄²×C₅	—	2	2	no	—
480	C₄²×C₅	—	2	1	no	—
481	C₄²×C₅	—	2	2	no	—
482	C₄²×C₅	—	2	2	no	—
483	C₄²×C₅	C₂×D₄	1	2	yes	—
484	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₅	C₂×D₄	1	2	yes	—
486	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
487	C₄²×C₅	C₂⁴	1	1	yes	characteristic
488	C₄²×C₅	C₂⁴	1	2	yes	—
489	C₄²×C₅	C₂⁴	1	1	yes	characteristic
490	C₂×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic
491	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	1	yes	characteristic
492	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	1	yes	characteristic
493	C₂×#135	C₂²×C₅	1	1	yes	characteristic
494	C₂×#135	C₂²×C₅	1	1	yes	characteristic
495	#553	—	2	2	no	—
496	#553	—	2	2	no	—
497	#553	—	2	1	no	—
498	#553	—	2	1	no	—
499	#552	—	2	1	no	—
500	#552	—	2	1	no	—
501	#541	C₂²×C₅	1	2	yes	complemented
502	#540	C₂²×C₅	1	2	yes	complemented
503	#537	C₂²×C₅	1	1	yes	characteristic
504	#537	C₂²×C₅	1	1	yes	characteristic
505	#532	C₂²×C₅	1	1	yes	characteristic, complemented
506	#529	C₂²×C₅	1	2	yes	complemented
507	#529	C₂²×C₅	1	2	yes	complemented
508	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
509	#520	—	2	1	no	—
510	#520	C₂²×C₅	1	2	yes	—
511	#520	C₂²×C₅	1	1	yes	characteristic
512	#520	C₂²×C₅	1	1	yes	characteristic
513	#520	C₂²×C₅	1	1	yes	characteristic, complemented
514	#520	C₂²×C₅	1	1	yes	characteristic, complemented
515	#518	—	2	2	no	—
516	#518	—	2	1	no	—
517	#518	C₂²×C₅	1	2	yes	—
518	#518	C₂²×C₅	1	1	yes	characteristic
519	C₄×#41	—	2	1	no	—
520	C₄×#41	C₂²×C₅	1	1	yes	characteristic
521	C₄×#41	C₂²×C₅	1	2	yes	—
522	C₄×#41	C₂²×C₅	1	1	yes	characteristic
523	C₂×C₄×D₄	—	2	2	no	—
524	C₂×C₄×D₄	—	2	1	no	—
525	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
526	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
527	#485	C₂²×C₅	1	2	yes	complemented
528	#485	C₂²×C₅	1	2	yes	complemented
529	#484	C₂²×C₅	1	2	yes	complemented
530	#483	C₂²×C₅	1	2	yes	complemented
531	#482	C₂²×C₅	1	2	yes	complemented
532	#482	C₂²×C₅	1	2	yes	complemented
533	#481	C₂²×C₅	1	2	yes	complemented
534	#480	C₂²×C₅	1	2	yes	complemented
535	#479	C₂²×C₅	1	2	yes	complemented
536	#479	C₂²×C₅	1	2	yes	complemented
537	#478	C₂²×C₅	1	2	yes	complemented
538	#478	C₂²×C₅	1	2	yes	complemented
539	#478	C₂²×C₅	1	2	yes	complemented
540	#478	C₂²×C₅	1	2	yes	complemented
541	#478	C₂²×C₅	1	2	yes	complemented
542	#478	C₂²×C₅	1	2	yes	complemented
543	#464	C₂²×C₅	1	1	yes	characteristic, complemented
544	#464	C₂²×C₅	1	1	yes	characteristic, complemented
545	#463	C₂²×C₅	1	2	yes	complemented
546	#463	C₂²×C₅	1	1	yes	characteristic, complemented
547	#463	C₂²×C₅	1	2	yes	complemented
548	#463	C₂²×C₅	1	1	yes	characteristic, complemented
549	#462	C₂²×C₅	1	1	yes	characteristic, complemented
550	#461	C₂²×C₅	1	2	yes	complemented
