Subgroups — #20256806

Order 6016.

1140 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689752	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689743	C₂	1	2	yes	maximal, complemented
3	#15689741	C₂	1	2	yes	maximal, complemented
4	#15689725	C₂	1	2	yes	maximal, complemented
5	#15689723	C₂	1	2	yes	maximal, complemented
6	#15689713	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689710	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689708	C₂	1	2	yes	maximal, complemented
9	#15689700	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689688	C₂	1	2	yes	maximal, complemented
11	#15689670	C₂	1	2	yes	maximal, complemented
12	#15689669	C₂	1	2	yes	maximal, complemented
13	#15689653	C₂	1	2	yes	maximal, complemented
14	#15689651	C₂	1	2	yes	maximal, complemented
15	#15689634	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689632	C₂	1	2	yes	maximal, complemented
17	C₄×#10625352	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625350	C₂²	1	2	yes	complemented
21	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10625352	C₂²	1	2	yes	—
23	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
25	#13094023	C₂²	1	2	yes	complemented
26	#13094022	C₂²	1	2	yes	complemented
27	#13094020	C₂²	1	2	yes	—
28	#13094020	C₂²	1	2	yes	—
29	#13094019	C₂²	1	2	yes	complemented
30	#13094019	C₂²	1	2	yes	complemented
31	#13094017	C₂²	1	2	yes	complemented
32	#13094017	C₂²	1	2	yes	complemented
33	#13094014	C₂²	1	2	yes	complemented
34	#13094014	C₂²	1	2	yes	complemented
35	#13094013	C₂²	1	2	yes	complemented
36	#13094011	C₂²	1	2	yes	complemented
37	#13094010	C₂²	1	2	yes	—
38	#13094010	C₂²	1	2	yes	—
39	#13094010	C₂²	1	2	yes	complemented
40	#13094010	C₂²	1	2	yes	complemented
41	#13094009	C₂²	1	2	yes	complemented
42	#13094009	C₂²	1	2	yes	complemented
43	#13094008	C₂²	1	2	yes	complemented
44	#13094007	C₂²	1	2	yes	complemented
45	#13094006	C₂²	1	2	yes	complemented
46	#13094006	C₂²	1	2	yes	complemented
47	#13094005	C₂²	1	2	yes	complemented
48	#13094003	C₂²	1	1	yes	characteristic
49	#13094003	C₂²	1	1	yes	characteristic, complemented
50	#13094002	C₂²	1	2	yes	complemented
51	#13094002	C₂²	1	2	yes	complemented
52	#13094001	C₂²	1	2	yes	—
53	#13094001	C₂²	1	2	yes	complemented
54	#13093999	C₂²	1	2	yes	complemented
55	#13093998	C₂²	1	1	yes	characteristic
56	#13093998	C₂²	1	1	yes	characteristic, complemented
57	#13093997	C₂²	1	2	yes	—
58	#13093997	C₂²	1	2	yes	—
59	#13093997	C₂²	1	2	yes	complemented
60	#13093997	C₂²	1	2	yes	complemented
61	#13093996	C₂²	1	2	yes	—
62	#13093996	C₂²	1	2	yes	—
63	#13093996	C₂²	1	2	yes	—
64	#13093996	C₂²	1	2	yes	complemented
