Subgroups — #20257849

Order 6016.

1022 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689868	C₂	1	2	yes	maximal, complemented
2	#15689868	C₂	1	2	yes	maximal, complemented
3	#15689859	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689856	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689856	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689850	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689830	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689829	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689793	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689779	C₂	1	2	yes	maximal, complemented
12	#15689773	C₂	1	2	yes	maximal, complemented
13	#15689744	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689741	C₂	1	2	yes	maximal, complemented
15	#15689740	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689726	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689717	C₂	1	2	yes	maximal, complemented
18	#15689716	C₂	1	2	yes	maximal, complemented
19	#15689695	C₂	1	2	yes	maximal, complemented
20	#15689676	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689668	C₂	1	1	yes	maximal, characteristic, complemented
22	#15689654	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625352	C₂²	1	2	yes	—
25	C₂×#10625352	C₂²	1	2	yes	—
26	C₂²×Dic₉₄	C₂²	1	2	yes	—
27	#13094024	C₂²	1	1	yes	characteristic
28	#13094023	C₂²	1	1	yes	characteristic
29	#13094023	C₂²	1	1	yes	characteristic
30	#13094023	C₂²	1	2	yes	—
31	#13094023	C₂²	1	1	yes	characteristic
32	#13094023	C₂²	1	1	yes	characteristic
33	#13094020	C₂²	1	1	yes	characteristic
34	#13094020	C₂²	1	1	yes	characteristic
35	#13094019	C₂²	1	2	yes	—
36	#13094017	C₂²	1	2	yes	—
37	#13094017	C₂²	1	2	yes	—
38	#13094015	C₂²	1	1	yes	characteristic
39	#13094015	C₂²	1	1	yes	characteristic
40	#13094015	C₂²	1	1	yes	characteristic
41	#13094015	C₂²	1	1	yes	characteristic
42	#13094014	C₂²	1	2	yes	—
43	#13094014	C₂²	1	2	yes	—
44	#13094012	C₂²	1	1	yes	characteristic
45	#13094011	C₂²	1	2	yes	—
46	#13094011	C₂²	1	1	yes	characteristic
47	#13094011	C₂²	1	2	yes	—
48	#13094011	C₂²	1	1	yes	characteristic
49	#13094010	C₂²	1	2	yes	—
50	#13094010	C₂²	1	2	yes	—
51	#13094010	C₂²	1	2	yes	—
52	#13094010	C₂²	1	2	yes	—
53	#13094008	C₂²	1	2	yes	—
54	#13094007	C₂²	1	2	yes	—
55	#13094007	C₂²	1	2	yes	—
56	#13094006	C₂²	1	2	yes	—
57	#13094006	C₂²	1	2	yes	—
58	#13094006	C₂²	1	2	yes	—
59	#13094006	C₂²	1	2	yes	—
60	#13094005	C₂²	1	2	yes	—
61	#13094005	C₂²	1	2	yes	—
62	#13094005	C₂²	1	2	yes	—
63	#13094005	C₂²	1	2	yes	—
64	#13094004	C₂²	1	2	yes	—
65	#13094003	C₂²	1	1	yes	characteristic
66	#13094003	C₂²	1	2	yes	—
67	#13094003	C₂²	1	2	yes	—
68	#13094002	C₂²	1	2	yes	—
69	#13094002	C₂²	1	2	yes	—
70	#13094002	C₂²	1	2	yes	—
71	#13094001	C₂²	1	2	yes	—
72	#13094001	C₂²	1	2	yes	—
