Subgroups — #16798323

Order 3328.

810 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	#13131314	C₂	1	2	yes	maximal
2	#13130773	C₂	1	1	yes	maximal, characteristic, complemented
3	#13130771	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130759	C₂	1	2	yes	maximal, complemented
5	#13130714	C₂	1	2	yes	maximal
6	#13130712	C₂	1	2	yes	maximal
7	#13130650	C₂	1	2	yes	maximal, complemented
8	C₄×#88101	C₂	1	2	yes	maximal, complemented
9	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
10	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	D₁₃×#117	C₂²	1	1	yes	characteristic
13	#11719136	C₂²	1	4	yes	—
14	C₂×#88102	C₂²	1	2	yes	—
15	C₂×#88101	C₂²	1	2	yes	—
16	C₂×#88101	C₂²	1	2	yes	—
17	C₂×#88101	C₂²	1	2	yes	—
18	#11719082	—	2	4	no	—
19	#11719071	—	2	4	no	—
20	#11719060	C₂²	1	2	yes	—
21	#11719059	C₂²	1	2	yes	—
22	C₄×C₄⋊#261	C₂²	1	4	yes	—
23	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
24	#11718783	C₄	1	1	yes	characteristic, complemented
25	#11718762	C₄	1	1	yes	characteristic, complemented
26	#11718658	C₄	1	1	yes	characteristic, complemented
27	#11718369	C₄	1	1	yes	characteristic, complemented
28	#11718369	C₄	1	1	yes	characteristic, complemented
29	D₁₃×#97	C₂²	1	1	yes	characteristic
30	D₁₃×#97	C₂²	1	1	yes	characteristic
31	#11718350	C₄	1	1	yes	characteristic, complemented
32	#11718350	C₄	1	1	yes	characteristic, complemented
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
35	#11718265	C₂²	1	4	yes	—
36	#11718265	C₂²	1	4	yes	—
37	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊#261	—	2	4	no	—
39	C₂×C₄⋊#261	—	2	4	no	—
40	C₂×C₄⋊#261	C₂³	1	4	yes	—
41	C₂×C₄⋊#261	C₂³	1	4	yes	—
42	C₂×C₄×#261	—	2	4	no	—
43	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
46	#88180	C₂×C₄	1	1	yes	characteristic
47	C₂×#6099	C₂×C₄	1	1	yes	characteristic
48	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
49	M₁₆×D₁₃	—	2	2	no	—
50	M₁₆×D₁₃	—	2	2	no	—
51	C₂×#6094	C₂×C₄	1	1	yes	characteristic
52	C₂×#6094	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	—	2	2	no	—
54	C₂×C₈×D₁₃	—	2	2	no	—
55	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
61	#88146	Q₈	1	2	yes	—
62	C₄⋊C₄×D₁₃	D₄	1	2	yes	—
63	C₂²⋊C₄×D₁₃	D₄	1	2	yes	—
64	#88131	Q₈	1	2	yes	—
65	#88126	C₂×C₄	1	1	yes	characteristic
66	#88126	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₄²×D₁₃	C₂³	1	1	yes	characteristic
69	(C₂×#261)⋊C₄	—	2	4	no	—
70	(C₂×#261)⋊C₄	—	2	4	no	—
71	(C₂×#261)⋊C₄	—	2	4	no	—
72	#88102	—	2	4	no	—
73	#88101	—	2	4	no	—
74	#88101	—	2	4	no	—
75	#88101	—	2	4	no	—
76	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	#88055	C₂×C₄	1	1	yes	characteristic
81	#88055	C₂×C₄	1	1	yes	characteristic
82	#88055	C₂×C₄	1	1	yes	characteristic
83	#88055	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
88	#88043	C₂×C₄	1	1	yes	characteristic
89	#88043	C₂×C₄	1	1	yes	characteristic
90	C₄×#1055	C₂×C₄	1	1	yes	characteristic
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	#20820	—	13	1	no	maximal, Sylow
