Subgroups — C₁₃×#25921 #15712260

Order 3328.

972 conjugacy classes of subgroups.

The subgroup lattice has 412 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×#3140	C₂	1	2	yes	maximal
3	C₁₃×#2545	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2028	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2027	C₂	1	2	yes	maximal
6	C₁₃×#1986	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1888	C₂	1	2	yes	maximal
8	C₁₃×#1886	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#101	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₁₃×#519	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#489	—	2	2	no	—
23	C₁₃×#489	—	2	2	no	—
24	C₁₃×#488	—	2	4	no	—
25	C₁₃×#419	C₂²	1	4	yes	—
26	C₁₃×#418	C₂²	1	4	yes	—
27	C₂×C₁₃×#101	C₂²	1	2	yes	—
28	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
29	C₁₃×#396	—	2	2	no	—
30	C₁₃×#391	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#388	—	2	2	no	—
33	C₄×C₁₃×C₄⋊C₄	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
47	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
48	C₁₃×#125	—	2	4	no	—
49	C₁₃×#125	—	2	8	no	—
50	C₁₃×#125	—	2	4	no	—
51	C₁₃×#125	D₄	1	4	yes	—
52	C₁₃×#124	—	2	4	no	—
53	C₁₃×#124	—	2	2	no	—
54	C₁₃×#124	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	4	no	—
60	C₄×Q₈×C₁₃	—	2	4	no	—
61	C₄×Q₈×C₁₃	—	2	4	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₁₃×#117	—	2	4	no	—
67	C₁₃×#117	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₁₃	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#101	—	2	4	no	—
85	C₁₃×#97	—	2	2	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	2	no	—
89	#25921	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	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	#41	1	4	yes	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₁₃×M₁₆	—	2	4	no	—
112	C₁₃×M₁₆	—	2	4	no	—
113	C₂×C₈×C₁₃	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	4	no	—
126	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
128	C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₁₃×C₂²⋊C₄	—	4	4	no	—
130	C₁₃×C₂²⋊C₄	—	4	1	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	4	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	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#3140	C₂×C₁₃	1	2	yes	—
144	#2545	C₂×C₁₃	1	1	yes	characteristic
145	#2028	C₂×C₁₃	1	2	yes	complemented
146	#2027	C₂×C₁₃	1	2	yes	—
147	#1986	C₂×C₁₃	1	2	yes	complemented
148	#1888	C₂×C₁₃	1	2	yes	—
149	#1886	C₂×C₁₃	1	2	yes	complemented
150	C₄×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₃	—	2	8	no	—
158	Q₈×C₁₃	—	4	4	no	—
159	Q₈×C₁₃	—	4	4	no	—
160	Q₈×C₁₃	—	8	2	no	—
161	Q₈×C₁₃	—	8	4	no	—
162	D₄×C₁₃	—	4	4	no	—
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	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#120	1	2	yes	—
183	C₂×C₄×C₁₃	#124	1	4	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
187	C₈×C₁₃	—	4	4	no	—
188	Q₈²	—	2	2	no	—
189	#557	—	2	2	no	—
190	#557	—	2	4	no	—
191	#544	—	2	2	no	—
192	#544	C₂²×C₁₃	1	2	yes	—
193	#533	—	2	2	no	—
194	#533	C₂²×C₁₃	1	2	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
198	#519	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
200	#489	—	2	2	no	—
201	#489	—	2	2	no	—
202	#488	—	2	4	no	—
203	#419	C₂²×C₁₃	1	4	yes	—
204	#418	C₂²×C₁₃	1	4	yes	—
205	C₂×#101	C₂²×C₁₃	1	2	yes	—
206	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
207	#396	—	2	2	no	—
208	#391	C₂²×C₁₃	1	1	yes	characteristic
209	#390	C₂²×C₁₃	1	1	yes	characteristic
210	#388	—	2	2	no	—
211	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
212	#343	C₂²×C₁₃	1	2	yes	—
213	#339	C₂²×C₁₃	1	4	yes	—
214	#339	C₂²×C₁₃	1	4	yes	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	—	8	1	no	—
220	C₂²×C₁₃	—	8	1	no	—
221	C₂²×C₁₃	—	8	1	no	—
222	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
223	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
224	C₂²×C₁₃	#536	1	1	yes	characteristic
225	C₄×C₁₃	—	2	4	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	#548	1	4	yes	—
236	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	8	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
246	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
247	#125	—	2	4	no	—
248	#125	—	2	8	no	—
249	#125	—	2	4	no	—
250	#125	D₄×C₁₃	1	4	yes	—
251	#124	—	2	4	no	—
252	#124	—	2	2	no	—
253	#124	—	2	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	4	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	4	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	—	2	2	no	—
265	#117	—	2	4	no	—
266	#117	C₂³×C₁₃	1	4	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	D₄×C₁₃	1	2	yes	—
276	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#102	—	2	4	no	—
282	#102	—	2	4	no	—
283	#101	—	2	4	no	—
284	#97	—	2	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	2	no	—
288	C₂×C₁₃	—	2	1	no	—
289	C₂×C₁₃	—	2	1	no	—
290	C₂×C₁₃	—	16	1	no	—
291	C₂×C₁₃	#2436	1	1	yes	characteristic
292	C₂×C₁₃	#3018	1	1	yes	characteristic
293	C₂×C₁₃	#3020	1	1	yes	characteristic
294	C₂⁴	—	2	1	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₁₃×#41	1	4	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
315	M₁₆	—	2	4	no	—
316	M₁₆	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
331	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₄²	—	2	8	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	C₂×D₄×C₁₃	1	2	yes	—
345	C₄²	C₂×D₄×C₁₃	1	2	yes	—
346	C₁₃	#25921	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
353	Q₈	—	2	8	no	—
354	Q₈	—	4	4	no	—
355	Q₈	—	4	4	no	—
356	Q₈	—	8	2	no	—
357	Q₈	—	8	4	no	—
358	D₄	—	4	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	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	1	no	—
376	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
377	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
378	C₂×C₄	C₁₃×#120	1	2	yes	—
379	C₂×C₄	C₁₃×#124	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
381	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
382	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
383	C₈	—	4	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
392	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
393	C₂²	C₁₃×#536	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	4	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	4	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	C₁₃×#548	1	4	yes	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	16	1	no	—
408	C₂	C₁₃×#2436	1	1	yes	characteristic
409	C₂	C₁₃×#3018	1	1	yes	characteristic
410	C₂	C₁₃×#3020	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×#2028	C₂	semidirect
6. C₁₃×#1986	C₂	semidirect
8. C₁₃×#1886	C₂	semidirect
9. C₄×C₁₃×#101	C₂	semidirect
89. #25921	C₁₃	direct (N × H)
142. #3502	C₂×C₁₃	semidirect
145. #2028	C₂×C₁₃	semidirect
147. #1986	C₂×C₁₃	semidirect
149. #1886	C₂×C₁₃	semidirect
150. C₄×#101	C₂×C₁₃	semidirect
346. C₁₃	#25921	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×#3140	2
C₁₃×#2545	2
C₁₃×#2028	2
C₁₃×#2027	2
C₁₃×#1986	2
C₁₃×#1888	2
C₁₃×#1886	2
C₄×C₁₃×#101	2
#25921	13

Subgroups — C13×#25921 #15712260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25921 #15712260