Subgroups — #20257101

Order 6016.

1040 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689846	C₂	1	2	yes	maximal, complemented
2	#15689841	C₂	1	2	yes	maximal, complemented
3	#15689838	C₂	1	2	yes	maximal, complemented
4	#15689836	C₂	1	2	yes	maximal, complemented
5	#15689823	C₂	1	2	yes	maximal, complemented
6	#15689821	C₂	1	2	yes	maximal, complemented
7	#15689814	C₂	1	2	yes	maximal, complemented
8	#15689808	C₂	1	2	yes	maximal, complemented
9	#15689751	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689706	C₂	1	4	yes	maximal, complemented
11	#15689701	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689653	C₂	1	4	yes	maximal, complemented
13	#15689635	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689630	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689604	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13093982	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625350	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
20	#13094024	C₂²	1	2	yes	complemented
21	#13094023	C₂²	1	2	yes	complemented
22	#13094019	C₂²	1	4	yes	—
23	#13094019	C₂²	1	4	yes	complemented
24	#13094018	C₂²	1	4	yes	—
25	#13094017	C₂²	1	4	yes	complemented
26	#13094016	C₂²	1	2	yes	complemented
27	#13094015	C₂²	1	2	yes	complemented
28	#13094014	C₂²	1	4	yes	complemented
29	#13094012	C₂²	1	4	yes	—
30	#13094010	C₂²	1	4	yes	—
31	#13094010	C₂²	1	4	yes	complemented
32	#13094009	C₂²	1	4	yes	—
33	#13094008	C₂²	1	2	yes	—
34	#13094007	C₂²	1	4	yes	—
35	#13094005	C₂²	1	2	yes	—
36	#13094004	C₂²	1	1	yes	characteristic
37	#13094004	C₂²	1	1	yes	characteristic
38	#13094003	C₂²	1	2	yes	complemented
39	#13094001	C₂²	1	4	yes	—
40	#13094000	C₂²	1	1	yes	characteristic
41	#13094000	C₂²	1	1	yes	characteristic
42	#13094000	C₂²	1	2	yes	complemented
43	#13093999	C₂²	1	1	yes	characteristic
44	#13093999	C₂²	1	1	yes	characteristic
45	#13093998	C₂²	1	4	yes	—
46	#13093998	C₂²	1	2	yes	complemented
47	#13093997	C₂²	1	4	yes	—
48	#13093996	C₂²	1	4	yes	—
49	#13093995	C₂²	1	1	yes	characteristic
50	#13093995	C₂²	1	1	yes	characteristic
51	#13093995	C₂²	1	2	yes	complemented
52	#13093994	C₂²	1	2	yes	—
53	#13093992	C₂²	1	2	yes	—
54	C₄×Dic₉₄	C₂²	1	4	yes	complemented
55	#13093989	C₂²	1	2	yes	complemented
56	C₄×D₁₈₈	C₂²	1	2	yes	—
57	C₄×D₁₈₈	C₂²	1	2	yes	—
58	#13093986	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
63	#13093983	C₂²	1	1	yes	characteristic
64	#13093983	C₂²	1	4	yes	complemented
65	#13093982	C₂²	1	2	yes	—
66	#13093982	C₂²	1	2	yes	—
67	#13093982	C₂²	1	2	yes	—
68	#13093982	C₂²	1	2	yes	—
69	#13093982	C₂²	1	2	yes	complemented
70	#13093981	C₂²	1	4	yes	complemented
71	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
74	C₂×C₄×Dic₄₇	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	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
96	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₂²×Dic₄₇	C₂³	1	2	yes	—
98	#10625350	—	2	4	no	—
99	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
100	C₂×D₁₈₈	C₂³	1	2	yes	—
101	C₂×D₁₈₈	C₂³	1	2	yes	—
102	C₂×C₄×D₄₇	—	2	4	no	—
103	C₂×C₄×D₄₇	C₂³	1	2	yes	—
104	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₄₇	C₂³	1	4	yes	—
109	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