93	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×#261	—	2	4	no	—
95	C₂²×#261	—	2	4	no	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₄×D₁₃	—	2	1	no	—
99	C₂×C₄×D₁₃	—	2	1	no	—
100	C₂×C₄×D₁₃	—	2	1	no	—
101	C₂×C₄×D₁₃	—	2	1	no	—
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
108	C₂²⋊#261	—	8	4	no	—
109	C₄⋊#261	—	2	4	no	—
110	C₄⋊#261	—	2	4	no	—
111	C₄⋊#261	—	2	4	no	—
112	C₄⋊#261	—	2	4	no	—
113	C₄⋊#261	—	8	4	no	—
114	C₄×#261	—	8	4	no	—
115	C₁₃×M₁₆	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
126	#6103	C₄⋊C₄	1	2	yes	—
127	#6103	C₄⋊C₄	1	2	yes	—
128	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
129	#6101	C₄⋊C₄	1	2	yes	—
130	#6101	C₄⋊C₄	1	2	yes	—
131	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
134	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
135	#6099	—	2	2	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
138	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
139	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	#6094	—	2	2	no	—
142	#6094	—	2	2	no	—
143	C₈×D₁₃	—	2	1	no	—
144	C₈×D₁₃	—	2	1	no	—
145	C₈×D₁₃	—	2	1	no	—
146	C₈×D₁₃	—	2	1	no	—
147	C₈×D₁₃	—	2	2	no	—
148	C₈×D₁₃	—	2	2	no	—
149	C₈×D₁₃	#41	1	2	yes	—
150	C₈×D₁₃	#41	1	2	yes	—
151	C₈×D₁₃	#41	1	2	yes	—
152	C₈×D₁₃	#41	1	2	yes	—
153	C₂×#405	—	13	1	no	—
154	#2314	—	13	2	no	—
155	#1846	—	13	1	no	—
156	#1844	—	13	1	no	—
157	#1836	—	13	2	no	—
158	#1809	—	13	2	no	—
159	#1807	—	13	2	no	—
160	#1776	—	13	2	no	—
161	C₄×#106	—	13	2	no	—
162	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×D₁₃	—	2	1	no	—
164	C₂²×D₁₃	—	2	1	no	—
165	C₂²×D₁₃	—	2	4	no	—
166	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×#261	—	4	4	no	—
169	C₂×#261	—	4	4	no	—
170	C₂×#261	—	4	4	no	—
171	C₂×#261	—	4	4	no	—
172	C₂×#261	—	4	4	no	—
173	C₂×#261	—	4	4	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	—	2	1	no	—
181	C₂×Dic₁₃	—	2	1	no	—
182	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
184	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
186	C₄×D₁₃	—	2	1	no	—
187	C₄×D₁₃	—	2	1	no	—
188	C₄×D₁₃	—	2	4	no	—
189	C₄×D₁₃	—	2	4	no	—
190	C₄×D₁₃	—	2	1	no	—
191	C₄×D₁₃	—	2	1	no	—
192	C₄×D₁₃	—	2	1	no	—
193	C₄×D₁₃	—	2	1	no	—
194	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
195	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
196	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
197	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	#117	1	2	yes	—
201	C₈×C₁₃	#117	1	2	yes	—
202	#1055	—	2	1	no	—
203	#1055	—	2	1	no	—
204	#1055	#117	1	2	yes	—
205	#1055	#117	1	2	yes	—
206	C₂²×M₁₆	—	13	1	no	—
207	C₂³×C₈	—	13	1	no	—
208	C₂×#117	—	13	1	no	—
209	C₂×#107	—	13	2	no	—
210	C₂×#106	—	13	2	no	—
211	C₂×#106	—	13	2	no	—
212	C₂×#106	—	13	2	no	—
213	#405	—	13	1	no	—
214	#405	—	13	1	no	—
215	#405	—	13	1	no	—
216	#405	—	13	1	no	—
217	#405	—	13	1	no	—
218	#405	—	13	1	no	—
219	#405	—	13	1	no	—
220	#405	#261	1	1	yes	characteristic, complemented
221	C₂×#97	—	13	1	no	—
222	C₂×#97	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	#388	—	26	4	no	—
