Subgroups — #20257120

Order 6016.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689837	C₂	1	2	yes	maximal, complemented
2	#15689825	C₂	1	2	yes	maximal, complemented
3	#15689820	C₂	1	2	yes	maximal, complemented
4	#15689804	C₂	1	4	yes	maximal, complemented
5	#15689773	C₂	1	2	yes	maximal, complemented
6	#15689760	C₂	1	4	yes	maximal, complemented
7	#15689751	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689742	C₂	1	2	yes	maximal, complemented
9	#15689727	C₂	1	2	yes	maximal, complemented
10	#15689671	C₂	1	2	yes	maximal, complemented
11	#15689652	C₂	1	2	yes	maximal, complemented
12	#15689630	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13093995	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689606	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689598	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625352	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	—
20	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
21	#13094024	C₂²	1	2	yes	complemented
22	#13094023	C₂²	1	2	yes	complemented
23	#13094017	C₂²	1	4	yes	complemented
24	#13094017	C₂²	1	4	yes	complemented
25	#13094016	C₂²	1	2	yes	complemented
26	#13094015	C₂²	1	2	yes	complemented
27	#13094011	C₂²	1	4	yes	complemented
28	#13094010	C₂²	1	4	yes	complemented
29	#13094008	C₂²	1	4	yes	complemented
30	#13094006	C₂²	1	4	yes	complemented
31	#13094005	C₂²	1	2	yes	—
32	#13094005	C₂²	1	4	yes	complemented
33	#13094005	C₂²	1	4	yes	complemented
34	#13094001	C₂²	1	4	yes	—
35	#13094001	C₂²	1	4	yes	complemented
36	#13094000	C₂²	1	1	yes	characteristic, complemented
37	#13094000	C₂²	1	1	yes	characteristic, complemented
38	#13093996	C₂²	1	4	yes	complemented
39	#13093996	C₂²	1	4	yes	complemented
40	#13093995	C₂²	1	2	yes	—
41	#13093995	C₂²	1	2	yes	—
42	#13093995	C₂²	1	2	yes	—
43	#13093995	C₂²	1	2	yes	—
44	#13093995	C₂²	1	4	yes	complemented
45	#13093995	C₂²	1	1	yes	characteristic, complemented
46	#13093995	C₂²	1	1	yes	characteristic, complemented
47	#13093992	C₂²	1	2	yes	—
48	Q₈×Dic₄₇	C₂²	1	2	yes	complemented
49	D₄×Dic₄₇	C₂²	1	4	yes	—
50	D₄×Dic₄₇	C₂²	1	2	yes	complemented
51	D₄×Dic₄₇	C₂²	1	2	yes	complemented
52	D₄×Dic₄₇	C₂²	1	4	yes	complemented
53	D₄×Dic₄₇	C₂²	1	2	yes	complemented
54	D₄×Dic₄₇	C₂²	1	2	yes	complemented
55	D₄×Dic₄₇	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
58	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
59	#13093983	C₂²	1	1	yes	characteristic
60	#13093983	C₂²	1	1	yes	characteristic
61	#13093983	C₂²	1	2	yes	complemented
62	#13093982	C₂²	1	1	yes	characteristic, complemented
63	#13093982	C₂²	1	1	yes	characteristic, complemented
64	#13093981	C₂²	1	2	yes	complemented
65	#13093980	C₂²	1	2	yes	—
66	#13093980	C₂²	1	4	yes	complemented
67	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
70	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
74	C₄²×D₄₇	C₂²	1	2	yes	complemented
75	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
76	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
