Subgroups — #20257621

Order 6016.

1270 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689862	C₂	1	2	yes	maximal, complemented
2	#15689860	C₂	1	2	yes	maximal, complemented
3	#15689820	C₂	1	2	yes	maximal, complemented
4	#15689817	C₂	1	2	yes	maximal, complemented
5	#15689758	C₂	1	2	yes	maximal, complemented
6	#15689757	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
8	#15689755	C₂	1	2	yes	maximal, complemented
9	#15689726	C₂	1	2	yes	maximal, complemented
10	#15689707	C₂	1	4	yes	maximal, complemented
11	#15689687	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689683	C₂	1	4	yes	maximal, complemented
13	#15689630	C₂	1	1	yes	maximal, characteristic, complemented
14	#121×D₄₇	C₂	1	2	yes	maximal, complemented
15	C₄₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
18	C₂×D₄×D₄₇	C₂²	1	4	yes	complemented
19	C₂×D₄×D₄₇	C₂²	1	2	yes	complemented
20	C₂×D₄×D₄₇	C₂²	1	4	yes	complemented
21	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
22	#13094020	C₂²	1	2	yes	complemented
23	#13094020	C₂²	1	2	yes	complemented
24	#13094018	C₂²	1	4	yes	complemented
25	#13094017	C₂²	1	4	yes	complemented
26	#13094015	C₂²	1	2	yes	complemented
27	#13094013	C₂²	1	2	yes	complemented
28	#13094008	C₂²	1	4	yes	complemented
29	#13094006	C₂²	1	4	yes	complemented
30	#13094006	C₂²	1	4	yes	complemented
31	#13094005	C₂²	1	4	yes	complemented
32	#13094005	C₂²	1	1	yes	characteristic, complemented
33	#13094005	C₂²	1	1	yes	characteristic, complemented
34	#13094000	C₂²	1	2	yes	complemented
35	#13093999	C₂²	1	2	yes	complemented
36	#13093998	C₂²	1	2	yes	complemented
37	#13093998	C₂²	1	2	yes	complemented
38	#13093997	C₂²	1	4	yes	complemented
39	#13093997	C₂²	1	4	yes	complemented
40	#13093997	C₂²	1	4	yes	complemented
41	#13093996	C₂²	1	4	yes	complemented
42	#13093996	C₂²	1	4	yes	complemented
43	#13093996	C₂²	1	4	yes	complemented
44	#13093995	C₂²	1	2	yes	complemented
45	#13093995	C₂²	1	4	yes	complemented
46	#13093995	C₂²	1	4	yes	complemented
47	#13093995	C₂²	1	2	yes	complemented
48	#13093994	C₂²	1	4	yes	complemented
49	#13093993	C₂²	1	4	yes	complemented
50	#13093992	C₂²	1	1	yes	characteristic, complemented
51	#13093992	C₂²	1	4	yes	complemented
52	#13093992	C₂²	1	4	yes	complemented
53	#13093992	C₂²	1	1	yes	characteristic, complemented
54	#13093992	C₂²	1	2	yes	complemented
55	#13093992	C₂²	1	2	yes	complemented
56	C₄×D₁₈₈	C₂²	1	4	yes	complemented
57	D₄×Dic₄₇	C₂²	1	2	yes	complemented
58	#13093986	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
61	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
62	#13093983	C₂²	1	1	yes	characteristic, complemented
63	#13093983	C₂²	1	1	yes	characteristic, complemented
64	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
65	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
66	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	#127×C₄₇	C₂²	1	2	yes	complemented
69	#124×C₄₇	C₂²	1	2	yes	complemented