226	#387	—	26	4	no	—
227	#384	—	13	2	no	—
228	#382	—	13	2	no	—
229	#380	—	13	4	no	—
230	C₄×C₄⋊C₄	—	13	4	no	—
231	#340	—	13	4	no	—
232	#340	—	13	4	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₁₃	—	2	2	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	4	2	no	—
239	C₂×D₁₃	—	4	2	no	—
240	C₂×D₁₃	#532	1	1	yes	characteristic
241	C₂×D₁₃	#532	1	1	yes	characteristic
242	C₂×D₁₃	#577	1	4	yes	—
243	#261	—	8	4	no	—
244	#261	—	8	4	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
249	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
250	Dic₁₃	—	2	2	no	—
251	Dic₁₃	—	2	2	no	—
252	Dic₁₃	—	2	1	no	—
253	Dic₁₃	#533	1	1	yes	characteristic
254	Dic₁₃	#533	1	1	yes	characteristic
255	C₂³×C₄	—	13	1	no	—
256	C₂×M₁₆	—	13	1	no	—
257	C₂×M₁₆	—	13	1	no	—
258	C₂×M₁₆	—	13	1	no	—
259	C₂×M₁₆	—	26	2	no	—
260	C₂×M₁₆	—	26	2	no	—
261	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	1	no	—
265	C₂²×C₈	—	13	1	no	—
266	C₂²×C₈	—	13	1	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	26	2	no	—
270	C₂²×C₈	—	26	2	no	—
271	C₂²×C₈	C₂×#261	1	1	yes	characteristic
272	#117	—	13	1	no	—
273	#117	—	13	2	no	—
274	#117	—	13	2	no	—
275	#117	—	13	1	no	—
276	#117	—	13	1	no	—
277	#117	C₂×#261	1	1	yes	characteristic
278	C₂×C₄⋊C₄	—	13	2	no	—
279	C₂×C₄⋊C₄	—	13	4	no	—
280	C₂×C₄⋊C₄	—	13	4	no	—
281	C₂×C₄⋊C₄	—	26	4	no	—
282	C₂×C₂²⋊C₄	—	13	2	no	—
283	C₂×C₂²⋊C₄	—	26	4	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	26	4	no	—
287	#107	—	26	4	no	—
288	#106	—	26	4	no	—
289	#106	—	26	4	no	—
290	#106	—	26	4	no	—
291	#97	—	13	1	no	—
292	#97	—	13	1	no	—
293	#97	—	13	1	no	—
294	#97	—	13	1	no	—
295	#97	—	13	1	no	—
296	#97	—	13	1	no	—
297	#97	C₂×#261	1	1	yes	characteristic
298	#97	C₂×#261	1	1	yes	characteristic
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	13	1	no	—
303	C₄×C₈	—	13	1	no	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	C₂×#261	1	1	yes	characteristic
306	C₄×C₈	C₂×#261	1	1	yes	characteristic
307	#95	—	26	4	no	—
308	#95	—	26	4	no	—
309	#95	—	26	4	no	—
310	C₂×C₁₃	—	4	1	no	—
311	C₂×C₁₃	#2285	1	1	yes	characteristic
312	C₂×C₁₃	#2912	1	2	yes	—
313	D₁₃	—	4	1	no	—
314	D₁₃	#3173	1	2	yes	—
315	D₁₃	#3174	1	2	yes	—
316	C₂⁴	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	2	no	—
321	C₂²×C₄	—	13	2	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	26	1	no	—
325	C₂²×C₄	—	26	1	no	—
326	C₂²×C₄	—	26	1	no	—
327	C₂²×C₄	—	26	1	no	—
328	C₂²×C₄	—	26	4	no	—
329	C₂²×C₄	—	26	4	no	—
330	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	26	2	no	—
333	M₁₆	—	26	2	no	—
334	M₁₆	—	26	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	13	1	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	2	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	2	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	13	1	no	—
343	C₂×C₈	—	13	1	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	1	no	—
346	C₂×C₈	—	26	1	no	—
347	C₂×C₈	—	26	1	no	—
348	C₂×C₈	—	26	1	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	C₂²×#261	1	1	yes	characteristic
