Subgroups — C₁₃×#25873 #15712212

Order 3328.

1206 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×#3497	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2040	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2039	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1980	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1793	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1793	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₁₃×#550	—	2	2	no	—
12	D₄×Q₈×C₁₃	—	2	2	no	—
13	C₁₃×#548	—	2	4	no	—
14	C₁₃×#537	—	2	2	no	—
15	C₁₃×#537	C₂²	1	2	yes	—
16	C₁₃×#532	—	2	2	no	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#491	—	2	2	no	—
21	C₁₃×#490	—	2	2	no	—
22	C₁₃×#488	—	2	4	no	—
23	C₂×C₁₃×#104	C₂²	1	4	yes	—
24	C₂×C₁₃×#104	C₂²	1	4	yes	—
25	C₁₃×#417	C₂²	1	4	yes	—
26	C₁₃×#417	C₂²	1	4	yes	—
27	C₂×C₁₃×#101	C₂²	1	2	yes	—
28	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
29	C₁₃×#398	—	2	2	no	—
30	C₁₃×#391	C₂²	1	1	yes	characteristic
31	C₁₃×#391	C₂²	1	1	yes	characteristic
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#343	C₂²	1	2	yes	—
37	C₁₃×2₋¹⁺⁴	—	2	4	no	—
38	C₁₃×2₋¹⁺⁴	—	2	4	no	—
39	C₁₃×2₋¹⁺⁴	—	4	4	no	—
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	2	4	no	—
42	C₂×C₁₃×#41	C₂³	1	4	yes	—
43	C₂²×Q₈×C₁₃	—	2	4	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
46	C₁₃×C₄⋊Q₈	—	2	2	no	—
47	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
48	C₁₃×#127	—	2	2	no	—
49	C₁₃×#127	D₄	1	2	yes	—
50	C₁₃×#125	—	2	2	no	—
51	C₁₃×#125	—	2	2	no	—
52	C₁₃×#124	—	2	4	no	—
53	C₁₃×#124	D₄	1	4	yes	—
54	C₁₃×C₂²⋊Q₈	—	2	8	no	—
55	C₁₃×C₂²⋊Q₈	—	2	4	no	—
56	C₁₃×#121	—	2	8	no	—
57	C₁₃×#121	—	2	4	no	—
58	C₁₃×#121	—	2	2	no	—
59	C₁₃×#121	—	2	4	no	—
60	C₁₃×#121	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	—	2	4	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×#104	—	4	4	no	—
80	C₁₃×#104	—	4	4	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#101	—	2	4	no	—
86	C₁₃×#97	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	#25873	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₁₃×#41	—	2	4	no	—
94	C₁₃×#41	—	2	4	no	—
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	2	4	no	—
97	C₁₃×#41	—	4	8	no	—
98	C₁₃×#41	—	4	8	no	—
99	C₁₃×#41	—	4	8	no	—
100	C₁₃×#41	—	4	8	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	4	8	no	—
105	C₂×Q₈×C₁₃	—	4	8	no	—
106	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
107	C₂×Q₈×C₁₃	#41	1	4	yes	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	4	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×M₁₆	—	2	4	no	—
126	C₁₃×M₁₆	—	2	4	no	—
127	C₂×C₈×C₁₃	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₄⋊C₄	—	4	1	no	—
138	C₁₃×C₄⋊C₄	—	4	1	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	#3497	C₂×C₁₃	1	1	yes	characteristic
150	#3142	C₂×C₁₃	1	2	yes	complemented
151	#2565	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2040	C₂×C₁₃	1	2	yes	complemented
153	#2039	C₂×C₁₃	1	2	yes	complemented
154	#1980	C₂×C₁₃	1	2	yes	complemented
155	#1793	C₂×C₁₃	1	2	yes	complemented
156	#1793	C₂×C₁₃	1	2	yes	complemented
157	C₄×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	8	no	—
161	Q₈×C₁₃	—	2	4	no	—
162	Q₈×C₁₃	—	2	4	no	—
163	Q₈×C₁₃	—	4	8	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	4	4	no	—
167	D₄×C₁₃	—	4	8	no	—
168	D₄×C₁₃	—	4	4	no	—
169	D₄×C₁₃	—	4	4	no	—
170	D₄×C₁₃	—	8	2	no	—
171	D₄×C₁₃	—	8	4	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	16	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
193	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#120	1	2	yes	—
195	C₂×C₄×C₁₃	#124	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₁₃	—	4	4	no	—
200	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
201	#550	—	2	2	no	—
202	D₄×Q₈	—	2	2	no	—
203	#548	—	2	4	no	—
204	#537	—	2	2	no	—
205	#537	C₂²×C₁₃	1	2	yes	—
206	#532	—	2	2	no	—