70	#121×C₄₇	C₂²	1	2	yes	complemented
71	#121×C₄₇	C₂²	1	2	yes	complemented
72	#120×C₄₇	C₂²	1	2	yes	complemented
73	#120×C₄₇	C₂²	1	2	yes	complemented
74	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₄₇	C₂³	1	2	yes	—
76	C₂³×D₄₇	C₂³	1	1	yes	characteristic
77	C₂³×D₄₇	C₂³	1	4	yes	—
78	C₂³×D₄₇	C₂³	1	2	yes	—
79	#41×C₄₇	—	4	2	no	—
80	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×D₄×C₄₇	—	4	2	no	—
82	C₂×D₄×C₄₇	C₂³	1	2	yes	—
83	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₄₇	C₂³	1	4	yes	—
86	C₂×D₄×C₄₇	C₂³	1	4	yes	—
87	C₂×D₄×C₄₇	C₂³	1	2	yes	—
88	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₄₇	—	4	8	no	—
93	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
101	C₂²×Dic₄₇	C₂³	1	4	yes	—
102	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
103	D₄×D₄₇	—	4	4	no	—
104	D₄×D₄₇	—	4	8	no	—
105	D₄×D₄₇	—	4	8	no	—
106	C₂×D₁₈₈	—	4	2	no	—
107	C₂×D₁₈₈	C₂³	1	2	yes	—
108	C₂×D₁₈₈	C₂³	1	4	yes	—
109	C₂×D₁₈₈	C₂³	1	2	yes	—
110	C₂×C₄×D₄₇	—	4	2	no	—
111	C₂×C₄×D₄₇	C₂³	1	2	yes	—
112	C₂×C₄×D₄₇	C₂³	1	2	yes	—
113	C₂×C₄×D₄₇	C₂³	1	4	yes	—
114	C₂×C₄×D₄₇	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
119	C₄²×C₄₇	C₂³	1	2	yes	—
120	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
121	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
123	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
124	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
126	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
133	C₄⋊Dic₄₇	C₂³	1	2	yes	—
134	C₄⋊Dic₄₇	C₂³	1	2	yes	—
135	C₄⋊Dic₄₇	C₂³	1	4	yes	—
136	Dic₄₇⋊C₄	C₂³	1	4	yes	—
137	Dic₄₇⋊C₄	C₂³	1	4	yes	—
138	Dic₄₇⋊C₄	C₂³	1	2	yes	—
139	Dic₄₇⋊C₄	C₂³	1	2	yes	—
140	C₄×Dic₄₇	C₂³	1	2	yes	—
141	C₄×Dic₄₇	C₂³	1	2	yes	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₄₇	C₂⁴	1	4	yes	—
146	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂²×D₄₇	—	2	4	no	—
149	C₂²×D₄₇	—	2	8	no	—
150	C₂²×D₄₇	—	4	1	no	—
151	C₂²×D₄₇	—	4	2	no	—
152	C₂²×D₄₇	—	4	4	no	—
153	C₂²×D₄₇	—	4	4	no	—
154	C₂²×D₄₇	—	4	4	no	—
155	C₂²×D₄₇	C₂⁴	1	4	yes	—
156	C₂²×D₄₇	C₂⁴	1	2	yes	—
157	Q₈×C₄₇	—	4	1	no	—
158	D₄×C₄₇	—	2	4	no	—
159	D₄×C₄₇	—	4	4	no	—
160	D₄×C₄₇	—	4	4	no	—
161	D₄×C₄₇	—	4	2	no	—
162	D₄×C₄₇	—	4	1	no	—
163	D₄×C₄₇	—	4	1	no	—
164	D₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
170	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₄₇	—	2	4	no	—
174	C₂²⋊D₄₇	—	2	8	no	—
175	C₂²⋊D₄₇	—	2	4	no	—
176	C₂²⋊D₄₇	—	4	4	no	—
177	C₂²⋊D₄₇	—	4	4	no	—
178	C₂²⋊D₄₇	—	4	4	no	—
179	C₂²⋊D₄₇	—	4	4	no	—
180	C₂²⋊D₄₇	—	4	4	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	4	4	no	—
183	C₂×Dic₄₇	C₂⁴	1	2	yes	—
184	C₂×Dic₄₇	C₂⁴	1	4	yes	—
185	C₂×Dic₄₇	C₂⁴	1	2	yes	—
186	C₂×Dic₄₇	C₂⁴	1	2	yes	—
187	D₁₈₈	—	2	8	no	—
188	D₁₈₈	—	2	4	no	—
189	D₁₈₈	—	4	2	no	—
190	C₄×D₄₇	—	2	4	no	—
191	C₄×D₄₇	—	4	2	no	—
192	C₄×D₄₇	—	4	4	no	—