77	#127×C₄₇	C₂²	1	2	yes	complemented
78	#124×C₄₇	C₂²	1	2	yes	complemented
79	#121×C₄₇	C₂²	1	2	yes	complemented
80	#121×C₄₇	C₂²	1	2	yes	complemented
81	#120×C₄₇	C₂²	1	4	yes	—
82	#117×C₄₇	C₂²	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂³	1	2	yes	—
84	C₂³×D₄₇	C₂³	1	1	yes	characteristic
85	#41×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×D₄×C₄₇	C₂³	1	2	yes	—
90	C₂×D₄×C₄₇	C₂³	1	2	yes	—
91	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₄₇	C₂³	1	4	yes	—
93	C₂×D₄×C₄₇	C₂³	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₄₇	—	4	4	no	—
97	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
101	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂³	1	2	yes	—
103	C₂²×Dic₄₇	C₂³	1	4	yes	—
104	C₂²×Dic₄₇	C₂³	1	4	yes	—
105	C₂²×Dic₄₇	C₂³	1	4	yes	—
106	#10625352	—	4	8	no	—
107	C₂×C₄×D₄₇	—	2	4	no	—
108	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₄₇	C₂³	1	2	yes	—
110	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₂³	1	2	yes	—
114	C₂×Dic₉₄	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
120	C₄²×C₄₇	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
123	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
124	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
126	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
127	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
128	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
129	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
134	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₄₇	C₂³	1	2	yes	—
137	C₄⋊Dic₄₇	C₂³	1	2	yes	—
138	C₄⋊Dic₄₇	C₂³	1	4	yes	—
139	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₄₇	C₂³	1	4	yes	—
142	Dic₄₇⋊C₄	C₂³	1	2	yes	—
143	Dic₄₇⋊C₄	C₂³	1	2	yes	—
144	Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	Dic₄₇⋊C₄	C₂³	1	4	yes	—
146	Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	Dic₄₇⋊C₄	C₂³	1	2	yes	—
148	C₄×Dic₄₇	C₂³	1	2	yes	—
149	C₄×Dic₄₇	C₂³	1	2	yes	—
150	C₄×Dic₄₇	C₂³	1	2	yes	—
151	C₄×Dic₄₇	C₂³	1	4	yes	—
152	C₄×Dic₄₇	C₂³	1	2	yes	—
153	C₂³×C₄₇	—	2	4	no	—
154	C₂³×C₄₇	—	4	2	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	C₂⁴	1	4	yes	—
157	C₂³×C₄₇	C₂⁴	1	2	yes	—
158	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	2	no	—
160	C₂²×D₄₇	—	2	2	no	—
161	C₂²×D₄₇	—	4	1	no	—
162	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
163	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	2	no	—
165	D₄×C₄₇	—	2	4	no	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	—	4	4	no	—
170	D₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	#41	1	4	yes	complemented
173	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
174	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
175	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
176	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₄₇	—	2	4	no	—
179	C₂²⋊D₄₇	—	2	8	no	—
180	C₂²⋊D₄₇	—	4	4	no	—
181	C₂²⋊D₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	4	4	no	—