551	#461	C₂²×C₅	1	1	yes	characteristic, complemented
552	#460	C₂²×C₅	1	1	yes	characteristic, complemented
553	#459	C₂²×C₅	1	2	yes	complemented
554	#459	C₂²×C₅	1	1	yes	characteristic, complemented
555	#452	C₂²×C₅	1	2	yes	—
556	#452	C₂²×C₅	1	2	yes	—
557	#450	C₂²×C₅	1	2	yes	—
558	#450	C₂²×C₅	1	2	yes	—
559	#449	C₂²×C₅	1	2	yes	—
560	#449	C₂²×C₅	1	2	yes	—
561	#447	C₂²×C₅	1	2	yes	—
562	#447	C₂²×C₅	1	2	yes	—
563	#442	C₂²×C₅	1	2	yes	complemented
564	#442	C₂²×C₅	1	2	yes	complemented
565	#442	C₂²×C₅	1	2	yes	complemented
566	#441	C₂²×C₅	1	2	yes	complemented
567	#440	C₂²×C₅	1	2	yes	complemented
568	#440	C₂²×C₅	1	2	yes	complemented
569	#440	C₂²×C₅	1	2	yes	complemented
570	#440	C₂²×C₅	1	2	yes	complemented
571	C₄×Q₁₆	C₂²×C₅	1	2	yes	complemented
572	C₄×SD₁₆	C₂²×C₅	1	2	yes	complemented
573	C₄×SD₁₆	C₂²×C₅	1	2	yes	complemented
574	C₄×SD₁₆	C₂²×C₅	1	2	yes	complemented
575	C₄×SD₁₆	C₂²×C₅	1	2	yes	complemented
576	C₄×D₈	C₂²×C₅	1	2	yes	complemented
577	C₄×D₈	C₂²×C₅	1	2	yes	complemented
578	C₄×D₈	C₂²×C₅	1	2	yes	complemented
579	#433	C₂²×C₅	1	2	yes	complemented
580	#433	C₂²×C₅	1	2	yes	complemented
581	#432	C₂²×C₅	1	2	yes	complemented
582	#431	C₂²×C₅	1	2	yes	complemented
583	#428	C₂²×C₅	1	1	yes	characteristic, complemented
584	#428	C₂²×C₅	1	1	yes	characteristic, complemented
585	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
586	C₂×#106	C₂²×C₅	1	1	yes	characteristic, complemented
587	#423	C₂²×C₅	1	1	yes	characteristic, complemented
588	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
589	#417	C₂²×C₅	1	1	yes	characteristic
590	#417	C₂²×C₅	1	1	yes	characteristic
591	#417	C₂²×C₅	1	1	yes	characteristic, complemented
592	#417	C₂²×C₅	1	1	yes	characteristic, complemented
593	#416	C₂²×C₅	1	1	yes	characteristic, complemented
594	#416	C₂²×C₅	1	1	yes	characteristic, complemented
595	C₂×#102	C₂²×C₅	1	1	yes	characteristic
596	C₂×#102	C₂²×C₅	1	1	yes	characteristic
597	#408	C₂²×C₅	1	1	yes	characteristic
598	#408	C₂²×C₅	1	1	yes	characteristic
599	#405	C₂²×C₅	1	1	yes	characteristic, complemented
600	#405	C₂²×C₅	1	1	yes	characteristic, complemented
601	C₂³×C₅	—	2	8	no	—
602	C₂³×C₅	—	2	2	no	—
603	C₂³×C₅	—	2	1	no	—
604	C₂³×C₅	—	2	4	no	—
605	C₂³×C₅	—	2	1	no	—
606	C₂³×C₅	—	2	1	no	—
607	C₂³×C₅	—	8	1	no	—
608	C₂³×C₅	—	8	2	no	—
609	C₂³×C₅	—	8	1	no	—
610	C₂³×C₅	—	8	2	no	—
611	C₂³×C₅	C₂²×D₄	1	2	yes	—
612	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
613	C₅×Q₈	—	2	2	no	—
614	C₅×Q₈	—	2	1	no	—
615	C₅×Q₈	—	2	1	no	—
616	C₅×Q₈	—	2	1	no	—
617	C₅×Q₈	—	2	1	no	—
618	C₅×Q₈	—	2	1	no	—
619	C₅×Q₈	C₂×#41	1	2	yes	—
620	C₅×D₄	—	2	8	no	—
621	C₅×D₄	—	2	8	no	—
622	C₅×D₄	—	2	4	no	—
623	C₅×D₄	—	2	4	no	—
624	C₅×D₄	—	2	2	no	—
625	C₅×D₄	—	2	4	no	—
626	C₅×D₄	—	2	2	no	—
627	C₅×D₄	—	2	1	no	—
628	C₅×D₄	—	2	1	no	—
629	C₅×D₄	—	2	1	no	—
630	C₅×D₄	—	2	1	no	—
