Subgroups — C₂×C₅×#3519 #11985491

Order 1280.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3519	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#546	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#546	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×D₄²	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#540	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#538	C₂	1	4	yes	maximal, complemented
13	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#525	C₂	1	2	yes	maximal, complemented
16	C₂²×C₅×#121	C₂	1	2	yes	maximal, complemented
17	C₂×C₅×#518	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₅×#41	C₂²	1	2	yes	complemented
20	C₂²×C₅×#41	C₂²	1	2	yes	complemented
21	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂³×C₅×D₄	C₂²	1	2	yes	—
23	C₂³×C₅×D₄	C₂²	1	2	yes	complemented
24	C₂³×C₅×D₄	C₂²	1	4	yes	complemented
25	C₂⁴×C₄×C₅	C₂²	1	2	yes	complemented
26	C₅×#555	C₂²	1	16	yes	complemented
27	C₅×#554	C₂²	1	16	yes	complemented
28	C₅×#553	C₂²	1	32	yes	complemented
29	C₅×#553	C₂²	1	32	yes	complemented
30	C₅×#550	C₂²	1	16	yes	complemented
31	C₅×#546	C₂²	1	64	yes	complemented
32	C₅×#546	C₂²	1	32	yes	complemented
33	C₅×D₄²	C₂²	1	16	yes	complemented
34	C₅×D₄²	C₂²	1	32	yes	complemented
35	C₅×#540	C₂²	1	32	yes	complemented
36	C₅×#538	C₂²	1	64	yes	complemented
37	C₅×#532	C₂²	1	16	yes	complemented
38	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×#127	C₂²	1	2	yes	complemented
41	C₅×#529	C₂²	1	16	yes	complemented
42	C₂×C₅×#126	C₂²	1	2	yes	complemented
43	C₂×C₅×#126	C₂²	1	4	yes	complemented
44	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×#125	C₂²	1	2	yes	complemented
46	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₅×#124	C₂²	1	2	yes	complemented
48	C₂×C₅×#124	C₂²	1	4	yes	complemented
49	C₅×#525	C₂²	1	32	yes	complemented
50	C₂×C₅×#123	C₂²	1	4	yes	complemented
51	C₂×C₅×#123	C₂²	1	2	yes	complemented
52	C₂×C₅×#123	C₂²	1	4	yes	complemented
53	C₂×C₅×#123	C₂²	1	4	yes	complemented
54	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₅×#121	C₂²	1	1	yes	characteristic
58	C₂×C₅×#121	C₂²	1	2	yes	complemented
59	C₂×C₅×#121	C₂²	1	4	yes	complemented
60	C₂×C₅×#121	C₂²	1	4	yes	complemented
61	C₂×C₅×#121	C₂²	1	2	yes	complemented
62	C₂×C₅×#121	C₂²	1	2	yes	complemented
63	C₂×C₅×#121	C₂²	1	2	yes	complemented
64	C₂×C₅×#121	C₂²	1	2	yes	complemented
65	C₂×C₅×#121	C₂²	1	4	yes	complemented
66	C₂×C₅×#121	C₂²	1	4	yes	complemented
67	C₂×C₅×#121	C₂²	1	2	yes	complemented
68	C₂×C₅×#121	C₂²	1	2	yes	complemented
69	C₂×C₅×#121	C₂²	1	4	yes	complemented
70	C₂×C₅×#121	C₂²	1	32	yes	complemented
71	C₂×C₅×#120	C₂²	1	4	yes	complemented
72	C₂×C₅×#120	C₂²	1	4	yes	complemented
73	C₂×C₅×#120	C₂²	1	4	yes	complemented
74	C₅×#518	C₂²	1	32	yes	complemented
75	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
77	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
78	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
79	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
80	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
82	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
84	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
85	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
86	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
87	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
88	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
89	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
91	C₂×C₄×C₅×D₄	C₂²	1	16	yes	complemented
92	C₂×C₅×#117	C₂²	1	2	yes	complemented
93	C₂×C₅×#117	C₂²	1	2	yes	complemented
94	C₂×C₅×#117	C₂²	1	2	yes	complemented
95	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
99	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
101	C₂×#3519	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁵×C₅	C₂³	1	2	yes	—
103	C₂⁵×C₅	C₂³	1	4	yes	—
104	C₂×C₅×#41	—	4	8	no	—
105	C₂×C₅×#41	—	4	8	no	—
106	C₂×C₅×#41	C₂³	1	16	yes	complemented
107	C₂×C₅×#41	C₂³	1	16	yes	complemented
108	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₅×Q₈	C₂³	1	2	yes	—
110	C₂²×C₅×D₄	—	2	8	no	—
111	C₂²×C₅×D₄	—	2	16	no	—
112	C₂²×C₅×D₄	—	4	8	no	—
113	C₂²×C₅×D₄	—	4	16	no	—
114	C₂²×C₅×D₄	C₂³	1	2	yes	—
115	C₂²×C₅×D₄	C₂³	1	4	yes	—
116	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₅×D₄	C₂³	1	2	yes	—
118	C₂²×C₅×D₄	C₂³	1	8	yes	—
119	C₂²×C₅×D₄	C₂³	1	4	yes	—
120	C₂²×C₅×D₄	C₂³	1	2	yes	—
121	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
122	C₂²×C₅×D₄	C₂³	1	2	yes	—
123	C₂²×C₅×D₄	C₂³	1	16	yes	—
124	C₂²×C₅×D₄	C₂³	1	4	yes	—
125	C₂²×C₅×D₄	C₂³	1	2	yes	—
126	C₂²×C₅×D₄	C₂³	1	4	yes	—
127	C₂²×C₅×D₄	C₂³	1	4	yes	—
128	C₂²×C₅×D₄	C₂³	1	4	yes	—
129	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₅×D₄	C₂³	1	16	yes	complemented
131	C₂²×C₅×D₄	C₂³	1	32	yes	complemented
132	C₂³×C₄×C₅	—	4	8	no	—
133	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₅	C₂³	1	2	yes	—
137	C₂³×C₄×C₅	C₂³	1	2	yes	—
138	C₂³×C₄×C₅	C₂³	1	2	yes	—
139	C₂³×C₄×C₅	C₂³	1	2	yes	—
140	C₂³×C₄×C₅	C₂³	1	4	yes	—
141	C₂³×C₄×C₅	C₂³	1	2	yes	—
142	C₂³×C₄×C₅	C₂³	1	4	yes	—
143	C₂³×C₄×C₅	C₂³	1	4	yes	—
144	C₂³×C₄×C₅	C₂³	1	2	yes	—
145	C₂³×C₄×C₅	C₂³	1	16	yes	complemented