110	C₂×Dic₉₄	C₂³	1	4	yes	—
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
118	C₄²×C₄₇	C₂³	1	2	yes	—
119	C₄²×C₄₇	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₄₇	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	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	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	2	yes	—
136	C₄⋊Dic₄₇	C₂³	1	2	yes	—
137	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₄₇	C₂³	1	2	yes	—
139	C₄⋊Dic₄₇	C₂³	1	4	yes	—
140	C₄⋊Dic₄₇	C₂³	1	2	yes	—
141	Dic₄₇⋊C₄	C₂³	1	4	yes	—
142	Dic₄₇⋊C₄	C₂³	1	2	yes	—
143	Dic₄₇⋊C₄	C₂³	1	4	yes	—
144	Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	Dic₄₇⋊C₄	C₂³	1	4	yes	—
146	Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	C₄×Dic₄₇	C₂³	1	4	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	—	4	1	no	—
155	C₂²×D₄₇	—	4	1	no	—
156	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
157	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
158	C₂²×D₄₇	C₂⁴	1	2	yes	—
159	Q₈×C₄₇	—	2	2	no	—
160	D₄×C₄₇	—	2	4	no	—
161	D₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	#41	1	4	yes	—
166	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
167	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₄₇	—	2	4	no	—
173	C₂²⋊D₄₇	—	4	2	no	—
174	C₂²⋊D₄₇	—	4	4	no	—
175	C₂²⋊D₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₄₇	C₂⁴	1	2	yes	—
181	C₂×Dic₄₇	C₂⁴	1	2	yes	—
182	C₂×Dic₄₇	C₂⁴	1	4	yes	—
183	C₂×Dic₄₇	C₂⁴	1	2	yes	—
184	D₁₈₈	—	2	2	no	—
185	D₁₈₈	—	4	2	no	—
186	D₁₈₈	—	4	2	no	—
187	C₄×D₄₇	—	2	2	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	4	no	—
192	C₄×D₄₇	—	4	4	no	—
193	Dic₉₄	—	2	2	no	—
194	Dic₉₄	—	4	4	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	C₂×#41	1	2	yes	—
201	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
202	C₂×D₄₇	—	2	1	no	—
203	C₂×D₄₇	—	2	1	no	—
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	2	2	no	—
206	C₂×D₄₇	—	2	1	no	—
207	C₂×D₄₇	—	2	1	no	—
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	—	2	1	no	—
210	C₂×D₄₇	—	2	1	no	—
211	C₂×D₄₇	—	4	4	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	C₂×#41	1	2	yes	—
217	C₄×C₄₇	C₂×#41	1	2	yes	—
218	Dic₄₇	—	2	2	no	—
219	Dic₄₇	—	2	1	no	—
220	Dic₄₇	—	2	1	no	—
221	Dic₄₇	—	2	2	no	—
222	Dic₄₇	—	2	4	no	—
223	Dic₄₇	—	2	2	no	—
224	#3493	—	47	1	no	maximal, Sylow
225	C₂×C₄₇	—	2	2	no	—
226	C₂×C₄₇	—	4	2	no	—
227	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
228	C₂×C₄₇	#585	1	1	yes	characteristic
229	C₂×C₄₇	#585	1	1	yes	characteristic
230	D₄₇	—	4	2	no	—
231	D₄₇	—	4	1	no	—
232	D₄₇	—	4	1	no	—
233	#556	—	47	2	no	—
234	#556	—	47	2	no	—
235	#555	—	47	2	no	—
236	#555	—	47	2	no	—
237	#553	—	47	2	no	—
238	#553	—	47	2	no	—
239	#552	—	47	2	no	—
240	#552	—	47	2	no	—
241	#544	—	47	1	no	—
242	#538	—	47	4	no	—
243	#537	—	47	1	no	—
244	#529	—	47	4	no	—
245	#525	—	47	1	no	—
246	#525	—	47	1	no	—
247	#520	—	47	1	no	—
248	#520	D₄₇	1	1	yes	characteristic, complemented
249	C₂×#117	—	47	1	no	—
250	C₄₇	#3493	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	47	1	no	—
252	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
253	C₂³×C₄	—	47	1	no	—
254	C₄⋊Q₈	—	47	2	no	—
255	C₄⋊Q₈	—	47	2	no	—