631	C₅×D₄	—	2	1	no	—
632	C₅×D₄	—	4	2	no	—
633	C₅×D₄	—	4	2	no	—
634	C₅×D₄	—	8	1	no	—
635	C₅×D₄	—	8	1	no	—
636	C₅×D₄	—	8	2	no	—
637	C₅×D₄	—	8	2	no	—
638	C₅×D₄	C₂×#41	1	2	yes	—
639	C₅×D₄	C₂×#41	1	4	yes	—
640	C₂×C₄×C₅	—	2	8	no	—
641	C₂×C₄×C₅	—	2	1	no	—
642	C₂×C₄×C₅	—	2	4	no	—
643	C₂×C₄×C₅	—	2	2	no	—
644	C₂×C₄×C₅	—	2	2	no	—
645	C₂×C₄×C₅	—	2	1	no	—
646	C₂×C₄×C₅	—	2	1	no	—
647	C₂×C₄×C₅	—	2	1	no	—
648	C₂×C₄×C₅	—	2	2	no	—
649	C₂×C₄×C₅	—	2	1	no	—
650	C₂×C₄×C₅	—	2	2	no	—
651	C₂×C₄×C₅	—	2	2	no	—
652	C₂×C₄×C₅	—	4	2	no	—
653	C₂×C₄×C₅	—	4	1	no	—
654	C₂×C₄×C₅	—	4	2	no	—
655	C₂×C₄×C₅	—	4	1	no	—
656	C₂×C₄×C₅	—	4	2	no	—
657	C₂×C₄×C₅	—	4	4	no	—
658	C₂×C₄×C₅	—	4	2	no	—
659	C₂×C₄×C₅	—	4	2	no	—
660	C₂×C₄×C₅	—	8	2	no	—
661	C₂×C₄×C₅	—	8	2	no	—
662	C₂×C₄×C₅	—	8	1	no	—
663	C₂×C₄×C₅	—	8	2	no	—
664	C₂×C₄×C₅	—	8	2	no	—
665	C₂×C₄×C₅	—	8	2	no	—
666	C₂×C₄×C₅	—	8	2	no	—
667	C₂×C₄×C₅	—	8	1	no	—
668	C₂×C₄×C₅	—	8	1	no	—
669	C₂×C₄×C₅	—	8	1	no	—
670	C₂×C₄×C₅	—	8	2	no	—
671	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
672	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
673	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
674	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
675	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
676	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
677	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
678	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
679	C₂×C₄×C₅	C₂×#41	1	2	yes	—
680	C₂×C₄×C₅	C₂×#41	1	2	yes	—
681	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
682	C₅×C₈	—	2	1	no	—
683	C₅×C₈	—	2	1	no	—
684	C₅×C₈	—	2	1	no	—
685	C₅×C₈	—	2	1	no	—
686	C₅×C₈	—	2	2	no	—
687	C₅×C₈	—	2	2	no	—
688	H(5,𝔽₂)	—	2	4	no	—
689	H(5,𝔽₂)	—	2	4	no	—
690	C₂×#41	—	2	1	no	—
691	C₂×#41	C₂³×C₅	1	2	yes	—
692	C₂×#41	C₂³×C₅	1	1	yes	characteristic
693	C₂×#41	C₂³×C₅	1	1	yes	characteristic
694	C₂×#41	C₂³×C₅	1	1	yes	characteristic
695	C₂×#41	C₂³×C₅	1	1	yes	characteristic
696	C₂²×D₄	—	2	2	no	—
697	C₂²×D₄	—	2	1	no	—
698	C₂²×D₄	C₂³×C₅	1	2	yes	—
699	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
700	C₂³×C₄	—	2	1	no	—
701	C₂³×C₄	—	2	2	no	—
702	AGL(1,ℤ/8)	—	2	4	no	—
703	AGL(1,ℤ/8)	—	2	4	no	—
704	#135	—	2	4	no	—
705	#135	—	2	4	no	—
706	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
707	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
710	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₅	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
714	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
715	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
716	C₂×D₈	C₂³×C₅	1	2	yes	—
717	C₂×D₈	C₂³×C₅	1	2	yes	—
718	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
723	#127	C₂³×C₅	1	1	yes	characteristic
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	1	no	—