146	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
147	C₅×#127	C₂³	1	8	yes	complemented
148	C₅×#127	C₂³	1	16	yes	complemented
149	C₅×#126	C₂³	1	16	yes	complemented
150	C₅×#126	C₂³	1	32	yes	complemented
151	C₅×#125	C₂³	1	8	yes	complemented
152	C₅×#125	C₂³	1	16	yes	complemented
153	C₅×#124	C₂³	1	8	yes	complemented
154	C₅×#124	C₂³	1	16	yes	complemented
155	C₅×#124	C₂³	1	32	yes	complemented
156	C₅×#123	C₂³	1	32	yes	complemented
157	C₅×#123	C₂³	1	16	yes	complemented
158	C₅×#123	C₂³	1	32	yes	complemented
159	C₅×#123	C₂³	1	32	yes	complemented
160	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
161	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
162	C₅×C₂²⋊Q₈	C₂³	1	32	yes	complemented
163	C₅×#121	C₂³	1	8	yes	—
164	C₅×#121	C₂³	1	16	yes	complemented
165	C₅×#121	C₂³	1	32	yes	complemented
166	C₅×#121	C₂³	1	32	yes	complemented
167	C₅×#121	C₂³	1	16	yes	complemented
168	C₅×#121	C₂³	1	16	yes	complemented
169	C₅×#121	C₂³	1	16	yes	complemented
170	C₅×#121	C₂³	1	16	yes	complemented
171	C₅×#121	C₂³	1	32	yes	complemented
172	C₅×#121	C₂³	1	32	yes	complemented
173	C₅×#121	C₂³	1	16	yes	complemented
174	C₅×#121	C₂³	1	16	yes	complemented
175	C₅×#121	C₂³	1	32	yes	complemented
176	C₅×#120	C₂³	1	32	yes	complemented
177	C₅×#120	C₂³	1	32	yes	complemented
178	C₅×#120	C₂³	1	32	yes	complemented
179	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
180	C₄×C₅×D₄	C₂³	1	8	yes	—
181	C₄×C₅×D₄	C₂³	1	8	yes	—
182	C₄×C₅×D₄	C₂³	1	16	yes	—
183	C₄×C₅×D₄	C₂³	1	16	yes	complemented
184	C₄×C₅×D₄	C₂³	1	8	yes	complemented
185	C₄×C₅×D₄	C₂³	1	16	yes	complemented
186	C₄×C₅×D₄	C₂³	1	8	yes	complemented
187	C₄×C₅×D₄	C₂³	1	32	yes	complemented
188	C₄×C₅×D₄	C₂³	1	16	yes	complemented
189	C₄×C₅×D₄	C₂³	1	32	yes	complemented
190	C₄×C₅×D₄	C₂³	1	16	yes	complemented
191	C₄×C₅×D₄	C₂³	1	32	yes	complemented
192	C₄×C₅×D₄	C₂³	1	16	yes	complemented
193	C₄×C₅×D₄	C₂³	1	8	yes	complemented
194	C₄×C₅×D₄	C₂³	1	16	yes	complemented
195	C₅×#117	C₂³	1	16	yes	complemented
196	C₅×#117	C₂³	1	16	yes	complemented
197	C₅×#117	C₂³	1	16	yes	complemented
198	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
210	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
212	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	complemented
213	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
228	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
229	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
230	C₂×C₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
231	C₂×C₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
232	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅	C₂³	1	4	yes	—
237	C₂×C₄²×C₅	C₂³	1	2	yes	—
238	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
239	#3519	C₂×C₅	1	32	yes	direct product factor
240	C₂×#555	C₂×C₅	1	1	yes	characteristic, complemented
241	C₂×#554	C₂×C₅	1	1	yes	characteristic, complemented
242	C₂×#553	C₂×C₅	1	2	yes	complemented
243	C₂×#553	C₂×C₅	1	2	yes	complemented
244	C₂×#550	C₂×C₅	1	1	yes	characteristic, complemented
245	C₂×#546	C₂×C₅	1	4	yes	complemented
246	C₂×#546	C₂×C₅	1	2	yes	complemented
247	C₂×D₄²	C₂×C₅	1	1	yes	characteristic, complemented
248	C₂×D₄²	C₂×C₅	1	2	yes	complemented
249	C₂×#540	C₂×C₅	1	2	yes	complemented
250	C₂×#538	C₂×C₅	1	4	yes	complemented
251	C₂×#532	C₂×C₅	1	1	yes	characteristic, complemented
252	C₂×#529	C₂×C₅	1	1	yes	characteristic, complemented
253	C₂×#525	C₂×C₅	1	2	yes	complemented
254	C₂²×#121	C₂×C₅	1	2	yes	complemented
255	C₂×#518	C₂×C₅	1	2	yes	complemented
256	C₂²×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
257	C₂⁴×C₅	—	2	8	no	—
258	C₂⁴×C₅	—	2	8	no	—
259	C₂⁴×C₅	—	2	16	no	—
260	C₂⁴×C₅	—	4	4	no	—
261	C₂⁴×C₅	—	4	8	no	—
262	C₂⁴×C₅	—	4	8	no	—
263	C₂⁴×C₅	C₂⁴	1	2	yes	—
264	C₂⁴×C₅	C₂⁴	1	2	yes	—
265	C₂⁴×C₅	C₂⁴	1	4	yes	—
266	C₂⁴×C₅	C₂⁴	1	8	yes	—
267	C₂⁴×C₅	C₂⁴	1	2	yes	—
268	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₅	C₂⁴	1	16	yes	—
270	C₅×#41	—	4	32	no	—
271	C₅×#41	—	4	32	no	—
272	C₂×C₅×Q₈	—	2	4	no	—
273	C₂×C₅×Q₈	—	4	4	no	—
274	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
275	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
276	C₂×C₅×D₄	—	2	8	no	—
277	C₂×C₅×D₄	—	2	16	no	—
278	C₂×C₅×D₄	—	2	8	no	—
279	C₂×C₅×D₄	—	2	16	no	—
280	C₂×C₅×D₄	—	2	32	no	—
281	C₂×C₅×D₄	—	2	64	no	—
282	C₂×C₅×D₄	—	2	4	no	—
283	C₂×C₅×D₄	—	2	8	no	—
284	C₂×C₅×D₄	—	2	4	no	—
285	C₂×C₅×D₄	—	2	8	no	—
286	C₂×C₅×D₄	—	4	32	no	—
287	C₂×C₅×D₄	—	4	8	no	—
288	C₂×C₅×D₄	—	4	8	no	—
289	C₂×C₅×D₄	—	4	8	no	—
290	C₂×C₅×D₄	—	4	4	no	—
291	C₂×C₅×D₄	—	4	8	no	—
292	C₂×C₅×D₄	—	4	64	no	—
293	C₂×C₅×D₄	#41	1	8	yes	complemented
294	C₂×C₅×D₄	C₂⁴	1	8	yes	—
295	C₂×C₅×D₄	C₂⁴	1	16	yes	—
296	C₂×C₅×D₄	C₂⁴	1	4	yes	—
297	C₂×C₅×D₄	C₂⁴	1	8	yes	—
298	C₂×C₅×D₄	C₂⁴	1	16	yes	—
299	C₂×C₅×D₄	C₂⁴	1	8	yes	—
300	C₂×C₅×D₄	C₂⁴	1	4	yes	—
301	C₂×C₅×D₄	C₂⁴	1	8	yes	—
302	C₂×C₅×D₄	C₂⁴	1	16	yes	—
303	C₂×C₅×D₄	C₂⁴	1	8	yes	—
304	C₂×C₅×D₄	C₂⁴	1	16	yes	—
305	C₂×C₅×D₄	C₂⁴	1	16	yes	—
306	C₂×C₅×D₄	C₂⁴	1	16	yes	—
307	C₂×C₅×D₄	C₂⁴	1	4	yes	—
308	C₂²×C₄×C₅	—	2	4	no	—
309	C₂²×C₄×C₅	—	2	4	no	—
310	C₂²×C₄×C₅	—	2	8	no	—
311	C₂²×C₄×C₅	—	2	4	no	—
312	C₂²×C₄×C₅	—	2	8	no	—
313	C₂²×C₄×C₅	—	2	8	no	—
314	C₂²×C₄×C₅	—	4	32	no	—
315	C₂²×C₄×C₅	—	4	4	no	—