193	C₄×D₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	2	4	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	4	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	4	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	8	4	no	—
204	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
205	C₂×D₄₇	—	2	2	no	—
206	C₂×D₄₇	—	2	2	no	—
207	C₂×D₄₇	—	2	4	no	—
208	C₂×D₄₇	—	2	4	no	—
209	C₂×D₄₇	—	2	4	no	—
210	C₂×D₄₇	—	4	4	no	—
211	C₂×D₄₇	—	8	8	no	—
212	C₂×D₄₇	—	8	4	no	—
213	C₂×D₄₇	H(5,𝔽₂)	1	4	yes	—
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
219	Dic₄₇	—	2	2	no	—
220	Dic₄₇	—	2	2	no	—
221	Dic₄₇	—	2	4	no	—
222	Dic₄₇	—	2	2	no	—
223	#3537	—	47	1	no	maximal, Sylow
224	C₂×C₄₇	—	4	1	no	—
225	C₂×C₄₇	—	4	1	no	—
226	C₂×C₄₇	—	4	4	no	—
227	C₂×C₄₇	—	4	1	no	—
228	C₂×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
229	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	D₄₇	—	2	4	no	—
231	D₄₇	—	4	4	no	—
232	#560	—	47	2	no	—
233	#560	—	47	2	no	—
234	#553	—	47	2	no	—
235	#553	—	47	2	no	—
236	D₄²	—	47	2	no	—
237	D₄²	—	47	2	no	—
238	D₄²	—	47	2	no	—
239	D₄²	—	47	2	no	—
240	#540	—	47	2	no	—
241	#538	—	47	4	no	—
242	#535	—	47	1	no	—
243	#535	D₄₇	1	1	yes	characteristic, complemented
244	#534	—	47	4	no	—
245	#525	—	47	1	no	—
246	C₂×#121	—	47	2	no	—
247	C₄₇	#3537	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
249	C₂²×D₄	—	47	4	no	—
250	C₂²×D₄	—	47	2	no	—
251	C₂²×D₄	—	47	4	no	—
252	C₂²×D₄	—	47	4	no	—
253	C₂²×D₄	—	47	1	no	—
254	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
255	C₂³×C₄	—	47	1	no	—
256	#127	—	47	2	no	—
257	#127	—	47	2	no	—
258	#127	C₂×D₄₇	1	2	yes	complemented
259	#126	—	47	4	no	—
260	#126	—	47	4	no	—
261	#125	—	47	2	no	—
262	#124	—	47	2	no	—
263	#124	C₂×D₄₇	1	2	yes	complemented
264	#123	—	47	1	no	—
265	#123	—	47	1	no	—
266	#123	—	47	4	no	—
267	#123	—	47	4	no	—
268	#123	—	47	4	no	—
269	#123	—	47	4	no	—
270	C₂²⋊Q₈	—	47	2	no	—
271	#121	—	47	2	no	—
272	#121	—	47	4	no	—
273	#121	—	47	2	no	—
274	#121	—	47	4	no	—
275	#121	—	47	4	no	—
276	#121	—	47	4	no	—
277	#121	—	47	4	no	—
278	#121	—	47	2	no	—
279	#121	—	47	2	no	—
280	#121	—	47	2	no	—
281	#121	—	47	4	no	—
282	#121	—	47	4	no	—
283	#121	—	47	4	no	—
284	#121	C₂×D₄₇	1	2	yes	complemented
285	#121	C₂×D₄₇	1	2	yes	complemented
286	#120	—	47	4	no	—
287	#120	—	47	1	no	—
288	#120	—	47	1	no	—
289	#120	—	47	2	no	—
290	#120	—	47	4	no	—
291	#120	—	47	2	no	—
292	#120	—	47	4	no	—
293	#120	—	47	4	no	—
294	#120	C₂×D₄₇	1	2	yes	complemented
295	#120	C₂×D₄₇	1	2	yes	complemented
296	C₄×D₄	—	47	2	no	—
297	C₄×D₄	—	47	2	no	—
298	C₄×D₄	—	47	2	no	—
299	C₄×D₄	—	47	2	no	—
300	C₄×D₄	—	47	4	no	—
301	C₄×D₄	—	47	4	no	—
302	#117	—	47	1	no	—
303	#117	—	47	1	no	—
304	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
305	C₂×C₄⋊C₄	—	47	2	no	—
306	C₂×C₂²⋊C₄	—	47	4	no	—
307	C₂⁴	—	47	1	no	—
308	C₂⁴	—	47	4	no	—
309	C₂⁴	—	47	2	no	—
310	C₂⁴	C₂²×D₄₇	1	2	yes	—
311	#41	—	4	2	no	—
312	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	47	2	no	—