732	#125	C₂³×C₅	1	2	yes	—
733	#125	C₂³×C₅	1	2	yes	—
734	#124	C₂³×C₅	1	1	yes	characteristic
735	#124	C₂³×C₅	1	1	yes	characteristic
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
743	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
744	#121	—	2	1	no	—
745	#121	—	2	1	no	—
746	#121	—	2	2	no	—
747	#121	—	2	2	no	—
748	#121	—	2	1	no	—
749	#121	—	2	1	no	—
750	#121	—	2	2	no	—
751	#121	—	2	2	no	—
752	#121	C₂³×C₅	1	2	yes	—
753	#121	C₂³×C₅	1	2	yes	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
756	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₅	1	2	yes	—
759	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
760	C₄×Q₈	C₂³×C₅	1	2	yes	—
761	C₄×Q₈	C₂³×C₅	1	2	yes	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	C₅×D₄	1	2	yes	—
786	C₄×D₄	C₅×D₄	1	1	yes	characteristic
787	C₄×D₄	C₅×D₄	1	2	yes	—
788	C₄×D₄	C₅×D₄	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₅	1	2	yes	—
790	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₅	1	2	yes	—
792	C₄×D₄	C₂³×C₅	1	2	yes	—
793	C₄×D₄	C₂³×C₅	1	2	yes	—
794	C₄×D₄	C₂³×C₅	1	2	yes	—
795	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₅	1	2	yes	—
797	C₄×D₄	C₂³×C₅	1	2	yes	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	C₂³×C₅	1	1	yes	characteristic
807	#117	C₂³×C₅	1	2	yes	—
808	#117	C₂³×C₅	1	1	yes	characteristic
809	#117	C₂³×C₅	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	2	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
817	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
818	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	—	2	1	no	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₄²	—	2	2	no	—
826	C₂×C₄²	—	2	1	no	—
827	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
828	C₂×C₄²	C₂³×C₅	1	2	yes	—
829	#107	C₂³×C₅	1	2	yes	—
830	#107	C₂³×C₅	1	2	yes	—
831	#107	C₂³×C₅	1	2	yes	—
832	#107	C₂³×C₅	1	2	yes	—
833	#106	C₂³×C₅	1	2	yes	—
834	#106	C₂³×C₅	1	2	yes	—
835	#106	C₂³×C₅	1	2	yes	—
836	#106	C₂³×C₅	1	2	yes	—
837	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₅	1	2	yes	—
842	C₄⋊C₈	C₂³×C₅	1	2	yes	—
843	#103	C₂³×C₅	1	1	yes	characteristic
844	#103	C₂³×C₅	1	1	yes	characteristic
845	#103	C₂³×C₅	1	1	yes	characteristic
846	#103	C₂³×C₅	1	1	yes	characteristic
847	#103	C₂³×C₅	1	2	yes	—
848	#103	C₂³×C₅	1	2	yes	—
849	#103	C₂³×C₅	1	2	yes	—
850	#103	C₂³×C₅	1	2	yes	—
851	#102	C₂³×C₅	1	2	yes	—
852	#102	C₂³×C₅	1	2	yes	—
853	#102	C₂³×C₅	1	2	yes	—
854	#102	C₂³×C₅	1	2	yes	—
855	#102	C₂³×C₅	1	1	yes	characteristic
856	#102	C₂³×C₅	1	1	yes	characteristic
857	#102	C₂³×C₅	1	1	yes	characteristic
858	#102	C₂³×C₅	1	1	yes	characteristic
859	#102	C₂³×C₅	1	2	yes	—
860	#102	C₂³×C₅	1	2	yes	—
861	#102	C₂³×C₅	1	2	yes	—
862	#102	C₂³×C₅	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
867	#97	C₂³×C₅	1	2	yes	—
