Subgroups — #16792626

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#13130054	C₂	1	4	yes	maximal, complemented
4	#13130053	C₂	1	4	yes	maximal, complemented
5	#13130032	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130032	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130030	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
10	C₂×D₁₃⋊M₁₆	C₄	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#11719125	C₄	1	2	yes	—
13	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
14	C₄×#6122	C₄	1	2	yes	—
15	C₄×#6122	C₂²	1	2	yes	—
16	#11719119	C₂²	1	2	yes	—
17	#11719051	C₄	1	2	yes	—
18	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
19	#11719049	C₂²	1	2	yes	—
20	C₄×#6118	C₄	1	2	yes	—
21	C₄×#6118	C₂²	1	2	yes	—
22	#11719047	C₄	1	2	yes	—
23	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
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	C₁₃×#431	C₄	1	1	yes	characteristic
28	#11718586	C₄	1	1	yes	characteristic
29	#11718494	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
32	#11718379	C₂²	1	2	yes	—
33	#11718346	C₄	1	1	yes	characteristic
34	#11718346	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	#1057⋊C₈	C₂²	1	4	yes	complemented
38	#1057⋊C₈	C₂²	1	4	yes	complemented
39	#11718251	C₂²	1	4	yes	complemented
40	C₈×#1057	C₂²	1	4	yes	complemented
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×#6122	C₂×C₄	1	4	yes	—
45	D₁₃⋊M₁₆	—	2	8	no	—
46	C₂×#6118	C₂×C₄	1	4	yes	—
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×C₈×D₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₂²⋊#1057	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	#88110	C₂×C₄	1	4	yes	—
70	C₄⋊#1057	C₂×C₄	1	4	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	2	yes	—
76	C₄×#1057	C₂³	1	2	yes	—
77	C₄×#1057	C₂³	1	2	yes	—
78	C₄×#1057	C₂³	1	2	yes	—
79	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
80	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂²⋊#1055	C₂×C₄	1	2	yes	—
84	#88060	C₂×C₄	1	2	yes	—
85	#88060	C₂×C₄	1	2	yes	—
86	#88054	C₂×C₄	1	2	yes	—
87	#88054	C₂×C₄	1	2	yes	—
88	C₈×Dic₁₃	C₂³	1	2	yes	—
89	C₈×Dic₁₃	C₂³	1	2	yes	—
90	C₄⋊#1055	C₂×C₄	1	2	yes	—
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	C₄×#1055	C₂×C₄	1	1	yes	characteristic
93	C₂×#1453	—	13	1	no	maximal, Sylow
94	C₂³×D₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	—	2	4	no	—
102	C₂×C₄×D₁₃	—	2	4	no	—
103	C₂×C₄×D₁₃	—	2	4	no	—
104	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₄²	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×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	#6122	—	2	8	no	—
117	C₂×#1057	C₂²×C₄	1	4	yes	—
118	C₂×#1057	C₂²×C₄	1	4	yes	—
119	C₂×#1057	C₂²×C₄	1	4	yes	—
120	C₂×#1057	C₂²×C₄	1	4	yes	—
121	#6118	—	2	8	no	—
122	D₁₃⋊C₈	—	2	4	no	—
123	D₁₃⋊C₈	—	2	4	no	—
124	D₁₃⋊C₈	—	2	4	no	—
125	D₁₃⋊C₈	M₁₆	1	8	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₃	C₄²	1	1	yes	characteristic
129	C₄²×C₁₃	C₄²	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄²	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	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
