Subgroups — C₅×#60591 #11983311

Order 1280.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
3	C₅×#3123	C₂	1	4	yes	maximal, complemented
4	C₅×#3120	C₂	1	4	yes	maximal, complemented
5	C₅×#3116	C₂	1	2	yes	maximal, complemented
6	C₅×#3110	C₂	1	2	yes	maximal, complemented
7	C₅×#3107	C₂	1	2	yes	maximal, complemented
8	C₅×#3101	C₂	1	2	yes	maximal, complemented
9	C₅×#3097	C₂	1	2	yes	maximal, complemented
10	C₅×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3009	C₂	1	2	yes	maximal
15	C₅×#2949	C₂	1	2	yes	maximal, complemented
16	C₅×#2947	C₂	1	2	yes	maximal, complemented
17	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×C₅×#137	C₂²	1	2	yes	—
20	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
21	C₅×#557	—	2	1	no	—
22	C₅×#557	—	2	1	no	—
23	C₅×#556	—	2	1	no	—
24	C₅×#556	—	2	1	no	—
25	C₅×#552	—	2	2	no	—
26	C₅×#552	—	2	2	no	—
27	C₅×#541	C₂²	1	4	yes	complemented
28	C₅×#536	C₂²	1	2	yes	—
29	C₅×#533	C₂²	1	2	yes	complemented
30	C₅×#533	C₂²	1	2	yes	complemented
31	C₅×#533	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₅×#520	—	2	1	no	—
34	C₅×#520	C₂²	1	2	yes	—
35	C₅×#520	C₂²	1	1	yes	characteristic
36	C₅×#520	C₂²	1	1	yes	characteristic
37	C₅×#519	C₂²	1	2	yes	complemented
38	C₅×#518	—	2	2	no	—
39	C₅×#518	—	2	1	no	—
40	C₅×#518	C₂²	1	2	yes	—
41	C₅×#518	C₂²	1	1	yes	characteristic
42	C₄×C₅×#41	—	2	1	no	—
43	C₄×C₅×#41	C₂²	1	1	yes	characteristic
44	C₄×C₅×#41	C₂²	1	2	yes	—
45	C₄×C₅×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×D₄	—	2	2	no	—
47	C₂×C₄×C₅×D₄	—	2	1	no	—
48	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
50	C₅×#485	C₂²	1	4	yes	complemented
51	C₅×#485	C₂²	1	4	yes	complemented
52	C₅×#484	C₂²	1	4	yes	complemented
53	C₅×#483	C₂²	1	4	yes	complemented
54	C₅×#479	C₂²	1	2	yes	complemented
55	C₅×#478	C₂²	1	2	yes	complemented
56	C₅×#478	C₂²	1	4	yes	complemented
57	C₅×#477	C₂²	1	1	yes	characteristic, complemented
58	C₅×#476	C₂²	1	1	yes	characteristic, complemented
59	C₅×#476	C₂²	1	2	yes	complemented
60	C₅×#475	C₂²	1	1	yes	characteristic, complemented
61	C₅×#474	C₂²	1	1	yes	characteristic, complemented
62	C₅×#474	C₂²	1	2	yes	complemented
63	C₅×#462	C₂²	1	2	yes	complemented
64	C₅×#462	C₂²	1	2	yes	complemented
65	C₅×#461	C₂²	1	2	yes	complemented
66	C₅×#461	C₂²	1	2	yes	complemented
67	C₅×#461	C₂²	1	4	yes	complemented
68	C₅×#461	C₂²	1	2	yes	complemented
69	C₅×#461	C₂²	1	2	yes	complemented
70	C₅×#452	C₂²	1	4	yes	—
71	C₅×#452	C₂²	1	4	yes	—
72	C₅×#450	C₂²	1	4	yes	—
73	C₅×#450	C₂²	1	4	yes	—
74	C₅×#441	C₂²	1	4	yes	complemented
75	C₅×#440	C₂²	1	4	yes	complemented
76	C₅×#440	C₂²	1	4	yes	complemented
77	C₅×#440	C₂²	1	4	yes	complemented
78	C₄×C₅×Q₁₆	C₂²	1	4	yes	complemented
79	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
80	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
81	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
82	C₅×#433	C₂²	1	4	yes	complemented
83	C₅×#432	C₂²	1	2	yes	complemented
84	C₅×#431	C₂²	1	2	yes	complemented
85	C₅×#428	C₂²	1	2	yes	complemented
86	C₅×#427	C₂²	1	2	yes	complemented
87	C₅×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₅×#419	C₂²	1	2	yes	complemented
90	C₅×#418	C₂²	1	2	yes	—
91	C₅×#416	C₂²	1	2	yes	—
92	C₂×C₅×#103	C₂²	1	2	yes	complemented
93	C₅×#408	C₂²	1	2	yes	—
94	C₅×#405	C₂²	1	2	yes	complemented
95	#60591	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₅×H(5,𝔽₂)	—	2	4	no	—
97	C₅×H(5,𝔽₂)	—	2	4	no	—
98	C₂×C₅×#41	—	2	1	no	—