868	#97	C₂³×C₅	1	2	yes	—
869	C₄×C₈	C₂³×C₅	1	2	yes	—
870	C₄×C₈	C₂³×C₅	1	2	yes	—
871	C₂²×C₅	—	2	1	no	—
872	C₂²×C₅	—	2	1	no	—
873	C₂²×C₅	—	2	2	no	—
874	C₂²×C₅	—	2	2	no	—
875	C₂²×C₅	—	2	2	no	—
876	C₂²×C₅	—	2	4	no	—
877	C₂²×C₅	—	2	2	no	—
878	C₂²×C₅	—	4	2	no	—
879	C₂²×C₅	—	4	1	no	—
880	C₂²×C₅	—	4	2	no	—
881	C₂²×C₅	—	4	1	no	—
882	C₂²×C₅	—	4	1	no	—
883	C₂²×C₅	—	4	1	no	—
884	C₂²×C₅	—	4	1	no	—
885	C₂²×C₅	—	4	1	no	—
886	C₂²×C₅	—	4	1	no	—
887	C₂²×C₅	—	4	1	no	—
888	C₂²×C₅	—	8	4	no	—
889	C₂²×C₅	—	8	8	no	—
890	C₂²×C₅	#525	1	2	yes	—
891	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
892	C₄×C₅	—	2	1	no	—
893	C₄×C₅	—	2	2	no	—
894	C₄×C₅	—	2	1	no	—
895	C₄×C₅	—	2	1	no	—
896	C₄×C₅	—	2	2	no	—
897	C₄×C₅	—	2	1	no	—
898	C₄×C₅	—	2	2	no	—
899	C₄×C₅	—	2	2	no	—
900	C₄×C₅	—	4	1	no	—
901	C₄×C₅	—	4	2	no	—
902	C₄×C₅	—	4	1	no	—
903	C₄×C₅	—	4	2	no	—
904	C₄×C₅	—	4	2	no	—
905	C₄×C₅	—	4	1	no	—
906	C₄×C₅	—	4	1	no	—
907	C₄×C₅	#525	1	2	yes	—
908	C₄×C₅	C₂²×#41	1	1	yes	characteristic
909	C₄×C₅	C₂²×#41	1	1	yes	characteristic
910	C₂⁴	—	2	2	no	—
911	C₂⁴	—	2	1	no	—
912	#41	—	2	8	no	—
913	#41	—	2	4	no	—
914	#41	—	2	4	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	2	2	no	—
922	#41	C₅×#41	1	4	yes	—
923	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
927	C₂×D₄	—	2	16	no	—
928	C₂×D₄	—	2	8	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	4	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
943	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
944	C₂×D₄	C₅×#41	1	4	yes	—
945	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
948	C₂×D₄	C₂⁴×C₅	1	2	yes	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	8	4	no	—
967	C₂²×C₄	—	8	2	no	—
968	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
969	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
970	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
971	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
972	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
973	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
974	Q₁₆	—	2	2	no	—
975	Q₁₆	—	2	2	no	—
976	SD₁₆	—	2	2	no	—
977	SD₁₆	—	2	2	no	—
978	SD₁₆	—	2	2	no	—
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	2	4	no	—
981	SD₁₆	—	2	4	no	—
982	D₈	—	2	2	no	—
983	D₈	—	2	2	no	—
984	D₈	—	2	4	no	—
985	D₈	—	2	4	no	—
986	M₁₆	—	2	2	no	—
987	M₁₆	—	2	2	no	—
988	C₂×C₈	—	2	2	no	—
989	C₂×C₈	—	2	2	no	—
990	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×C₅	1	2	yes	—
993	C₂×C₈	C₂⁴×C₅	1	2	yes	—
994	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
1016	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1042	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1043	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	C₂×C₅×D₄	1	2	yes	—
1052	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1053	C₄²	C₂×C₅×D₄	1	2	yes	—