73	#13094001	C₂²	1	1	yes	characteristic
74	#13094001	C₂²	1	1	yes	characteristic
75	#13094001	C₂²	1	2	yes	—
76	#13094001	C₂²	1	2	yes	—
77	#13094001	C₂²	1	2	yes	—
78	#13094001	C₂²	1	1	yes	characteristic
79	#13094001	C₂²	1	1	yes	characteristic
80	#13093998	C₂²	1	1	yes	characteristic
81	#13093996	C₂²	1	2	yes	—
82	#13093996	C₂²	1	2	yes	—
83	#13093996	C₂²	1	2	yes	—
84	#13093996	C₂²	1	2	yes	—
85	#13093995	C₂²	1	2	yes	—
86	#13093995	C₂²	1	2	yes	—
87	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
88	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
89	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
90	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
91	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
92	#13093989	C₂²	1	1	yes	characteristic
93	#13093989	C₂²	1	2	yes	—
94	#13093989	C₂²	1	1	yes	characteristic
95	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
96	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
97	D₄×Dic₄₇	C₂²	1	2	yes	—
98	D₄×Dic₄₇	C₂²	1	2	yes	—
99	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
100	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
101	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
102	#13093986	C₂²	1	1	yes	characteristic
103	#13093986	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
105	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
106	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
107	#13093983	C₂²	1	1	yes	characteristic
108	#13093980	C₂²	1	2	yes	—
109	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
110	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
111	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
112	#127×C₄₇	C₂²	1	1	yes	characteristic
113	#125×C₄₇	C₂²	1	1	yes	characteristic
114	#123×C₄₇	C₂²	1	2	yes	—
115	#123×C₄₇	C₂²	1	2	yes	—
116	#121×C₄₇	C₂²	1	1	yes	characteristic
117	#121×C₄₇	C₂²	1	2	yes	—
118	#121×C₄₇	C₂²	1	2	yes	—
119	#121×C₄₇	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
122	#117×C₄₇	C₂²	1	1	yes	characteristic
123	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₄₇	C₂³	1	2	yes	—
126	C₂×D₄×C₄₇	C₂³	1	2	yes	—
127	C₂×D₄×C₄₇	C₂³	1	2	yes	—
128	C₂×D₄×C₄₇	C₂³	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
137	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
138	C₂²×Dic₄₇	C₂³	1	2	yes	—
139	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂³	1	2	yes	—
141	C₂²×Dic₄₇	C₂³	1	2	yes	—
142	C₂²×Dic₄₇	C₂³	1	2	yes	—
143	#10625352	—	4	4	no	—
144	#10625352	—	4	4	no	—
145	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₄₇	C₂³	1	2	yes	—
147	C₂×C₄×D₄₇	C₂³	1	2	yes	—
148	C₂×C₄×D₄₇	C₂³	1	2	yes	—
149	C₂×Dic₉₄	—	4	4	no	—
150	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
151	C₂×Dic₉₄	C₂³	1	2	yes	—
152	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
153	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