316	C₂²×C₄×C₅	—	4	4	no	—
317	C₂²×C₄×C₅	—	4	4	no	—
318	C₂²×C₄×C₅	—	4	8	no	—
319	C₂²×C₄×C₅	—	4	8	no	—
320	C₂²×C₄×C₅	—	4	8	no	—
321	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
322	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
323	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
324	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
326	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
327	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
338	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
339	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
340	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
341	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
342	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
343	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
345	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
346	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
347	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
348	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
349	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
350	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
351	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
352	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
353	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
354	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
355	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
356	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
357	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
358	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
359	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
360	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
361	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
362	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
363	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
364	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
365	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
366	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
367	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
368	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
369	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
370	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
371	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
372	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
373	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
374	C₄²×C₅	C₂⁴	1	4	yes	—
375	C₄²×C₅	C₂⁴	1	4	yes	—
376	C₄²×C₅	C₂⁴	1	4	yes	—
377	C₄²×C₅	C₂⁴	1	4	yes	—
378	C₄²×C₅	C₂⁴	1	16	yes	—
379	C₄²×C₅	C₂⁴	1	8	yes	—
380	C₂²×#41	C₂²×C₅	1	2	yes	complemented
381	C₂²×#41	C₂²×C₅	1	2	yes	complemented
382	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
383	C₂³×D₄	C₂²×C₅	1	2	yes	—
384	C₂³×D₄	C₂²×C₅	1	2	yes	complemented
385	C₂³×D₄	C₂²×C₅	1	4	yes	complemented
386	C₂⁴×C₄	C₂²×C₅	1	2	yes	complemented
387	#555	C₂²×C₅	1	16	yes	complemented
388	#554	C₂²×C₅	1	16	yes	complemented
389	#553	C₂²×C₅	1	32	yes	complemented
390	#553	C₂²×C₅	1	32	yes	complemented
391	#550	C₂²×C₅	1	16	yes	complemented
392	#546	C₂²×C₅	1	64	yes	complemented
393	#546	C₂²×C₅	1	32	yes	complemented
394	D₄²	C₂²×C₅	1	16	yes	complemented
395	D₄²	C₂²×C₅	1	32	yes	complemented
396	#540	C₂²×C₅	1	32	yes	complemented
397	#538	C₂²×C₅	1	64	yes	complemented
398	#532	C₂²×C₅	1	16	yes	complemented
399	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
400	C₂×#127	C₂²×C₅	1	1	yes	characteristic, complemented
401	C₂×#127	C₂²×C₅	1	2	yes	complemented
402	#529	C₂²×C₅	1	16	yes	complemented
403	C₂×#126	C₂²×C₅	1	2	yes	complemented
404	C₂×#126	C₂²×C₅	1	4	yes	complemented
405	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
406	C₂×#125	C₂²×C₅	1	2	yes	complemented
407	C₂×#124	C₂²×C₅	1	1	yes	characteristic, complemented
408	C₂×#124	C₂²×C₅	1	2	yes	complemented
409	C₂×#124	C₂²×C₅	1	4	yes	complemented
410	#525	C₂²×C₅	1	32	yes	complemented
411	C₂×#123	C₂²×C₅	1	4	yes	complemented
412	C₂×#123	C₂²×C₅	1	2	yes	complemented
413	C₂×#123	C₂²×C₅	1	4	yes	complemented
414	C₂×#123	C₂²×C₅	1	4	yes	complemented
415	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
416	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
417	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
418	C₂×#121	C₂²×C₅	1	1	yes	characteristic
419	C₂×#121	C₂²×C₅	1	2	yes	complemented
420	C₂×#121	C₂²×C₅	1	4	yes	complemented
421	C₂×#121	C₂²×C₅	1	4	yes	complemented
422	C₂×#121	C₂²×C₅	1	2	yes	complemented
423	C₂×#121	C₂²×C₅	1	2	yes	complemented
424	C₂×#121	C₂²×C₅	1	2	yes	complemented
425	C₂×#121	C₂²×C₅	1	2	yes	complemented
426	C₂×#121	C₂²×C₅	1	4	yes	complemented
427	C₂×#121	C₂²×C₅	1	4	yes	complemented
428	C₂×#121	C₂²×C₅	1	2	yes	complemented
429	C₂×#121	C₂²×C₅	1	2	yes	complemented
430	C₂×#121	C₂²×C₅	1	4	yes	complemented
431	C₂×#121	C₂²×C₅	1	32	yes	complemented
432	C₂×#120	C₂²×C₅	1	4	yes	complemented
433	C₂×#120	C₂²×C₅	1	4	yes	complemented
434	C₂×#120	C₂²×C₅	1	4	yes	complemented
435	#518	C₂²×C₅	1	32	yes	complemented
436	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