184	C₂×Dic₄₇	—	4	4	no	—
185	C₂×Dic₄₇	—	4	4	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₄₇	C₂⁴	1	2	yes	—
189	C₂×Dic₄₇	C₂⁴	1	2	yes	—
190	C₂×Dic₄₇	C₂⁴	1	2	yes	—
191	C₂×Dic₄₇	C₂⁴	1	4	yes	—
192	C₂×Dic₄₇	C₂⁴	1	2	yes	—
193	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
194	C₄×D₄₇	—	2	4	no	—
195	C₄×D₄₇	—	2	2	no	—
196	C₄×D₄₇	—	2	2	no	—
197	C₄×D₄₇	—	2	2	no	—
198	C₄×D₄₇	—	2	2	no	—
199	C₄×D₄₇	—	4	2	no	—
200	Dic₉₄	—	4	4	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	8	4	no	—
210	C₂²×C₄₇	C₂×#41	1	2	yes	—
211	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
212	C₂×D₄₇	—	2	1	no	—
213	C₂×D₄₇	—	2	1	no	—
214	C₂×D₄₇	—	2	1	no	—
215	C₂×D₄₇	—	2	1	no	—
216	C₂×D₄₇	—	2	1	no	—
217	C₂×D₄₇	—	4	4	no	—
218	C₂×D₄₇	H(5,𝔽₂)	1	2	yes	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	C₂×#41	1	2	yes	—
223	C₄×C₄₇	C₂×#41	1	2	yes	—
224	Dic₄₇	—	2	1	no	—
225	Dic₄₇	—	2	1	no	—
226	Dic₄₇	—	2	2	no	—
227	Dic₄₇	—	2	4	no	—
228	Dic₄₇	—	2	2	no	—
229	Dic₄₇	—	2	2	no	—
230	Dic₄₇	—	2	2	no	—
231	#3494	—	47	1	no	maximal, Sylow
232	C₂×C₄₇	—	2	2	no	—
233	C₂×C₄₇	—	4	2	no	—
234	C₂×C₄₇	—	4	4	no	—
235	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
236	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄₇	#585	1	1	yes	characteristic
238	D₄₇	—	2	2	no	—
239	D₄₇	—	4	1	no	—
240	#555	—	47	2	no	—
241	#553	—	47	2	no	—
242	#553	—	47	2	no	—
243	#551	—	47	4	no	—
244	#547	—	47	2	no	—
245	#546	—	47	4	no	—
246	#544	—	47	1	no	—
247	#542	—	47	2	no	—
248	#540	—	47	2	no	—
249	#535	D₄₇	1	1	yes	characteristic, complemented
250	#532	—	47	2	no	—
251	#529	—	47	2	no	—
252	#525	—	47	1	no	—
253	C₂×#121	—	47	1	no	—
254	#520	—	47	1	no	—
255	#518	—	47	1	no	—
256	C₂×#117	—	47	1	no	—
257	C₄₇	#3494	1	1	yes	characteristic, complemented, Sylow
258	C₂×#41	—	47	4	no	—
259	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
260	C₂²×D₄	—	47	2	no	—
261	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
262	C₂³×C₄	—	47	1	no	—
263	C₄⋊Q₈	—	47	2	no	—
264	C₄⋊Q₈	—	47	2	no	—
265	#127	C₂×D₄₇	1	2	yes	complemented
266	#126	—	47	4	no	—
267	#126	—	47	4	no	—
268	#125	—	47	2	no	—
269	#125	—	47	2	no	—
270	#124	—	47	4	no	—
271	#124	—	47	4	no	—
272	#124	C₂×D₄₇	1	2	yes	complemented
273	#123	—	47	2	no	—
274	#123	—	47	4	no	—
275	#123	—	47	4	no	—
276	#123	—	47	4	no	—
277	#123	—	47	4	no	—
278	C₂²⋊Q₈	—	47	1	no	—
279	C₂²⋊Q₈	—	47	1	no	—
280	C₂²⋊Q₈	—	47	4	no	—
281	C₂²⋊Q₈	—	47	4	no	—
282	#121	—	47	2	no	—
283	#121	—	47	2	no	—
284	#121	—	47	2	no	—
285	#121	—	47	2	no	—
286	#121	—	47	1	no	—
287	#121	—	47	1	no	—
288	#121	—	47	4	no	—
289	#121	—	47	4	no	—
290	#121	—	47	4	no	—
291	#121	C₂×D₄₇	1	2	yes	complemented
292	#121	C₂×D₄₇	1	2	yes	complemented
293	#120	—	47	2	no	—
294	#120	C₂×D₄₇	1	4	yes	—
295	C₄×Q₈	—	47	2	no	—
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	2	no	—
301	C₄×D₄	—	47	4	no	—
302	C₄×D₄	—	47	4	no	—
303	C₄×D₄	—	47	2	no	—
304	C₄×D₄	—	47	2	no	—
305	C₄×D₄	—	47	4	no	—
306	#117	—	47	1	no	—
307	#117	—	47	1	no	—
