Subgroups — #16792635

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131515	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13130051	C₂	1	2	yes	maximal, complemented
4	#13130048	C₂	1	2	yes	maximal, complemented
5	#13130044	C₂	1	2	yes	maximal, complemented
6	#13130041	C₂	1	2	yes	maximal, complemented
7	#13130038	C₂	1	2	yes	maximal, complemented
8	#13130034	C₂	1	2	yes	maximal, complemented
9	#13123466	C₂	1	1	yes	maximal, characteristic
10	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#11719128	C₄	1	2	yes	—
13	#11719127	C₄	1	2	yes	—
14	#11719125	C₂²	1	2	yes	—
15	C₂×C₄×#1057	C₄	1	2	yes	—
16	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
17	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
18	#11719055	C₄	1	2	yes	—
19	#11719053	C₄	1	2	yes	—
20	#11719049	C₂²	1	2	yes	—
21	C₄×#6118	C₂²	1	2	yes	—
22	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
23	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
24	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×#432	C₄	1	1	yes	characteristic
29	#11718587	C₄	1	1	yes	characteristic
30	#11718498	C₄	1	2	yes	—
31	#11718494	C₂²	1	2	yes	—
32	#11718387	C₄	1	2	yes	—
33	#11718379	C₂²	1	2	yes	—
34	#11718368	C₂²	1	2	yes	—
35	#11718366	C₄	1	2	yes	—
36	#1057⋊C₈	C₂²	1	4	yes	complemented
37	#1057⋊C₈	C₂²	1	4	yes	complemented
38	#11718251	C₂²	1	4	yes	complemented
39	C₈×#1057	C₂²	1	4	yes	complemented
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×#1057	C₂×C₄	1	2	yes	—
44	C₂²×#1057	C₂×C₄	1	2	yes	—
45	C₂×#6118	C₂×C₄	1	4	yes	—
46	C₂×D₁₃⋊C₈	—	2	8	no	—
47	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
48	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
49	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
50	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6094	C₂×C₄	1	4	yes	—
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₁₃	C₂³	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₂²⋊#1057	C₂×C₄	1	4	yes	—
65	#88112	C₂×C₄	1	4	yes	—
66	#88112	C₂×C₄	1	4	yes	—
67	#88111	C₂×C₄	1	4	yes	—
68	#88110	C₂×C₄	1	4	yes	—
69	C₄×#1057	C₂×C₄	1	2	yes	—
70	C₄×#1057	C₂×C₄	1	2	yes	—
71	C₄×#1057	C₂×C₄	1	2	yes	—
72	C₄×#1057	C₂×C₄	1	2	yes	—
73	C₄×#1057	C₂×C₄	1	2	yes	—
74	C₄×#1057	C₂×C₄	1	2	yes	—
75	C₄×#1057	C₂³	1	1	yes	characteristic
76	C₄×#1057	C₂³	1	4	yes	—
77	C₄×#1057	C₂³	1	1	yes	characteristic
78	C₄×#1057	C₂³	1	1	yes	characteristic
79	C₄×#1057	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
81	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
82	C₁₃×#97	C₂×C₄	1	2	yes	—
83	C₂²⋊#1055	C₂×C₄	1	2	yes	—
84	#88060	C₂×C₄	1	4	yes	—
85	#88054	C₂×C₄	1	4	yes	—
86	C₈×Dic₁₃	C₂³	1	4	yes	—
87	C₄⋊#1055	C₂×C₄	1	2	yes	—
88	#88043	C₂×C₄	1	2	yes	—
89	#17323	—	13	1	no	maximal, Sylow
90	C₂³×D₁₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	—	2	4	no	—
98	C₂×C₄×D₁₃	—	2	4	no	—
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×#1057	—	2	4	no	—
113	C₂×#1057	M₁₆	1	8	yes	complemented
114	C₂×#1057	C₂²×C₄	1	2	yes	—
115	C₂×#1057	C₂²×C₄	1	2	yes	—
116	C₂×#1057	C₂²×C₄	1	8	yes	—
117	C₂×#1057	C₂²×C₄	1	2	yes	—
118	C₂×#1057	C₂²×C₄	1	2	yes	—
119	#6118	—	2	8	no	—
120	D₁₃⋊C₈	—	2	4	no	—
121	D₁₃⋊C₈	—	2	4	no	—
122	D₁₃⋊C₈	—	2	4	no	—
