Subgroups — C₁₃×#24317 #15710656

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3077	C₂	1	2	yes	maximal
3	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2060	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2027	C₂	1	2	yes	maximal
6	C₁₃×#1995	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1888	C₂	1	2	yes	maximal
8	C₁₃×#1857	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈²×C₁₃	—	2	2	no	—
11	C₁₃×#557	—	2	2	no	—
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#544	—	2	2	no	—
14	C₁₃×#544	C₂²	1	2	yes	—
15	C₁₃×#533	—	2	2	no	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
18	C₁₃×#519	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#478	—	2	4	no	—
22	C₁₃×#476	—	2	2	no	—
23	C₁₃×#474	—	2	2	no	—
24	C₁₃×#428	C₂²	1	4	yes	—
25	C₁₃×#423	C₂²	1	2	yes	—
26	C₁₃×#418	C₂²	1	4	yes	—
27	C₂×C₁₃×#101	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#388	—	2	2	no	—
31	C₁₃×#385	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#376	C₂²	1	1	yes	characteristic
34	C₁₃×#343	C₂²	1	2	yes	—
35	C₁₃×#339	C₂²	1	4	yes	—
36	C₁₃×#339	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	—	2	1	no	—
40	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	—	2	2	no	—
43	C₁₃×C₄⋊Q₈	—	2	8	no	—
44	C₁₃×C₄⋊Q₈	—	2	4	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
47	C₁₃×#125	—	2	4	no	—
48	C₁₃×#125	—	2	8	no	—
49	C₁₃×#125	—	2	4	no	—
50	C₁₃×#125	D₄	1	4	yes	—
51	C₁₃×#124	—	2	2	no	—
52	C₁₃×#124	Q₈	1	4	yes	complemented
53	C₁₃×C₂²⋊Q₈	—	2	2	no	—
54	C₁₃×C₂²⋊Q₈	—	2	4	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	4	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₁₃×#117	—	2	4	no	—
67	C₁₃×#117	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₁₃	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#101	—	2	4	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	#24317	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
97	C₂×Q₈×C₁₃	#41	1	2	yes	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	8	2	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₁₃×M₁₆	—	2	4	no	—
113	C₁₃×M₁₆	—	2	4	no	—
114	C₂×C₈×C₁₃	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	—	2	8	no	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	8	2	no	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₁₃×C₂²⋊C₄	—	2	8	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	8	2	no	—
134	C₄²×C₁₃	—	2	8	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	4	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
143	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#3077	C₂×C₁₃	1	2	yes	—
145	#2326	C₂×C₁₃	1	1	yes	characteristic
146	#2060	C₂×C₁₃	1	2	yes	complemented
147	#2027	C₂×C₁₃	1	2	yes	—
148	#1995	C₂×C₁₃	1	2	yes	complemented
149	#1888	C₂×C₁₃	1	2	yes	—
150	#1857	C₂×C₁₃	1	2	yes	complemented
151	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	4	4	no	—
161	Q₈×C₁₃	—	8	2	no	—
162	Q₈×C₁₃	—	8	4	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	8	4	no	—
182	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#120	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
190	C₈×C₁₃	—	4	4	no	—
191	Q₈²	—	2	2	no	—
192	#557	—	2	2	no	—
193	#557	—	2	4	no	—
194	#544	—	2	2	no	—
195	#544	C₂²×C₁₃	1	2	yes	—
196	#533	—	2	2	no	—
197	#533	C₂²×C₁₃	1	2	yes	—
198	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
199	#519	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
202	#478	—	2	4	no	—
203	#476	—	2	2	no	—
204	#474	—	2	2	no	—
205	#428	C₂²×C₁₃	1	4	yes	—
206	#423	C₂²×C₁₃	1	2	yes	—
207	#418	C₂²×C₁₃	1	4	yes	—
208	C₂×#101	C₂²×C₁₃	1	2	yes	—
209	#391	C₂²×C₁₃	1	1	yes	characteristic
210	#390	C₂²×C₁₃	1	1	yes	characteristic
211	#388	—	2	2	no	—
212	#385	—	2	2	no	—
213	#384	C₂²×C₁₃	1	1	yes	characteristic
214	#376	C₂²×C₁₃	1	1	yes	characteristic
215	#343	C₂²×C₁₃	1	2	yes	—