154	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
155	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
156	C₂×Dic₉₄	C₂³	1	2	yes	—
157	C₂×Dic₉₄	C₂³	1	2	yes	—
158	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
163	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
170	C₄²×C₄₇	C₂³	1	1	yes	characteristic
171	C₄²×C₄₇	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
183	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
189	C₄⋊Dic₄₇	C₂³	1	2	yes	—
190	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₄₇	C₂³	1	2	yes	—
192	C₄⋊Dic₄₇	C₂³	1	2	yes	—
193	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
200	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₄₇⋊C₄	C₂³	1	2	yes	—
202	Dic₄₇⋊C₄	C₂³	1	2	yes	—
203	Dic₄₇⋊C₄	C₂³	1	2	yes	—
204	Dic₄₇⋊C₄	C₂³	1	2	yes	—
205	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₄₇⋊C₄	C₂³	1	2	yes	—
209	Dic₄₇⋊C₄	C₂³	1	2	yes	—
210	Dic₄₇⋊C₄	C₂³	1	2	yes	—
211	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₄₇⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₄₇	C₂³	1	2	yes	—
221	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₂³×C₄₇	C₂⁴	1	2	yes	—
226	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
227	C₂³×C₄₇	C₂⁴	1	2	yes	—
228	C₂²×D₄₇	C₂⁴	1	2	yes	—
229	D₄×C₄₇	—	2	2	no	—
230	D₄×C₄₇	—	2	2	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	4	2	no	—
237	C₂×C₄×C₄₇	—	4	2	no	—
238	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
242	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂²⋊D₄₇	—	2	4	no	—
247	C₂²⋊D₄₇	—	4	2	no	—
248	C₂²⋊D₄₇	—	4	2	no	—
249	C₂²⋊D₄₇	—	4	2	no	—
250	C₂²⋊D₄₇	—	4	2	no	—
251	C₂×Dic₄₇	—	2	4	no	—
252	C₂×Dic₄₇	—	2	2	no	—
253	C₂×Dic₄₇	—	4	2	no	—
254	C₂×Dic₄₇	—	4	2	no	—
255	C₂×Dic₄₇	—	4	2	no	—
256	C₂×Dic₄₇	—	4	1	no	—
257	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₄₇	C₂⁴	1	2	yes	—
259	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₄₇	C₂⁴	1	2	yes	—
265	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₄₇	C₂⁴	1	2	yes	—
267	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
268	D₁₈₈	—	2	2	no	—
269	C₄×D₄₇	—	4	2	no	—
270	C₄×D₄₇	—	4	2	no	—
271	C₄×D₄₇	—	4	2	no	—
272	Dic₉₄	—	2	2	no	—
273	Dic₉₄	—	2	2	no	—
274	Dic₉₄	—	2	4	no	—
275	Dic₉₄	—	2	2	no	—
276	Dic₉₄	—	4	2	no	—
277	Dic₉₄	—	4	2	no	—
278	Dic₉₄	—	4	1	no	—
279	Dic₉₄	—	4	1	no	—
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	—	2	1	no	—
282	C₂²×C₄₇	—	2	2	no	—
283	C₂²×C₄₇	—	2	1	no	—
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	2	1	no	—
287	C₂²×C₄₇	—	2	2	no	—
288	C₂²×C₄₇	—	2	2	no	—
289	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
290	C₂×D₄₇	—	2	2	no	—
291	C₂×D₄₇	—	2	2	no	—
292	C₂×D₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	2	no	—
295	C₄×C₄₇	—	2	1	no	—
296	C₄×C₄₇	—	2	1	no	—
297	C₄×C₄₇	—	2	1	no	—