144	C₂×#1055	C₂²×C₄	1	2	yes	—
145	C₂×#1055	C₂²×C₄	1	2	yes	—
146	C₈×D₁₃	—	2	4	no	—
147	C₈×D₁₃	—	2	4	no	—
148	C₂×#431	—	13	1	no	—
149	C₂×#431	—	13	1	no	—
150	C₂×C₄×M₁₆	—	13	1	no	—
151	#1453	—	13	4	no	—
152	#1453	—	13	4	no	—
153	C₂×#322	—	13	1	no	—
154	C₂×#322	—	13	1	no	—
155	C₂×#322	—	13	1	no	—
156	C₂×C₈²	—	13	1	no	—
157	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₁₃	—	2	2	no	—
159	C₂²×D₁₃	—	2	2	no	—
160	C₂²×D₁₃	—	2	2	no	—
161	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
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	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
191	C₄×D₁₃	#131	1	4	yes	—
192	C₄×D₁₃	#131	1	4	yes	—
193	#1057	—	2	4	no	—
194	#1057	—	2	4	no	—
195	#1057	—	2	4	no	—
196	#1057	C₂×M₁₆	1	8	yes	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	2	2	no	—
199	#1055	—	2	2	no	—
200	#1055	—	2	2	no	—
201	C₂²×M₁₆	—	13	2	no	—
202	C₂²×C₄²	—	13	1	no	—
203	#431	—	13	2	no	—
204	#431	—	13	2	no	—
205	#431	—	13	2	no	—
206	#431	—	13	2	no	—
207	#431	—	13	1	no	—
208	#431	—	13	2	no	—
209	#431	—	13	2	no	—
210	#431	—	13	1	no	—
211	#431	—	13	1	no	—
212	#431	#261	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	13	2	no	—
214	C₂×C₄⋊C₈	—	13	2	no	—
215	C₂×C₂²⋊C₈	—	13	2	no	—
216	C₂×C₂²⋊C₈	—	13	2	no	—
217	C₄×M₁₆	—	13	2	no	—
218	C₄×M₁₆	—	13	2	no	—
219	C₄×M₁₆	—	13	2	no	—
220	C₄×M₁₆	—	13	2	no	—
221	C₂×#97	—	13	2	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	C₂×C₄×C₈	—	13	1	no	—
226	C₂×C₄×C₈	—	13	1	no	—
227	C₂×C₄×C₈	—	13	1	no	—
228	#322	—	13	4	no	—
229	#322	—	13	4	no	—
230	#322	—	13	4	no	—
231	C₈²	—	13	4	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	—	4	4	no	—
240	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
241	C₂×D₁₃	#405	1	2	yes	—
242	C₂×D₁₃	#405	1	2	yes	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
247	C₄×C₁₃	#405	1	2	yes	—
248	C₄×C₁₃	C₂×#131	1	2	yes	—
249	Dic₁₃	—	2	1	no	—
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	#405	1	2	yes	—
253	Dic₁₃	C₂²×M₁₆	1	2	yes	—
254	Dic₁₃	C₂×#131	1	2	yes	—
255	C₂³×C₄	—	13	1	no	—
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	—	13	1	no	—
258	C₂×M₁₆	—	13	4	no	—
259	C₂×M₁₆	—	13	4	no	—
260	C₂×M₁₆	—	26	8	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	13	2	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	13	2	no	—
266	C₂²×C₈	—	13	2	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	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	C₂×#261	1	1	yes	characteristic
279	C₄⋊C₈	—	13	4	no	—
280	C₄⋊C₈	—	13	4	no	—
281	C₄⋊C₈	—	13	2	no	—
282	C₄⋊C₈	—	13	2	no	—
283	C₄⋊C₈	—	13	2	no	—
284	C₄⋊C₈	C₂×#261	1	2	yes	—
285	C₂²⋊C₈	—	13	4	no	—
286	C₂²⋊C₈	—	13	4	no	—
287	C₂²⋊C₈	—	13	2	no	—
288	C₂²⋊C₈	—	13	2	no	—
289	C₂²⋊C₈	—	13	2	no	—
290	C₂²⋊C₈	C₂×#261	1	2	yes	—
291	#97	—	13	4	no	—
292	#97	—	13	4	no	—
293	C₄×C₈	—	13	2	no	—
294	C₄×C₈	—	13	2	no	—
295	C₄×C₈	—	13	2	no	—
296	C₄×C₈	—	13	2	no	—
297	C₄×C₈	—	13	2	no	—