99	C₂×C₅×#41	C₂³	1	2	yes	—
100	C₂×C₅×#41	C₂³	1	1	yes	characteristic
101	C₂×C₅×#41	C₂³	1	1	yes	characteristic
102	C₂²×C₅×Q₈	C₂³	1	2	yes	—
103	C₂²×C₅×D₄	—	2	2	no	—
104	C₂²×C₅×D₄	—	2	1	no	—
105	C₂²×C₅×D₄	C₂³	1	2	yes	—
106	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅	—	2	1	no	—
108	C₂³×C₄×C₅	—	2	2	no	—
109	C₅×#137	—	2	8	no	—
110	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₅×SD₁₆	—	2	8	no	—
112	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₅×M₁₆	C₂³	1	2	yes	—
116	C₂²×C₅×C₈	C₂³	1	2	yes	—
117	C₅×C₄⋊Q₈	—	2	2	no	—
118	C₅×C₄⋊Q₈	—	2	1	no	—
119	C₅×C₄⋊Q₈	—	2	1	no	—
120	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₅×#126	—	2	4	no	—
125	C₅×#126	—	2	4	no	—
126	C₅×#125	—	2	4	no	—
127	C₅×#125	—	2	4	no	—
128	C₅×#125	—	2	2	no	—
129	C₅×#125	—	2	2	no	—
130	C₅×#125	C₂³	1	2	yes	—
131	C₅×#124	—	2	2	no	—
132	C₅×#123	—	2	4	no	—
133	C₅×C₂²⋊Q₈	—	2	1	no	—
134	C₅×C₂²⋊Q₈	—	2	1	no	—
135	C₅×C₂²⋊Q₈	—	2	2	no	—
136	C₅×C₂²⋊Q₈	—	2	2	no	—
137	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₄×C₅×Q₈	—	2	1	no	—
140	C₄×C₅×Q₈	—	2	2	no	—
141	C₄×C₅×Q₈	—	2	2	no	—
142	C₄×C₅×Q₈	—	2	2	no	—
143	C₄×C₅×Q₈	—	2	2	no	—
144	C₄×C₅×Q₈	—	2	1	no	—
145	C₄×C₅×Q₈	—	2	1	no	—
146	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
147	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
148	C₄×C₅×Q₈	C₂³	1	4	yes	—
149	C₄×C₅×Q₈	C₂³	1	4	yes	—
150	C₄×C₅×Q₈	C₂³	1	2	yes	—
151	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
152	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
153	C₄×C₅×D₄	—	2	2	no	—
154	C₄×C₅×D₄	—	2	1	no	—
155	C₄×C₅×D₄	—	2	1	no	—
156	C₄×C₅×D₄	—	2	2	no	—
157	C₄×C₅×D₄	—	2	1	no	—
158	C₄×C₅×D₄	—	2	2	no	—
159	C₄×C₅×D₄	—	2	1	no	—
160	C₄×C₅×D₄	—	2	2	no	—
161	C₄×C₅×D₄	—	2	1	no	—
162	C₄×C₅×D₄	—	2	2	no	—
163	C₄×C₅×D₄	—	2	2	no	—
164	C₄×C₅×D₄	—	2	2	no	—
165	C₄×C₅×D₄	—	2	2	no	—
166	C₄×C₅×D₄	—	2	2	no	—
167	C₄×C₅×D₄	—	2	1	no	—
168	C₄×C₅×D₄	—	2	2	no	—
169	C₄×C₅×D₄	—	2	1	no	—
170	C₄×C₅×D₄	D₄	1	2	yes	—
171	C₄×C₅×D₄	D₄	1	1	yes	characteristic
172	C₄×C₅×D₄	D₄	1	2	yes	—
173	C₄×C₅×D₄	D₄	1	1	yes	characteristic
174	C₄×C₅×D₄	C₂³	1	2	yes	—
175	C₄×C₅×D₄	C₂³	1	2	yes	—
176	C₄×C₅×D₄	C₂³	1	2	yes	—
177	C₄×C₅×D₄	C₂³	1	2	yes	—
178	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
179	C₄×C₅×D₄	C₂³	1	2	yes	—
180	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
181	C₅×#117	—	2	2	no	—
182	C₅×#117	—	2	2	no	—
183	C₅×#117	—	2	1	no	—
184	C₅×#117	—	2	2	no	—
185	C₅×#117	—	2	4	no	—
186	C₅×#117	—	2	2	no	—
187	C₅×#117	—	2	1	no	—
188	C₅×#117	C₂³	1	2	yes	—
189	C₅×#117	C₂³	1	1	yes	characteristic
190	C₅×#117	C₂³	1	2	yes	—
191	C₅×#117	C₂³	1	1	yes	characteristic
192	C₅×#117	C₂³	1	2	yes	—
193	C₂×C₅×C₄⋊C₄	—	2	1	no	—
194	C₂×C₅×C₄⋊C₄	—	2	1	no	—
195	C₂×C₅×C₄⋊C₄	—	2	1	no	—
196	C₂×C₅×C₄⋊C₄	—	2	2	no	—
197	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₄²×C₅	—	2	2	no	—
205	C₂×C₄²×C₅	—	2	1	no	—
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₅×#107	C₂³	1	2	yes	—
209	C₅×#107	C₂³	1	2	yes	—
210	C₅×#107	C₂³	1	4	yes	—
211	C₅×#106	C₂³	1	2	yes	—
212	C₅×#106	C₂³	1	2	yes	—
213	C₅×#106	C₂³	1	4	yes	—
214	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₅×C₄⋊C₈	C₂³	1	2	yes	—
217	C₅×C₄⋊C₈	C₂³	1	2	yes	—
218	C₅×C₄⋊C₈	C₂³	1	2	yes	—
219	C₅×#103	C₂³	1	4	yes	—
220	C₅×#103	C₂³	1	4	yes	—
221	C₅×#103	C₂³	1	2	yes	—
222	C₅×#103	C₂³	1	2	yes	—
223	C₅×#103	C₂³	1	4	yes	—
224	C₅×#103	C₂³	1	4	yes	—
225	C₅×#102	C₂³	1	2	yes	—
226	C₅×#102	C₂³	1	2	yes	—
227	C₅×#102	C₂³	1	4	yes	—
