Subgroups — #20257141

Order 6016.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689841	C₂	1	2	yes	maximal, complemented
2	#15689828	C₂	1	2	yes	maximal, complemented
3	#15689813	C₂	1	4	yes	maximal, complemented
4	#15689812	C₂	1	2	yes	maximal, complemented
5	#15689808	C₂	1	2	yes	maximal, complemented
6	#15689802	C₂	1	4	yes	maximal, complemented
7	#15689754	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689738	C₂	1	2	yes	maximal, complemented
9	#15689731	C₂	1	2	yes	maximal, complemented
10	#15689694	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689677	C₂	1	2	yes	maximal, complemented
12	#15689655	C₂	1	2	yes	maximal, complemented
13	#15689630	C₂	1	1	yes	maximal, characteristic
14	C₂×#13094004	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689600	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
20	#13094023	C₂²	1	2	yes	complemented
21	#13094023	C₂²	1	2	yes	complemented
22	#13094022	C₂²	1	2	yes	complemented
23	#13094019	C₂²	1	4	yes	—
24	#13094018	C₂²	1	4	yes	—
25	#13094017	C₂²	1	4	yes	complemented
26	#13094017	C₂²	1	4	yes	complemented
27	#13094016	C₂²	1	4	yes	complemented
28	#13094015	C₂²	1	2	yes	complemented
29	#13094015	C₂²	1	2	yes	complemented
30	#13094014	C₂²	1	4	yes	complemented
31	#13094014	C₂²	1	4	yes	complemented
32	#13094011	C₂²	1	2	yes	complemented
33	#13094010	C₂²	1	4	yes	—
34	#13094007	C₂²	1	4	yes	—
35	#13094006	C₂²	1	4	yes	—
36	#13094005	C₂²	1	4	yes	—
37	#13094005	C₂²	1	2	yes	—
38	#13094004	C₂²	1	2	yes	—
39	#13094004	C₂²	1	2	yes	—
40	#13094004	C₂²	1	2	yes	—
41	#13094004	C₂²	1	2	yes	—
42	#13094003	C₂²	1	4	yes	—
43	#13094003	C₂²	1	4	yes	complemented
44	#13094003	C₂²	1	2	yes	complemented
45	#13094003	C₂²	1	2	yes	complemented
46	#13094002	C₂²	1	4	yes	—
47	#13094000	C₂²	1	1	yes	characteristic
48	#13094000	C₂²	1	1	yes	characteristic
49	#13093995	C₂²	1	1	yes	characteristic
50	#13093995	C₂²	1	1	yes	characteristic
51	#13093992	C₂²	1	2	yes	—
52	C₄×Dic₉₄	C₂²	1	2	yes	complemented
53	C₄×Dic₉₄	C₂²	1	2	yes	complemented
54	C₄×Dic₉₄	C₂²	1	4	yes	complemented
55	#13093989	C₂²	1	2	yes	complemented
56	#13093989	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
58	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
60	#13093983	C₂²	1	1	yes	characteristic
61	#13093983	C₂²	1	1	yes	characteristic
62	#13093983	C₂²	1	4	yes	complemented
63	#13093982	C₂²	1	1	yes	characteristic
64	#13093982	C₂²	1	1	yes	characteristic
65	#13093981	C₂²	1	2	yes	—
66	#13093981	C₂²	1	4	yes	—
67	#13093980	C₂²	1	4	yes	—
68	#13093980	C₂²	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
70	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
72	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
74	C₄²×D₄₇	C₂²	1	2	yes	—
75	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
76	C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
77	C₄×D₄×C₄₇	C₂²	1	4	yes	—
78	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
79	#117×C₄₇	C₂²	1	1	yes	characteristic
80	#117×C₄₇	C₂²	1	2	yes	complemented
81	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
83	C₂³×D₄₇	C₂³	1	1	yes	characteristic
84	#41×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₇	C₂³	1	2	yes	—
87	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
94	C₂²×Dic₄₇	C₂³	1	2	yes	—
95	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₄₇	—	2	4	no	—
97	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₂³	1	2	yes	—