298	C₄×C₈	—	13	2	no	—
299	C₄×C₈	—	13	2	no	—
300	C₄×C₈	—	13	2	no	—
301	C₄×C₈	—	13	2	no	—
302	C₄×C₈	—	13	2	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	C₂×C₁₃	—	4	1	no	—
308	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
311	D₁₃	—	4	1	no	—
312	D₁₃	#1453	1	4	yes	complemented
313	C₂⁴	—	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	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	26	4	no	—
330	C₂²×C₄	—	26	4	no	—
331	C₂²×C₄	—	26	4	no	—
332	C₂²×C₄	C₄×#261	1	1	yes	characteristic
333	C₂²×C₄	C₄×#261	1	1	yes	characteristic
334	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
335	M₁₆	—	26	8	no	—
336	M₁₆	—	26	8	no	—
337	C₂×C₈	—	13	4	no	—
338	C₂×C₈	—	13	8	no	—
339	C₂×C₈	—	13	4	no	—
340	C₂×C₈	—	13	4	no	—
341	C₂×C₈	—	13	4	no	—
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	26	4	no	—
345	C₂×C₈	—	26	4	no	—
346	C₂×C₈	—	26	4	no	—
347	C₂×C₈	—	26	4	no	—
348	C₂×C₈	—	26	4	no	—
349	C₂×C₈	C₂²×#261	1	2	yes	—
350	C₂×C₈	C₂²×#261	1	2	yes	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	C₄×#261	1	1	yes	characteristic
364	C₄²	C₄×#261	1	1	yes	characteristic
365	C₄²	C₂²×#261	1	1	yes	characteristic
366	C₄²	C₂²×#261	1	1	yes	characteristic
367	C₁₃	C₂×#1453	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	13	1	no	—
369	C₂³	—	13	1	no	—
370	C₂³	—	26	2	no	—
371	C₂³	—	26	2	no	—
372	C₂³	—	26	2	no	—
373	C₂³	C₂×C₄×#261	1	1	yes	characteristic
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	4	no	—
381	C₂×C₄	—	13	4	no	—
382	C₂×C₄	—	13	4	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
399	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
403	C₂×C₄	C₂³×#261	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	2	2	no	—
406	C₈	—	13	8	no	—
407	C₈	—	26	4	no	—
408	C₈	—	26	4	no	—
409	C₈	—	26	4	no	—
410	C₈	—	26	2	no	—
411	C₈	—	26	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	13	2	no	—
416	C₂²	—	13	2	no	—
417	C₂²	—	13	2	no	—
418	C₂²	—	26	1	no	—
419	C₂²	—	26	1	no	—
420	C₂²	—	26	1	no	—
421	C₂²	—	52	4	no	—
422	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	13	2	no	—
427	C₄	—	13	2	no	—
428	C₄	—	13	2	no	—
429	C₄	—	26	1	no	—
430	C₄	—	26	1	no	—
431	C₄	—	26	1	no	—
432	C₄	#11719089	1	2	yes	—
433	C₄	M₁₆×#261	1	2	yes	—
434	C₄	D₁₃⋊#131	1	2	yes	—
435	C₂	—	4	1	no	—
436	C₂	—	13	4	no	—
437	C₂	—	52	1	no	—
438	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
439	C₂	C₂×#11719089	1	1	yes	characteristic
440	C₂	#13131396	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	C₂×#1453
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130054	C₂	semidirect
4. #13130053	C₂	semidirect
5. #13130032	C₂	semidirect
6. #13130032	C₂	semidirect
7. #13130030	C₂	semidirect
8. C₈×D₁₃⋊C₈	C₂	semidirect
37. #1057⋊C₈	C₂²	semidirect
38. #1057⋊C₈	C₂²	semidirect
39. #11718251	C₂²	semidirect
40. C₈×#1057	C₂²	semidirect
312. D₁₃	#1453	semidirect
367. C₁₃	C₂×#1453	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
C₄×D₁₃⋊M₁₆	2
#13130054	2
#13130053	2
#13130032	2
#13130030	2
C₈×D₁₃⋊C₈	2
D₁₃×#431	2
C₂×#1453	13