Subgroups — #20256801

Order 6016.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689751	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689742	C₂	1	2	yes	maximal, complemented
3	#15689740	C₂	1	2	yes	maximal, complemented
4	#15689727	C₂	1	2	yes	maximal, complemented
5	#15689726	C₂	1	2	yes	maximal, complemented
6	#15689708	C₂	1	4	yes	maximal, complemented
7	#15689701	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689690	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689671	C₂	1	2	yes	maximal, complemented
10	#15689668	C₂	1	2	yes	maximal, complemented
11	#15689654	C₂	1	2	yes	maximal, complemented
12	#15689652	C₂	1	2	yes	maximal, complemented
13	#15689629	C₂	1	4	yes	maximal, complemented
14	#41×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689591	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625350	C₂²	1	1	yes	characteristic
19	C₂×#10625352	C₂²	1	4	yes	complemented
20	C₂³×Dic₄₇	C₂²	1	2	yes	—
21	#13094024	C₂²	1	2	yes	complemented
22	#13094023	C₂²	1	2	yes	complemented
23	#13094020	C₂²	1	2	yes	—
24	#13094017	C₂²	1	4	yes	complemented
25	#13094017	C₂²	1	4	yes	complemented
26	#13094016	C₂²	1	2	yes	complemented
27	#13094015	C₂²	1	2	yes	complemented
28	#13094011	C₂²	1	2	yes	—
29	#13094011	C₂²	1	4	yes	complemented
30	#13094010	C₂²	1	4	yes	complemented
31	#13094008	C₂²	1	4	yes	complemented
32	#13094006	C₂²	1	4	yes	complemented
33	#13094005	C₂²	1	4	yes	complemented
34	#13094005	C₂²	1	4	yes	complemented
35	#13094003	C₂²	1	2	yes	complemented
36	#13094001	C₂²	1	4	yes	—
37	#13094001	C₂²	1	4	yes	complemented
38	#13094000	C₂²	1	2	yes	complemented
39	#13093998	C₂²	1	2	yes	complemented
40	#13093996	C₂²	1	4	yes	—
41	#13093996	C₂²	1	4	yes	complemented
42	#13093996	C₂²	1	4	yes	complemented
43	#13093995	C₂²	1	2	yes	—
44	#13093995	C₂²	1	2	yes	—
45	#13093995	C₂²	1	2	yes	complemented
46	#13093995	C₂²	1	4	yes	complemented
47	#13093993	C₂²	1	4	yes	—
48	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
50	#13093989	C₂²	1	1	yes	characteristic, complemented
51	#13093989	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₄₇	C₂²	1	2	yes	—
53	D₄×Dic₄₇	C₂²	1	2	yes	—
54	D₄×Dic₄₇	C₂²	1	2	yes	—
55	D₄×Dic₄₇	C₂²	1	2	yes	—
56	D₄×Dic₄₇	C₂²	1	2	yes	—
57	D₄×Dic₄₇	C₂²	1	2	yes	—
58	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
60	D₄×Dic₄₇	C₂²	1	4	yes	complemented
61	#13093986	C₂²	1	1	yes	characteristic, complemented
62	#13093986	C₂²	1	1	yes	characteristic, complemented
63	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
64	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
65	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
66	#13093983	C₂²	1	1	yes	characteristic
67	#13093983	C₂²	1	2	yes	complemented
68	#13093981	C₂²	1	2	yes	complemented
69	#13093980	C₂²	1	4	yes	complemented
70	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
71	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂²	1	2	yes	complemented
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	—
78	#124×C₄₇	C₂²	1	2	yes	—
79	#121×C₄₇	C₂²	1	2	yes	—
80	#121×C₄₇	C₂²	1	2	yes	—
81	#120×C₄₇	C₂²	1	4	yes	—
82	#117×C₄₇	C₂²	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂³	1	2	yes	—
84	#41×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	C₂³	1	2	yes	—
88	C₂×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×D₄×C₄₇	C₂³	1	2	yes	—
90	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×D₄×C₄₇	C₂³	1	4	yes	—