65	#13093996	C₂²	1	2	yes	complemented
66	#13093996	C₂²	1	2	yes	complemented
67	#13093995	C₂²	1	2	yes	complemented
68	#13093994	C₂²	1	2	yes	—
69	#13093993	C₂²	1	2	yes	—
70	#13093992	C₂²	1	2	yes	—
71	C₄×Dic₉₄	C₂²	1	2	yes	complemented
72	#13093989	C₂²	1	2	yes	complemented
73	C₄×D₁₈₈	C₂²	1	2	yes	complemented
74	D₄×Dic₄₇	C₂²	1	2	yes	—
75	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
76	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
77	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
78	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
80	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
84	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
85	#13093983	C₂²	1	1	yes	characteristic, complemented
86	#13093982	C₂²	1	2	yes	complemented
87	#13093981	C₂²	1	2	yes	complemented
88	#13093980	C₂²	1	2	yes	—
89	#13093980	C₂²	1	2	yes	complemented
90	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
92	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₄₇	C₂²	1	2	yes	complemented
95	C₄²×D₄₇	C₂²	1	2	yes	complemented
96	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
98	#123×C₄₇	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
100	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
101	#121×C₄₇	C₂²	1	1	yes	characteristic
102	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
103	#120×C₄₇	C₂²	1	2	yes	—
104	C₄×D₄×C₄₇	C₂²	1	2	yes	—
105	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
106	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
108	C₂³×D₄₇	C₂³	1	1	yes	characteristic
109	#41×C₄₇	—	4	2	no	—
110	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₄₇	C₂³	1	2	yes	—
112	C₂×D₄×C₄₇	C₂³	1	2	yes	—
113	C₂×D₄×C₄₇	C₂³	1	2	yes	—
114	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	—	4	2	no	—
116	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊D₄₇	—	2	4	no	—
124	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
133	C₂²×Dic₄₇	C₂³	1	2	yes	—
134	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂³	1	2	yes	—
136	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
138	#10625352	—	2	8	no	—
139	#10625350	—	4	4	no	—
140	#10625350	—	4	2	no	—
141	C₂×D₁₈₈	C₂³	1	2	yes	—
142	C₂×D₁₈₈	C₂³	1	2	yes	—
143	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₄₇	—	4	2	no	—
145	C₂×C₄×D₄₇	C₂³	1	2	yes	—
146	C₂×C₄×D₄₇	C₂³	1	2	yes	—
147	C₂×C₄×D₄₇	C₂³	1	2	yes	—
148	C₂×C₄×D₄₇	C₂³	1	2	yes	—
149	C₂×C₄×D₄₇	C₂³	1	2	yes	—
150	C₂×Dic₉₄	C₂³	1	2	yes	—
151	C₂×Dic₉₄	C₂³	1	2	yes	—
152	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
156	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₄²×C₄₇	C₂³	1	2	yes	—