228	C₅×#102	C₂³	1	4	yes	—
229	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₅×#97	C₂³	1	4	yes	—
232	C₄×C₅×C₈	C₂³	1	4	yes	—
233	#3509	C₂×C₅	1	1	yes	characteristic, complemented
234	C₄×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic
235	#3123	C₂×C₅	1	4	yes	complemented
236	#3120	C₂×C₅	1	4	yes	complemented
237	#3116	C₂×C₅	1	2	yes	complemented
238	#3110	C₂×C₅	1	2	yes	complemented
239	#3107	C₂×C₅	1	2	yes	complemented
240	#3101	C₂×C₅	1	2	yes	complemented
241	#3097	C₂×C₅	1	2	yes	complemented
242	#3077	C₂×C₅	1	1	yes	characteristic, complemented
243	#3076	C₂×C₅	1	1	yes	characteristic, complemented
244	#3039	C₂×C₅	1	1	yes	characteristic, complemented
245	C₂×#461	C₂×C₅	1	1	yes	characteristic, complemented
246	#3009	C₂×C₅	1	2	yes	—
247	#2949	C₂×C₅	1	2	yes	complemented
248	#2947	C₂×C₅	1	2	yes	complemented
249	#2925	C₂×C₅	1	1	yes	characteristic, complemented
250	C₂⁴×C₅	—	2	2	no	—
251	C₂⁴×C₅	—	2	1	no	—
252	C₅×#41	—	2	8	no	—
253	C₅×#41	—	2	4	no	—
254	C₅×#41	—	2	4	no	—
255	C₅×#41	—	2	2	no	—
256	C₅×#41	—	2	2	no	—
257	C₅×#41	—	2	2	no	—
258	C₅×#41	#41	1	4	yes	—
259	C₂×C₅×Q₈	—	2	1	no	—
260	C₂×C₅×Q₈	—	2	1	no	—
261	C₂×C₅×Q₈	—	2	2	no	—
262	C₂×C₅×Q₈	—	2	4	no	—
263	C₂×C₅×Q₈	—	2	4	no	—
264	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
265	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
266	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₅×D₄	—	2	16	no	—
268	C₂×C₅×D₄	—	2	8	no	—
269	C₂×C₅×D₄	—	2	2	no	—
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	2	4	no	—
272	C₂×C₅×D₄	—	2	4	no	—
273	C₂×C₅×D₄	—	2	2	no	—
274	C₂×C₅×D₄	—	2	1	no	—
275	C₂×C₅×D₄	—	2	2	no	—
276	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
277	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
278	C₂×C₅×D₄	#41	1	4	yes	—
279	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
280	C₂×C₅×D₄	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	1	no	—
283	C₂²×C₄×C₅	—	2	2	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	2	1	no	—
286	C₂²×C₄×C₅	—	2	2	no	—
287	C₂²×C₄×C₅	—	2	1	no	—
288	C₂²×C₄×C₅	—	2	2	no	—
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	—	2	2	no	—
291	C₂²×C₄×C₅	—	2	2	no	—
292	C₂²×C₄×C₅	—	2	2	no	—
293	C₂²×C₄×C₅	—	8	2	no	—
294	C₂²×C₄×C₅	—	8	4	no	—
295	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
301	C₅×Q₁₆	—	2	8	no	—
302	C₅×SD₁₆	—	2	8	no	—
303	C₅×SD₁₆	—	2	8	no	—
304	C₅×SD₁₆	—	2	8	no	—
305	C₅×M₁₆	—	2	4	no	—
306	C₂×C₅×C₈	—	2	4	no	—
307	C₂×C₅×C₈	C₂⁴	1	2	yes	—
308	C₂×C₅×C₈	C₂⁴	1	2	yes	—
309	C₂×C₅×C₈	C₂⁴	1	4	yes	—
310	C₅×C₄⋊C₄	—	2	2	no	—
311	C₅×C₄⋊C₄	—	2	1	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	2	1	no	—
314	C₅×C₄⋊C₄	—	2	2	no	—
315	C₅×C₄⋊C₄	—	2	2	no	—
316	C₅×C₄⋊C₄	—	2	2	no	—
317	C₅×C₄⋊C₄	—	2	2	no	—
318	C₅×C₄⋊C₄	—	2	1	no	—
319	C₅×C₄⋊C₄	—	2	1	no	—
320	C₅×C₄⋊C₄	—	2	1	no	—
321	C₅×C₄⋊C₄	—	2	4	no	—
322	C₅×C₄⋊C₄	—	2	4	no	—
323	C₅×C₄⋊C₄	—	2	2	no	—
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	2	4	no	—
326	C₅×C₄⋊C₄	—	2	4	no	—
327	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
329	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
331	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
332	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
333	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
334	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
335	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
336	C₅×C₂²⋊C₄	—	2	2	no	—
337	C₅×C₂²⋊C₄	—	2	1	no	—