315	C₂×D₄	—	47	4	no	—
316	C₂×D₄	—	47	2	no	—
317	C₂×D₄	—	47	4	no	—
318	C₂×D₄	—	47	4	no	—
319	C₂×D₄	—	47	4	no	—
320	C₂×D₄	—	47	4	no	—
321	C₂×D₄	—	47	4	no	—
322	C₂×D₄	—	47	4	no	—
323	C₂×D₄	—	47	2	no	—
324	C₂×D₄	—	47	2	no	—
325	C₂×D₄	—	188	2	no	—
326	C₂×D₄	—	188	4	no	—
327	C₂×D₄	—	188	8	no	—
328	C₂×D₄	—	188	8	no	—
329	C₂×D₄	—	188	8	no	—
330	C₂×D₄	C₂²×D₄₇	1	2	yes	—
331	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₂×D₄	C₂²×D₄₇	1	2	yes	—
334	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
335	C₂×D₄	C₂²×D₄₇	1	4	yes	—
336	C₂×D₄	C₂²×D₄₇	1	4	yes	—
337	C₂²×C₄	—	47	4	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	2	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	4	no	—
342	C₂²×C₄	—	47	4	no	—
343	C₂²×C₄	—	188	2	no	—
344	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
347	C₄⋊C₄	—	47	4	no	—
348	C₄⋊C₄	—	47	2	no	—
349	C₄⋊C₄	—	47	2	no	—
350	C₄⋊C₄	—	47	4	no	—
351	C₄⋊C₄	—	47	2	no	—
352	C₄⋊C₄	—	47	2	no	—
353	C₄⋊C₄	—	47	4	no	—
354	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
355	C₂²⋊C₄	—	47	4	no	—
356	C₂²⋊C₄	—	47	2	no	—
357	C₂²⋊C₄	—	47	1	no	—
358	C₂²⋊C₄	—	47	1	no	—
359	C₂²⋊C₄	—	47	4	no	—
360	C₂²⋊C₄	—	47	2	no	—
361	C₂²⋊C₄	—	47	2	no	—
362	C₂²⋊C₄	—	47	4	no	—
363	C₂²⋊C₄	—	47	4	no	—
364	C₂²⋊C₄	—	47	2	no	—
365	C₂²⋊C₄	—	47	2	no	—
366	C₂²⋊C₄	—	47	4	no	—
367	C₂²⋊C₄	—	47	4	no	—
368	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
369	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
371	C₄²	—	47	2	no	—
372	C₄²	—	47	2	no	—
373	C₄²	C₂²×D₄₇	1	2	yes	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	47	2	no	—
377	C₂³	—	47	4	no	—
378	C₂³	—	94	8	no	—
379	C₂³	—	94	4	no	—
380	C₂³	—	188	4	no	—
381	C₂³	—	188	4	no	—
382	C₂³	—	188	2	no	—
383	C₂³	—	188	4	no	—
384	C₂³	—	188	1	no	—
385	C₂³	C₂³×D₄₇	1	1	yes	characteristic
386	C₂³	C₂³×D₄₇	1	4	yes	—
387	C₂³	C₂³×D₄₇	1	1	yes	characteristic
388	C₂³	C₂³×D₄₇	1	1	yes	characteristic
389	Q₈	—	4	1	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	94	8	no	—
398	D₄	—	94	4	no	—
399	D₄	—	94	8	no	—
400	D₄	—	94	4	no	—
401	D₄	—	94	4	no	—
402	D₄	—	188	2	no	—
403	D₄	—	188	4	no	—
404	D₄	—	188	4	no	—
405	D₄	—	188	4	no	—
406	D₄	—	188	4	no	—
407	D₄	—	188	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	47	2	no	—
412	C₂×C₄	—	47	4	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	47	2	no	—
415	C₂×C₄	—	94	4	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	4	no	—
418	C₂×C₄	—	188	4	no	—
419	C₂×C₄	—	188	1	no	—
420	C₂×C₄	—	188	4	no	—
421	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₄₇	1	4	yes	—
424	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
426	C₂²	—	2	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	47	4	no	—
437	C₂²	—	94	2	no	—
438	C₂²	—	94	2	no	—
439	C₂²	—	94	4	no	—
440	C₂²	—	94	4	no	—
441	C₂²	—	94	4	no	—
442	C₂²	—	376	8	no	—
443	C₂²	—	376	4	no	—
444	C₂²	—	188	4	no	—
445	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	94	2	no	—