437	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
440	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
441	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
442	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
443	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
444	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
445	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
446	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
447	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
448	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
449	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
450	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
451	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
452	C₂×C₄×D₄	C₂²×C₅	1	16	yes	complemented
453	C₂×#117	C₂²×C₅	1	2	yes	complemented
454	C₂×#117	C₂²×C₅	1	2	yes	complemented
455	C₂×#117	C₂²×C₅	1	2	yes	complemented
456	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
457	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
458	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
459	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
460	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
461	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
462	C₂³×C₅	—	2	2	no	—
463	C₂³×C₅	—	2	2	no	—
464	C₂³×C₅	—	2	4	no	—
465	C₂³×C₅	—	2	4	no	—
466	C₂³×C₅	—	2	4	no	—
467	C₂³×C₅	—	2	16	no	—
468	C₂³×C₅	—	2	4	no	—
469	C₂³×C₅	—	2	8	no	—
470	C₂³×C₅	—	2	4	no	—
471	C₂³×C₅	—	2	8	no	—
472	C₂³×C₅	—	2	8	no	—
473	C₂³×C₅	—	2	4	no	—
474	C₂³×C₅	—	2	4	no	—
475	C₂³×C₅	—	2	16	no	—
476	C₂³×C₅	—	2	4	no	—
477	C₂³×C₅	—	2	32	no	—
478	C₂³×C₅	—	4	8	no	—
479	C₂³×C₅	—	4	16	no	—
480	C₂³×C₅	—	4	16	no	—
481	C₂³×C₅	—	4	32	no	—
482	C₂³×C₅	—	8	32	no	—
483	C₂³×C₅	C₂×#41	1	8	yes	—
484	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
485	C₂³×C₅	C₂⁵	1	4	yes	—
486	C₂³×C₅	C₂⁵	1	4	yes	—
487	C₂³×C₅	C₂⁵	1	8	yes	—
488	C₂³×C₅	C₂⁵	1	4	yes	—
489	C₂³×C₅	C₂⁵	1	2	yes	—
490	C₂³×C₅	C₂⁵	1	1	yes	characteristic
491	C₅×Q₈	—	2	8	no	—
492	C₅×Q₈	—	4	8	no	—
493	C₅×D₄	—	2	16	no	—
494	C₅×D₄	—	2	32	no	—
495	C₅×D₄	—	2	16	no	—
496	C₅×D₄	—	2	32	no	—
497	C₅×D₄	—	2	8	no	—
498	C₅×D₄	—	2	16	no	—
499	C₅×D₄	—	2	8	no	—
500	C₅×D₄	—	2	16	no	—
501	C₅×D₄	—	4	16	no	—
502	C₅×D₄	—	4	16	no	—
503	C₅×D₄	—	4	16	no	—
504	C₅×D₄	—	4	8	no	—
505	C₅×D₄	—	4	16	no	—
506	C₅×D₄	C₂×#41	1	16	yes	complemented
507	C₂×C₄×C₅	—	2	2	no	—
508	C₂×C₄×C₅	—	2	4	no	—
509	C₂×C₄×C₅	—	2	2	no	—
510	C₂×C₄×C₅	—	2	2	no	—
511	C₂×C₄×C₅	—	2	4	no	—
512	C₂×C₄×C₅	—	2	4	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	8	no	—
515	C₂×C₄×C₅	—	2	4	no	—
516	C₂×C₄×C₅	—	2	8	no	—
517	C₂×C₄×C₅	—	2	4	no	—
518	C₂×C₄×C₅	—	2	8	no	—
519	C₂×C₄×C₅	—	2	16	no	—
520	C₂×C₄×C₅	—	2	8	no	—
521	C₂×C₄×C₅	—	2	16	no	—
522	C₂×C₄×C₅	—	2	16	no	—
523	C₂×C₄×C₅	—	4	8	no	—
524	C₂×C₄×C₅	—	4	8	no	—
525	C₂×C₄×C₅	—	4	8	no	—
526	C₂×C₄×C₅	—	4	16	no	—
527	C₂×C₄×C₅	—	4	16	no	—
528	C₂×C₄×C₅	—	4	16	no	—
529	C₂×C₄×C₅	C₂×#41	1	4	yes	—
530	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
531	C₂×C₄×C₅	C₂⁵	1	2	yes	—
532	C₂×C₄×C₅	C₂⁵	1	4	yes	—
533	C₂×C₄×C₅	C₂⁵	1	2	yes	—
534	C₂×C₄×C₅	C₂⁵	1	2	yes	—
535	C₂×C₄×C₅	C₂⁵	1	4	yes	—
536	C₂×C₄×C₅	C₂⁵	1	2	yes	—
537	C₂×C₄×C₅	C₂⁵	1	8	yes	—
538	C₂×C₄×C₅	C₂⁵	1	4	yes	—
539	C₂×C₄×C₅	C₂⁵	1	4	yes	—
540	C₂×C₄×C₅	C₂⁵	1	4	yes	—
541	C₂×C₄×C₅	C₂⁵	1	2	yes	—
542	C₂×C₄×C₅	C₂⁵	1	2	yes	—
543	C₂⁵	C₂³×C₅	1	2	yes	—
544	C₂⁵	C₂³×C₅	1	4	yes	—
545	C₂×#41	—	4	8	no	—
546	C₂×#41	—	4	8	no	—
547	C₂×#41	C₂³×C₅	1	16	yes	complemented
548	C₂×#41	C₂³×C₅	1	16	yes	complemented
549	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₅	1	2	yes	—
551	C₂²×D₄	—	2	8	no	—
552	C₂²×D₄	—	2	16	no	—
553	C₂²×D₄	—	4	8	no	—
554	C₂²×D₄	—	4	16	no	—
555	C₂²×D₄	C₂³×C₅	1	2	yes	—
556	C₂²×D₄	C₂³×C₅	1	4	yes	—
557	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₅	1	2	yes	—
559	C₂²×D₄	C₂³×C₅	1	8	yes	—
560	C₂²×D₄	C₂³×C₅	1	4	yes	—
561	C₂²×D₄	C₂³×C₅	1	2	yes	—
562	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₅	1	2	yes	—
564	C₂²×D₄	C₂³×C₅	1	16	yes	—
565	C₂²×D₄	C₂³×C₅	1	4	yes	—
566	C₂²×D₄	C₂³×C₅	1	2	yes	—
567	C₂²×D₄	C₂³×C₅	1	4	yes	—
568	C₂²×D₄	C₂³×C₅	1	4	yes	—
569	C₂²×D₄	C₂³×C₅	1	4	yes	—
570	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₅	1	16	yes	complemented
572	C₂²×D₄	C₂³×C₅	1	32	yes	complemented
573	C₂³×C₄	—	4	8	no	—
574	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₅	1	2	yes	—
576	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₅	1	2	yes	—
578	C₂³×C₄	C₂³×C₅	1	2	yes	—
579	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₅	1	2	yes	—
581	C₂³×C₄	C₂³×C₅	1	4	yes	—
582	C₂³×C₄	C₂³×C₅	1	2	yes	—
583	C₂³×C₄	C₂³×C₅	1	4	yes	—
584	C₂³×C₄	C₂³×C₅	1	4	yes	—
585	C₂³×C₄	C₂³×C₅	1	2	yes	—
586	C₂³×C₄	C₂³×C₅	1	16	yes	complemented
587	C₄⋊Q₈	C₂³×C₅	1	8	yes	complemented
588	#127	C₂³×C₅	1	8	yes	complemented
589	#127	C₂³×C₅	1	16	yes	complemented
590	#126	C₂³×C₅	1	16	yes	complemented
591	#126	C₂³×C₅	1	32	yes	complemented
592	#125	C₂³×C₅	1	8	yes	complemented
593	#125	C₂³×C₅	1	16	yes	complemented
594	#124	C₂³×C₅	1	8	yes	complemented
595	#124	C₂³×C₅	1	16	yes	complemented
596	#124	C₂³×C₅	1	32	yes	complemented
597	#123	C₂³×C₅	1	32	yes	complemented