1054	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₅	1	2	yes	—
1056	C₄²	C₂⁴×C₅	1	1	yes	characteristic
1057	C₄²	C₂⁴×C₅	1	1	yes	characteristic
1058	C₂×C₅	—	2	2	no	—
1059	C₂×C₅	—	4	2	no	—
1060	C₂×C₅	—	4	4	no	—
1061	C₂×C₅	—	4	2	no	—
1062	C₂×C₅	—	8	1	no	—
1063	C₂×C₅	—	8	1	no	—
1064	C₂×C₅	C₂×#525	1	1	yes	characteristic
1065	C₂×C₅	#3584	1	1	yes	characteristic
1066	C₂×C₅	#3585	1	1	yes	characteristic
1067	C₂³	—	2	8	no	—
1068	C₂³	—	2	2	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	4	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	8	1	no	—
1074	C₂³	—	8	2	no	—
1075	C₂³	—	8	1	no	—
1076	C₂³	—	8	2	no	—
1077	C₂³	C₂²×C₅×D₄	1	2	yes	—
1078	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	2	1	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	1	no	—
1084	Q₈	—	2	1	no	—
1085	Q₈	C₂×C₅×#41	1	2	yes	—
1086	D₄	—	2	8	no	—
1087	D₄	—	2	8	no	—
1088	D₄	—	2	4	no	—
1089	D₄	—	2	4	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	2	4	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	C₂×C₅×#41	1	2	yes	—
1105	D₄	C₂×C₅×#41	1	4	yes	—
1106	C₂×C₄	—	2	8	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	4	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	1	no	—
1137	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1138	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1139	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1140	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1141	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1142	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1143	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1144	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1145	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1146	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1147	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
1148	C₈	—	2	1	no	—
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	2	no	—
1153	C₈	—	2	2	no	—
1154	C₅	#60601	1	1	yes	characteristic, direct product factor, Sylow
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	1	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	8	4	no	—
1173	C₂²	—	8	8	no	—
1174	C₂²	C₅×#525	1	2	yes	—
1175	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	4	2	no	—
1191	C₄	C₅×#525	1	2	yes	—
1192	C₄	C₂²×C₅×#41	1	1	yes	characteristic
1193	C₄	C₂²×C₅×#41	1	1	yes	characteristic
1194	C₂	—	2	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	4	4	no	—
1197	C₂	—	4	2	no	—
1198	C₂	—	8	1	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₂×C₅×#525	1	1	yes	characteristic
1201	C₂	C₅×#3584	1	1	yes	characteristic
1202	C₂	C₅×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅×#3512	C₂	semidirect
2. C₄×C₅×H(5,𝔽₂)	C₂	semidirect
3. C₅×#3123	C₂	semidirect