308	#117	—	47	2	no	—
309	#117	—	47	1	no	—
310	#117	—	47	1	no	—
311	#117	—	47	2	no	—
312	#117	—	47	4	no	—
313	#117	—	47	2	no	—
314	#117	C₂×D₄₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	47	1	no	—
316	C₂×C₄⋊C₄	—	47	2	no	—
317	C₂×C₄⋊C₄	—	47	1	no	—
318	C₂×C₄⋊C₄	—	47	1	no	—
319	C₂×C₂²⋊C₄	—	47	4	no	—
320	C₂×C₂²⋊C₄	—	47	2	no	—
321	C₂×C₂²⋊C₄	—	47	2	no	—
322	C₂×C₄²	—	47	2	no	—
323	C₂⁴	—	47	1	no	—
324	C₂⁴	C₂²×D₄₇	1	2	yes	—
325	#41	—	2	4	no	—
326	#41	—	188	8	no	—
327	C₂×Q₈	—	47	4	no	—
328	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	47	2	no	—
331	C₂×D₄	—	47	4	no	—
332	C₂×D₄	—	47	2	no	—
333	C₂×D₄	—	47	4	no	—
334	C₂×D₄	—	188	4	no	—
335	C₂×D₄	C₂²×D₄₇	1	2	yes	—
336	C₂×D₄	C₂²×D₄₇	1	2	yes	—
337	C₂×D₄	C₂²×D₄₇	1	2	yes	—
338	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
339	C₂×D₄	C₂²×D₄₇	1	4	yes	—
340	C₂×D₄	C₂²×D₄₇	1	4	yes	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	4	no	—
344	C₂²×C₄	—	47	4	no	—
345	C₂²×C₄	—	47	4	no	—
346	C₂²×C₄	—	47	1	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	1	no	—
350	C₂²×C₄	—	47	1	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	94	4	no	—
353	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
354	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	—	47	2	no	—
357	C₄⋊C₄	—	47	2	no	—
358	C₄⋊C₄	—	47	4	no	—
359	C₄⋊C₄	—	47	4	no	—
360	C₄⋊C₄	—	47	2	no	—
361	C₄⋊C₄	—	47	1	no	—
362	C₄⋊C₄	—	47	2	no	—
363	C₄⋊C₄	—	47	1	no	—
364	C₄⋊C₄	—	47	2	no	—
365	C₄⋊C₄	—	47	4	no	—
366	C₄⋊C₄	—	47	1	no	—
367	C₄⋊C₄	—	47	1	no	—
368	C₄⋊C₄	—	47	4	no	—
369	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
371	C₂²⋊C₄	—	47	2	no	—
372	C₂²⋊C₄	—	47	2	no	—
373	C₂²⋊C₄	—	47	4	no	—
374	C₂²⋊C₄	—	47	4	no	—
375	C₂²⋊C₄	—	47	4	no	—
376	C₂²⋊C₄	—	47	4	no	—
377	C₂²⋊C₄	—	47	4	no	—
378	C₂²⋊C₄	—	47	2	no	—
379	C₂²⋊C₄	—	47	2	no	—
380	C₂²⋊C₄	—	47	2	no	—
381	C₂²⋊C₄	—	47	2	no	—
382	C₂²⋊C₄	—	47	2	no	—
383	C₂²⋊C₄	—	47	2	no	—
384	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
386	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
387	C₄²	—	47	2	no	—
388	C₄²	—	47	2	no	—
389	C₄²	—	47	2	no	—
390	C₄²	—	47	4	no	—
391	C₄²	—	47	2	no	—
392	C₄²	C₂²×D₄₇	1	2	yes	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	47	1	no	—
397	C₂³	—	47	1	no	—
398	C₂³	—	94	2	no	—
399	C₂³	—	94	2	no	—
400	C₂³	—	188	1	no	—
401	C₂³	C₂³×D₄₇	1	4	yes	—
402	C₂³	C₂³×D₄₇	1	2	yes	—
403	C₂³	C₂³×D₄₇	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	188	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	94	8	no	—
413	D₄	—	94	4	no	—
414	D₄	—	188	2	no	—
415	D₄	—	188	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	47	1	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	47	2	no	—
421	C₂×C₄	—	47	2	no	—
422	C₂×C₄	—	47	4	no	—
423	C₂×C₄	—	47	1	no	—
424	C₂×C₄	—	94	4	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	94	2	no	—
428	C₂×C₄	—	94	2	no	—
429	C₂×C₄	—	94	2	no	—
430	C₂×C₄	—	188	2	no	—
431	C₂×C₄	—	188	4	no	—
432	C₂×C₄	—	188	2	no	—
433	C₂×C₄	—	188	4	no	—
434	C₂×C₄	—	188	4	no	—