598	#123	C₂³×C₅	1	16	yes	complemented
599	#123	C₂³×C₅	1	32	yes	complemented
600	#123	C₂³×C₅	1	32	yes	complemented
601	C₂²⋊Q₈	C₂³×C₅	1	8	yes	complemented
602	C₂²⋊Q₈	C₂³×C₅	1	16	yes	complemented
603	C₂²⋊Q₈	C₂³×C₅	1	32	yes	complemented
604	#121	C₂³×C₅	1	8	yes	—
605	#121	C₂³×C₅	1	16	yes	complemented
606	#121	C₂³×C₅	1	32	yes	complemented
607	#121	C₂³×C₅	1	32	yes	complemented
608	#121	C₂³×C₅	1	16	yes	complemented
609	#121	C₂³×C₅	1	16	yes	complemented
610	#121	C₂³×C₅	1	16	yes	complemented
611	#121	C₂³×C₅	1	16	yes	complemented
612	#121	C₂³×C₅	1	32	yes	complemented
613	#121	C₂³×C₅	1	32	yes	complemented
614	#121	C₂³×C₅	1	16	yes	complemented
615	#121	C₂³×C₅	1	16	yes	complemented
616	#121	C₂³×C₅	1	32	yes	complemented
617	#120	C₂³×C₅	1	32	yes	complemented
618	#120	C₂³×C₅	1	32	yes	complemented
619	#120	C₂³×C₅	1	32	yes	complemented
620	C₄×Q₈	C₂³×C₅	1	8	yes	complemented
621	C₄×D₄	C₂³×C₅	1	8	yes	—
622	C₄×D₄	C₂³×C₅	1	8	yes	—
623	C₄×D₄	C₂³×C₅	1	16	yes	—
624	C₄×D₄	C₂³×C₅	1	16	yes	complemented
625	C₄×D₄	C₂³×C₅	1	8	yes	complemented
626	C₄×D₄	C₂³×C₅	1	16	yes	complemented
627	C₄×D₄	C₂³×C₅	1	8	yes	complemented
628	C₄×D₄	C₂³×C₅	1	32	yes	complemented
629	C₄×D₄	C₂³×C₅	1	16	yes	complemented
630	C₄×D₄	C₂³×C₅	1	32	yes	complemented
631	C₄×D₄	C₂³×C₅	1	16	yes	complemented
632	C₄×D₄	C₂³×C₅	1	32	yes	complemented
633	C₄×D₄	C₂³×C₅	1	16	yes	complemented
634	C₄×D₄	C₂³×C₅	1	8	yes	complemented
635	C₄×D₄	C₂³×C₅	1	16	yes	complemented
636	#117	C₂³×C₅	1	16	yes	complemented
637	#117	C₂³×C₅	1	16	yes	complemented
638	#117	C₂³×C₅	1	16	yes	complemented
639	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	complemented
653	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	complemented
654	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	complemented
671	C₂×C₂²⋊C₄	C₂³×C₅	1	32	yes	complemented
672	C₂×C₂²⋊C₄	C₂³×C₅	1	32	yes	complemented
673	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₅	1	4	yes	—
675	C₂×C₄²	C₂³×C₅	1	2	yes	—
676	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₅	1	8	yes	complemented
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	4	no	—
683	C₂²×C₅	—	2	4	no	—
684	C₂²×C₅	—	2	8	no	—
685	C₂²×C₅	—	2	16	no	—
686	C₂²×C₅	—	2	4	no	—
687	C₂²×C₅	—	2	4	no	—
688	C₂²×C₅	—	2	8	no	—
689	C₂²×C₅	—	2	4	no	—
690	C₂²×C₅	—	2	8	no	—
691	C₂²×C₅	—	2	8	no	—
692	C₂²×C₅	—	2	4	no	—
693	C₂²×C₅	—	2	4	no	—
694	C₂²×C₅	—	2	4	no	—
695	C₂²×C₅	—	4	32	no	—
696	C₂²×C₅	—	4	8	no	—
697	C₂²×C₅	—	4	16	no	—
698	C₂²×C₅	—	4	8	no	—
699	C₂²×C₅	—	8	32	no	—
700	C₂²×C₅	C₂²×#41	1	8	yes	—
701	C₂²×C₅	C₂²×#41	1	2	yes	—
702	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
703	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
704	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
705	C₂²×C₅	C₂⁶	1	1	yes	characteristic
706	C₄×C₅	—	2	2	no	—
707	C₄×C₅	—	2	4	no	—
708	C₄×C₅	—	2	2	no	—
709	C₄×C₅	—	2	2	no	—
710	C₄×C₅	—	2	4	no	—
711	C₄×C₅	—	2	4	no	—
712	C₄×C₅	—	2	2	no	—
713	C₄×C₅	—	2	4	no	—
714	C₄×C₅	—	2	8	no	—
715	C₄×C₅	—	2	4	no	—
716	C₄×C₅	C₂²×#41	1	4	yes	—
717	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
718	C₂⁴	—	2	8	no	—
719	C₂⁴	—	2	8	no	—
720	C₂⁴	—	2	16	no	—
721	C₂⁴	—	4	4	no	—
722	C₂⁴	—	4	8	no	—
723	C₂⁴	—	4	8	no	—
724	C₂⁴	C₂⁴×C₅	1	2	yes	—
725	C₂⁴	C₂⁴×C₅	1	2	yes	—
726	C₂⁴	C₂⁴×C₅	1	4	yes	—
727	C₂⁴	C₂⁴×C₅	1	8	yes	—
728	C₂⁴	C₂⁴×C₅	1	2	yes	—
729	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
730	C₂⁴	C₂⁴×C₅	1	16	yes	—
731	#41	—	4	32	no	—
732	#41	—	4	32	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	4	4	no	—
735	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
736	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	16	no	—
739	C₂×D₄	—	2	8	no	—
740	C₂×D₄	—	2	16	no	—
741	C₂×D₄	—	2	32	no	—
742	C₂×D₄	—	2	64	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	8	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	4	32	no	—
748	C₂×D₄	—	4	8	no	—
749	C₂×D₄	—	4	8	no	—
750	C₂×D₄	—	4	8	no	—
751	C₂×D₄	—	4	4	no	—
752	C₂×D₄	—	4	8	no	—
753	C₂×D₄	—	4	64	no	—
754	C₂×D₄	C₅×#41	1	8	yes	complemented
755	C₂×D₄	C₂⁴×C₅	1	8	yes	—
756	C₂×D₄	C₂⁴×C₅	1	16	yes	—
757	C₂×D₄	C₂⁴×C₅	1	4	yes	—
758	C₂×D₄	C₂⁴×C₅	1	8	yes	—
759	C₂×D₄	C₂⁴×C₅	1	16	yes	—
760	C₂×D₄	C₂⁴×C₅	1	8	yes	—
761	C₂×D₄	C₂⁴×C₅	1	4	yes	—
762	C₂×D₄	C₂⁴×C₅	1	8	yes	—
763	C₂×D₄	C₂⁴×C₅	1	16	yes	—
764	C₂×D₄	C₂⁴×C₅	1	8	yes	—
765	C₂×D₄	C₂⁴×C₅	1	16	yes	—
766	C₂×D₄	C₂⁴×C₅	1	16	yes	—
767	C₂×D₄	C₂⁴×C₅	1	16	yes	—
768	C₂×D₄	C₂⁴×C₅	1	4	yes	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	8	no	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	2	8	no	—
774	C₂²×C₄	—	2	8	no	—
775	C₂²×C₄	—	4	32	no	—
776	C₂²×C₄	—	4	4	no	—
777	C₂²×C₄	—	4	4	no	—
778	C₂²×C₄	—	4	4	no	—
779	C₂²×C₄	—	4	8	no	—
780	C₂²×C₄	—	4	8	no	—
781	C₂²×C₄	—	4	8	no	—
782	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
789	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
792	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
793	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
794	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
796	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
797	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
798	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