163	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
164	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
165	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
166	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
168	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
170	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
180	C₄⋊Dic₄₇	C₂³	1	2	yes	—
181	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₄₇	C₂³	1	2	yes	—
184	Dic₄₇⋊C₄	C₂³	1	2	yes	—
185	Dic₄₇⋊C₄	C₂³	1	2	yes	—
186	Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	Dic₄₇⋊C₄	C₂³	1	2	yes	—
188	Dic₄₇⋊C₄	C₂³	1	2	yes	—
189	Dic₄₇⋊C₄	C₂³	1	2	yes	—
190	Dic₄₇⋊C₄	C₂³	1	2	yes	—
191	Dic₄₇⋊C₄	C₂³	1	2	yes	—
192	Dic₄₇⋊C₄	C₂³	1	2	yes	—
193	Dic₄₇⋊C₄	C₂³	1	2	yes	—
194	C₄×Dic₄₇	C₂³	1	2	yes	—
195	C₄×Dic₄₇	C₂³	1	2	yes	—
196	C₄×Dic₄₇	C₂³	1	2	yes	—
197	C₄×Dic₄₇	C₂³	1	2	yes	—
198	C₄×Dic₄₇	C₂³	1	2	yes	—
199	C₄×Dic₄₇	C₂³	1	2	yes	—
200	C₄×Dic₄₇	C₂³	1	2	yes	—
201	C₂³×C₄₇	—	2	2	no	—
202	C₂³×C₄₇	—	4	1	no	—
203	C₂³×C₄₇	—	4	1	no	—
204	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
205	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
206	C₂³×C₄₇	C₂⁴	1	2	yes	—
207	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
208	C₂²×D₄₇	—	2	2	no	—
209	C₂²×D₄₇	—	4	1	no	—
210	C₂²×D₄₇	—	4	1	no	—
211	C₂²×D₄₇	C₂⁴	1	2	yes	—
212	C₂²×D₄₇	C₂⁴	1	2	yes	—
213	Q₈×C₄₇	—	4	1	no	—
214	D₄×C₄₇	—	2	4	no	—
215	D₄×C₄₇	—	4	2	no	—
216	D₄×C₄₇	—	4	2	no	—
217	D₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	4	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	4	1	no	—
224	C₂×C₄×C₄₇	—	4	1	no	—
225	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
226	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
228	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
229	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
232	C₂²⋊D₄₇	—	2	4	no	—
233	C₂²⋊D₄₇	—	2	4	no	—
234	C₂²⋊D₄₇	—	2	4	no	—
235	C₂²⋊D₄₇	—	2	4	no	—
236	C₂²⋊D₄₇	—	4	2	no	—
237	C₂²⋊D₄₇	—	4	2	no	—
238	C₂²⋊D₄₇	—	4	2	no	—
239	C₂²⋊D₄₇	—	4	2	no	—
240	C₂²⋊D₄₇	—	4	2	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	4	1	no	—
243	C₂×Dic₄₇	—	4	1	no	—
244	C₂×Dic₄₇	—	4	2	no	—
245	C₂×Dic₄₇	#41	1	4	yes	complemented
246	C₂×Dic₄₇	C₂⁴	1	2	yes	—
247	C₂×Dic₄₇	C₂⁴	1	2	yes	—
248	C₂×Dic₄₇	C₂⁴	1	2	yes	—
249	C₂×Dic₄₇	C₂⁴	1	2	yes	—
250	C₂×Dic₄₇	C₂⁴	1	2	yes	—
251	C₂×Dic₄₇	C₂⁴	1	2	yes	—
252	D₁₈₈	—	4	2	no	—
253	D₁₈₈	—	4	1	no	—
254	D₁₈₈	—	4	2	no	—
255	C₄×D₄₇	—	2	4	no	—
256	C₄×D₄₇	—	2	4	no	—
257	C₄×D₄₇	—	2	4	no	—
258	C₄×D₄₇	—	4	2	no	—
259	C₄×D₄₇	—	4	2	no	—
260	Dic₉₄	—	2	4	no	—
261	Dic₉₄	—	4	1	no	—