338	C₅×C₂²⋊C₄	—	2	2	no	—
339	C₅×C₂²⋊C₄	—	2	4	no	—
340	C₅×C₂²⋊C₄	—	2	4	no	—
341	C₅×C₂²⋊C₄	—	2	2	no	—
342	C₅×C₂²⋊C₄	—	2	1	no	—
343	C₅×C₂²⋊C₄	—	2	2	no	—
344	C₅×C₂²⋊C₄	—	2	2	no	—
345	C₅×C₂²⋊C₄	—	2	2	no	—
346	C₅×C₂²⋊C₄	—	2	2	no	—
347	C₅×C₂²⋊C₄	—	2	1	no	—
348	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
349	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
350	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
351	C₄²×C₅	—	2	1	no	—
352	C₄²×C₅	—	2	2	no	—
353	C₄²×C₅	—	2	1	no	—
354	C₄²×C₅	—	2	2	no	—
355	C₄²×C₅	—	2	1	no	—
356	C₄²×C₅	—	2	4	no	—
357	C₄²×C₅	—	2	4	no	—
358	C₄²×C₅	—	2	2	no	—
359	C₄²×C₅	C₂×D₄	1	2	yes	—
360	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₅	C₂×D₄	1	2	yes	—
362	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₅	C₂⁴	1	1	yes	characteristic
364	C₄²×C₅	C₂⁴	1	2	yes	—
365	C₄²×C₅	C₂⁴	1	1	yes	characteristic
366	C₂×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic
367	C₂×#137	C₂²×C₅	1	2	yes	—
368	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
369	#557	—	2	1	no	—
370	#557	—	2	1	no	—
371	#556	—	2	1	no	—
372	#556	—	2	1	no	—
373	#552	—	2	2	no	—
374	#552	—	2	2	no	—
375	#541	C₂²×C₅	1	4	yes	complemented
376	#536	C₂²×C₅	1	2	yes	—
377	#533	C₂²×C₅	1	2	yes	complemented
378	#533	C₂²×C₅	1	2	yes	complemented
379	#533	C₂²×C₅	1	1	yes	characteristic, complemented
380	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
381	#520	—	2	1	no	—
382	#520	C₂²×C₅	1	2	yes	—
383	#520	C₂²×C₅	1	1	yes	characteristic
384	#520	C₂²×C₅	1	1	yes	characteristic
385	#519	C₂²×C₅	1	2	yes	complemented
386	#518	—	2	2	no	—
387	#518	—	2	1	no	—
388	#518	C₂²×C₅	1	2	yes	—
389	#518	C₂²×C₅	1	1	yes	characteristic
390	C₄×#41	—	2	1	no	—
391	C₄×#41	C₂²×C₅	1	1	yes	characteristic
392	C₄×#41	C₂²×C₅	1	2	yes	—
393	C₄×#41	C₂²×C₅	1	1	yes	characteristic
394	C₂×C₄×D₄	—	2	2	no	—
395	C₂×C₄×D₄	—	2	1	no	—
396	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
398	#485	C₂²×C₅	1	4	yes	complemented
399	#485	C₂²×C₅	1	4	yes	complemented
400	#484	C₂²×C₅	1	4	yes	complemented
401	#483	C₂²×C₅	1	4	yes	complemented
402	#479	C₂²×C₅	1	2	yes	complemented
403	#478	C₂²×C₅	1	2	yes	complemented
404	#478	C₂²×C₅	1	4	yes	complemented
405	#477	C₂²×C₅	1	1	yes	characteristic, complemented
406	#476	C₂²×C₅	1	1	yes	characteristic, complemented
407	#476	C₂²×C₅	1	2	yes	complemented
408	#475	C₂²×C₅	1	1	yes	characteristic, complemented
409	#474	C₂²×C₅	1	1	yes	characteristic, complemented
410	#474	C₂²×C₅	1	2	yes	complemented
411	#462	C₂²×C₅	1	2	yes	complemented
412	#462	C₂²×C₅	1	2	yes	complemented
413	#461	C₂²×C₅	1	2	yes	complemented
414	#461	C₂²×C₅	1	2	yes	complemented
415	#461	C₂²×C₅	1	2	yes	complemented
416	#461	C₂²×C₅	1	4	yes	complemented
417	#461	C₂²×C₅	1	2	yes	complemented
418	#452	C₂²×C₅	1	4	yes	—
419	#452	C₂²×C₅	1	4	yes	—
420	#450	C₂²×C₅	1	4	yes	—
421	#450	C₂²×C₅	1	4	yes	—
422	#441	C₂²×C₅	1	4	yes	complemented
423	#440	C₂²×C₅	1	4	yes	complemented
424	#440	C₂²×C₅	1	4	yes	complemented
425	#440	C₂²×C₅	1	4	yes	complemented
426	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
427	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
428	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
429	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
430	#433	C₂²×C₅	1	4	yes	complemented
431	#432	C₂²×C₅	1	2	yes	complemented
432	#431	C₂²×C₅	1	2	yes	complemented
433	#428	C₂²×C₅	1	2	yes	complemented
434	#427	C₂²×C₅	1	2	yes	complemented