799	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
800	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
801	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
802	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
803	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
804	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
806	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
807	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
808	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
809	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
810	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
811	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
812	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
813	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
814	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
815	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
816	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
817	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
818	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
819	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
820	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
821	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
822	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
823	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
825	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
826	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
827	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
828	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
829	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
830	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
831	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
834	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
835	C₄²	C₂⁴×C₅	1	4	yes	—
836	C₄²	C₂⁴×C₅	1	4	yes	—
837	C₄²	C₂⁴×C₅	1	4	yes	—
838	C₄²	C₂⁴×C₅	1	4	yes	—
839	C₄²	C₂⁴×C₅	1	16	yes	—
840	C₄²	C₂⁴×C₅	1	8	yes	—
841	C₂×C₅	—	2	4	no	—
842	C₂×C₅	—	2	8	no	—
843	C₂×C₅	—	4	4	no	—
844	C₂×C₅	—	4	8	no	—
845	C₂×C₅	—	4	4	no	—
846	C₂×C₅	#3519	1	4	yes	direct product factor
847	C₂×C₅	C₂³×#41	1	1	yes	characteristic
848	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	4	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	16	no	—
856	C₂³	—	2	4	no	—
857	C₂³	—	2	8	no	—
858	C₂³	—	2	4	no	—
859	C₂³	—	2	8	no	—
860	C₂³	—	2	8	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	16	no	—
864	C₂³	—	2	4	no	—
865	C₂³	—	2	32	no	—
866	C₂³	—	4	8	no	—
867	C₂³	—	4	16	no	—
868	C₂³	—	4	16	no	—
869	C₂³	—	4	32	no	—
870	C₂³	—	8	32	no	—
871	C₂³	C₂×C₅×#41	1	8	yes	—
872	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
873	C₂³	C₂⁵×C₅	1	4	yes	—
874	C₂³	C₂⁵×C₅	1	4	yes	—
875	C₂³	C₂⁵×C₅	1	8	yes	—
876	C₂³	C₂⁵×C₅	1	4	yes	—
877	C₂³	C₂⁵×C₅	1	2	yes	—
878	C₂³	C₂⁵×C₅	1	1	yes	characteristic
879	Q₈	—	2	8	no	—
880	Q₈	—	4	8	no	—
881	D₄	—	2	16	no	—
882	D₄	—	2	32	no	—
883	D₄	—	2	16	no	—
884	D₄	—	2	32	no	—
885	D₄	—	2	8	no	—
886	D₄	—	2	16	no	—
887	D₄	—	2	8	no	—
888	D₄	—	2	16	no	—
889	D₄	—	4	16	no	—
890	D₄	—	4	16	no	—
891	D₄	—	4	16	no	—
892	D₄	—	4	8	no	—
893	D₄	—	4	16	no	—
894	D₄	C₂×C₅×#41	1	16	yes	complemented
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	4	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	8	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	16	no	—
908	C₂×C₄	—	2	8	no	—
909	C₂×C₄	—	2	16	no	—
910	C₂×C₄	—	2	16	no	—
911	C₂×C₄	—	4	8	no	—
912	C₂×C₄	—	4	8	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	16	no	—
915	C₂×C₄	—	4	16	no	—
916	C₂×C₄	—	4	16	no	—
917	C₂×C₄	C₂×C₅×#41	1	4	yes	—
918	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
919	C₂×C₄	C₂⁵×C₅	1	2	yes	—
920	C₂×C₄	C₂⁵×C₅	1	4	yes	—
921	C₂×C₄	C₂⁵×C₅	1	2	yes	—
922	C₂×C₄	C₂⁵×C₅	1	2	yes	—
923	C₂×C₄	C₂⁵×C₅	1	4	yes	—
924	C₂×C₄	C₂⁵×C₅	1	2	yes	—
925	C₂×C₄	C₂⁵×C₅	1	8	yes	—
926	C₂×C₄	C₂⁵×C₅	1	4	yes	—
927	C₂×C₄	C₂⁵×C₅	1	4	yes	—
928	C₂×C₄	C₂⁵×C₅	1	4	yes	—
929	C₂×C₄	C₂⁵×C₅	1	2	yes	—
930	C₂×C₄	C₂⁵×C₅	1	2	yes	—
931	C₅	C₂×#3519	1	1	yes	characteristic, direct product factor, Sylow
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	8	no	—
937	C₂²	—	2	16	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	8	no	—
943	C₂²	—	2	8	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	4	32	no	—
948	C₂²	—	4	8	no	—
949	C₂²	—	4	8	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	8	32	no	—
952	C₂²	C₂²×C₅×#41	1	8	yes	—
953	C₂²	C₂²×C₅×#41	1	2	yes	—
954	C₂²	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
955	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
956	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
957	C₂²	C₂⁶×C₅	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	4	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	4	no	—
966	C₄	—	2	8	no	—
967	C₄	—	2	4	no	—
968	C₄	C₂²×C₅×#41	1	4	yes	—
969	C₄	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	2	8	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	—	4	8	no	—
975	C₂	C₅×#3519	1	4	yes	direct product factor
976	C₂	C₂³×C₅×#41	1	1	yes	characteristic
977	C₂	C₂²×C₅×H(5,𝔽₂)	1	1	yes	characteristic