4. C₅×#3122	C₂	semidirect
5. C₅×#3120	C₂	semidirect
6. C₅×#3119	C₂	semidirect
7. C₅×#3114	C₂	semidirect
8. C₅×#3111	C₂	semidirect
9. C₅×#3105	C₂	semidirect
10. C₅×#3102	C₂	semidirect
11. C₅×#3099	C₂	semidirect
12. C₅×#3098	C₂	semidirect
13. C₅×#3080	C₂	semidirect
14. C₂×C₅×#478	C₂	semidirect
15. C₅×#3036	C₂	semidirect
16. C₅×#3035	C₂	semidirect
17. C₅×#3012	C₂	semidirect
18. C₅×#3012	C₂	semidirect
19. C₅×#2952	C₂	semidirect
20. C₅×#2951	C₂	semidirect
21. C₅×#2946	C₂	semidirect
22. C₅×#2946	C₂	semidirect
23. C₅×#2925	C₂	semidirect
35. C₅×#541	C₂²	semidirect
36. C₅×#540	C₂²	semidirect
39. C₅×#532	C₂²	semidirect
40. C₅×#529	C₂²	semidirect
41. C₅×#529	C₂²	semidirect
42. C₂×C₅×#125	C₂²	semidirect
47. C₅×#520	C₂²	semidirect
48. C₅×#520	C₂²	semidirect
61. C₅×#485	C₂²	semidirect
62. C₅×#485	C₂²	semidirect
63. C₅×#484	C₂²	semidirect
64. C₅×#483	C₂²	semidirect
65. C₅×#482	C₂²	semidirect
66. C₅×#482	C₂²	semidirect
67. C₅×#481	C₂²	semidirect
68. C₅×#480	C₂²	semidirect
69. C₅×#479	C₂²	semidirect
70. C₅×#479	C₂²	semidirect
71. C₅×#478	C₂²	semidirect
72. C₅×#478	C₂²	semidirect
73. C₅×#478	C₂²	semidirect
74. C₅×#478	C₂²	semidirect
75. C₅×#478	C₂²	semidirect
76. C₅×#478	C₂²	semidirect
77. C₅×#464	C₂²	semidirect
78. C₅×#464	C₂²	semidirect
79. C₅×#463	C₂²	semidirect
80. C₅×#463	C₂²	semidirect
81. C₅×#463	C₂²	semidirect
82. C₅×#463	C₂²	semidirect
83. C₅×#462	C₂²	semidirect
84. C₅×#461	C₂²	semidirect
85. C₅×#461	C₂²	semidirect
86. C₅×#460	C₂²	semidirect
87. C₅×#459	C₂²	semidirect
88. C₅×#459	C₂²	semidirect
97. C₅×#442	C₂²	semidirect
98. C₅×#442	C₂²	semidirect
99. C₅×#442	C₂²	semidirect
100. C₅×#441	C₂²	semidirect
101. C₅×#440	C₂²	semidirect
102. C₅×#440	C₂²	semidirect
103. C₅×#440	C₂²	semidirect
104. C₅×#440	C₂²	semidirect
105. C₄×C₅×Q₁₆	C₂²	semidirect
106. C₄×C₅×SD₁₆	C₂²	semidirect
107. C₄×C₅×SD₁₆	C₂²	semidirect
108. C₄×C₅×SD₁₆	C₂²	semidirect
109. C₄×C₅×SD₁₆	C₂²	semidirect
110. C₄×C₅×D₈	C₂²	semidirect
111. C₄×C₅×D₈	C₂²	semidirect
112. C₄×C₅×D₈	C₂²	semidirect
113. C₅×#433	C₂²	semidirect
114. C₅×#433	C₂²	semidirect
115. C₅×#432	C₂²	semidirect
116. C₅×#431	C₂²	semidirect
117. C₅×#428	C₂²	semidirect
118. C₅×#428	C₂²	semidirect
119. C₂×C₅×#107	C₂²	semidirect
120. C₂×C₅×#106	C₂²	semidirect
121. C₅×#423	C₂²	semidirect
122. C₂×C₅×C₄⋊C₈	C₂²	semidirect
125. C₅×#417	C₂²	semidirect
126. C₅×#417	C₂²	semidirect
127. C₅×#416	C₂²	semidirect
128. C₅×#416	C₂²	semidirect
133. C₅×#405	C₂²	semidirect
134. C₅×#405	C₂²	semidirect
135. #60601	C₅	direct (N × H)
319. #3512	C₂×C₅	semidirect
320. C₄×H(5,𝔽₂)	C₂×C₅	semidirect
321. #3123	C₂×C₅	semidirect
322. #3122	C₂×C₅	semidirect
323. #3120	C₂×C₅	semidirect
324. #3119	C₂×C₅	semidirect
325. #3114	C₂×C₅	semidirect
326. #3111	C₂×C₅	semidirect
327. #3105	C₂×C₅	semidirect