298	C₄×C₄₇	—	2	1	no	—
299	C₄×C₄₇	—	2	2	no	—
300	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
301	Dic₄₇	—	2	1	no	—
302	Dic₄₇	—	2	2	no	—
303	Dic₄₇	—	2	1	no	—
304	Dic₄₇	—	2	2	no	—
305	Dic₄₇	—	2	1	no	—
306	Dic₄₇	—	2	2	no	—
307	Dic₄₇	—	2	1	no	—
308	Dic₄₇	—	2	1	no	—
309	Dic₄₇	—	2	1	no	—
310	Dic₄₇	—	2	1	no	—
311	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
312	#3554	—	47	1	no	maximal, Sylow
313	C₂×C₄₇	—	4	2	no	—
314	C₂×C₄₇	—	4	1	no	—
315	C₂×C₄₇	—	4	2	no	—
316	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂×C₄₇	#585	1	1	yes	characteristic
319	D₄₇	—	4	2	no	—
320	#562	—	47	2	no	—
321	#562	—	47	2	no	—
322	#559	—	47	1	no	—
323	#559	—	47	1	no	—
324	#559	—	47	1	no	—
325	#557	—	47	1	no	—
326	#554	—	47	1	no	—
327	#554	—	47	1	no	—
328	#550	—	47	1	no	—
329	D₄×Q₈	—	47	1	no	—
330	#548	—	47	2	no	—
331	#547	—	47	2	no	—
332	#542	—	47	2	no	—
333	#542	—	47	1	no	—
334	#542	—	47	1	no	—
335	#540	—	47	1	no	—
336	#540	D₄₇	1	1	yes	characteristic, complemented
337	#539	—	47	2	no	—
338	#539	—	47	2	no	—
339	#536	—	47	2	no	—
340	#533	—	47	1	no	—
341	#532	—	47	1	no	—
342	#529	—	47	1	no	—
343	C₄₇	#3554	1	1	yes	characteristic, complemented, Sylow
344	C₂×#41	—	47	2	no	—
345	C₂×#41	—	47	2	no	—
346	C₂²×Q₈	—	47	2	no	—
347	C₄⋊Q₈	—	47	1	no	—
348	C₄⋊Q₈	—	47	1	no	—
349	C₄⋊Q₈	—	47	1	no	—
350	C₄⋊Q₈	—	47	2	no	—
351	C₄⋊Q₈	—	47	1	no	—
352	C₄⋊Q₈	—	47	1	no	—
353	#127	—	47	1	no	—
354	#127	—	47	1	no	—
355	#127	C₂×D₄₇	1	1	yes	characteristic
356	#126	—	47	2	no	—
357	#126	—	47	2	no	—
358	#126	—	47	2	no	—
359	#125	—	47	1	no	—
360	#125	—	47	1	no	—
361	#125	—	47	1	no	—
362	#125	—	47	2	no	—
363	#125	—	47	2	no	—
364	#125	—	47	1	no	—
365	#125	C₂×D₄₇	1	1	yes	characteristic
366	#124	—	47	1	no	—
367	#124	—	47	2	no	—
368	#124	—	47	1	no	—
369	#124	—	47	2	no	—
370	#124	—	47	2	no	—
371	#124	—	47	2	no	—
372	#124	—	47	2	no	—
373	#124	—	47	2	no	—
374	#124	—	47	1	no	—
375	#123	—	47	2	no	—
376	#123	—	47	2	no	—
377	#123	—	47	2	no	—
378	#123	—	47	2	no	—
379	#123	—	47	2	no	—
380	#123	—	47	2	no	—
381	#123	—	47	2	no	—
382	#123	—	47	2	no	—
383	#123	—	47	2	no	—
384	#123	—	47	2	no	—
385	#123	—	47	2	no	—
386	#123	C₂×D₄₇	1	2	yes	—
387	#123	C₂×D₄₇	1	2	yes	—
388	C₂²⋊Q₈	—	47	1	no	—
389	C₂²⋊Q₈	—	47	2	no	—
390	C₂²⋊Q₈	—	47	2	no	—
391	C₂²⋊Q₈	—	47	2	no	—
392	C₂²⋊Q₈	—	47	2	no	—
393	C₂²⋊Q₈	—	47	2	no	—
394	C₂²⋊Q₈	—	47	2	no	—
395	C₂²⋊Q₈	—	47	1	no	—
396	C₂²⋊Q₈	—	47	1	no	—
397	C₂²⋊Q₈	—	47	1	no	—
398	C₂²⋊Q₈	—	47	1	no	—
399	C₂²⋊Q₈	—	47	2	no	—
400	C₂²⋊Q₈	—	47	2	no	—
401	C₂²⋊Q₈	—	47	2	no	—
402	C₂²⋊Q₈	—	47	2	no	—
403	C₂²⋊Q₈	—	47	2	no	—
404	#121	—	47	2	no	—
405	#121	—	47	2	no	—
406	#121	—	47	2	no	—
407	#121	—	47	2	no	—
408	#121	—	47	2	no	—
409	#121	—	47	2	no	—
410	#121	—	47	1	no	—
411	#121	C₂×D₄₇	1	1	yes	characteristic
412	#121	C₂×D₄₇	1	1	yes	characteristic
413	#121	C₂×D₄₇	1	2	yes	—
414	#121	C₂×D₄₇	1	2	yes	—