978	C₂	C₂²×C₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3519	C₂	direct (N × H)
2. C₂×C₅×#555	C₂	semidirect
3. C₂×C₅×#554	C₂	semidirect
4. C₂×C₅×#553	C₂	semidirect
5. C₂×C₅×#553	C₂	semidirect
6. C₂×C₅×#550	C₂	semidirect
7. C₂×C₅×#546	C₂	semidirect
8. C₂×C₅×#546	C₂	semidirect
9. C₂×C₅×D₄²	C₂	semidirect
10. C₂×C₅×D₄²	C₂	semidirect
11. C₂×C₅×#540	C₂	semidirect
12. C₂×C₅×#538	C₂	semidirect
13. C₂×C₅×#532	C₂	semidirect
14. C₂×C₅×#529	C₂	semidirect
15. C₂×C₅×#525	C₂	semidirect
16. C₂²×C₅×#121	C₂	semidirect
17. C₂×C₅×#518	C₂	semidirect
18. C₂²×C₄×C₅×D₄	C₂	semidirect
19. C₂²×C₅×#41	C₂²	semidirect
20. C₂²×C₅×#41	C₂²	semidirect
23. C₂³×C₅×D₄	C₂²	semidirect
24. C₂³×C₅×D₄	C₂²	semidirect
25. C₂⁴×C₄×C₅	C₂²	semidirect
26. C₅×#555	C₂²	semidirect
27. C₅×#554	C₂²	semidirect
28. C₅×#553	C₂²	semidirect
29. C₅×#553	C₂²	semidirect
30. C₅×#550	C₂²	semidirect
31. C₅×#546	C₂²	semidirect
32. C₅×#546	C₂²	semidirect
33. C₅×D₄²	C₂²	semidirect
34. C₅×D₄²	C₂²	semidirect
35. C₅×#540	C₂²	semidirect
36. C₅×#538	C₂²	semidirect
37. C₅×#532	C₂²	semidirect
38. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₅×#127	C₂²	semidirect
40. C₂×C₅×#127	C₂²	semidirect
41. C₅×#529	C₂²	semidirect
42. C₂×C₅×#126	C₂²	semidirect
43. C₂×C₅×#126	C₂²	semidirect
44. C₂×C₅×#125	C₂²	semidirect
45. C₂×C₅×#125	C₂²	semidirect
46. C₂×C₅×#124	C₂²	semidirect
47. C₂×C₅×#124	C₂²	semidirect
48. C₂×C₅×#124	C₂²	semidirect
49. C₅×#525	C₂²	semidirect
50. C₂×C₅×#123	C₂²	semidirect
51. C₂×C₅×#123	C₂²	semidirect
52. C₂×C₅×#123	C₂²	semidirect
53. C₂×C₅×#123	C₂²	semidirect
54. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₅×#121	C₂²	semidirect
59. C₂×C₅×#121	C₂²	semidirect
60. C₂×C₅×#121	C₂²	semidirect
61. C₂×C₅×#121	C₂²	semidirect
62. C₂×C₅×#121	C₂²	semidirect
63. C₂×C₅×#121	C₂²	semidirect
64. C₂×C₅×#121	C₂²	semidirect
65. C₂×C₅×#121	C₂²	semidirect
66. C₂×C₅×#121	C₂²	semidirect
67. C₂×C₅×#121	C₂²	semidirect
68. C₂×C₅×#121	C₂²	semidirect
69. C₂×C₅×#121	C₂²	semidirect
70. C₂×C₅×#121	C₂²	semidirect
71. C₂×C₅×#120	C₂²	semidirect
72. C₂×C₅×#120	C₂²	semidirect
73. C₂×C₅×#120	C₂²	semidirect
74. C₅×#518	C₂²	semidirect
75. C₂×C₄×C₅×Q₈	C₂²	semidirect
79. C₂×C₄×C₅×D₄	C₂²	semidirect
80. C₂×C₄×C₅×D₄	C₂²	semidirect
81. C₂×C₄×C₅×D₄	C₂²	semidirect
82. C₂×C₄×C₅×D₄	C₂²	semidirect
83. C₂×C₄×C₅×D₄	C₂²	semidirect
84. C₂×C₄×C₅×D₄	C₂²	semidirect
85. C₂×C₄×C₅×D₄	C₂²	semidirect
86. C₂×C₄×C₅×D₄	C₂²	semidirect
87. C₂×C₄×C₅×D₄	C₂²	semidirect
88. C₂×C₄×C₅×D₄	C₂²	semidirect
89. C₂×C₄×C₅×D₄	C₂²	semidirect
90. C₂×C₄×C₅×D₄	C₂²	semidirect
91. C₂×C₄×C₅×D₄	C₂²	semidirect
92. C₂×C₅×#117	C₂²	semidirect
93. C₂×C₅×#117	C₂²	semidirect
94. C₂×C₅×#117	C₂²	semidirect
95. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
97. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
98. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
99. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
100. C₂²×C₄²×C₅	C₂²	semidirect
101. C₂×#3519	C₅	direct (N × H)
106. C₂×C₅×#41	C₂³	semidirect
107. C₂×C₅×#41	C₂³	semidirect
130. C₂²×C₅×D₄	C₂³	semidirect
131. C₂²×C₅×D₄	C₂³	semidirect
145. C₂³×C₄×C₅	C₂³	semidirect
146. C₅×C₄⋊Q₈	C₂³	semidirect
147. C₅×#127	C₂³	semidirect
148. C₅×#127	C₂³	semidirect
149. C₅×#126	C₂³	semidirect
150. C₅×#126	C₂³	semidirect
151. C₅×#125	C₂³	semidirect
152. C₅×#125	C₂³	semidirect
153. C₅×#124	C₂³	semidirect
154. C₅×#124	C₂³	semidirect
155. C₅×#124	C₂³	semidirect
156. C₅×#123	C₂³	semidirect
157. C₅×#123	C₂³	semidirect
158. C₅×#123	C₂³	semidirect
159. C₅×#123	C₂³	semidirect
160. C₅×C₂²⋊Q₈	C₂³	semidirect
161. C₅×C₂²⋊Q₈	C₂³	semidirect
162. C₅×C₂²⋊Q₈	C₂³	semidirect
164. C₅×#121	C₂³	semidirect
165. C₅×#121	C₂³	semidirect
166. C₅×#121	C₂³	semidirect
167. C₅×#121	C₂³	semidirect
168. C₅×#121	C₂³	semidirect
169. C₅×#121	C₂³	semidirect
170. C₅×#121	C₂³	semidirect
171. C₅×#121	C₂³	semidirect
172. C₅×#121	C₂³	semidirect
173. C₅×#121	C₂³	semidirect
174. C₅×#121	C₂³	semidirect
175. C₅×#121	C₂³	semidirect
176. C₅×#120	C₂³	semidirect
177. C₅×#120	C₂³	semidirect
178. C₅×#120	C₂³	semidirect
179. C₄×C₅×Q₈	C₂³	semidirect
183. C₄×C₅×D₄	C₂³	semidirect
184. C₄×C₅×D₄	C₂³	semidirect
185. C₄×C₅×D₄	C₂³	semidirect
186. C₄×C₅×D₄	C₂³	semidirect
187. C₄×C₅×D₄	C₂³	semidirect
188. C₄×C₅×D₄	C₂³	semidirect
189. C₄×C₅×D₄	C₂³	semidirect
190. C₄×C₅×D₄	C₂³	semidirect
191. C₄×C₅×D₄	C₂³	semidirect
192. C₄×C₅×D₄	C₂³	semidirect
193. C₄×C₅×D₄	C₂³	semidirect
194. C₄×C₅×D₄	C₂³	semidirect
195. C₅×#117	C₂³	semidirect
196. C₅×#117	C₂³	semidirect
197. C₅×#117	C₂³	semidirect
211. C₂×C₅×C₄⋊C₄	C₂³	semidirect
212. C₂×C₅×C₄⋊C₄	C₂³	semidirect
229. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
230. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
231. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
238. C₂×C₄²×C₅	C₂³	semidirect
239. #3519	C₂×C₅	direct (N × H)
240. C₂×#555	C₂×C₅	semidirect
241. C₂×#554	C₂×C₅	semidirect
242. C₂×#553	C₂×C₅	semidirect
243. C₂×#553	C₂×C₅	semidirect
244. C₂×#550	C₂×C₅	semidirect
245. C₂×#546	C₂×C₅	semidirect
246. C₂×#546	C₂×C₅	semidirect
247. C₂×D₄²	C₂×C₅	semidirect
248. C₂×D₄²	C₂×C₅	semidirect
249. C₂×#540	C₂×C₅	semidirect
250. C₂×#538	C₂×C₅	semidirect
251. C₂×#532	C₂×C₅	semidirect