262	Dic₉₄	—	4	2	no	—
263	C₂²×C₄₇	—	2	1	no	—
264	C₂²×C₄₇	—	2	1	no	—
265	C₂²×C₄₇	—	2	2	no	—
266	C₂²×C₄₇	—	2	1	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	2	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	2	2	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	4	4	no	—
275	C₂²×C₄₇	C₂×#41	1	2	yes	—
276	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
277	C₂×D₄₇	—	2	2	no	—
278	C₂×D₄₇	—	2	2	no	—
279	C₂×D₄₇	—	2	2	no	—
280	C₂×D₄₇	—	2	2	no	—
281	C₂×D₄₇	—	2	2	no	—
282	C₂×D₄₇	—	2	2	no	—
283	C₂×D₄₇	—	4	4	no	—
284	C₄×C₄₇	—	2	2	no	—
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	2	2	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
291	Dic₄₇	—	2	2	no	—
292	Dic₄₇	—	2	2	no	—
293	Dic₄₇	—	2	2	no	—
294	Dic₄₇	—	2	2	no	—
295	Dic₄₇	—	2	2	no	—
296	Dic₄₇	C₂×#41	1	4	yes	—
297	#3460	—	47	1	no	maximal, Sylow
298	C₂×C₄₇	—	2	2	no	—
299	C₂×C₄₇	—	4	2	no	—
300	C₂×C₄₇	—	4	1	no	—
301	C₂×C₄₇	—	4	1	no	—
302	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
303	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄₇	#585	1	1	yes	characteristic
305	D₄₇	—	4	2	no	—
306	D₄₇	—	4	2	no	—
307	#544	—	47	1	no	—
308	#542	—	47	2	no	—
309	#542	—	47	2	no	—
310	#540	—	47	2	no	—
311	#540	—	47	2	no	—
312	#538	—	47	1	no	—
313	#538	—	47	1	no	—
314	#538	—	47	2	no	—
315	#537	—	47	1	no	—
316	#535	—	47	2	no	—
317	#532	—	47	2	no	—
318	#532	—	47	2	no	—
319	#529	—	47	2	no	—
320	#529	—	47	2	no	—
321	#525	—	47	1	no	—
322	#525	—	47	2	no	—
323	#525	D₄₇	1	1	yes	characteristic, complemented
324	C₄×#41	—	47	2	no	—
325	C₂×C₄×D₄	—	47	1	no	—
326	C₄₇	#3460	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	47	2	no	—
328	C₂×#41	—	47	1	no	—
329	C₂×#41	—	47	2	no	—
330	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
331	C₂²×D₄	—	47	1	no	—
332	C₂³×C₄	—	47	1	no	—
333	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
334	C₄⋊Q₈	—	47	2	no	—
335	C₄⋊Q₈	—	47	2	no	—
336	#127	—	47	2	no	—
337	#127	—	47	2	no	—
338	#126	—	47	2	no	—
339	#126	—	47	2	no	—
340	#126	—	47	2	no	—
341	#126	—	47	2	no	—
342	#125	—	47	2	no	—
343	#125	—	47	2	no	—
344	#124	—	47	2	no	—
345	#124	—	47	2	no	—
346	#124	—	47	2	no	—
347	#124	—	47	2	no	—
348	#124	—	47	2	no	—
349	#124	—	47	2	no	—
350	#123	—	47	2	no	—
351	#123	—	47	2	no	—
352	#123	—	47	2	no	—
353	#123	—	47	2	no	—
354	#123	—	47	2	no	—
355	#123	—	47	2	no	—
356	#123	—	47	2	no	—
357	#123	C₂×D₄₇	1	2	yes	complemented
358	C₂²⋊Q₈	—	47	1	no	—
359	C₂²⋊Q₈	—	47	1	no	—
360	C₂²⋊Q₈	—	47	2	no	—
361	C₂²⋊Q₈	—	47	2	no	—
362	C₂²⋊Q₈	—	47	2	no	—
363	C₂²⋊Q₈	—	47	2	no	—
364	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
365	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