92	C₂×D₄×C₄₇	C₂³	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₂²×Dic₄₇	—	4	4	no	—
100	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂³	1	2	yes	—
102	C₂²×Dic₄₇	C₂³	1	4	yes	—
103	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂³	1	2	yes	—
105	C₂²×Dic₄₇	C₂³	1	2	yes	—
106	C₂²×Dic₄₇	C₂³	1	4	yes	—
107	#10625352	—	4	8	no	—
108	#10625350	—	2	4	no	—
109	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₄₇	C₂³	1	2	yes	—
111	C₂×C₄×D₄₇	C₂³	1	2	yes	—
112	C₂×C₄×D₄₇	C₂³	1	2	yes	—
113	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
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	4	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
124	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
126	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
127	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
128	C₂²⋊Dic₄₇	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	C₄⋊Dic₄₇	C₂³	1	2	yes	—
133	C₄⋊Dic₄₇	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	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	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
145	C₄×Dic₄₇	C₂³	1	2	yes	—
146	C₄×Dic₄₇	C₂³	1	2	yes	—
147	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
148	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
149	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
150	C₄×Dic₄₇	C₂³	1	2	yes	—
151	C₄×Dic₄₇	C₂³	1	2	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	C₂⁴	1	2	yes	—
160	Q₈×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	4	no	—
162	D₄×C₄₇	—	2	4	no	—
163	D₄×C₄₇	—	2	4	no	—
164	D₄×C₄₇	—	2	2	no	—
165	D₄×C₄₇	—	4	4	no	—
166	D₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	#41	1	4	yes	complemented
169	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
171	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
172	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₄₇	—	2	4	no	—
175	C₂²⋊D₄₇	—	4	4	no	—
176	C₂²⋊D₄₇	—	4	4	no	—
177	C₂²⋊D₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	2	4	no	—
179	C₂×Dic₄₇	—	2	8	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	4	no	—
183	C₂×Dic₄₇	—	4	1	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₄₇	C₂⁴	1	2	yes	—
188	C₂×Dic₄₇	C₂⁴	1	2	yes	—
189	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
190	C₂×Dic₄₇	C₂⁴	1	2	yes	—
191	C₂×Dic₄₇	C₂⁴	1	4	yes	—
192	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
193	D₁₈₈	—	2	2	no	—
194	C₄×D₄₇	—	2	4	no	—
195	C₄×D₄₇	—	2	4	no	—
196	C₄×D₄₇	—	4	2	no	—
197	Dic₉₄	—	2	2	no	—
198	Dic₉₄	—	4	4	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	4	no	—
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	4	8	no	—
208	C₂²×C₄₇	C₂×#41	1	2	yes	—
209	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	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	2	no	—
220	Dic₄₇	—	2	4	no	—
221	Dic₄₇	—	2	1	no	—
222	Dic₄₇	—	2	1	no	—
223	Dic₄₇	—	2	1	no	—
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
226	#3460	—	47	1	no	maximal, Sylow
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	4	2	no	—
229	C₂×C₄₇	—	4	4	no	—
230	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
231	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄₇	#585	1	1	yes	characteristic
233	D₄₇	—	4	2	no	—
234	#544	—	47	1	no	—
235	#542	—	47	2	no	—
236	#542	—	47	2	no	—
237	#540	—	47	2	no	—
238	#540	—	47	2	no	—
239	#538	—	47	4	no	—
240	#537	—	47	1	no	—
241	#535	—	47	1	no	—