252. C₂×#529	C₂×C₅	semidirect
253. C₂×#525	C₂×C₅	semidirect
254. C₂²×#121	C₂×C₅	semidirect
255. C₂×#518	C₂×C₅	semidirect
256. C₂²×C₄×D₄	C₂×C₅	semidirect
293. C₂×C₅×D₄	#41	semidirect
380. C₂²×#41	C₂²×C₅	semidirect
381. C₂²×#41	C₂²×C₅	semidirect
384. C₂³×D₄	C₂²×C₅	semidirect
385. C₂³×D₄	C₂²×C₅	semidirect
386. C₂⁴×C₄	C₂²×C₅	semidirect
387. #555	C₂²×C₅	semidirect
388. #554	C₂²×C₅	semidirect
389. #553	C₂²×C₅	semidirect
390. #553	C₂²×C₅	semidirect
391. #550	C₂²×C₅	semidirect
392. #546	C₂²×C₅	semidirect
393. #546	C₂²×C₅	semidirect
394. D₄²	C₂²×C₅	semidirect
395. D₄²	C₂²×C₅	semidirect
396. #540	C₂²×C₅	semidirect
397. #538	C₂²×C₅	semidirect
398. #532	C₂²×C₅	semidirect
399. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
400. C₂×#127	C₂²×C₅	semidirect
401. C₂×#127	C₂²×C₅	semidirect
402. #529	C₂²×C₅	semidirect
403. C₂×#126	C₂²×C₅	semidirect
404. C₂×#126	C₂²×C₅	semidirect
405. C₂×#125	C₂²×C₅	semidirect
406. C₂×#125	C₂²×C₅	semidirect
407. C₂×#124	C₂²×C₅	semidirect
408. C₂×#124	C₂²×C₅	semidirect
409. C₂×#124	C₂²×C₅	semidirect
410. #525	C₂²×C₅	semidirect
411. C₂×#123	C₂²×C₅	semidirect
412. C₂×#123	C₂²×C₅	semidirect
413. C₂×#123	C₂²×C₅	semidirect
414. C₂×#123	C₂²×C₅	semidirect
415. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
416. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
417. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
419. C₂×#121	C₂²×C₅	semidirect
420. C₂×#121	C₂²×C₅	semidirect
421. C₂×#121	C₂²×C₅	semidirect
422. C₂×#121	C₂²×C₅	semidirect
423. C₂×#121	C₂²×C₅	semidirect
424. C₂×#121	C₂²×C₅	semidirect
425. C₂×#121	C₂²×C₅	semidirect
426. C₂×#121	C₂²×C₅	semidirect
427. C₂×#121	C₂²×C₅	semidirect
428. C₂×#121	C₂²×C₅	semidirect
429. C₂×#121	C₂²×C₅	semidirect
430. C₂×#121	C₂²×C₅	semidirect
431. C₂×#121	C₂²×C₅	semidirect
432. C₂×#120	C₂²×C₅	semidirect
433. C₂×#120	C₂²×C₅	semidirect
434. C₂×#120	C₂²×C₅	semidirect
435. #518	C₂²×C₅	semidirect
436. C₂×C₄×Q₈	C₂²×C₅	semidirect
440. C₂×C₄×D₄	C₂²×C₅	semidirect
441. C₂×C₄×D₄	C₂²×C₅	semidirect
442. C₂×C₄×D₄	C₂²×C₅	semidirect
443. C₂×C₄×D₄	C₂²×C₅	semidirect
444. C₂×C₄×D₄	C₂²×C₅	semidirect
445. C₂×C₄×D₄	C₂²×C₅	semidirect
446. C₂×C₄×D₄	C₂²×C₅	semidirect
447. C₂×C₄×D₄	C₂²×C₅	semidirect
448. C₂×C₄×D₄	C₂²×C₅	semidirect
449. C₂×C₄×D₄	C₂²×C₅	semidirect
450. C₂×C₄×D₄	C₂²×C₅	semidirect
451. C₂×C₄×D₄	C₂²×C₅	semidirect
452. C₂×C₄×D₄	C₂²×C₅	semidirect
453. C₂×#117	C₂²×C₅	semidirect
454. C₂×#117	C₂²×C₅	semidirect
455. C₂×#117	C₂²×C₅	semidirect
456. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
457. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
458. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
459. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
460. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
461. C₂²×C₄²	C₂²×C₅	semidirect
506. C₅×D₄	C₂×#41	semidirect
547. C₂×#41	C₂³×C₅	semidirect
548. C₂×#41	C₂³×C₅	semidirect
571. C₂²×D₄	C₂³×C₅	semidirect
572. C₂²×D₄	C₂³×C₅	semidirect
586. C₂³×C₄	C₂³×C₅	semidirect
587. C₄⋊Q₈	C₂³×C₅	semidirect
588. #127	C₂³×C₅	semidirect
589. #127	C₂³×C₅	semidirect
590. #126	C₂³×C₅	semidirect
591. #126	C₂³×C₅	semidirect
592. #125	C₂³×C₅	semidirect
593. #125	C₂³×C₅	semidirect
594. #124	C₂³×C₅	semidirect
595. #124	C₂³×C₅	semidirect
596. #124	C₂³×C₅	semidirect
597. #123	C₂³×C₅	semidirect
598. #123	C₂³×C₅	semidirect
599. #123	C₂³×C₅	semidirect
600. #123	C₂³×C₅	semidirect
601. C₂²⋊Q₈	C₂³×C₅	semidirect
602. C₂²⋊Q₈	C₂³×C₅	semidirect
603. C₂²⋊Q₈	C₂³×C₅	semidirect
605. #121	C₂³×C₅	semidirect
606. #121	C₂³×C₅	semidirect
607. #121	C₂³×C₅	semidirect
608. #121	C₂³×C₅	semidirect
609. #121	C₂³×C₅	semidirect
610. #121	C₂³×C₅	semidirect
611. #121	C₂³×C₅	semidirect
612. #121	C₂³×C₅	semidirect
613. #121	C₂³×C₅	semidirect
614. #121	C₂³×C₅	semidirect
615. #121	C₂³×C₅	semidirect
616. #121	C₂³×C₅	semidirect
617. #120	C₂³×C₅	semidirect
618. #120	C₂³×C₅	semidirect
619. #120	C₂³×C₅	semidirect
620. C₄×Q₈	C₂³×C₅	semidirect
624. C₄×D₄	C₂³×C₅	semidirect
625. C₄×D₄	C₂³×C₅	semidirect
626. C₄×D₄	C₂³×C₅	semidirect
627. C₄×D₄	C₂³×C₅	semidirect
628. C₄×D₄	C₂³×C₅	semidirect
629. C₄×D₄	C₂³×C₅	semidirect
630. C₄×D₄	C₂³×C₅	semidirect
631. C₄×D₄	C₂³×C₅	semidirect
632. C₄×D₄	C₂³×C₅	semidirect
633. C₄×D₄	C₂³×C₅	semidirect
634. C₄×D₄	C₂³×C₅	semidirect
635. C₄×D₄	C₂³×C₅	semidirect
636. #117	C₂³×C₅	semidirect
637. #117	C₂³×C₅	semidirect
638. #117	C₂³×C₅	semidirect
652. C₂×C₄⋊C₄	C₂³×C₅	semidirect
653. C₂×C₄⋊C₄	C₂³×C₅	semidirect
670. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
671. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
672. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
679. C₂×C₄²	C₂³×C₅	semidirect
754. C₂×D₄	C₅×#41	semidirect
846. C₂×C₅	#3519	direct (N × H)
894. D₄	C₂×C₅×#41	semidirect
931. C₅	C₂×#3519	direct (N × H)
975. C₂	C₅×#3519	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×#3519	2
C₂×C₅×#555	2
C₂×C₅×#554	2
C₂×C₅×#553	2
C₂×C₅×#550	2
C₂×C₅×#546	2
C₂×C₅×D₄²	2
C₂×C₅×#540	2
C₂×C₅×#538	2
C₂×C₅×#532	2
C₂×C₅×#529	2
C₂×C₅×#525	2
C₂²×C₅×#121	2
C₂×C₅×#518	2
C₂²×C₄×C₅×D₄	2
C₂×#3519	5

Subgroups — C2×C5×#3519 #11985491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3519 #11985491