99	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₂³	1	2	yes	—
103	C₂×Dic₉₄	—	2	4	no	—
104	C₂×Dic₉₄	C₂³	1	2	yes	—
105	C₂×Dic₉₄	C₂³	1	2	yes	—
106	C₂×Dic₉₄	C₂³	1	4	yes	—
107	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
109	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
111	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₄²×C₄₇	C₂³	1	2	yes	—
115	C₄²×C₄₇	C₂³	1	4	yes	—
116	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
117	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
118	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
119	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
128	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₄₇	C₂³	1	4	yes	—
131	C₄⋊Dic₄₇	C₂³	1	4	yes	—
132	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₄₇	C₂³	1	4	yes	—
135	Dic₄₇⋊C₄	C₂³	1	2	yes	—
136	Dic₄₇⋊C₄	C₂³	1	2	yes	—
137	Dic₄₇⋊C₄	C₂³	1	4	yes	—
138	Dic₄₇⋊C₄	C₂³	1	4	yes	—
139	Dic₄₇⋊C₄	C₂³	1	4	yes	—
140	Dic₄₇⋊C₄	C₂³	1	4	yes	—
141	Dic₄₇⋊C₄	C₂³	1	2	yes	—
142	Dic₄₇⋊C₄	C₂³	1	2	yes	—
143	Dic₄₇⋊C₄	C₂³	1	4	yes	—
144	Dic₄₇⋊C₄	C₂³	1	4	yes	—
145	C₄×Dic₄₇	C₂³	1	2	yes	—
146	C₄×Dic₄₇	C₂³	1	2	yes	—
147	C₄×Dic₄₇	C₂³	1	2	yes	—
148	C₄×Dic₄₇	C₂³	1	4	yes	—
149	C₄×Dic₄₇	C₂³	1	4	yes	—
150	C₄×Dic₄₇	C₂³	1	2	yes	—
151	C₂³×C₄₇	C₂⁴	1	2	yes	—
152	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	2	no	—
154	C₂²×D₄₇	—	2	2	no	—
155	C₂²×D₄₇	—	4	1	no	—
156	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
157	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
158	Q₈×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	2	4	no	—
160	D₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	#41	1	4	yes	—
165	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
166	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
167	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
169	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₄₇	—	2	4	no	—
172	C₂²⋊D₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₄₇	C₂⁴	1	2	yes	—
177	C₂×Dic₄₇	C₂⁴	1	2	yes	—
178	C₂×Dic₄₇	C₂⁴	1	2	yes	—
179	C₂×Dic₄₇	C₂⁴	1	2	yes	—
180	C₂×Dic₄₇	C₂⁴	1	4	yes	—
181	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
182	C₄×D₄₇	—	2	4	no	—
183	C₄×D₄₇	—	2	2	no	—
184	C₄×D₄₇	—	2	2	no	—
185	C₄×D₄₇	—	2	2	no	—
186	C₄×D₄₇	—	2	2	no	—
187	C₄×D₄₇	—	4	2	no	—
188	Dic₉₄	—	2	4	no	—
189	Dic₉₄	—	2	4	no	—
190	Dic₉₄	—	4	4	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	C₂×#41	1	2	yes	—
197	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
198	C₂×D₄₇	—	2	1	no	—
199	C₂×D₄₇	—	2	1	no	—
200	C₂×D₄₇	—	2	1	no	—
201	C₂×D₄₇	—	2	1	no	—
202	C₂×D₄₇	—	2	1	no	—
203	C₂×D₄₇	—	4	4	no	—
204	C₂×D₄₇	2₋¹⁺⁴	1	2	yes	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	C₂×#41	1	2	yes	—
210	C₄×C₄₇	C₂×#41	1	2	yes	—
211	Dic₄₇	—	2	4	no	—
212	Dic₄₇	—	2	1	no	—
213	Dic₄₇	—	2	1	no	—
214	Dic₄₇	—	2	2	no	—
215	Dic₄₇	—	2	2	no	—
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	2	2	no	—
218	#3495	—	47	1	no	maximal, Sylow
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	—	4	2	no	—
221	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
222	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×C₄₇	#585	1	1	yes	characteristic
224	D₄₇	—	2	2	no	—
225	D₄₇	—	4	1	no	—
226	#556	—	47	2	no	—
227	#554	—	47	2	no	—
228	#552	—	47	4	no	—
229	#552	—	47	2	no	—
230	#552	—	47	2	no	—
231	#551	—	47	4	no	—
232	#544	—	47	1	no	—
233	#542	—	47	2	no	—