123	D₁₃⋊C₈	—	2	4	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
125	C₄²×C₁₃	C₄²	1	1	yes	characteristic
126	C₄²×C₁₃	C₄²	1	1	yes	characteristic
127	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×#1055	C₂²×C₄	1	4	yes	—
142	#6094	—	2	8	no	—
143	#2920	—	13	1	no	—
144	#2920	—	13	1	no	—
145	C₂²×C₄×C₈	—	13	1	no	—
146	#1452	—	13	2	no	—
147	#1451	—	13	2	no	—
148	#1451	—	13	2	no	—
149	#1450	—	13	2	no	—
150	C₈×M₁₆	—	13	2	no	—
151	C₈×M₁₆	—	13	2	no	—
152	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂²×D₁₃	—	2	2	no	—
154	C₂²×D₁₃	—	2	2	no	—
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
174	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	#131	1	4	yes	—
187	C₄×D₁₃	#131	1	4	yes	—
188	#1057	—	2	2	no	—
189	#1057	—	2	2	no	—
190	#1057	—	2	8	no	—
191	#1057	C₂×M₁₆	1	4	yes	—
192	#1057	C₂×M₁₆	1	4	yes	—
193	C₈×C₁₃	—	2	4	no	—
194	#1055	—	2	4	no	—
195	C₂³×C₈	—	13	2	no	—
196	C₂²×C₄²	—	13	1	no	—
197	#432	—	13	2	no	—
198	#432	—	13	2	no	—
199	#432	—	13	1	no	—
200	#432	—	13	2	no	—
201	#432	#261	1	1	yes	characteristic
202	#431	—	13	2	no	—
203	#431	—	13	2	no	—
204	#431	—	13	2	no	—
205	#431	—	13	2	no	—
206	#423	—	13	2	no	—
207	#423	—	13	2	no	—
208	#407	—	13	2	no	—
209	#407	—	13	2	no	—
210	C₄×M₁₆	—	13	2	no	—
211	C₄×M₁₆	—	13	2	no	—
212	C₂×C₄×C₈	—	13	2	no	—
213	C₂×C₄×C₈	—	13	2	no	—
214	C₂×C₄×C₈	—	13	1	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	C₂×C₄×C₈	—	13	1	no	—
217	C₂×C₄×C₈	—	13	1	no	—
218	C₂×C₄×C₈	—	13	1	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	—	13	2	no	—
221	#322	—	13	4	no	—
222	#322	—	13	4	no	—
223	#322	—	13	4	no	—
224	C₈²	—	13	4	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
228	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
229	C₂×D₁₃	—	2	8	no	—
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	—	2	1	no	—
233	C₂×D₁₃	—	2	1	no	—
234	C₂×D₁₃	#405	1	2	yes	—
235	C₂×D₁₃	#405	1	2	yes	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	#405	1	2	yes	—
241	C₄×C₁₃	C₂×#131	1	2	yes	—
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	C₄×M₁₆	1	2	yes	—
245	Dic₁₃	#405	1	2	yes	—
246	Dic₁₃	C₂²×M₁₆	1	2	yes	—
247	Dic₁₃	C₂×#131	1	2	yes	—
248	C₂³×C₄	—	13	1	no	—
249	C₂³×C₄	—	13	1	no	—
250	C₂³×C₄	—	13	1	no	—
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	13	4	no	—
253	C₂²×C₈	—	13	2	no	—
254	C₂²×C₈	—	13	2	no	—
255	C₂²×C₈	—	13	2	no	—
256	C₂²×C₈	—	13	2	no	—
257	C₂²×C₈	—	13	2	no	—
258	C₂²×C₈	—	13	2	no	—
259	C₂²×C₈	—	26	8	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	C₂×#261	1	1	yes	characteristic
272	C₄⋊C₈	—	13	4	no	—
273	C₄⋊C₈	—	13	4	no	—
274	C₄⋊C₈	—	13	4	no	—
275	C₄⋊C₈	—	13	2	no	—
276	C₄⋊C₈	C₂×#261	1	2	yes	—
277	C₂²⋊C₈	—	13	4	no	—
278	C₂²⋊C₈	—	13	4	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	C₂²⋊C₈	—	13	4	no	—
281	C₂²⋊C₈	C₂×#261	1	2	yes	—
282	#97	—	13	4	no	—
283	#97	—	13	2	no	—
284	#97	C₂×#261	1	2	yes	—
285	C₄×C₈	—	13	2	no	—
286	C₄×C₈	—	13	2	no	—
287	C₄×C₈	—	13	2	no	—
288	C₄×C₈	—	13	2	no	—
289	C₄×C₈	—	13	2	no	—
290	C₄×C₈	—	13	2	no	—
291	C₄×C₈	—	13	1	no	—
292	C₄×C₈	—	13	4	no	—
293	C₄×C₈	—	13	1	no	—
294	C₄×C₈	—	13	1	no	—
295	C₄×C₈	—	13	1	no	—
296	C₄×C₈	—	13	4	no	—
297	C₂×C₁₃	—	2	2	no	—
298	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