435	#423	C₂²×C₅	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
437	#419	C₂²×C₅	1	2	yes	complemented
438	#418	C₂²×C₅	1	2	yes	—
439	#416	C₂²×C₅	1	2	yes	—
440	C₂×#103	C₂²×C₅	1	2	yes	complemented
441	#408	C₂²×C₅	1	2	yes	—
442	#405	C₂²×C₅	1	2	yes	complemented
443	C₂³×C₅	—	2	8	no	—
444	C₂³×C₅	—	2	2	no	—
445	C₂³×C₅	—	2	1	no	—
446	C₂³×C₅	—	2	4	no	—
447	C₂³×C₅	—	8	1	no	—
448	C₂³×C₅	—	8	2	no	—
449	C₂³×C₅	—	8	1	no	—
450	C₂³×C₅	—	8	2	no	—
451	C₂³×C₅	C₂²×D₄	1	2	yes	—
452	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
453	C₅×Q₈	—	2	2	no	—
454	C₅×Q₈	—	2	1	no	—
455	C₅×Q₈	—	2	4	no	—
456	C₅×Q₈	—	2	4	no	—
457	C₅×Q₈	—	4	2	no	—
458	C₅×Q₈	—	4	4	no	—
459	C₅×Q₈	—	4	2	no	—
460	C₅×Q₈	C₂×#41	1	2	yes	—
461	C₅×D₄	—	2	8	no	—
462	C₅×D₄	—	2	8	no	—
463	C₅×D₄	—	2	4	no	—
464	C₅×D₄	—	2	4	no	—
465	C₅×D₄	—	2	2	no	—
466	C₅×D₄	—	2	4	no	—
467	C₅×D₄	—	2	2	no	—
468	C₅×D₄	—	2	1	no	—
469	C₅×D₄	C₂×#41	1	2	yes	—
470	C₅×D₄	C₂×#41	1	4	yes	—
471	C₂×C₄×C₅	—	2	8	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	4	no	—
474	C₂×C₄×C₅	—	2	2	no	—
475	C₂×C₄×C₅	—	2	4	no	—
476	C₂×C₄×C₅	—	2	2	no	—
477	C₂×C₄×C₅	—	2	2	no	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	2	no	—
480	C₂×C₄×C₅	—	2	2	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	4	no	—
484	C₂×C₄×C₅	—	4	1	no	—
485	C₂×C₄×C₅	—	4	2	no	—
486	C₂×C₄×C₅	—	4	4	no	—
487	C₂×C₄×C₅	—	4	4	no	—
488	C₂×C₄×C₅	—	4	2	no	—
489	C₂×C₄×C₅	—	8	2	no	—
490	C₂×C₄×C₅	—	8	1	no	—
491	C₂×C₄×C₅	—	8	2	no	—
492	C₂×C₄×C₅	—	8	2	no	—
493	C₂×C₄×C₅	—	8	2	no	—
494	C₂×C₄×C₅	—	8	1	no	—
495	C₂×C₄×C₅	—	8	2	no	—
496	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅	C₂×#41	1	2	yes	—
505	C₂×C₄×C₅	C₂×#41	1	2	yes	—
506	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
507	C₅×C₈	—	2	2	no	—
508	C₅×C₈	—	2	2	no	—
509	C₅×C₈	—	2	4	no	—
510	H(5,𝔽₂)	—	2	4	no	—
511	H(5,𝔽₂)	—	2	4	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	C₂³×C₅	1	2	yes	—
514	C₂×#41	C₂³×C₅	1	1	yes	characteristic
515	C₂×#41	C₂³×C₅	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₅	1	2	yes	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	C₂³×C₅	1	2	yes	—
520	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	2	no	—
523	#137	—	2	8	no	—
524	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
525	C₂×SD₁₆	—	2	8	no	—
526	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
527	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
528	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
529	C₂×M₁₆	C₂³×C₅	1	2	yes	—
530	C₂²×C₈	C₂³×C₅	1	2	yes	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#125	—	2	4	no	—
541	#125	—	2	4	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₅	1	2	yes	—
545	#124	—	2	2	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
552	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
561	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
563	C₄×Q₈	C₂³×C₅	1	2	yes	—
564	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₅	1	4	yes	—
566	C₄×Q₈	C₂³×C₅	1	4	yes	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	C₅×D₄	1	2	yes	—
585	C₄×D₄	C₅×D₄	1	1	yes	characteristic
586	C₄×D₄	C₅×D₄	1	2	yes	—
587	C₄×D₄	C₅×D₄	1	1	yes	characteristic
588	C₄×D₄	C₂³×C₅	1	2	yes	—
589	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
590	C₄×D₄	C₂³×C₅	1	2	yes	—
591	C₄×D₄	C₂³×C₅	1	2	yes	—
592	C₄×D₄	C₂³×C₅	1	2	yes	—
593	C₄×D₄	C₂³×C₅	1	2	yes	—
594	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	1	no	—
598	#117	—	2	2	no	—