352	C₂×C₈	C₂²×#261	1	1	yes	characteristic
353	C₂×C₈	C₂²×#261	1	1	yes	characteristic
354	C₂×C₈	C₂²×#261	1	1	yes	characteristic
355	C₄⋊C₄	—	13	2	no	—
356	C₄⋊C₄	—	13	2	no	—
357	C₄⋊C₄	—	13	2	no	—
358	C₄⋊C₄	—	26	4	no	—
359	C₄⋊C₄	—	26	4	no	—
360	C₄⋊C₄	—	26	4	no	—
361	C₄⋊C₄	—	26	4	no	—
362	C₄⋊C₄	—	104	4	no	—
363	C₄⋊C₄	C₄⋊#261	1	2	yes	—
364	C₂²⋊C₄	—	13	2	no	—
365	C₂²⋊C₄	—	13	2	no	—
366	C₂²⋊C₄	—	13	2	no	—
367	C₂²⋊C₄	—	104	4	no	—
368	C₂²⋊C₄	C₄⋊#261	1	2	yes	—
369	C₄²	—	13	2	no	—
370	C₄²	—	13	2	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	104	4	no	—
374	C₄²	C₂²×#261	1	1	yes	characteristic
375	C₄²	C₂²×#261	1	1	yes	characteristic
376	C₁₃	#20820	1	1	yes	characteristic, complemented, Sylow
377	C₂³	—	13	1	no	—
378	C₂³	—	13	1	no	—
379	C₂³	—	26	4	no	—
380	C₂³	—	26	1	no	—
381	C₂³	—	26	1	no	—
382	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	2	no	—
391	C₂×C₄	—	13	2	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	1	no	—
395	C₂×C₄	—	26	4	no	—
396	C₂×C₄	—	26	4	no	—
397	C₂×C₄	—	26	1	no	—
398	C₂×C₄	—	26	1	no	—
399	C₂×C₄	—	26	1	no	—
400	C₂×C₄	—	26	1	no	—
401	C₂×C₄	—	26	1	no	—
402	C₂×C₄	—	26	1	no	—
403	C₂×C₄	—	52	4	no	—
404	C₂×C₄	—	52	4	no	—
405	C₂×C₄	—	52	4	no	—
406	C₂×C₄	—	52	4	no	—
407	C₂×C₄	—	52	4	no	—
408	C₂×C₄	—	52	4	no	—
409	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
410	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
411	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
412	C₂×C₄	C₂³×#261	1	1	yes	characteristic
413	C₈	—	2	1	no	—
414	C₈	—	2	1	no	—
415	C₈	—	13	2	no	—
416	C₈	—	13	2	no	—
417	C₈	—	26	1	no	—
418	C₈	—	26	1	no	—
419	C₈	#88237	1	2	yes	—
420	C₈	#88237	1	2	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	13	1	no	—
424	C₂²	—	13	1	no	—
425	C₂²	—	13	4	no	—
426	C₂²	—	26	1	no	—
427	C₂²	—	26	2	no	—
428	C₂²	—	52	2	no	—
429	C₂²	—	52	2	no	—
430	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	13	1	no	—
435	C₄	—	13	1	no	—
436	C₄	—	26	1	no	—
437	C₄	—	26	2	no	—
438	C₄	—	26	2	no	—
439	C₄	—	104	4	no	—
440	C₄	—	104	4	no	—
441	C₄	C₂×#88237	1	1	yes	characteristic
442	C₄	C₂×#88237	1	1	yes	characteristic
443	C₂	—	4	1	no	—
444	C₂	—	13	2	no	—
445	C₂	—	13	2	no	—
446	C₂	—	52	1	no	—
447	C₂	#13131285	1	1	yes	characteristic
448	C₂	#13131490	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20820
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13130773	C₂	semidirect
3. #13130771	C₂	semidirect
4. #13130759	C₂	semidirect
7. #13130650	C₂	semidirect
8. C₄×#88101	C₂	semidirect
23. C₁₃×#405	C₄	semidirect
24. #11718783	C₄	semidirect
25. #11718762	C₄	semidirect
26. #11718658	C₄	semidirect
27. #11718369	C₄	semidirect
28. #11718369	C₄	semidirect
31. #11718350	C₄	semidirect
32. #11718350	C₄	semidirect
220. #405	#261	semidirect
376. C₁₃	#20820	semidirect

Maximal subgroups

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

subgroup	index
#13131314	2
#13130773	2
#13130771	2
#13130759	2
#13130714	2
#13130712	2
#13130650	2
C₄×#88101	2
D₁₃×#405	2
#20820	13