Subgroups — #15869740

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124445	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123530	C₂	1	2	yes	maximal, complemented
4	#13115729	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115589	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115547	C₂	1	2	yes	maximal, complemented
7	#13115284	C₂	1	2	yes	maximal, complemented
8	#13114878	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114673	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	#11719496	C₂²	1	2	yes	—
16	C₂×#88158	C₂²	1	1	yes	characteristic
17	C₂×#88155	C₂²	1	2	yes	—
18	C₁₃×#405	—	2	4	no	—
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	#11718868	C₂²	1	2	yes	—
24	#11718798	C₄	1	2	yes	complemented
25	#11718796	C₄	1	2	yes	complemented
26	#11718795	C₄	1	4	yes	complemented
27	#11718774	C₂²	1	2	yes	—
28	#11718772	—	2	4	no	—
29	#11718771	C₂²	1	2	yes	—
30	C₈×C₂²⋊D₁₃	—	2	4	no	—
31	C₂×#88059	C₂²	1	1	yes	characteristic
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	#11718767	C₂²	1	1	yes	characteristic
34	#11718763	C₂²	1	2	yes	—
35	#11718762	C₂²	1	2	yes	—
36	C₂×#88045	C₂²	1	2	yes	—
37	C₂×#88045	C₂²	1	2	yes	—
38	#11718361	—	2	4	no	—
39	#11718144	C₂²	1	2	yes	—
40	#11718115	C₂²	1	2	yes	—
41	#11718115	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×#6127	C₂³	1	2	yes	—
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₂×C₁₃×M₁₆	—	2	2	no	—
46	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	D₄	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	#88207	—	2	2	no	—
63	#88184	C₂×C₄	1	4	yes	—
64	#88183	—	2	2	no	—
65	C₄×C₂²⋊D₁₃	—	2	4	no	—
66	#88180	C₂³	1	2	yes	—
67	#88178	C₂×C₄	1	4	yes	—
68	C₂×#6099	C₂³	1	2	yes	—
69	C₂×#6099	C₂³	1	2	yes	—
70	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
71	#88158	—	2	2	no	—
72	#88158	—	2	2	no	—
73	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
74	C₂×#6095	C₂×C₄	1	2	yes	—
75	#88155	—	2	4	no	—
76	#88155	—	2	4	no	—
77	C₂×#6094	—	2	2	no	—
78	C₂×C₈×D₁₃	—	2	2	no	—
79	C₁₃×#97	—	2	2	no	—
80	C₁₃×#97	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
83	C₂²⋊#1055	—	2	4	no	—
84	#88061	C₂×C₄	1	4	yes	—
85	#88060	—	2	4	no	—
86	#88059	—	2	2	no	—
87	#88059	—	2	2	no	—
88	#88058	C₂×C₄	1	2	yes	—
89	#88057	C₂×C₄	1	2	yes	—
90	#88056	C₂×C₄	1	4	yes	—
91	#88055	—	2	2	no	—
92	#88054	—	2	4	no	—
93	C₈×Dic₁₃	—	2	2	no	—
94	#88045	—	2	4	no	—
95	#88045	—	2	4	no	—
96	#21548	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₂²⋊D₁₃	—	2	4	no	—
109	C₂×C₂²⋊D₁₃	—	2	2	no	—
110	#6127	—	2	2	no	—
111	#6127	—	2	2	no	—
112	#6127	—	2	2	no	—
113	#6127	—	2	2	no	—
114	C₂×D₅₂	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₁₃	—	2	2	no	—
116	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
117	C₁₃×M₁₆	—	2	4	no	—
118	C₁₃×M₁₆	—	2	4	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃	#41	1	2	yes	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	C₂×D₄	1	2	yes	—
140	C₄²×C₁₃	#41	1	2	yes	—
141	C₂²⋊Dic₁₃	—	2	4	no	—
142	C₂²⋊Dic₁₃	—	2	2	no	—
143	#6103	—	2	4	no	—
144	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
145	#6101	—	2	4	no	—
146	C₄×Dic₁₃	—	2	2	no	—
147	#6099	—	2	2	no	—
148	#6099	—	2	2	no	—
149	#6099	—	2	2	no	—
150	#6099	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	Dic₅₂	—	2	2	no	—
154	D₁₀₄	—	2	2	no	—
155	#6095	—	2	4	no	—
156	#6094	—	4	4	no	—
157	C₈×D₁₃	—	4	4	no	—
158	#3054	—	13	1	no	—
159	C₂×#443	—	13	1	no	—
160	#2929	—	13	2	no	—
161	C₂×#405	D₁₃	1	1	yes	characteristic, complemented