242	#535	D₄₇	1	1	yes	characteristic, complemented
243	#532	—	47	2	no	—
244	#532	—	47	2	no	—
245	#529	—	47	2	no	—
246	#529	—	47	2	no	—
247	#525	—	47	4	no	—
248	C₄×#41	—	47	1	no	—
249	C₄×#41	—	47	1	no	—
250	C₂×C₄×D₄	—	47	1	no	—
251	C₄₇	#3460	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	47	4	no	—
253	C₂×#41	—	47	1	no	—
254	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
255	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
256	C₂³×C₄	—	47	2	no	—
257	C₄⋊Q₈	—	47	2	no	—
258	C₄⋊Q₈	—	47	2	no	—
259	#127	—	47	2	no	—
260	#127	C₂×D₄₇	1	2	yes	—
261	#126	—	47	4	no	—
262	#126	—	47	4	no	—
263	#125	—	47	2	no	—
264	#125	—	47	2	no	—
265	#124	—	47	2	no	—
266	#124	—	47	4	no	—
267	#124	—	47	4	no	—
268	#124	C₂×D₄₇	1	2	yes	—
269	#123	—	47	4	no	—
270	#123	—	47	4	no	—
271	#123	—	47	4	no	—
272	#123	—	47	4	no	—
273	C₂²⋊Q₈	—	47	2	no	—
274	C₂²⋊Q₈	—	47	2	no	—
275	C₂²⋊Q₈	—	47	4	no	—
276	C₂²⋊Q₈	—	47	4	no	—
277	#121	—	47	4	no	—
278	#121	—	47	4	no	—
279	#121	—	47	2	no	—
280	#121	—	47	2	no	—
281	#121	—	47	2	no	—
282	#121	—	47	4	no	—
283	#121	—	47	4	no	—
284	#121	—	47	2	no	—
285	#121	C₂×D₄₇	1	2	yes	—
286	#121	C₂×D₄₇	1	2	yes	—
287	#120	—	47	4	no	—
288	#120	C₂×D₄₇	1	4	yes	—
289	C₄×Q₈	—	47	1	no	—
290	C₄×Q₈	—	47	1	no	—
291	C₄×Q₈	—	47	1	no	—
292	C₄×Q₈	—	47	1	no	—
293	C₄×D₄	—	47	2	no	—
294	C₄×D₄	—	47	2	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	47	2	no	—
297	C₄×D₄	—	47	2	no	—
298	C₄×D₄	—	47	1	no	—
299	C₄×D₄	—	47	2	no	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	47	4	no	—
302	C₄×D₄	—	47	1	no	—
303	C₄×D₄	—	47	1	no	—
304	C₄×D₄	—	47	2	no	—
305	C₄×D₄	—	47	2	no	—
306	C₄×D₄	—	47	4	no	—
307	#117	—	47	1	no	—
308	#117	—	47	2	no	—
309	#117	—	47	4	no	—
310	#117	—	47	2	no	—
311	#117	C₂×D₄₇	1	1	yes	characteristic
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₂²⋊C₄	—	47	2	no	—
314	C₂×C₄²	—	47	1	no	—
315	C₂×C₄²	—	47	2	no	—
316	C₂×C₄²	—	47	2	no	—
317	C₂⁴	C₂²×D₄₇	1	2	yes	—
318	#41	—	2	4	no	—
319	#41	—	94	4	no	—
320	#41	—	188	8	no	—
321	C₂×Q₈	—	47	1	no	—
322	C₂×Q₈	—	47	4	no	—
323	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	47	2	no	—
326	C₂×D₄	—	47	4	no	—
327	C₂×D₄	—	47	4	no	—
328	C₂×D₄	—	47	4	no	—
329	C₂×D₄	—	47	1	no	—
330	C₂×D₄	C₂²×D₄₇	1	2	yes	—
331	C₂×D₄	C₂²×D₄₇	1	2	yes	—
332	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₂×D₄	C₂²×D₄₇	1	2	yes	—
334	C₂×D₄	C₂²×D₄₇	1	4	yes	—
335	C₂×D₄	C₂²×D₄₇	1	4	yes	—
336	C₂²×C₄	—	47	1	no	—
337	C₂²×C₄	—	47	2	no	—
338	C₂²×C₄	—	47	4	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	2	no	—
342	C₂²×C₄	—	47	4	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	2	no	—
345	C₂²×C₄	—	47	2	no	—
346	C₂²×C₄	—	188	4	no	—
347	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
348	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
349	C₄⋊C₄	—	47	2	no	—
350	C₄⋊C₄	—	47	2	no	—
351	C₄⋊C₄	—	47	4	no	—
352	C₄⋊C₄	—	47	4	no	—
353	C₄⋊C₄	—	47	4	no	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	—	47	1	no	—
357	C₄⋊C₄	—	47	1	no	—
358	C₄⋊C₄	—	47	2	no	—
359	C₄⋊C₄	—	47	2	no	—
360	C₄⋊C₄	—	47	4	no	—
361	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
368	C₂²⋊C₄	—	47	4	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	4	no	—
374	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
377	C₄²	—	47	1	no	—
378	C₄²	—	47	1	no	—
379	C₄²	—	47	2	no	—
380	C₄²	—	47	2	no	—
381	C₄²	—	47	1	no	—
382	C₄²	—	47	1	no	—
383	C₄²	—	47	2	no	—
384	C₄²	—	47	2	no	—
385	C₄²	—	47	2	no	—