256	#126	—	47	4	no	—
257	#126	—	47	4	no	—
258	#126	—	47	4	no	—
259	#126	—	47	4	no	—
260	#125	—	47	4	no	—
261	#125	—	47	2	no	—
262	#125	—	47	2	no	—
263	#124	—	47	4	no	—
264	#124	—	47	4	no	—
265	#124	—	47	4	no	—
266	#123	—	47	2	no	—
267	#123	—	47	4	no	—
268	#123	—	47	4	no	—
269	#123	—	47	2	no	—
270	C₂²⋊Q₈	—	47	1	no	—
271	C₂²⋊Q₈	—	47	1	no	—
272	C₂²⋊Q₈	—	47	2	no	—
273	C₂²⋊Q₈	—	47	2	no	—
274	C₂²⋊Q₈	—	47	1	no	—
275	C₂²⋊Q₈	—	47	1	no	—
276	C₂²⋊Q₈	—	47	4	no	—
277	#121	—	47	1	no	—
278	#121	—	47	1	no	—
279	#121	—	47	4	no	—
280	#121	—	47	2	no	—
281	#121	—	47	2	no	—
282	#121	—	47	4	no	—
283	#121	—	47	1	no	—
284	#121	—	47	1	no	—
285	#121	—	47	4	no	—
286	#120	—	47	2	no	—
287	#120	—	47	2	no	—
288	C₄×Q₈	—	47	2	no	—
289	C₄×Q₈	—	47	4	no	—
290	C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
291	C₄×D₄	—	47	4	no	—
292	C₄×D₄	—	47	2	no	—
293	C₄×D₄	—	47	2	no	—
294	C₄×D₄	—	47	4	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	47	2	no	—
297	C₄×D₄	—	47	2	no	—
298	C₄×D₄	C₂×D₄₇	1	4	yes	—
299	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
300	#117	—	47	1	no	—
301	#117	—	47	4	no	—
302	#117	—	47	2	no	—
303	#117	—	47	2	no	—
304	#117	—	47	2	no	—
305	#117	—	47	2	no	—
306	#117	—	47	2	no	—
307	#117	—	47	4	no	—
308	#117	C₂×D₄₇	1	1	yes	characteristic
309	#117	C₂×D₄₇	1	2	yes	complemented
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₄⋊C₄	—	47	2	no	—
312	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
314	C₂×C₂²⋊C₄	—	47	2	no	—
315	C₂×C₄²	—	47	2	no	—
316	C₂⁴	—	47	1	no	—
317	#41	—	2	4	no	—
318	#41	—	94	4	no	—
319	C₂×Q₈	—	47	1	no	—
320	C₂×Q₈	—	47	4	no	—
321	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
322	C₂×D₄	—	47	2	no	—
323	C₂×D₄	—	47	2	no	—
324	C₂×D₄	—	47	2	no	—
325	C₂×D₄	—	47	4	no	—
326	C₂×D₄	—	47	1	no	—
327	C₂×D₄	—	47	2	no	—
328	C₂×D₄	—	47	2	no	—
329	C₂×D₄	C₂²×D₄₇	1	2	yes	—
330	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	—	47	1	no	—
332	C₂²×C₄	—	47	2	no	—
333	C₂²×C₄	—	47	2	no	—
334	C₂²×C₄	—	47	1	no	—
335	C₂²×C₄	—	47	1	no	—
336	C₂²×C₄	—	47	1	no	—
337	C₂²×C₄	—	47	1	no	—
338	C₂²×C₄	—	47	4	no	—
339	C₂²×C₄	—	94	4	no	—
340	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
341	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
342	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
343	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
344	C₄⋊C₄	—	47	4	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	47	4	no	—
347	C₄⋊C₄	—	47	2	no	—
348	C₄⋊C₄	—	47	4	no	—
349	C₄⋊C₄	—	47	4	no	—
350	C₄⋊C₄	—	47	1	no	—
351	C₄⋊C₄	—	47	2	no	—
352	C₄⋊C₄	—	47	2	no	—
353	C₄⋊C₄	—	47	1	no	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	47	4	no	—
356	C₄⋊C₄	—	47	2	no	—
357	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
358	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
359	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
361	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
362	C₂²⋊C₄	—	47	2	no	—
363	C₂²⋊C₄	—	47	2	no	—
364	C₂²⋊C₄	—	47	4	no	—
365	C₂²⋊C₄	—	47	2	no	—
366	C₂²⋊C₄	—	47	4	no	—
367	C₂²⋊C₄	—	47	4	no	—
368	C₂²⋊C₄	—	47	2	no	—
369	C₂²⋊C₄	—	47	4	no	—
370	C₂²⋊C₄	—	47	4	no	—
371	C₂²⋊C₄	—	47	2	no	—
372	C₂²⋊C₄	—	47	2	no	—
373	C₂²⋊C₄	—	47	2	no	—