415	C₄×Q₈	—	47	1	no	—
416	C₄×Q₈	—	47	2	no	—
417	C₄×Q₈	—	47	1	no	—
418	C₄×Q₈	—	47	1	no	—
419	C₄×Q₈	—	47	1	no	—
420	C₄×Q₈	—	47	1	no	—
421	C₄×Q₈	—	47	1	no	—
422	C₄×Q₈	—	47	1	no	—
423	C₄×D₄	—	47	2	no	—
424	C₄×D₄	—	47	1	no	—
425	C₄×D₄	—	47	1	no	—
426	C₄×D₄	—	47	2	no	—
427	C₄×D₄	—	47	1	no	—
428	C₄×D₄	—	47	1	no	—
429	C₄×D₄	—	47	2	no	—
430	C₄×D₄	—	47	2	no	—
431	C₄×D₄	—	47	1	no	—
432	C₄×D₄	—	47	1	no	—
433	C₄×D₄	—	47	2	no	—
434	C₄×D₄	—	47	1	no	—
435	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
436	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
437	#117	—	47	1	no	—
438	#117	—	47	2	no	—
439	#117	C₂×D₄₇	1	1	yes	characteristic
440	C₂×C₄⋊C₄	—	47	2	no	—
441	C₂×C₄⋊C₄	—	47	2	no	—
442	C₂×C₄²	—	47	1	no	—
443	#41	—	188	4	no	—
444	#41	—	188	4	no	—
445	C₂×Q₈	—	47	1	no	—
446	C₂×Q₈	—	47	1	no	—
447	C₂×Q₈	—	47	2	no	—
448	C₂×Q₈	—	47	1	no	—
449	C₂×Q₈	—	47	1	no	—
450	C₂×Q₈	—	47	1	no	—
451	C₂×Q₈	—	47	2	no	—
452	C₂×Q₈	—	47	2	no	—
453	C₂×Q₈	—	188	4	no	—
454	C₂×D₄	—	47	2	no	—
455	C₂×D₄	—	47	2	no	—
456	C₂×D₄	—	47	2	no	—
457	C₂×D₄	—	47	2	no	—
458	C₂×D₄	—	47	2	no	—
459	C₂×D₄	—	47	1	no	—
460	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
462	C₂×D₄	C₂²×D₄₇	1	2	yes	—
463	C₂×D₄	C₂²×D₄₇	1	2	yes	—
464	C₂×D₄	C₂²×D₄₇	1	2	yes	—
465	C₂×D₄	C₂²×D₄₇	1	2	yes	—
466	C₂²×C₄	—	47	1	no	—
467	C₂²×C₄	—	47	2	no	—
468	C₂²×C₄	—	47	1	no	—
469	C₂²×C₄	—	47	2	no	—
470	C₂²×C₄	—	47	2	no	—
471	C₂²×C₄	—	47	2	no	—
472	C₂²×C₄	—	47	2	no	—
473	C₂²×C₄	—	47	2	no	—
474	C₂²×C₄	—	47	2	no	—
475	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
477	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
478	C₄⋊C₄	—	47	1	no	—
479	C₄⋊C₄	—	47	2	no	—
480	C₄⋊C₄	—	47	2	no	—
481	C₄⋊C₄	—	47	2	no	—
482	C₄⋊C₄	—	47	1	no	—
483	C₄⋊C₄	—	47	1	no	—
484	C₄⋊C₄	—	47	2	no	—
485	C₄⋊C₄	—	47	1	no	—
486	C₄⋊C₄	—	47	1	no	—
487	C₄⋊C₄	—	47	2	no	—
488	C₄⋊C₄	—	47	1	no	—
489	C₄⋊C₄	—	47	1	no	—
490	C₄⋊C₄	—	47	1	no	—
491	C₄⋊C₄	—	47	2	no	—
492	C₄⋊C₄	—	47	2	no	—
493	C₄⋊C₄	—	47	2	no	—
494	C₄⋊C₄	—	47	2	no	—
495	C₄⋊C₄	—	47	1	no	—
496	C₄⋊C₄	—	47	2	no	—
497	C₄⋊C₄	—	47	2	no	—
498	C₄⋊C₄	—	47	1	no	—
499	C₄⋊C₄	—	47	1	no	—
500	C₄⋊C₄	—	47	1	no	—
501	C₄⋊C₄	—	47	1	no	—
502	C₄⋊C₄	—	47	1	no	—
503	C₄⋊C₄	—	47	1	no	—
504	C₄⋊C₄	—	47	1	no	—
505	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
506	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
511	C₂²⋊C₄	—	47	1	no	—
512	C₂²⋊C₄	—	47	1	no	—
513	C₂²⋊C₄	—	47	2	no	—
514	C₂²⋊C₄	—	47	2	no	—
515	C₂²⋊C₄	—	47	2	no	—
516	C₂²⋊C₄	—	47	2	no	—
517	C₂²⋊C₄	—	47	2	no	—
518	C₂²⋊C₄	—	47	2	no	—
519	C₂²⋊C₄	—	47	2	no	—
520	C₂²⋊C₄	—	47	2	no	—
521	C₂²⋊C₄	—	47	2	no	—
522	C₂²⋊C₄	—	47	2	no	—
523	C₂²⋊C₄	—	47	2	no	—
524	C₂²⋊C₄	—	47	2	no	—
525	C₂²⋊C₄	—	47	2	no	—
526	C₂²⋊C₄	—	47	2	no	—
527	C₂²⋊C₄	—	47	2	no	—
528	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