599	#117	—	2	4	no	—
600	#117	—	2	2	no	—
601	#117	—	2	1	no	—
602	#117	C₂³×C₅	1	1	yes	characteristic
603	#117	C₂³×C₅	1	2	yes	—
604	#117	C₂³×C₅	1	2	yes	—
605	#117	C₂³×C₅	1	1	yes	characteristic
606	#117	C₂³×C₅	1	2	yes	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	2	no	—
615	C₂×C₂²⋊C₄	—	2	2	no	—
616	C₂×C₂²⋊C₄	—	2	2	no	—
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₄²	—	2	2	no	—
619	C₂×C₄²	—	2	1	no	—
620	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₅	1	2	yes	—
622	#107	C₂³×C₅	1	2	yes	—
623	#107	C₂³×C₅	1	2	yes	—
624	#107	C₂³×C₅	1	4	yes	—
625	#106	C₂³×C₅	1	2	yes	—
626	#106	C₂³×C₅	1	2	yes	—
627	#106	C₂³×C₅	1	4	yes	—
628	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
629	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
630	C₄⋊C₈	C₂³×C₅	1	2	yes	—
631	C₄⋊C₈	C₂³×C₅	1	2	yes	—
632	C₄⋊C₈	C₂³×C₅	1	2	yes	—
633	#103	C₂³×C₅	1	4	yes	—
634	#103	C₂³×C₅	1	4	yes	—
635	#103	C₂³×C₅	1	2	yes	—
636	#103	C₂³×C₅	1	2	yes	—
637	#103	C₂³×C₅	1	4	yes	—
638	#103	C₂³×C₅	1	4	yes	—
639	#102	C₂³×C₅	1	2	yes	—
640	#102	C₂³×C₅	1	2	yes	—
641	#102	C₂³×C₅	1	4	yes	—
642	#102	C₂³×C₅	1	4	yes	—
643	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
644	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
645	#97	C₂³×C₅	1	4	yes	—
646	C₄×C₈	C₂³×C₅	1	4	yes	—
647	C₂²×C₅	—	2	1	no	—
648	C₂²×C₅	—	2	1	no	—
649	C₂²×C₅	—	2	2	no	—
650	C₂²×C₅	—	2	2	no	—
651	C₂²×C₅	—	2	4	no	—
652	C₂²×C₅	—	2	2	no	—
653	C₂²×C₅	—	2	2	no	—
654	C₂²×C₅	—	4	2	no	—
655	C₂²×C₅	—	4	1	no	—
656	C₂²×C₅	—	4	2	no	—
657	C₂²×C₅	—	4	1	no	—
658	C₂²×C₅	—	8	4	no	—
659	C₂²×C₅	—	8	8	no	—
660	C₂²×C₅	#525	1	2	yes	—
661	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
662	C₄×C₅	—	2	1	no	—
663	C₄×C₅	—	2	2	no	—
664	C₄×C₅	—	2	1	no	—
665	C₄×C₅	—	2	2	no	—
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	—	2	2	no	—
668	C₄×C₅	—	2	1	no	—
669	C₄×C₅	—	4	1	no	—
670	C₄×C₅	—	4	2	no	—
671	C₄×C₅	—	4	4	no	—
672	C₄×C₅	—	4	2	no	—
673	C₄×C₅	—	4	1	no	—
674	C₄×C₅	—	4	2	no	—
675	C₄×C₅	#525	1	2	yes	—
676	C₄×C₅	#577	1	2	yes	—
677	C₄×C₅	C₂²×#41	1	1	yes	characteristic
678	C₄×C₅	C₂²×#41	1	1	yes	characteristic
679	C₂⁴	—	2	2	no	—
680	C₂⁴	—	2	1	no	—
681	#41	—	2	8	no	—
682	#41	—	2	4	no	—
683	#41	—	2	4	no	—
684	#41	—	2	2	no	—
685	#41	—	2	2	no	—
686	#41	—	2	2	no	—
687	#41	C₅×#41	1	4	yes	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	4	no	—
692	C₂×Q₈	—	2	4	no	—
693	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
694	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
695	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
696	C₂×D₄	—	2	16	no	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
706	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
707	C₂×D₄	C₅×#41	1	4	yes	—
708	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
709	C₂×D₄	C₂⁴×C₅	1	2	yes	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	8	2	no	—
723	C₂²×C₄	—	8	4	no	—
724	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
725	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
726	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
727	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
730	Q₁₆	—	2	8	no	—
731	SD₁₆	—	2	8	no	—
732	SD₁₆	—	2	8	no	—
733	SD₁₆	—	2	8	no	—
734	M₁₆	—	2	4	no	—
735	C₂×C₈	—	2	4	no	—
736	C₂×C₈	C₂⁴×C₅	1	2	yes	—
737	C₂×C₈	C₂⁴×C₅	1	4	yes	—
738	C₂×C₈	C₂⁴×C₅	1	2	yes	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
757	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
