Subgroups — D₁₃⋊#1454 #16792632

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 436 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	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
3	#13130058	C₂	1	4	yes	maximal, complemented
4	#13130057	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×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719125	C₄	1	2	yes	—
12	#11719125	C₂²	1	2	yes	—
13	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
14	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
15	#11719119	C₄	1	2	yes	—
16	#11719119	C₂²	1	2	yes	—
17	#11719051	C₄	1	2	yes	—
18	#11719051	C₂²	1	2	yes	—
19	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
20	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
21	#11719049	C₄	1	2	yes	—
22	#11719049	C₂²	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×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
45	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
46	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	C₂²⋊#1057	C₂×C₄	1	4	yes	—
63	C₂²⋊#1057	C₂×C₄	1	4	yes	—
64	#88112	C₂×C₄	1	4	yes	—
65	#88112	C₂×C₄	1	4	yes	—
66	#88111	C₂×C₄	1	4	yes	—
67	#88111	C₂×C₄	1	4	yes	—
68	C₄⋊#1057	C₂×C₄	1	4	yes	—
69	C₄⋊#1057	C₂×C₄	1	4	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	C₂³	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	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊#1055	C₂×C₄	1	2	yes	—
83	#88060	C₂×C₄	1	2	yes	—
84	#88060	C₂×C₄	1	2	yes	—
85	#88054	C₂×C₄	1	2	yes	—
86	#88054	C₂×C₄	1	2	yes	—
87	C₈×Dic₁₃	C₂³	1	2	yes	—
88	C₈×Dic₁₃	C₂³	1	2	yes	—
89	C₄⋊#1055	C₂×C₄	1	2	yes	—
90	C₄×#1055	C₂×C₄	1	1	yes	characteristic
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	C₂×#1454	—	13	1	no	maximal, Sylow
93	C₂³×D₁₃	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	—	2	4	no	—
101	C₂×C₄×D₁₃	—	2	4	no	—
102	C₂×C₄×D₁₃	—	2	4	no	—
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	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	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×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×#1057	C₂²×C₄	1	4	yes	—
116	C₂×#1057	C₂²×C₄	1	4	yes	—
117	C₂×#1057	C₂²×C₄	1	4	yes	—
118	C₂×#1057	C₂²×C₄	1	4	yes	—
119	D₁₃⋊C₈	—	2	4	no	—
120	D₁₃⋊C₈	—	2	4	no	—
121	D₁₃⋊C₈	—	2	4	no	—
122	D₁₃⋊C₈	—	2	4	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	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	2	yes	—
142	C₂×#1055	C₂²×C₄	1	2	yes	—
143	C₈×D₁₃	—	2	4	no	—
144	C₈×D₁₃	—	2	4	no	—
145	C₂×#431	—	13	1	no	—
146	C₂×#431	—	13	1	no	—
147	C₂×#431	—	13	1	no	—
148	#1454	—	13	4	no	—
149	#1454	—	13	4	no	—
150	C₂×#322	—	13	1	no	—
151	C₂×#322	—	13	1	no	—
152	C₂×#322	—	13	1	no	—
153	C₂×C₈²	—	13	1	no	—
154	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	—	2	2	no	—
157	C₂²×D₁₃	—	2	2	no	—
158	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
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	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×Dic₁₃	—	2	2	no	—
170	C₂×Dic₁₃	—	2	2	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
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	—	2	2	no	—
187	C₄×D₁₃	#131	1	4	yes	—
188	C₄×D₁₃	#131	1	4	yes	—
189	C₄×D₁₃	#131	1	4	yes	—
190	#1057	—	2	4	no	—
191	#1057	—	2	4	no	—
192	#1057	—	2	4	no	—
193	#1057	—	2	4	no	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	2	2	no	—
196	#1055	—	2	2	no	—
197	#1055	—	2	2	no	—
198	C₂²×C₄²	—	13	1	no	—
199	#431	—	13	2	no	—
200	#431	—	13	2	no	—
201	#431	—	13	2	no	—
202	#431	—	13	2	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×C₄⋊C₈	—	13	2	no	—
216	C₂×C₂²⋊C₈	—	13	2	no	—
217	C₂×C₂²⋊C₈	—	13	2	no	—
218	C₂×C₂²⋊C₈	—	13	2	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	#322	—	13	4	no	—
226	#322	—	13	4	no	—
227	#322	—	13	4	no	—
228	C₈²	—	13	4	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
233	C₂×D₁₃	—	2	1	no	—
234	C₂×D₁₃	—	2	1	no	—
235	C₂×D₁₃	—	2	1	no	—
236	C₂×D₁₃	—	4	4	no	—
237	C₂×D₁₃	#405	1	2	yes	—
238	C₂×D₁₃	#405	1	2	yes	—
239	C₂×D₁₃	#405	1	2	yes	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	#405	1	2	yes	—
244	C₄×C₁₃	#405	1	2	yes	—