162	#1975	—	13	1	no	—
163	#1946	—	13	1	no	—
164	#1938	—	13	2	no	—
165	#1897	—	13	2	no	—
166	#1811	—	13	1	no	—
167	#1772	—	13	1	no	—
168	#1764	—	13	2	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	C₄×D₄	1	2	yes	—
173	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
174	C₂²×D₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₁₃	—	4	8	no	—
193	C₂²⋊D₁₃	—	4	2	no	—
194	C₂²⋊D₁₃	—	4	2	no	—
195	C₂×Dic₁₃	—	2	4	no	—
196	C₂×Dic₁₃	—	2	2	no	—
197	D₅₂	—	2	2	no	—
198	D₅₂	—	2	2	no	—
199	C₄×D₁₃	—	4	2	no	—
200	C₄×D₁₃	—	4	2	no	—
201	Dic₂₆	—	2	2	no	—
202	Dic₂₆	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	C₄×D₄	1	2	yes	—
206	C₈×C₁₃	C₄×D₄	1	2	yes	—
207	C₈×C₁₃	#121	1	2	yes	—
208	C₈×C₁₃	#121	1	2	yes	—
209	#1055	—	4	2	no	—
210	#1055	—	4	2	no	—
211	C₂×#135	—	13	1	no	—
212	C₂×#131	—	13	2	no	—
213	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
214	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
215	#525	—	13	2	no	—
216	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
217	#470	—	13	2	no	—
218	#469	—	13	2	no	—
219	#468	—	13	4	no	—
220	#443	—	26	4	no	—
221	#435	—	26	4	no	—
222	C₈×D₄	—	26	4	no	—
223	C₂×#108	—	13	1	no	—
224	C₂×#108	—	13	1	no	—
225	#427	—	13	1	no	—
226	#424	—	13	2	no	—
227	C₂×#104	—	13	2	no	—
228	C₂×#104	—	13	2	no	—
229	#416	—	13	2	no	—
230	#408	—	13	2	no	—
231	#407	—	13	2	no	—
232	#405	—	2	4	no	—
233	#405	—	13	2	no	—
234	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
235	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
238	#341	—	13	2	no	—
239	#339	—	13	2	no	—
240	#339	—	13	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₁₃	#525	1	1	yes	characteristic
248	C₂²×C₁₃	#529	1	1	yes	characteristic
249	C₂×D₁₃	—	4	4	no	—
250	C₂×D₁₃	—	4	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
256	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₁₃	#532	1	1	yes	characteristic
258	Dic₁₃	—	4	4	no	—
259	Dic₁₃	—	4	2	no	—
260	C₂×#41	—	13	2	no	—
261	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
262	#135	—	26	2	no	—
263	#135	—	26	2	no	—
264	C₂×Q₁₆	—	13	1	no	—
265	C₂×SD₁₆	—	13	2	no	—
266	C₂×D₈	—	13	1	no	—
267	#131	—	26	4	no	—
268	#131	—	26	4	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	13	2	no	—
272	C₂×M₁₆	—	13	2	no	—
273	C₂×M₁₆	—	26	2	no	—
274	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
275	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	26	2	no	—
279	C₂²×C₈	D₅₂	1	2	yes	—
280	C₂²×C₈	D₅₂	1	2	yes	—
281	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
284	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
285	#123	—	26	2	no	—
286	C₂²⋊Q₈	—	13	4	no	—
287	#121	—	13	4	no	—
288	#120	—	26	2	no	—
289	C₄×D₄	—	26	4	no	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	#117	—	13	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
297	#108	—	26	2	no	—
298	#108	—	26	2	no	—
299	#107	—	13	2	no	—
300	#106	—	13	2	no	—
301	C₄⋊C₈	—	26	4	no	—
302	#104	—	26	4	no	—
303	#104	—	26	4	no	—
304	#103	—	13	4	no	—
305	#102	—	13	4	no	—
306	C₂²⋊C₈	—	26	4	no	—
307	C₂²⋊C₈	—	26	4	no	—
308	#97	—	2	2	no	—
309	#97	—	2	2	no	—
310	#97	—	26	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	26	2	no	—
313	C₄×C₈	C₂²⋊D₁₃	1	4	yes	complemented
314	C₂×C₁₃	—	2	1	no	—
315	C₂×C₁₃	—	2	1	no	—
316	C₂×C₁₃	—	4	2	no	—
317	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
318	C₂×C₁₃	#2955	1	2	yes	—
319	D₁₃	—	8	2	no	—
320	C₂⁴	#6127	1	1	yes	characteristic
321	#41	—	26	2	no	—
322	#41	—	26	2	no	—
323	#41	—	26	2	no	—