451	C₄	—	94	4	no	—
452	C₄	—	94	2	no	—
453	C₄	—	94	2	no	—
454	C₄	#13094069	1	2	yes	—
455	C₂	—	4	1	no	—
456	C₂	—	4	4	no	—
457	C₂	—	4	1	no	—
458	C₂	—	4	1	no	—
459	C₂	—	94	4	no	—
460	C₂	—	188	4	no	—
461	C₂	H(5,𝔽₂)×D₄₇	1	2	yes	—
462	C₂	C₂×#13094069	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#535	C₂
hypercenter	#535	D₄₇
hypocenter	C₄₇	#3537
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #15689862	C₂	semidirect
2. #15689860	C₂	semidirect
3. #15689820	C₂	semidirect
4. #15689817	C₂	semidirect
5. #15689758	C₂	semidirect
6. #15689757	C₂	semidirect
7. D₄×C₂²⋊D₄₇	C₂	semidirect
8. #15689755	C₂	semidirect
9. #15689726	C₂	semidirect
10. #15689707	C₂	semidirect
11. #15689687	C₂	semidirect
12. #15689683	C₂	semidirect
13. #15689630	C₂	semidirect
14. #121×D₄₇	C₂	semidirect
15. C₄₇×#535	C₂	semidirect
16. C₂²×D₁₈₈	C₂²	semidirect
17. C₂²×C₂²⋊D₄₇	C₂²	semidirect
18. C₂×D₄×D₄₇	C₂²	semidirect
19. C₂×D₄×D₄₇	C₂²	semidirect
20. C₂×D₄×D₄₇	C₂²	semidirect
21. C₂²×C₄×D₄₇	C₂²	semidirect
22. #13094020	C₂²	semidirect
23. #13094020	C₂²	semidirect
24. #13094018	C₂²	semidirect
25. #13094017	C₂²	semidirect
26. #13094015	C₂²	semidirect
27. #13094013	C₂²	semidirect
28. #13094008	C₂²	semidirect
29. #13094006	C₂²	semidirect
30. #13094006	C₂²	semidirect
31. #13094005	C₂²	semidirect
32. #13094005	C₂²	semidirect
33. #13094005	C₂²	semidirect
34. #13094000	C₂²	semidirect
35. #13093999	C₂²	semidirect
36. #13093998	C₂²	semidirect
37. #13093998	C₂²	semidirect
38. #13093997	C₂²	semidirect
39. #13093997	C₂²	semidirect
40. #13093997	C₂²	semidirect
41. #13093996	C₂²	semidirect
42. #13093996	C₂²	semidirect
43. #13093996	C₂²	semidirect
44. #13093995	C₂²	semidirect
45. #13093995	C₂²	semidirect
46. #13093995	C₂²	semidirect
47. #13093995	C₂²	semidirect
48. #13093994	C₂²	semidirect
49. #13093993	C₂²	semidirect
50. #13093992	C₂²	semidirect
51. #13093992	C₂²	semidirect
52. #13093992	C₂²	semidirect
53. #13093992	C₂²	semidirect
54. #13093992	C₂²	semidirect
55. #13093992	C₂²	semidirect
56. C₄×D₁₈₈	C₂²	semidirect
57. D₄×Dic₄₇	C₂²	semidirect
58. #13093986	C₂²	semidirect
59. C₄×C₂²⋊D₄₇	C₂²	semidirect
60. C₄×C₂²⋊D₄₇	C₂²	semidirect
61. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
62. #13093983	C₂²	semidirect
63. #13093983	C₂²	semidirect
64. C₄⋊C₄×D₄₇	C₂²	semidirect
65. C₂²⋊C₄×D₄₇	C₂²	semidirect
66. C₂×#41×C₄₇	C₂²	semidirect
67. C₂²×D₄×C₄₇	C₂²	semidirect
68. #127×C₄₇	C₂²	semidirect
69. #124×C₄₇	C₂²	semidirect
70. #121×C₄₇	C₂²	semidirect
71. #121×C₄₇	C₂²	semidirect
72. #120×C₄₇	C₂²	semidirect
73. #120×C₄₇	C₂²	semidirect
74. #117×C₄₇	C₂²	semidirect
243. #535	D₄₇	semidirect
247. C₄₇	#3537	semidirect
248. C₂×#41	C₂×D₄₇	semidirect
254. C₂²×D₄	C₂×D₄₇	semidirect
258. #127	C₂×D₄₇	semidirect
263. #124	C₂×D₄₇	semidirect
284. #121	C₂×D₄₇	semidirect
285. #121	C₂×D₄₇	semidirect
294. #120	C₂×D₄₇	semidirect
295. #120	C₂×D₄₇	semidirect
304. #117	C₂×D₄₇	semidirect