234	#541	—	47	2	no	—
235	#536	—	47	1	no	—
236	#533	—	47	2	no	—
237	#529	—	47	2	no	—
238	#525	—	47	1	no	—
239	C₂×C₂²⋊Q₈	—	47	1	no	—
240	#520	D₄₇	1	1	yes	characteristic, complemented
241	#519	—	47	1	no	—
242	C₂×#117	—	47	1	no	—
243	C₄₇	#3495	1	1	yes	characteristic, complemented, Sylow
244	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
245	C₂²×Q₈	—	47	1	no	—
246	C₂³×C₄	—	47	1	no	—
247	C₄⋊Q₈	—	47	2	no	—
248	C₄⋊Q₈	—	47	2	no	—
249	C₄⋊Q₈	—	47	2	no	—
250	#126	—	47	4	no	—
251	#126	—	47	4	no	—
252	#126	—	47	4	no	—
253	#126	—	47	4	no	—
254	#125	—	47	2	no	—
255	#125	—	47	4	no	—
256	#125	—	47	4	no	—
257	#125	—	47	2	no	—
258	#125	—	47	4	no	—
259	#124	—	47	2	no	—
260	#124	—	47	4	no	—
261	#123	—	47	2	no	—
262	#123	—	47	4	no	—
263	#123	—	47	4	no	—
264	#123	—	47	4	no	—
265	C₂²⋊Q₈	—	47	1	no	—
266	C₂²⋊Q₈	—	47	1	no	—
267	C₂²⋊Q₈	—	47	2	no	—
268	C₂²⋊Q₈	—	47	2	no	—
269	C₂²⋊Q₈	—	47	4	no	—
270	C₂²⋊Q₈	—	47	4	no	—
271	C₂²⋊Q₈	—	47	2	no	—
272	C₂²⋊Q₈	—	47	2	no	—
273	C₂²⋊Q₈	—	47	2	no	—
274	C₂²⋊Q₈	—	47	2	no	—
275	C₂²⋊Q₈	—	47	4	no	—
276	#121	—	47	1	no	—
277	#121	—	47	1	no	—
278	#120	—	47	2	no	—
279	C₄×Q₈	—	47	2	no	—
280	C₄×Q₈	—	47	2	no	—
281	C₄×Q₈	—	47	2	no	—
282	C₄×Q₈	—	47	2	no	—
283	C₄×Q₈	—	47	4	no	—
284	C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
285	C₄×D₄	—	47	2	no	—
286	C₄×D₄	—	47	2	no	—
287	C₄×D₄	—	47	4	no	—
288	C₄×D₄	C₂×D₄₇	1	4	yes	—
289	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
290	#117	—	47	1	no	—
291	#117	—	47	1	no	—
292	#117	—	47	4	no	—
293	#117	—	47	1	no	—
294	#117	—	47	1	no	—
295	#117	—	47	2	no	—
296	#117	—	47	4	no	—
297	#117	—	47	2	no	—
298	#117	—	47	4	no	—
299	#117	C₂×D₄₇	1	1	yes	characteristic
300	#117	C₂×D₄₇	1	2	yes	complemented
301	C₂×C₄⋊C₄	—	47	2	no	—
302	C₂×C₄⋊C₄	—	47	1	no	—
303	C₂×C₄⋊C₄	—	47	1	no	—
304	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
306	C₂×C₂²⋊C₄	—	47	2	no	—
307	C₂×C₂²⋊C₄	—	47	2	no	—
308	C₂×C₄²	—	47	2	no	—
309	C₂⁴	—	47	1	no	—
310	#41	—	2	4	no	—
311	C₂×Q₈	—	47	2	no	—
312	C₂×Q₈	—	47	2	no	—
313	C₂×Q₈	—	47	4	no	—
314	C₂×Q₈	—	94	4	no	—
315	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
316	C₂×D₄	—	47	2	no	—
317	C₂×D₄	—	47	2	no	—
318	C₂×D₄	C₂²×D₄₇	1	2	yes	—
319	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	1	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	47	1	no	—
325	C₂²×C₄	—	47	1	no	—
326	C₂²×C₄	—	47	1	no	—
327	C₂²×C₄	—	47	2	no	—
328	C₂²×C₄	—	94	4	no	—
329	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
330	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
331	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
332	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₄⋊C₄	—	47	2	no	—
334	C₄⋊C₄	—	47	2	no	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	47	4	no	—
337	C₄⋊C₄	—	47	4	no	—
338	C₄⋊C₄	—	47	4	no	—
339	C₄⋊C₄	—	47	2	no	—
340	C₄⋊C₄	—	47	2	no	—
341	C₄⋊C₄	—	47	4	no	—
342	C₄⋊C₄	—	47	4	no	—
343	C₄⋊C₄	—	47	1	no	—
344	C₄⋊C₄	—	47	1	no	—
345	C₄⋊C₄	—	47	4	no	—
346	C₄⋊C₄	—	47	4	no	—
347	C₄⋊C₄	—	47	1	no	—
348	C₄⋊C₄	—	47	1	no	—
349	C₄⋊C₄	—	47	4	no	—
350	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
353	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
354	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
355	C₂²⋊C₄	—	47	2	no	—
356	C₂²⋊C₄	—	47	2	no	—
357	C₂²⋊C₄	—	47	2	no	—
358	C₂²⋊C₄	—	47	4	no	—
359	C₂²⋊C₄	—	47	2	no	—
360	C₂²⋊C₄	—	47	4	no	—
361	C₂²⋊C₄	—	47	2	no	—