758	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
759	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
760	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
763	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
778	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
779	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	4	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	2	no	—
788	C₄²	C₂×C₅×D₄	1	2	yes	—
789	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
790	C₄²	C₂×C₅×D₄	1	2	yes	—
791	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
792	C₄²	C₂⁴×C₅	1	2	yes	—
793	C₄²	C₂⁴×C₅	1	1	yes	characteristic
794	C₄²	C₂⁴×C₅	1	1	yes	characteristic
795	C₂×C₅	—	2	2	no	—
796	C₂×C₅	—	4	2	no	—
797	C₂×C₅	—	4	4	no	—
798	C₂×C₅	—	4	2	no	—
799	C₂×C₅	C₂×#525	1	1	yes	characteristic
800	C₂×C₅	C₂×#577	1	1	yes	characteristic
801	C₂×C₅	#3586	1	1	yes	characteristic
802	C₂³	—	2	8	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	8	1	no	—
807	C₂³	—	8	2	no	—
808	C₂³	—	8	1	no	—
809	C₂³	—	8	2	no	—
810	C₂³	C₂²×C₅×D₄	1	2	yes	—
811	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
812	Q₈	—	2	2	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	2	4	no	—
816	Q₈	—	4	2	no	—
817	Q₈	—	4	4	no	—
818	Q₈	—	4	2	no	—
819	Q₈	C₂×C₅×#41	1	2	yes	—
820	D₄	—	2	8	no	—
821	D₄	—	2	8	no	—
822	D₄	—	2	4	no	—
823	D₄	—	2	4	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	1	no	—
828	D₄	C₂×C₅×#41	1	2	yes	—
829	D₄	C₂×C₅×#41	1	4	yes	—
830	C₂×C₄	—	2	8	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	8	2	no	—
849	C₂×C₄	—	8	2	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	1	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
856	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
857	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
858	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
859	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
860	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
861	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
862	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
863	C₂×C₄	C₂×C₅×#41	1	2	yes	—
864	C₂×C₄	C₂×C₅×#41	1	2	yes	—
865	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
866	C₈	—	2	2	no	—
867	C₈	—	2	2	no	—
868	C₈	—	2	4	no	—
869	C₅	#60591	1	1	yes	characteristic, direct product factor, Sylow
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	8	4	no	—
882	C₂²	—	8	8	no	—
883	C₂²	C₅×#525	1	2	yes	—
884	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	1	no	—
892	C₄	—	4	4	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	2	no	—
898	C₄	C₅×#525	1	2	yes	—
899	C₄	C₅×#577	1	2	yes	—
900	C₄	C₂²×C₅×#41	1	1	yes	characteristic
901	C₄	C₂²×C₅×#41	1	1	yes	characteristic
902	C₂	—	2	2	no	—
903	C₂	—	4	2	no	—
904	C₂	—	4	4	no	—
905	C₂	—	4	2	no	—
906	C₂	C₂×C₅×#525	1	1	yes	characteristic
907	C₂	C₂×C₅×#577	1	1	yes	characteristic
908	C₂	C₅×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×H(5,𝔽₂)	C₂²
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×#3509	C₂	semidirect
3. C₅×#3123	C₂	semidirect
4. C₅×#3120	C₂	semidirect
5. C₅×#3116	C₂	semidirect
6. C₅×#3110	C₂	semidirect
7. C₅×#3107	C₂	semidirect
8. C₅×#3101	C₂	semidirect
9. C₅×#3097	C₂	semidirect
10. C₅×#3077	C₂	semidirect
11. C₅×#3076	C₂	semidirect
12. C₅×#3039	C₂	semidirect
13. C₂×C₅×#461	C₂	semidirect
15. C₅×#2949	C₂	semidirect
16. C₅×#2947	C₂	semidirect
17. C₅×#2925	C₂	semidirect