299	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
301	D₁₃	—	2	2	no	—
302	D₁₃	—	2	2	no	—
303	C₂⁴	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	26	4	no	—
320	C₂²×C₄	—	26	4	no	—
321	C₂²×C₄	—	26	4	no	—
322	C₂²×C₄	C₄×#261	1	1	yes	characteristic
323	C₂²×C₄	C₄×#261	1	1	yes	characteristic
324	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
325	M₁₆	—	26	8	no	—
326	M₁₆	—	26	8	no	—
327	C₂×C₈	—	13	2	no	—
328	C₂×C₈	—	13	2	no	—
329	C₂×C₈	—	13	8	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	13	2	no	—
332	C₂×C₈	—	13	8	no	—
333	C₂×C₈	—	13	4	no	—
334	C₂×C₈	—	26	4	no	—
335	C₂×C₈	—	26	4	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	—	26	4	no	—
338	C₂×C₈	—	26	4	no	—
339	C₂×C₈	C₂²×#261	1	4	yes	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	1	no	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	C₄×#261	1	1	yes	characteristic
353	C₄²	C₄×#261	1	1	yes	characteristic
354	C₄²	C₂²×#261	1	1	yes	characteristic
355	C₄²	C₂²×#261	1	1	yes	characteristic
356	C₁₃	#17323	1	1	yes	characteristic, complemented, Sylow
357	C₂³	—	13	1	no	—
358	C₂³	—	13	1	no	—
359	C₂³	—	26	2	no	—
360	C₂³	—	26	2	no	—
361	C₂³	—	26	2	no	—
362	C₂³	C₂×C₄×#261	1	1	yes	characteristic
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	13	4	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	4	no	—
372	C₂×C₄	—	13	4	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	2	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	2	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
388	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
389	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
392	C₂×C₄	C₂³×#261	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	13	4	no	—
395	C₈	—	13	4	no	—
396	C₈	—	26	2	no	—
397	C₈	—	26	2	no	—
398	C₈	—	26	8	no	—
399	C₈	—	26	4	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	13	2	no	—
403	C₂²	—	13	2	no	—
404	C₂²	—	26	8	no	—
405	C₂²	—	26	1	no	—
406	C₂²	—	26	1	no	—
407	C₂²	—	26	1	no	—
408	C₂²	—	26	1	no	—
409	C₂²	M₁₆×#261	1	2	yes	—
410	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	13	2	no	—
416	C₄	—	13	2	no	—
417	C₄	—	13	2	no	—
418	C₄	—	13	2	no	—
419	C₄	—	26	1	no	—
420	C₄	—	26	1	no	—
421	C₄	#11719099	1	2	yes	—
422	C₄	D₁₃⋊#131	1	2	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	26	2	no	—
425	C₂	—	26	2	no	—
426	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
427	C₂	#13131396	1	1	yes	characteristic
428	C₂	C₂×#11719099	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#432	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#432	#261
hypocenter	C₁₃	#17323
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
3. #13130051	C₂	semidirect
4. #13130048	C₂	semidirect
5. #13130044	C₂	semidirect
6. #13130041	C₂	semidirect
7. #13130038	C₂	semidirect
8. #13130034	C₂	semidirect
36. #1057⋊C₈	C₂²	semidirect
37. #1057⋊C₈	C₂²	semidirect
38. #11718251	C₂²	semidirect
39. C₈×#1057	C₂²	semidirect
113. C₂×#1057	M₁₆	semidirect
356. C₁₃	#17323	semidirect

Maximal subgroups

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

subgroup	index
#13131515	2
C₂×C₄×D₁₃⋊C₈	2
#13130051	2
#13130048	2
#13130044	2
#13130041	2
#13130038	2
#13130034	2
#13123466	2
#17323	13