324	#41	—	26	2	no	—
325	C₂×Q₈	—	13	2	no	—
326	C₂×D₄	—	13	2	no	—
327	C₂×D₄	—	26	4	no	—
328	C₂×D₄	—	26	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	26	2	no	—
336	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
337	C₂²×C₄	C₂×D₅₂	1	2	yes	—
338	C₂²×C₄	#6127	1	1	yes	characteristic
339	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
340	Q₁₆	—	26	2	no	—
341	SD₁₆	—	26	4	no	—
342	D₈	—	26	2	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	26	2	no	—
346	M₁₆	—	26	2	no	—
347	M₁₆	—	26	2	no	—
348	M₁₆	—	26	2	no	—
349	M₁₆	—	52	4	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	—	52	4	no	—
359	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
362	C₂×C₈	C₂×D₅₂	1	2	yes	—
363	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
364	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
365	C₂×C₈	#6127	1	2	yes	—
366	C₂×C₈	#6127	1	2	yes	—
367	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
368	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	13	4	no	—
371	C₄⋊C₄	—	26	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	26	4	no	—
374	C₂²⋊C₄	—	26	2	no	—
375	C₂²⋊C₄	—	26	4	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	26	2	no	—
379	C₄²	#6127	1	2	yes	—
380	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
381	C₁₃	#21548	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	26	2	no	—
386	C₂³	C₄×D₅₂	1	2	yes	—
387	C₂³	C₂×#6127	1	1	yes	characteristic
388	Q₈	—	26	2	no	—
389	Q₈	—	26	2	no	—
390	D₄	—	26	2	no	—
391	D₄	—	26	2	no	—
392	D₄	—	52	8	no	—
393	D₄	—	52	2	no	—
394	D₄	—	52	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	C₄×D₅₂	1	2	yes	—
410	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
412	C₂×C₄	C₂×#6127	1	1	yes	characteristic
413	C₂×C₄	C₂×#6127	1	1	yes	characteristic
414	C₂×C₄	C₂×#6127	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	52	2	no	—
419	C₈	—	52	2	no	—
420	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
421	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
422	C₈	#88184	1	2	yes	—
423	C₈	#88184	1	2	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	52	4	no	—
430	C₂²	—	52	2	no	—
431	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
432	C₂²	#11719184	1	1	yes	characteristic
433	C₂²	#11719496	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	52	4	no	—
438	C₄	—	52	2	no	—
439	C₄	C₄×#6127	1	1	yes	characteristic
440	C₄	#11719182	1	1	yes	characteristic
441	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
442	C₄	C₂×#88184	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	4	2	no	—
446	C₂	—	104	2	no	—
447	C₂	C₄×#88184	1	1	yes	characteristic
448	C₂	#13123740	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124445	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#21548
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#11718361	C₂	semidirect
3. #13123530	C₂	semidirect
4. #13115729	C₂	semidirect
5. #13115589	C₂	semidirect
6. #13115547	C₂	semidirect
7. #13115284	C₂	semidirect
8. #13114878	C₂	semidirect
9. #13114715	C₂	semidirect
10. #13114673	C₂	semidirect
11. C₂×C₁₃×#405	C₂	semidirect
24. #11718798	C₄	semidirect
25. #11718796	C₄	semidirect
26. #11718795	C₄	semidirect
82. C₄×C₈×C₁₃	D₄	semidirect
161. C₂×#405	D₁₃	semidirect
313. C₄×C₈	C₂²⋊D₁₃	semidirect
381. C₁₃	#21548	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13124445	2
C₂×#11718361	2
#13123530	2
#13115729	2
#13115589	2
#13115547	2
#13115284	2
#13114878	2
#13114715	2
#13114673	2
C₂×C₁₃×#405	2
#21548	13