531	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
534	C₄²	—	47	1	no	—
535	C₄²	—	47	1	no	—
536	C₄²	—	47	1	no	—
537	C₄²	—	47	1	no	—
538	C₄²	—	47	2	no	—
539	C₄²	—	47	1	no	—
540	C₄²	—	47	1	no	—
541	C₄²	—	47	2	no	—
542	C₄²	—	47	2	no	—
543	C₄²	C₂²×D₄₇	1	1	yes	characteristic
544	C₄²	C₂²×D₄₇	1	1	yes	characteristic
545	C₂³	—	47	2	no	—
546	C₂³	C₂³×D₄₇	1	2	yes	—
547	C₂³	C₂³×D₄₇	1	1	yes	characteristic
548	C₂³	C₂³×D₄₇	1	2	yes	—
549	Q₈	—	94	2	no	—
550	Q₈	—	94	4	no	—
551	Q₈	—	94	2	no	—
552	Q₈	—	94	2	no	—
553	Q₈	—	188	1	no	—
554	Q₈	—	188	1	no	—
555	Q₈	—	188	2	no	—
556	Q₈	—	188	2	no	—
557	D₄	—	2	2	no	—
558	D₄	—	2	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	94	4	no	—
564	D₄	—	94	2	no	—
565	D₄	—	188	2	no	—
566	D₄	—	188	2	no	—
567	D₄	—	188	2	no	—
568	D₄	—	188	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	47	1	no	—
573	C₂×C₄	—	47	2	no	—
574	C₂×C₄	—	47	1	no	—
575	C₂×C₄	—	47	1	no	—
576	C₂×C₄	—	47	1	no	—
577	C₂×C₄	—	47	1	no	—
578	C₂×C₄	—	47	1	no	—
579	C₂×C₄	—	47	1	no	—
580	C₂×C₄	—	47	2	no	—
581	C₂×C₄	—	47	1	no	—
582	C₂×C₄	—	47	2	no	—
583	C₂×C₄	—	94	4	no	—
584	C₂×C₄	—	94	2	no	—
585	C₂×C₄	—	188	2	no	—
586	C₂×C₄	—	188	2	no	—
587	C₂×C₄	—	188	2	no	—
588	C₂×C₄	—	188	1	no	—
589	C₂×C₄	—	188	2	no	—
590	C₂×C₄	—	188	2	no	—
591	C₂×C₄	—	188	2	no	—
592	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₄₇	1	2	yes	—
595	C₂×C₄	C₂³×D₄₇	1	2	yes	—
596	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	94	2	no	—
610	C₂²	—	94	2	no	—
611	C₂²	—	94	2	no	—
612	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	47	2	no	—
621	C₄	—	94	1	no	—
622	C₄	—	94	2	no	—
623	C₄	—	94	1	no	—
624	C₄	—	94	2	no	—
625	C₄	—	94	1	no	—
626	C₄	—	94	2	no	—
627	C₄	—	94	1	no	—
628	C₄	—	94	1	no	—
629	C₄	—	94	1	no	—
630	C₄	—	94	1	no	—
631	C₄	#13094071	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	4	1	no	—
634	C₂	—	4	2	no	—
635	C₂	—	188	2	no	—
636	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
637	C₂	C₂×#13094071	1	1	yes	characteristic
638	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#540	C₂
hypercenter	#540	D₄₇
hypocenter	C₄₇	#3554
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #15689868	C₂	semidirect
2. #15689868	C₂	semidirect
3. #15689859	C₂	semidirect
4. #15689856	C₂	semidirect
5. #15689856	C₂	semidirect
6. #15689850	C₂	semidirect
7. #15689830	C₂	semidirect
8. #15689829	C₂	semidirect
9. #15689793	C₂	semidirect
10. D₄×Dic₉₄	C₂	semidirect
11. #15689779	C₂	semidirect
12. #15689773	C₂	semidirect
13. #15689744	C₂	semidirect
14. #15689741	C₂	semidirect
15. #15689740	C₂	semidirect
16. #15689726	C₂	semidirect
17. #15689717	C₂	semidirect
18. #15689716	C₂	semidirect
19. #15689695	C₂	semidirect
20. #15689676	C₂	semidirect
21. #15689668	C₂	semidirect
22. #15689654	C₂	semidirect
23. C₄₇×#540	C₂	semidirect
336. #540	D₄₇	semidirect
343. C₄₇	#3554	semidirect