362	C₂²⋊C₄	—	47	2	no	—
363	C₂²⋊C₄	—	47	4	no	—
364	C₂²⋊C₄	—	47	4	no	—
365	C₂²⋊C₄	—	47	2	no	—
366	C₂²⋊C₄	—	47	2	no	—
367	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
368	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
369	C₄²	—	47	2	no	—
370	C₄²	—	47	2	no	—
371	C₄²	—	47	2	no	—
372	C₄²	—	47	4	no	—
373	C₄²	—	47	4	no	—
374	C₄²	—	47	2	no	—
375	C₄²	C₂²×D₄₇	1	2	yes	—
376	C₄²	C₂²×D₄₇	1	4	yes	—
377	C₂³	—	47	1	no	—
378	C₂³	—	47	1	no	—
379	C₂³	—	94	2	no	—
380	C₂³	—	94	2	no	—
381	C₂³	—	188	1	no	—
382	C₂³	C₂³×D₄₇	1	2	yes	—
383	C₂³	C₂³×D₄₇	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	94	4	no	—
386	Q₈	—	94	4	no	—
387	Q₈	—	188	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	2	no	—
390	D₄	—	94	4	no	—
391	D₄	—	188	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	47	1	no	—
396	C₂×C₄	—	47	2	no	—
397	C₂×C₄	—	47	2	no	—
398	C₂×C₄	—	47	2	no	—
399	C₂×C₄	—	47	4	no	—
400	C₂×C₄	—	47	2	no	—
401	C₂×C₄	—	47	1	no	—
402	C₂×C₄	—	94	4	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	4	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	#10625350	1	4	yes	—
411	C₂×C₄	C₂³×D₄₇	1	2	yes	—
412	C₂×C₄	C₂³×D₄₇	1	2	yes	—
413	C₂×C₄	C₂³×D₄₇	1	2	yes	—
414	C₂×C₄	C₂³×D₄₇	1	4	yes	—
415	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	47	2	no	—
423	C₂²	—	94	1	no	—
424	C₂²	—	94	1	no	—
425	C₂²	—	94	1	no	—
426	C₂²	—	94	1	no	—
427	C₂²	—	94	1	no	—
428	C₂²	—	188	4	no	—
429	C₂²	C₂×#10625350	1	2	yes	—
430	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	94	1	no	—
436	C₄	—	94	1	no	—
437	C₄	—	94	4	no	—
438	C₄	—	94	2	no	—
439	C₄	—	94	2	no	—
440	C₄	—	94	2	no	—
441	C₄	—	94	2	no	—
442	C₄	C₂×#10625350	1	2	yes	—
443	C₄	C₂×#10625350	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	4	2	no	—
446	C₂	—	94	2	no	—
447	C₂	—	188	1	no	—
448	C₂	C₂²×#10625350	1	1	yes	characteristic
449	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
450	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#520	C₂
hypercenter	#520	D₄₇
hypocenter	C₄₇	#3495
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #15689841	C₂	semidirect
2. #15689828	C₂	semidirect
3. #15689813	C₂	semidirect
4. #15689812	C₂	semidirect
5. #15689808	C₂	semidirect
6. #15689802	C₂	semidirect
7. #15689754	C₂	semidirect
8. #15689738	C₂	semidirect
9. #15689731	C₂	semidirect
10. #15689694	C₂	semidirect
11. #15689677	C₂	semidirect
12. #15689655	C₂	semidirect
14. C₂×#13094004	C₂	semidirect
15. #15689600	C₂	semidirect
16. #117×D₄₇	C₂	semidirect
17. C₄₇×#520	C₂	semidirect
20. #13094023	C₂²	semidirect
21. #13094023	C₂²	semidirect
22. #13094022	C₂²	semidirect
25. #13094017	C₂²	semidirect
26. #13094017	C₂²	semidirect
27. #13094016	C₂²	semidirect
28. #13094015	C₂²	semidirect
29. #13094015	C₂²	semidirect
30. #13094014	C₂²	semidirect
31. #13094014	C₂²	semidirect
32. #13094011	C₂²	semidirect
43. #13094003	C₂²	semidirect
44. #13094003	C₂²	semidirect
45. #13094003	C₂²	semidirect
52. C₄×Dic₉₄	C₂²	semidirect
53. C₄×Dic₉₄	C₂²	semidirect
54. C₄×Dic₉₄	C₂²	semidirect
55. #13093989	C₂²	semidirect
56. #13093989	C₂²	semidirect
62. #13093983	C₂²	semidirect
76. C₄×Q₈×C₄₇	C₂²	semidirect
78. C₄×D₄×C₄₇	C₂²	semidirect
80. #117×C₄₇	C₂²	semidirect
82. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
240. #520	D₄₇	semidirect
243. C₄₇	#3495	semidirect
284. C₄×Q₈	C₂×D₄₇	semidirect
289. C₄×D₄	C₂×D₄₇	semidirect
300. #117	C₂×D₄₇	semidirect
305. C₂×C₄⋊C₄	C₂×D₄₇	semidirect