27. C₅×#541	C₂²	semidirect
29. C₅×#533	C₂²	semidirect
30. C₅×#533	C₂²	semidirect
31. C₅×#533	C₂²	semidirect
32. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
37. C₅×#519	C₂²	semidirect
50. C₅×#485	C₂²	semidirect
51. C₅×#485	C₂²	semidirect
52. C₅×#484	C₂²	semidirect
53. C₅×#483	C₂²	semidirect
54. C₅×#479	C₂²	semidirect
55. C₅×#478	C₂²	semidirect
56. C₅×#478	C₂²	semidirect
57. C₅×#477	C₂²	semidirect
58. C₅×#476	C₂²	semidirect
59. C₅×#476	C₂²	semidirect
60. C₅×#475	C₂²	semidirect
61. C₅×#474	C₂²	semidirect
62. C₅×#474	C₂²	semidirect
63. C₅×#462	C₂²	semidirect
64. C₅×#462	C₂²	semidirect
65. C₅×#461	C₂²	semidirect
66. C₅×#461	C₂²	semidirect
67. C₅×#461	C₂²	semidirect
68. C₅×#461	C₂²	semidirect
69. C₅×#461	C₂²	semidirect
74. C₅×#441	C₂²	semidirect
75. C₅×#440	C₂²	semidirect
76. C₅×#440	C₂²	semidirect
77. C₅×#440	C₂²	semidirect
78. C₄×C₅×Q₁₆	C₂²	semidirect
79. C₄×C₅×SD₁₆	C₂²	semidirect
80. C₄×C₅×SD₁₆	C₂²	semidirect
81. C₄×C₅×SD₁₆	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
83. C₅×#432	C₂²	semidirect
84. C₅×#431	C₂²	semidirect
85. C₅×#428	C₂²	semidirect
86. C₅×#427	C₂²	semidirect
87. C₅×#423	C₂²	semidirect
88. C₂×C₅×C₄⋊C₈	C₂²	semidirect
89. C₅×#419	C₂²	semidirect
92. C₂×C₅×#103	C₂²	semidirect
94. C₅×#405	C₂²	semidirect
95. #60591	C₅	direct (N × H)
233. #3509	C₂×C₅	semidirect
235. #3123	C₂×C₅	semidirect
236. #3120	C₂×C₅	semidirect
237. #3116	C₂×C₅	semidirect
238. #3110	C₂×C₅	semidirect
239. #3107	C₂×C₅	semidirect
240. #3101	C₂×C₅	semidirect
241. #3097	C₂×C₅	semidirect
242. #3077	C₂×C₅	semidirect
243. #3076	C₂×C₅	semidirect
244. #3039	C₂×C₅	semidirect
245. C₂×#461	C₂×C₅	semidirect
247. #2949	C₂×C₅	semidirect
248. #2947	C₂×C₅	semidirect
249. #2925	C₂×C₅	semidirect
375. #541	C₂²×C₅	semidirect
377. #533	C₂²×C₅	semidirect
378. #533	C₂²×C₅	semidirect
379. #533	C₂²×C₅	semidirect
380. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
385. #519	C₂²×C₅	semidirect
398. #485	C₂²×C₅	semidirect
399. #485	C₂²×C₅	semidirect
400. #484	C₂²×C₅	semidirect
401. #483	C₂²×C₅	semidirect
402. #479	C₂²×C₅	semidirect
403. #478	C₂²×C₅	semidirect
404. #478	C₂²×C₅	semidirect
405. #477	C₂²×C₅	semidirect
406. #476	C₂²×C₅	semidirect
407. #476	C₂²×C₅	semidirect
408. #475	C₂²×C₅	semidirect
409. #474	C₂²×C₅	semidirect
410. #474	C₂²×C₅	semidirect
411. #462	C₂²×C₅	semidirect
412. #462	C₂²×C₅	semidirect
413. #461	C₂²×C₅	semidirect
414. #461	C₂²×C₅	semidirect
415. #461	C₂²×C₅	semidirect
416. #461	C₂²×C₅	semidirect
417. #461	C₂²×C₅	semidirect
422. #441	C₂²×C₅	semidirect
423. #440	C₂²×C₅	semidirect
424. #440	C₂²×C₅	semidirect
425. #440	C₂²×C₅	semidirect
426. C₄×Q₁₆	C₂²×C₅	semidirect
427. C₄×SD₁₆	C₂²×C₅	semidirect
428. C₄×SD₁₆	C₂²×C₅	semidirect
429. C₄×SD₁₆	C₂²×C₅	semidirect
430. #433	C₂²×C₅	semidirect
431. #432	C₂²×C₅	semidirect
432. #431	C₂²×C₅	semidirect
433. #428	C₂²×C₅	semidirect
434. #427	C₂²×C₅	semidirect
435. #423	C₂²×C₅	semidirect
436. C₂×C₄⋊C₈	C₂²×C₅	semidirect
437. #419	C₂²×C₅	semidirect
440. C₂×#103	C₂²×C₅	semidirect
442. #405	C₂²×C₅	semidirect
869. C₅	#60591	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×#3509	2
C₄×C₅×H(5,𝔽₂)	2
C₅×#3123	2
C₅×#3120	2
C₅×#3116	2
C₅×#3110	2
C₅×#3107	2
C₅×#3101	2
C₅×#3097	2
C₅×#3077	2
C₅×#3076	2
C₅×#3039	2
C₂×C₅×#461	2
C₅×#3009	2
C₅×#2949	2
C₅×#2947	2
C₅×#2925	2
#60591	5

Subgroups — C5×#60591 #11983311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60591 #11983311