386	C₄²	C₂²×D₄₇	1	2	yes	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	47	2	no	—
391	C₂³	C₂³×D₄₇	1	4	yes	—
392	C₂³	C₂³×D₄₇	1	2	yes	—
393	C₂³	C₂³×D₄₇	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	94	2	no	—
396	Q₈	—	188	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	4	no	—
403	D₄	—	94	4	no	—
404	D₄	—	94	2	no	—
405	D₄	—	188	4	no	—
406	D₄	—	188	4	no	—
407	D₄	—	188	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	47	1	no	—
410	C₂×C₄	—	47	1	no	—
411	C₂×C₄	—	47	1	no	—
412	C₂×C₄	—	47	2	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	47	1	no	—
415	C₂×C₄	—	47	2	no	—
416	C₂×C₄	—	47	4	no	—
417	C₂×C₄	—	94	4	no	—
418	C₂×C₄	—	94	2	no	—
419	C₂×C₄	—	94	8	no	—
420	C₂×C₄	—	94	4	no	—
421	C₂×C₄	—	94	4	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	1	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	4	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	#10625352	1	4	yes	complemented
428	C₂×C₄	C₂³×D₄₇	1	2	yes	—
429	C₂×C₄	C₂³×D₄₇	1	2	yes	—
430	C₂×C₄	C₂³×D₄₇	1	2	yes	—
431	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	94	2	no	—
444	C₂²	—	94	2	no	—
445	C₂²	C₂×#10625352	1	2	yes	—
446	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	47	2	no	—
451	C₄	—	94	2	no	—
452	C₄	—	94	1	no	—
453	C₄	—	94	4	no	—
454	C₄	—	94	2	no	—
455	C₄	—	94	1	no	—
456	C₄	—	94	1	no	—
457	C₄	—	94	2	no	—
458	C₄	C₂×#10625352	1	2	yes	—
459	C₄	C₂×#10625352	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	4	4	no	—
462	C₂	—	4	2	no	—
463	C₂	—	188	2	no	—
464	C₂	C₂²×#10625352	1	1	yes	characteristic
465	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
466	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	#3460
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. #15689751	C₂	semidirect
2. #15689742	C₂	semidirect
3. #15689740	C₂	semidirect
4. #15689727	C₂	semidirect
5. #15689726	C₂	semidirect
6. #15689708	C₂	semidirect
7. #15689701	C₂	semidirect
8. #15689690	C₂	semidirect
9. #15689671	C₂	semidirect
10. #15689668	C₂	semidirect
11. #15689654	C₂	semidirect
12. #15689652	C₂	semidirect
13. #15689629	C₂	semidirect
14. #41×Dic₄₇	C₂	semidirect
15. #15689591	C₂	semidirect
16. C₂×D₄×Dic₄₇	C₂	semidirect
17. C₄₇×#535	C₂	semidirect
19. C₂×#10625352	C₂²	semidirect
21. #13094024	C₂²	semidirect
22. #13094023	C₂²	semidirect
24. #13094017	C₂²	semidirect
25. #13094017	C₂²	semidirect
26. #13094016	C₂²	semidirect
27. #13094015	C₂²	semidirect
29. #13094011	C₂²	semidirect
30. #13094010	C₂²	semidirect
31. #13094008	C₂²	semidirect
32. #13094006	C₂²	semidirect
33. #13094005	C₂²	semidirect
34. #13094005	C₂²	semidirect
35. #13094003	C₂²	semidirect
37. #13094001	C₂²	semidirect
38. #13094000	C₂²	semidirect
39. #13093998	C₂²	semidirect
41. #13093996	C₂²	semidirect
42. #13093996	C₂²	semidirect
45. #13093995	C₂²	semidirect
46. #13093995	C₂²	semidirect
48. Q₈×Dic₄₇	C₂²	semidirect
49. Q₈×Dic₄₇	C₂²	semidirect
50. #13093989	C₂²	semidirect
51. #13093989	C₂²	semidirect
58. D₄×Dic₄₇	C₂²	semidirect
59. D₄×Dic₄₇	C₂²	semidirect
60. D₄×Dic₄₇	C₂²	semidirect
61. #13093986	C₂²	semidirect
62. #13093986	C₂²	semidirect
65. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
67. #13093983	C₂²	semidirect
68. #13093981	C₂²	semidirect
69. #13093980	C₂²	semidirect
73. C₂×C₄×Dic₄₇	C₂²	semidirect
74. C₄²×D₄₇	C₂²	semidirect
168. C₂×C₄×C₄₇	#41	semidirect
242. #535	D₄₇	semidirect
251. C₄₇	#3460	semidirect
427. C₂×C₄	#10625352	semidirect