328. #3102	C₂×C₅	semidirect
329. #3099	C₂×C₅	semidirect
330. #3098	C₂×C₅	semidirect
331. #3080	C₂×C₅	semidirect
332. C₂×#478	C₂×C₅	semidirect
333. #3036	C₂×C₅	semidirect
334. #3035	C₂×C₅	semidirect
335. #3012	C₂×C₅	semidirect
336. #3012	C₂×C₅	semidirect
337. #2952	C₂×C₅	semidirect
338. #2951	C₂×C₅	semidirect
339. #2946	C₂×C₅	semidirect
340. #2946	C₂×C₅	semidirect
341. #2925	C₂×C₅	semidirect
501. #541	C₂²×C₅	semidirect
502. #540	C₂²×C₅	semidirect
505. #532	C₂²×C₅	semidirect
506. #529	C₂²×C₅	semidirect
507. #529	C₂²×C₅	semidirect
508. C₂×#125	C₂²×C₅	semidirect
513. #520	C₂²×C₅	semidirect
514. #520	C₂²×C₅	semidirect
527. #485	C₂²×C₅	semidirect
528. #485	C₂²×C₅	semidirect
529. #484	C₂²×C₅	semidirect
530. #483	C₂²×C₅	semidirect
531. #482	C₂²×C₅	semidirect
532. #482	C₂²×C₅	semidirect
533. #481	C₂²×C₅	semidirect
534. #480	C₂²×C₅	semidirect
535. #479	C₂²×C₅	semidirect
536. #479	C₂²×C₅	semidirect
537. #478	C₂²×C₅	semidirect
538. #478	C₂²×C₅	semidirect
539. #478	C₂²×C₅	semidirect
540. #478	C₂²×C₅	semidirect
541. #478	C₂²×C₅	semidirect
542. #478	C₂²×C₅	semidirect
543. #464	C₂²×C₅	semidirect
544. #464	C₂²×C₅	semidirect
545. #463	C₂²×C₅	semidirect
546. #463	C₂²×C₅	semidirect
547. #463	C₂²×C₅	semidirect
548. #463	C₂²×C₅	semidirect
549. #462	C₂²×C₅	semidirect
550. #461	C₂²×C₅	semidirect
551. #461	C₂²×C₅	semidirect
552. #460	C₂²×C₅	semidirect
553. #459	C₂²×C₅	semidirect
554. #459	C₂²×C₅	semidirect
563. #442	C₂²×C₅	semidirect
564. #442	C₂²×C₅	semidirect
565. #442	C₂²×C₅	semidirect
566. #441	C₂²×C₅	semidirect
567. #440	C₂²×C₅	semidirect
568. #440	C₂²×C₅	semidirect
569. #440	C₂²×C₅	semidirect
570. #440	C₂²×C₅	semidirect
571. C₄×Q₁₆	C₂²×C₅	semidirect
572. C₄×SD₁₆	C₂²×C₅	semidirect
573. C₄×SD₁₆	C₂²×C₅	semidirect
574. C₄×SD₁₆	C₂²×C₅	semidirect
575. C₄×SD₁₆	C₂²×C₅	semidirect
576. C₄×D₈	C₂²×C₅	semidirect
577. C₄×D₈	C₂²×C₅	semidirect
578. C₄×D₈	C₂²×C₅	semidirect
579. #433	C₂²×C₅	semidirect
580. #433	C₂²×C₅	semidirect
581. #432	C₂²×C₅	semidirect
582. #431	C₂²×C₅	semidirect
583. #428	C₂²×C₅	semidirect
584. #428	C₂²×C₅	semidirect
585. C₂×#107	C₂²×C₅	semidirect
586. C₂×#106	C₂²×C₅	semidirect
587. #423	C₂²×C₅	semidirect
588. C₂×C₄⋊C₈	C₂²×C₅	semidirect
591. #417	C₂²×C₅	semidirect
592. #417	C₂²×C₅	semidirect
593. #416	C₂²×C₅	semidirect
594. #416	C₂²×C₅	semidirect
599. #405	C₂²×C₅	semidirect
600. #405	C₂²×C₅	semidirect
1154. C₅	#60601	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3512	2
C₄×C₅×H(5,𝔽₂)	2
C₅×#3123	2
C₅×#3122	2
C₅×#3120	2
C₅×#3119	2
C₅×#3114	2
C₅×#3111	2
C₅×#3105	2
C₅×#3102	2
C₅×#3099	2
C₅×#3098	2
C₅×#3080	2
C₂×C₅×#478	2
C₅×#3036	2
C₅×#3035	2
C₅×#3012	2
C₅×#2952	2
C₅×#2951	2
C₅×#2946	2
C₅×#2925	2
#60601	5

Subgroups — C5×#60601 #11983321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60601 #11983321