366	#121	—	47	2	no	—
367	#121	—	47	2	no	—
368	#121	—	47	2	no	—
369	#121	—	47	2	no	—
370	#121	—	47	2	no	—
371	#121	—	47	2	no	—
372	#121	—	47	2	no	—
373	#121	—	47	1	no	—
374	#121	—	47	1	no	—
375	#121	—	47	2	no	—
376	#121	—	47	2	no	—
377	#121	—	47	2	no	—
378	#121	—	47	2	no	—
379	#121	—	47	2	no	—
380	#121	C₂×D₄₇	1	1	yes	characteristic
381	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
382	#120	—	47	2	no	—
383	#120	—	47	2	no	—
384	#120	—	47	2	no	—
385	#120	C₂×D₄₇	1	2	yes	—
386	C₄×Q₈	—	47	2	no	—
387	C₄×Q₈	—	47	2	no	—
388	C₄×D₄	—	47	2	no	—
389	C₄×D₄	—	47	2	no	—
390	C₄×D₄	—	47	2	no	—
391	C₄×D₄	—	47	2	no	—
392	C₄×D₄	—	47	2	no	—
393	C₄×D₄	—	47	2	no	—
394	C₄×D₄	—	47	2	no	—
395	C₄×D₄	—	47	2	no	—
396	C₄×D₄	—	47	2	no	—
397	C₄×D₄	—	47	2	no	—
398	C₄×D₄	—	47	2	no	—
399	C₄×D₄	—	47	2	no	—
400	C₄×D₄	C₂×D₄₇	1	2	yes	—
401	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
402	#117	—	47	1	no	—
403	#117	—	47	2	no	—
404	#117	—	47	2	no	—
405	#117	—	47	2	no	—
406	#117	—	47	2	no	—
407	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
408	C₂×C₄⋊C₄	—	47	1	no	—
409	C₂×C₂²⋊C₄	—	47	1	no	—
410	C₂×C₂²⋊C₄	—	47	1	no	—
411	C₂×C₄²	—	47	1	no	—
412	C₂×C₄²	—	47	2	no	—
413	C₂×C₄²	—	47	2	no	—
414	C₂⁴	—	47	1	no	—
415	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
416	#41	—	4	2	no	—
417	#41	—	94	8	no	—
418	#41	—	188	2	no	—
419	#41	—	188	4	no	—
420	C₂×Q₈	—	47	2	no	—
421	C₂×Q₈	—	47	1	no	—
422	C₂×Q₈	—	47	2	no	—
423	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
424	C₂×D₄	—	47	2	no	—
425	C₂×D₄	—	47	2	no	—
426	C₂×D₄	—	47	2	no	—
427	C₂×D₄	—	47	2	no	—
428	C₂×D₄	—	47	2	no	—
429	C₂×D₄	—	47	2	no	—
430	C₂×D₄	—	47	2	no	—
431	C₂×D₄	—	47	2	no	—
432	C₂×D₄	—	47	2	no	—
433	C₂×D₄	—	47	2	no	—
434	C₂×D₄	—	47	2	no	—
435	C₂×D₄	—	47	1	no	—
436	C₂×D₄	—	94	4	no	—
437	C₂×D₄	C₂²×D₄₇	1	2	yes	—
438	C₂×D₄	C₂²×D₄₇	1	2	yes	—
439	C₂×D₄	C₂²×D₄₇	1	2	yes	—
440	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	47	1	no	—
443	C₂²×C₄	—	47	2	no	—
444	C₂²×C₄	—	47	1	no	—
445	C₂²×C₄	—	47	2	no	—
446	C₂²×C₄	—	47	1	no	—
447	C₂²×C₄	—	47	2	no	—
448	C₂²×C₄	—	47	2	no	—
449	C₂²×C₄	—	47	2	no	—
450	C₂²×C₄	—	47	2	no	—
451	C₂²×C₄	—	47	2	no	—
452	C₂²×C₄	—	188	2	no	—
453	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
455	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
460	C₄⋊C₄	—	47	2	no	—
461	C₄⋊C₄	—	47	2	no	—
462	C₄⋊C₄	—	47	2	no	—
463	C₄⋊C₄	—	47	2	no	—
464	C₄⋊C₄	—	47	2	no	—
465	C₄⋊C₄	—	47	2	no	—
466	C₄⋊C₄	—	47	2	no	—
467	C₄⋊C₄	—	47	2	no	—
468	C₄⋊C₄	—	47	2	no	—
469	C₄⋊C₄	—	47	2	no	—
470	C₄⋊C₄	—	47	2	no	—
471	C₄⋊C₄	—	47	1	no	—
472	C₄⋊C₄	—	47	1	no	—