216	#339	C₂²×C₁₃	1	4	yes	—
217	#339	C₂²×C₁₃	1	4	yes	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	—	8	1	no	—
225	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂²×C₁₃	#536	1	1	yes	characteristic
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	4	4	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	4	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	—	8	1	no	—
238	C₄×C₁₃	#548	1	2	yes	—
239	C₄×C₁₃	D₄×Q₈	1	2	yes	—
240	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	—	2	8	no	—
247	C₄⋊Q₈	—	2	4	no	—
248	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
249	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
250	#125	—	2	4	no	—
251	#125	—	2	8	no	—
252	#125	—	2	4	no	—
253	#125	D₄×C₁₃	1	4	yes	—
254	#124	—	2	2	no	—
255	#124	Q₈×C₁₃	1	4	yes	complemented
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	4	no	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	—	2	2	no	—
269	#117	—	2	4	no	—
270	#117	C₂³×C₁₃	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	D₄×C₁₃	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
282	#107	—	2	4	no	—
283	#106	—	2	4	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	#102	—	2	4	no	—
287	#102	—	2	4	no	—
288	#101	—	2	4	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	2	no	—
292	C₂×C₁₃	—	2	1	no	—
293	C₂×C₁₃	—	2	1	no	—
294	C₂×C₁₃	—	8	2	no	—
295	C₂×C₁₃	#2409	1	1	yes	characteristic
296	C₂×C₁₃	#3020	1	1	yes	characteristic
297	C₂×C₁₃	#3021	1	1	yes	characteristic
298	C₂⁴	—	2	1	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
305	C₂×Q₈	C₁₃×#41	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	8	2	no	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
336	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₄²	—	2	8	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂×D₄×C₁₃	1	2	yes	—
349	C₄²	C₂×D₄×C₁₃	1	2	yes	—
350	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
351	C₁₃	#24317	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
358	Q₈	—	2	4	no	—
359	Q₈	—	2	4	no	—
360	Q₈	—	4	4	no	—
361	Q₈	—	8	2	no	—
362	Q₈	—	8	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	4	no	—
382	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
383	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
384	C₂×C₄	C₁₃×#120	1	2	yes	—
385	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
386	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
387	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
389	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
390	C₈	—	4	4	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
399	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
400	C₂²	C₁₃×#536	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	4	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	4	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	1	no	—
411	C₄	C₁₃×#548	1	2	yes	—
412	C₄	D₄×Q₈×C₁₃	1	2	yes	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	8	2	no	—
416	C₂	C₁₃×#2409	1	1	yes	characteristic
417	C₂	C₁₃×#3020	1	1	yes	characteristic
418	C₂	C₁₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3502	C₂	semidirect
4. C₁₃×#2060	C₂	semidirect
6. C₁₃×#1995	C₂	semidirect
8. C₁₃×#1857	C₂	semidirect
9. C₁₃×#1801	C₂	semidirect
52. C₁₃×#124	Q₈	semidirect
89. #24317	C₁₃	direct (N × H)
143. #3502	C₂×C₁₃	semidirect
146. #2060	C₂×C₁₃	semidirect
148. #1995	C₂×C₁₃	semidirect
150. #1857	C₂×C₁₃	semidirect
151. #1801	C₂×C₁₃	semidirect
255. #124	Q₈×C₁₃	semidirect
351. C₁₃	#24317	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×#3502	2
C₁₃×#3077	2
C₁₃×#2326	2
C₁₃×#2060	2
C₁₃×#2027	2
C₁₃×#1995	2
C₁₃×#1888	2
C₁₃×#1857	2
C₁₃×#1801	2
#24317	13

Subgroups — C13×#24317 #15710656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24317 #15710656