374	C₂²⋊C₄	—	47	2	no	—
375	C₂²⋊C₄	—	47	2	no	—
376	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
378	C₄²	—	47	4	no	—
379	C₄²	—	47	4	no	—
380	C₄²	—	47	4	no	—
381	C₄²	—	47	2	no	—
382	C₄²	C₂²×D₄₇	1	4	yes	—
383	C₄²	C₂²×D₄₇	1	2	yes	—
384	C₂³	—	47	1	no	—
385	C₂³	—	47	1	no	—
386	C₂³	—	47	2	no	—
387	C₂³	—	94	2	no	—
388	C₂³	—	188	1	no	—
389	C₂³	—	188	1	no	—
390	C₂³	C₂³×D₄₇	1	2	yes	—
391	C₂³	C₂³×D₄₇	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	94	2	no	—
394	Q₈	—	188	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	94	4	no	—
398	D₄	—	94	2	no	—
399	D₄	—	188	2	no	—
400	D₄	—	188	2	no	—
401	D₄	—	188	2	no	—
402	D₄	—	188	4	no	—
403	D₄	—	188	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	47	1	no	—
408	C₂×C₄	—	47	1	no	—
409	C₂×C₄	—	47	2	no	—
410	C₂×C₄	—	47	2	no	—
411	C₂×C₄	—	47	4	no	—
412	C₂×C₄	—	47	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	4	no	—
419	C₂×C₄	—	188	4	no	—
420	C₂×C₄	—	188	2	no	—
421	C₂×C₄	#10625350	1	4	yes	—
422	C₂×C₄	C₂³×D₄₇	1	4	yes	—
423	C₂×C₄	C₂³×D₄₇	1	2	yes	—
424	C₂×C₄	C₂³×D₄₇	1	2	yes	—
425	C₂×C₄	C₂³×D₄₇	1	2	yes	—
426	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	94	1	no	—
434	C₂²	—	94	1	no	—
435	C₂²	—	94	2	no	—
436	C₂²	—	94	2	no	—
437	C₂²	—	94	1	no	—
438	C₂²	—	94	1	no	—
439	C₂²	—	94	2	no	—
440	C₂²	—	94	1	no	—
441	C₂²	—	94	1	no	—
442	C₂²	—	188	4	no	—
443	C₂²	C₂×#10625350	1	2	yes	—
444	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	94	1	no	—
450	C₄	—	94	1	no	—
451	C₄	—	94	2	no	—
452	C₄	—	94	2	no	—
453	C₄	—	94	4	no	—
454	C₄	—	94	2	no	—
455	C₄	C₂×#10625350	1	2	yes	—
456	C₄	C₂×#10625350	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	188	1	no	—
460	C₂	—	188	1	no	—
461	C₂	—	188	2	no	—
462	C₂	C₂²×#10625350	1	1	yes	characteristic
463	C₂	#15689958	1	1	yes	characteristic
464	C₂	#15689960	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	#3493
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. #15689846	C₂	semidirect
2. #15689841	C₂	semidirect
3. #15689838	C₂	semidirect
4. #15689836	C₂	semidirect
5. #15689823	C₂	semidirect
6. #15689821	C₂	semidirect
7. #15689814	C₂	semidirect
8. #15689808	C₂	semidirect
9. #15689751	C₂	semidirect
10. #15689706	C₂	semidirect
11. #15689701	C₂	semidirect
12. #15689653	C₂	semidirect
13. #15689635	C₂	semidirect
14. #15689630	C₂	semidirect
15. #15689604	C₂	semidirect
16. C₂×#13093982	C₂	semidirect
17. C₄₇×#520	C₂	semidirect
20. #13094024	C₂²	semidirect
21. #13094023	C₂²	semidirect
23. #13094019	C₂²	semidirect
25. #13094017	C₂²	semidirect
26. #13094016	C₂²	semidirect
27. #13094015	C₂²	semidirect
28. #13094014	C₂²	semidirect
31. #13094010	C₂²	semidirect
38. #13094003	C₂²	semidirect
42. #13094000	C₂²	semidirect
46. #13093998	C₂²	semidirect
51. #13093995	C₂²	semidirect
54. C₄×Dic₉₄	C₂²	semidirect
55. #13093989	C₂²	semidirect
58. #13093986	C₂²	semidirect
62. C₄×C₂²⋊D₄₇	C₂²	semidirect
64. #13093983	C₂²	semidirect
69. #13093982	C₂²	semidirect
70. #13093981	C₂²	semidirect
72. C₄⋊C₄×D₄₇	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
248. #520	D₄₇	semidirect
250. C₄₇	#3493	semidirect
290. C₄×Q₈	C₂×D₄₇	semidirect
299. C₄×D₄	C₂×D₄₇	semidirect
309. #117	C₂×D₄₇	semidirect
313. C₂×C₄⋊C₄	C₂×D₄₇	semidirect