473	C₄⋊C₄	—	47	2	no	—
474	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
475	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
478	C₂²⋊C₄	—	47	2	no	—
479	C₂²⋊C₄	—	47	2	no	—
480	C₂²⋊C₄	—	47	2	no	—
481	C₂²⋊C₄	—	47	2	no	—
482	C₂²⋊C₄	—	47	2	no	—
483	C₂²⋊C₄	—	47	2	no	—
484	C₂²⋊C₄	—	47	2	no	—
485	C₂²⋊C₄	—	47	2	no	—
486	C₂²⋊C₄	—	47	2	no	—
487	C₂²⋊C₄	—	47	2	no	—
488	C₂²⋊C₄	—	47	2	no	—
489	C₂²⋊C₄	—	47	2	no	—
490	C₂²⋊C₄	—	47	2	no	—
491	C₂²⋊C₄	—	47	2	no	—
492	C₂²⋊C₄	—	47	2	no	—
493	C₂²⋊C₄	—	47	2	no	—
494	C₂²⋊C₄	—	47	2	no	—
495	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
496	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
500	C₄²	—	47	2	no	—
501	C₄²	—	47	2	no	—
502	C₄²	—	47	2	no	—
503	C₄²	—	47	2	no	—
504	C₄²	—	47	2	no	—
505	C₄²	—	47	2	no	—
506	C₄²	—	47	2	no	—
507	C₄²	C₂²×D₄₇	1	2	yes	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	47	2	no	—
512	C₂³	—	47	2	no	—
513	C₂³	—	94	2	no	—
514	C₂³	—	188	1	no	—
515	C₂³	—	188	1	no	—
516	C₂³	C₂³×D₄₇	1	1	yes	characteristic
517	C₂³	C₂³×D₄₇	1	1	yes	characteristic
518	C₂³	C₂³×D₄₇	1	2	yes	—
519	C₂³	C₂³×D₄₇	1	1	yes	characteristic
520	Q₈	—	4	1	no	—
521	Q₈	—	94	4	no	—
522	Q₈	—	188	1	no	—
523	Q₈	—	188	2	no	—
524	D₄	—	2	4	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	2	no	—
528	D₄	—	94	4	no	—
529	D₄	—	94	4	no	—
530	D₄	—	94	4	no	—
531	D₄	—	94	4	no	—
532	D₄	—	188	2	no	—
533	D₄	—	188	1	no	—
534	D₄	—	188	2	no	—
535	D₄	—	188	2	no	—
536	D₄	—	188	2	no	—
537	D₄	—	188	2	no	—
538	D₄	—	188	2	no	—
539	D₄	—	188	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	47	4	no	—
548	C₂×C₄	—	47	2	no	—
549	C₂×C₄	—	47	2	no	—
550	C₂×C₄	—	47	2	no	—
551	C₂×C₄	—	47	2	no	—
552	C₂×C₄	—	47	2	no	—
553	C₂×C₄	—	47	2	no	—
554	C₂×C₄	—	94	4	no	—
555	C₂×C₄	—	94	4	no	—
556	C₂×C₄	—	94	4	no	—
557	C₂×C₄	—	94	4	no	—
558	C₂×C₄	—	188	2	no	—
559	C₂×C₄	—	188	2	no	—
560	C₂×C₄	—	188	1	no	—
561	C₂×C₄	—	188	2	no	—
562	C₂×C₄	—	188	1	no	—
563	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₄₇	1	2	yes	—
565	C₂×C₄	C₂³×D₄₇	1	2	yes	—
566	C₂×C₄	C₂³×D₄₇	1	2	yes	—
567	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	94	2	no	—
583	C₂²	—	94	2	no	—
584	C₂²	—	94	2	no	—
585	C₂²	—	94	2	no	—
586	C₂²	—	94	2	no	—
587	C₂²	—	94	2	no	—
588	C₂²	—	188	4	no	—
589	C₂²	#41×D₄₇	1	2	yes	—
590	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	47	4	no	—
598	C₄	—	94	2	no	—
599	C₄	—	94	2	no	—
600	C₄	—	94	2	no	—
601	C₄	—	94	2	no	—
602	C₄	—	94	2	no	—
603	C₄	#13094069	1	2	yes	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	1	no	—
607	C₂	—	4	2	no	—
608	C₂	—	188	2	no	—
609	C₂	—	188	2	no	—