435	C₂×C₄	#10625352	1	4	yes	complemented
436	C₂×C₄	C₂³×D₄₇	1	2	yes	—
437	C₂×C₄	C₂³×D₄₇	1	2	yes	—
438	C₂×C₄	C₂³×D₄₇	1	2	yes	—
439	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	8	4	no	—
450	C₂²	—	47	2	no	—
451	C₂²	—	94	1	no	—
452	C₂²	—	94	1	no	—
453	C₂²	—	94	1	no	—
454	C₂²	—	94	1	no	—
455	C₂²	—	94	1	no	—
456	C₂²	—	188	4	no	—
457	C₂²	C₂×#10625352	1	2	yes	—
458	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	94	1	no	—
463	C₄	—	94	1	no	—
464	C₄	—	94	2	no	—
465	C₄	—	94	4	no	—
466	C₄	—	94	2	no	—
467	C₄	—	94	2	no	—
468	C₄	—	94	2	no	—
469	C₄	C₂×#10625352	1	2	yes	—
470	C₄	C₂×#10625352	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	—	4	2	no	—
474	C₂	—	94	2	no	—
475	C₂	—	188	1	no	—
476	C₂	C₂²×#10625352	1	1	yes	characteristic
477	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
478	C₂	#15689958	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	#3494
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. #15689837	C₂	semidirect
2. #15689825	C₂	semidirect
3. #15689820	C₂	semidirect
4. #15689804	C₂	semidirect
5. #15689773	C₂	semidirect
6. #15689760	C₂	semidirect
7. #15689751	C₂	semidirect
8. #15689742	C₂	semidirect
9. #15689727	C₂	semidirect
10. #15689671	C₂	semidirect
11. #15689652	C₂	semidirect
12. #15689630	C₂	semidirect
13. C₂×#13093995	C₂	semidirect
14. #15689606	C₂	semidirect
15. #15689598	C₂	semidirect
16. #117×D₄₇	C₂	semidirect
17. C₄₇×#535	C₂	semidirect
18. C₂×#10625352	C₂²	semidirect
21. #13094024	C₂²	semidirect
22. #13094023	C₂²	semidirect
23. #13094017	C₂²	semidirect
24. #13094017	C₂²	semidirect
25. #13094016	C₂²	semidirect
26. #13094015	C₂²	semidirect
27. #13094011	C₂²	semidirect
28. #13094010	C₂²	semidirect
29. #13094008	C₂²	semidirect
30. #13094006	C₂²	semidirect
32. #13094005	C₂²	semidirect
33. #13094005	C₂²	semidirect
35. #13094001	C₂²	semidirect
36. #13094000	C₂²	semidirect
37. #13094000	C₂²	semidirect
38. #13093996	C₂²	semidirect
39. #13093996	C₂²	semidirect
44. #13093995	C₂²	semidirect
45. #13093995	C₂²	semidirect
46. #13093995	C₂²	semidirect
48. Q₈×Dic₄₇	C₂²	semidirect
50. D₄×Dic₄₇	C₂²	semidirect
51. D₄×Dic₄₇	C₂²	semidirect
52. D₄×Dic₄₇	C₂²	semidirect
53. D₄×Dic₄₇	C₂²	semidirect
54. D₄×Dic₄₇	C₂²	semidirect
55. D₄×Dic₄₇	C₂²	semidirect
56. C₄×C₂²⋊D₄₇	C₂²	semidirect
57. C₄×C₂²⋊D₄₇	C₂²	semidirect
58. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
61. #13093983	C₂²	semidirect
62. #13093982	C₂²	semidirect
63. #13093982	C₂²	semidirect
64. #13093981	C₂²	semidirect
66. #13093980	C₂²	semidirect
68. C₂×C₄⋊Dic₄₇	C₂²	semidirect
69. C₄⋊C₄×D₄₇	C₂²	semidirect
70. C₄⋊C₄×D₄₇	C₂²	semidirect
74. C₄²×D₄₇	C₂²	semidirect
77. #127×C₄₇	C₂²	semidirect
78. #124×C₄₇	C₂²	semidirect
79. #121×C₄₇	C₂²	semidirect
80. #121×C₄₇	C₂²	semidirect
172. C₂×C₄×C₄₇	#41	semidirect
249. #535	D₄₇	semidirect
257. C₄₇	#3494	semidirect
265. #127	C₂×D₄₇	semidirect
272. #124	C₂×D₄₇	semidirect
291. #121	C₂×D₄₇	semidirect
292. #121	C₂×D₄₇	semidirect
435. C₂×C₄	#10625352	semidirect