245	C₄×C₁₃	C₂×#131	1	2	yes	—
246	Dic₁₃	—	2	1	no	—
247	Dic₁₃	—	2	1	no	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	#405	1	2	yes	—
250	Dic₁₃	C₂×#131	1	2	yes	—
251	Dic₁₃	C₂×#131	1	2	yes	—
252	C₂³×C₄	—	13	1	no	—
253	C₂³×C₄	—	13	1	no	—
254	C₂³×C₄	—	13	1	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	—	13	2	no	—
260	C₂²×C₈	—	13	2	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	—	13	1	no	—
272	C₂×C₄²	C₂×#261	1	1	yes	characteristic
273	C₄⋊C₈	—	13	4	no	—
274	C₄⋊C₈	—	13	4	no	—
275	C₄⋊C₈	—	13	4	no	—
276	C₄⋊C₈	—	13	4	no	—
277	C₄⋊C₈	—	13	2	no	—
278	C₄⋊C₈	—	13	2	no	—
279	C₄⋊C₈	—	13	2	no	—
280	C₄⋊C₈	C₂×#261	1	2	yes	—
281	C₂²⋊C₈	—	13	4	no	—
282	C₂²⋊C₈	—	13	4	no	—
283	C₂²⋊C₈	—	13	4	no	—
284	C₂²⋊C₈	—	13	4	no	—
285	C₂²⋊C₈	—	13	2	no	—
286	C₂²⋊C₈	—	13	2	no	—
287	C₂²⋊C₈	—	13	2	no	—
288	C₂²⋊C₈	C₂×#261	1	2	yes	—
289	C₄×C₈	—	13	2	no	—
290	C₄×C₈	—	13	2	no	—
291	C₄×C₈	—	13	2	no	—
292	C₄×C₈	—	13	2	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	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	C₂×#261	1	1	yes	characteristic
302	C₄×C₈	C₂×#261	1	1	yes	characteristic
303	C₂×C₁₃	—	4	1	no	—
304	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
305	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
307	D₁₃	—	4	1	no	—
308	D₁₃	#1454	1	4	yes	complemented
309	C₂⁴	—	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	—	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	—	26	4	no	—
326	C₂²×C₄	—	26	4	no	—
327	C₂²×C₄	—	26	4	no	—
328	C₂²×C₄	C₄×#261	1	1	yes	characteristic
329	C₂²×C₄	C₄×#261	1	1	yes	characteristic
330	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
331	C₂×C₈	—	13	4	no	—
332	C₂×C₈	—	13	4	no	—
333	C₂×C₈	—	13	4	no	—
334	C₂×C₈	—	13	4	no	—
335	C₂×C₈	—	13	2	no	—
336	C₂×C₈	—	13	2	no	—
337	C₂×C₈	—	26	4	no	—
338	C₂×C₈	—	26	4	no	—
339	C₂×C₈	—	26	4	no	—
340	C₂×C₈	—	26	4	no	—
341	C₂×C₈	—	26	4	no	—
342	C₂×C₈	—	26	4	no	—
343	C₂×C₈	C₂²×#261	1	2	yes	—
344	C₂×C₈	C₂²×#261	1	2	yes	—
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	—	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	C₄×#261	1	1	yes	characteristic
358	C₄²	C₄×#261	1	1	yes	characteristic
359	C₄²	C₂²×#261	1	1	yes	characteristic
360	C₄²	C₂²×#261	1	1	yes	characteristic
361	C₁₃	C₂×#1454	1	1	yes	characteristic, complemented, Sylow
362	C₂³	—	13	1	no	—
363	C₂³	—	13	1	no	—
364	C₂³	—	26	2	no	—
365	C₂³	—	26	2	no	—
366	C₂³	—	26	2	no	—
367	C₂³	C₂×C₄×#261	1	1	yes	characteristic
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	4	no	—
375	C₂×C₄	—	13	4	no	—
376	C₂×C₄	—	13	4	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	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	—	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	C₂×C₄×#261	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
396	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
397	C₂×C₄	C₂³×#261	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	26	4	no	—
401	C₈	—	26	4	no	—
402	C₈	—	26	4	no	—
403	C₈	—	26	4	no	—
404	C₈	—	26	2	no	—
405	C₈	—	26	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	13	2	no	—
410	C₂²	—	13	2	no	—
411	C₂²	—	13	2	no	—
412	C₂²	—	26	1	no	—
413	C₂²	—	26	1	no	—
414	C₂²	—	26	1	no	—
415	C₂²	—	52	4	no	—
416	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	13	2	no	—
421	C₄	—	13	2	no	—
422	C₄	—	13	2	no	—
423	C₄	—	26	1	no	—
424	C₄	—	26	1	no	—
425	C₄	—	26	1	no	—
426	C₄	#11719089	1	2	yes	—
427	C₄	#11719099	1	2	yes	—
428	C₄	D₁₃⋊#131	1	2	yes	—
429	C₂	—	4	1	no	—
430	C₂	—	13	4	no	—
431	C₂	—	52	1	no	—
432	C₂	C₂×#11719089	1	1	yes	characteristic
433	C₂	#13131396	1	1	yes	characteristic
434	C₂	C₂×#11719099	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×#1454
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. #13130058	C₂	semidirect
4. #13130057	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
308. D₁₃	#1454	semidirect
361. C₁₃	C₂×#1454	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
#13130058	2
#13130057	2
#13130032	2
#13130030	2
C₈×D₁₃⋊C₈	2
D₁₃×#431	2
C₂×#1454	13

Subgroups — D13⋊#1454 #16792632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1454 #16792632