610	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
611	C₂	C₂×#13094069	1	1	yes	characteristic
612	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₄₇×#525	C₂
hypercenter	#525	D₄₇
hypocenter	C₄₇	#3460
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #15689752	C₂	semidirect
2. #15689743	C₂	semidirect
3. #15689741	C₂	semidirect
4. #15689725	C₂	semidirect
5. #15689723	C₂	semidirect
6. #15689713	C₂	semidirect
7. #15689710	C₂	semidirect
8. #15689708	C₂	semidirect
9. #15689700	C₂	semidirect
10. #15689688	C₂	semidirect
11. #15689670	C₂	semidirect
12. #15689669	C₂	semidirect
13. #15689653	C₂	semidirect
14. #15689651	C₂	semidirect
15. #15689634	C₂	semidirect
16. #15689632	C₂	semidirect
17. C₄×#10625352	C₂	semidirect
18. C₂×C₄×C₂²⋊D₄₇	C₂	semidirect
19. C₄₇×#525	C₂	semidirect
20. C₂×#10625350	C₂²	semidirect
21. C₂×#10625350	C₂²	semidirect
25. #13094023	C₂²	semidirect
26. #13094022	C₂²	semidirect
29. #13094019	C₂²	semidirect
30. #13094019	C₂²	semidirect
31. #13094017	C₂²	semidirect
32. #13094017	C₂²	semidirect
33. #13094014	C₂²	semidirect
34. #13094014	C₂²	semidirect
35. #13094013	C₂²	semidirect
36. #13094011	C₂²	semidirect
39. #13094010	C₂²	semidirect
40. #13094010	C₂²	semidirect
41. #13094009	C₂²	semidirect
42. #13094009	C₂²	semidirect
43. #13094008	C₂²	semidirect
44. #13094007	C₂²	semidirect
45. #13094006	C₂²	semidirect
46. #13094006	C₂²	semidirect
47. #13094005	C₂²	semidirect
49. #13094003	C₂²	semidirect
50. #13094002	C₂²	semidirect
51. #13094002	C₂²	semidirect
53. #13094001	C₂²	semidirect
54. #13093999	C₂²	semidirect
56. #13093998	C₂²	semidirect
59. #13093997	C₂²	semidirect
60. #13093997	C₂²	semidirect
64. #13093996	C₂²	semidirect
65. #13093996	C₂²	semidirect
66. #13093996	C₂²	semidirect
67. #13093995	C₂²	semidirect
71. C₄×Dic₉₄	C₂²	semidirect
72. #13093989	C₂²	semidirect
73. C₄×D₁₈₈	C₂²	semidirect
80. C₄×C₂²⋊D₄₇	C₂²	semidirect
81. C₄×C₂²⋊D₄₇	C₂²	semidirect
82. C₄×C₂²⋊D₄₇	C₂²	semidirect
84. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
85. #13093983	C₂²	semidirect
86. #13093982	C₂²	semidirect
87. #13093981	C₂²	semidirect
89. #13093980	C₂²	semidirect
94. C₂×C₄×Dic₄₇	C₂²	semidirect
95. C₄²×D₄₇	C₂²	semidirect
96. C₂×#41×C₄₇	C₂²	semidirect
98. #123×C₄₇	C₂²	semidirect
100. C₂²⋊Q₈×C₄₇	C₂²	semidirect
102. #121×C₄₇	C₂²	semidirect
105. C₄×D₄×C₄₇	C₂²	semidirect
106. #117×C₄₇	C₂²	semidirect
245. C₂×Dic₄₇	#41	semidirect
323. #525	D₄₇	semidirect
326. C₄₇	#3460	semidirect
330. C₂×#41	C₂×D₄₇	semidirect
357. #123	C₂×D₄₇	semidirect
365. C₂²⋊Q₈	C₂×D₄₇	semidirect
381. #121	C₂×D₄₇	semidirect
401. C₄×D₄	C₂×D₄₇	semidirect
407. #117	C₂×D₄₇	semidirect