Subgroups — C₁₃×#29114 #15715453

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1935	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1825	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1788	C₂	1	2	yes	maximal
11	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#103	C₂²	1	2	yes	—
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	2	yes	—
22	C₁₃×#391	C₂²	1	1	yes	characteristic
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#386	—	2	2	no	—
29	C₁₃×#385	—	2	2	no	—
30	C₁₃×#382	C₂²	1	1	yes	characteristic
31	C₁₃×#380	C₂²	1	2	yes	—
32	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	4	no	—
42	C₂×C₁₃×#41	—	4	2	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	D₄	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×#125	—	4	2	no	—
52	C₁₃×#117	—	2	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	4	2	no	—
65	C₂×C₄²×C₁₃	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#103	—	2	4	no	—
69	C₁₃×#103	—	4	2	no	—
70	C₁₃×#102	—	2	4	no	—
71	C₁₃×#102	—	4	2	no	—
72	C₁₃×C₂²⋊C₈	—	2	4	no	—
73	C₁₃×#97	—	4	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	#29114	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	—	2	1	no	—
81	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₁₃×#41	—	4	8	no	—
83	C₁₃×#41	—	4	8	no	—
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	#41	1	2	yes	—
88	C₂×D₄×C₁₃	—	2	4	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	#41	1	2	yes	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₂²⋊C₄	—	4	4	no	—
129	C₁₃×C₂²⋊C₄	—	4	4	no	—
130	C₁₃×C₂²⋊C₄	—	4	4	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	4	2	no	—
135	C₄²×C₁₃	—	4	2	no	—
136	#2851	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2297	C₂×C₁₃	1	1	yes	characteristic
138	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#1936	C₂×C₁₃	1	2	yes	complemented
143	#1935	C₂×C₁₃	1	2	yes	complemented
144	#1825	C₂×C₁₃	1	2	yes	complemented
145	#1788	C₂×C₁₃	1	2	yes	—
146	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂³×C₁₃	—	2	1	no	—
148	C₂³×C₁₃	—	2	1	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	#124	1	2	yes	—
157	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	2	4	no	—
161	D₄×C₁₃	—	4	8	no	—
162	D₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	8	no	—
175	C₂×C₄×C₁₃	—	4	8	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	#124	1	2	yes	—
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	2	yes	—
192	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
193	C₈×C₁₃	—	4	2	no	—
194	C₈×C₁₃	—	4	2	no	—
195	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
198	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#103	C₂²×C₁₃	1	2	yes	—
200	C₂×#103	C₂²×C₁₃	1	2	yes	—
201	C₂×#102	C₂²×C₁₃	1	2	yes	—
202	C₂×#102	C₂²×C₁₃	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
204	C₂×#97	C₂²×C₁₃	1	2	yes	—
205	#391	C₂²×C₁₃	1	1	yes	characteristic
206	#391	C₂²×C₁₃	1	1	yes	characteristic
207	#390	C₂²×C₁₃	1	1	yes	characteristic
208	#390	C₂²×C₁₃	1	1	yes	characteristic
209	#389	C₂²×C₁₃	1	2	yes	—
210	#387	—	2	2	no	—
211	#386	—	2	2	no	—
212	#385	—	2	2	no	—
213	#382	C₂²×C₁₃	1	1	yes	characteristic
214	#380	C₂²×C₁₃	1	2	yes	—
215	C₄×C₂²⋊C₄	—	2	2	no	—
216	#340	C₂²×C₁₃	1	2	yes	—
217	#340	C₂²×C₁₃	1	2	yes	—
218	#340	C₂²×C₁₃	1	2	yes	—
219	#340	C₂²×C₁₃	1	2	yes	—
220	#336	C₂²×C₁₃	1	1	yes	characteristic
221	#336	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	—	8	1	no	—
230	C₂²×C₁₃	—	8	1	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	#525	1	1	yes	characteristic
233	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
234	C₂²×C₁₃	#534	1	1	yes	characteristic
235	C₂²×C₁₃	#575	1	2	yes	—
236	C₂²×C₁₃	#575	1	2	yes	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	2	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	8	2	no	—
242	C₄×C₁₃	—	8	1	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	#551	1	2	yes	—
246	C₄×C₁₃	#551	1	2	yes	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	4	2	no	—
251	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	D₄×C₁₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
259	#125	—	4	2	no	—
260	#117	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	4	2	no	—
273	C₂×C₄²	D₄×C₁₃	1	2	yes	—
274	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
276	#103	—	2	4	no	—
277	#103	—	4	2	no	—
278	#102	—	2	4	no	—
279	#102	—	4	2	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	#97	—	4	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	C₂×C₁₃	—	4	2	no	—
288	C₂×C₁₃	—	8	2	no	—
289	C₂×C₁₃	#2561	1	1	yes	characteristic
290	C₂×C₁₃	#3111	1	2	yes	—
291	C₂×C₁₃	#3135	1	1	yes	characteristic
292	C₂×C₁₃	#3142	1	1	yes	characteristic
293	C₂×C₁₃	#3197	1	2	yes	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
296	#41	—	4	8	no	—
297	#41	—	4	8	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₁₃×#41	1	2	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	C₁₃×#41	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₁₃×#41	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	4	2	no	—
349	C₄²	—	4	2	no	—
350	C₁₃	#29114	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₁₃×#124	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	4	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₁₃×#124	1	2	yes	—
393	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
394	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
396	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₁₃×#525	1	1	yes	characteristic
410	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
411	C₂²	C₁₃×#534	1	1	yes	characteristic
412	C₂²	C₁₃×#575	1	2	yes	—
413	C₂²	C₁₃×#575	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	2	no	—
422	C₄	C₁₃×#551	1	2	yes	—
423	C₄	C₁₃×#551	1	2	yes	—
424	C₂	—	4	2	no	—
425	C₂	—	8	2	no	—
426	C₂	C₁₃×#2561	1	1	yes	characteristic
427	C₂	C₁₃×#3111	1	2	yes	—
428	C₂	C₁₃×#3135	1	1	yes	characteristic
429	C₂	C₁₃×#3142	1	1	yes	characteristic
430	C₂	C₁₃×#3197	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2851	C₂	semidirect
3. C₁₃×#2074	C₂	semidirect
4. C₁₃×#2073	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
7. C₁₃×#1936	C₂	semidirect
8. C₁₃×#1935	C₂	semidirect
9. C₁₃×#1825	C₂	semidirect
11. C₁₃×#1749	C₂	semidirect
79. #29114	C₁₃	direct (N × H)
136. #2851	C₂×C₁₃	semidirect
138. #2074	C₂×C₁₃	semidirect
139. #2073	C₂×C₁₃	semidirect
140. #2026	C₂×C₁₃	semidirect
141. #2025	C₂×C₁₃	semidirect
142. #1936	C₂×C₁₃	semidirect
143. #1935	C₂×C₁₃	semidirect
144. #1825	C₂×C₁₃	semidirect
146. #1749	C₂×C₁₃	semidirect
350. C₁₃	#29114	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2851	2
C₁₃×#2297	2
C₁₃×#2074	2
C₁₃×#2073	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1936	2
C₁₃×#1935	2
C₁₃×#1825	2
C₁₃×#1788	2
C₁₃×#1749	2
#29114	13

Subgroups — C13×#29114 #15715453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29114 #15715453