207	#532	C₂²×C₁₃	1	2	yes	—
208	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	#491	—	2	2	no	—
211	#490	—	2	2	no	—
212	#488	—	2	4	no	—
213	C₂×#104	C₂²×C₁₃	1	4	yes	—
214	C₂×#104	C₂²×C₁₃	1	4	yes	—
215	#417	C₂²×C₁₃	1	4	yes	—
216	#417	C₂²×C₁₃	1	4	yes	—
217	C₂×#101	C₂²×C₁₃	1	2	yes	—
218	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
219	#398	—	2	2	no	—
220	#391	C₂²×C₁₃	1	1	yes	characteristic
221	#391	C₂²×C₁₃	1	1	yes	characteristic
222	#387	—	2	2	no	—
223	#384	C₂²×C₁₃	1	1	yes	characteristic
224	#382	C₂²×C₁₃	1	1	yes	characteristic
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	#343	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	4	4	no	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	4	4	no	—
232	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
233	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
234	C₂²×C₁₃	#535	1	1	yes	characteristic
235	C₄×C₁₃	—	2	4	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	4	2	no	—
240	C₄×C₁₃	—	4	4	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	8	1	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	—	8	1	no	—
245	C₄×C₁₃	#546	1	4	yes	—
246	2₋¹⁺⁴	—	2	4	no	—
247	2₋¹⁺⁴	—	2	4	no	—
248	2₋¹⁺⁴	—	4	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	C₂³×C₁₃	1	4	yes	—
252	C₂²×Q₈	—	2	4	no	—
253	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
257	#127	—	2	2	no	—
258	#127	D₄×C₁₃	1	2	yes	—
259	#125	—	2	2	no	—
260	#125	—	2	2	no	—
261	#124	—	2	4	no	—
262	#124	D₄×C₁₃	1	4	yes	—
263	C₂²⋊Q₈	—	2	8	no	—
264	C₂²⋊Q₈	—	2	4	no	—
265	#121	—	2	8	no	—
266	#121	—	2	4	no	—
267	#121	—	2	2	no	—
268	#121	—	2	4	no	—
269	#121	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	#104	—	4	4	no	—
289	#104	—	4	4	no	—
290	#103	—	2	4	no	—
291	#103	—	2	4	no	—
292	#102	—	2	4	no	—
293	#102	—	2	4	no	—
294	#101	—	2	4	no	—
295	#97	—	2	2	no	—
296	C₄×C₈	—	2	2	no	—
297	#95	—	2	1	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	C₂×C₁₃	—	2	1	no	—
302	C₂×C₁₃	—	2	1	no	—
303	C₂×C₁₃	—	8	4	no	—
304	C₂×C₁₃	#2435	1	1	yes	characteristic
305	C₂×C₁₃	#3018	1	1	yes	characteristic
306	C₂×C₁₃	#3020	1	1	yes	characteristic
307	#41	—	2	4	no	—
308	#41	—	2	4	no	—
309	#41	—	2	4	no	—
310	#41	—	2	4	no	—
311	#41	—	4	8	no	—
312	#41	—	4	8	no	—
313	#41	—	4	8	no	—
314	#41	—	4	8	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	8	no	—
319	C₂×Q₈	—	4	8	no	—
320	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
321	C₂×Q₈	C₁₃×#41	1	4	yes	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	C₂×D₄×C₁₃	1	2	yes	—
362	C₄²	C₂×D₄×C₁₃	1	2	yes	—
363	C₁₃	#25873	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	2	4	no	—
365	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
366	Q₈	—	2	8	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	4	no	—
369	Q₈	—	4	8	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	8	2	no	—
377	D₄	—	8	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	16	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
399	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
400	C₂×C₄	C₁₃×#120	1	2	yes	—
401	C₂×C₄	C₁₃×#124	1	4	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
403	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
404	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
405	C₈	—	4	4	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
412	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
413	C₂²	C₁₃×#535	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	C₁₃×#546	1	4	yes	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	8	4	no	—
428	C₂	C₁₃×#2435	1	1	yes	characteristic
429	C₂	C₁₃×#3018	1	1	yes	characteristic
430	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	C₁₃×#3497	C₂
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
2. C₁₃×#3142	C₂	semidirect
3. C₁₃×#2565	C₂	semidirect
4. C₁₃×#2040	C₂	semidirect
5. C₁₃×#2039	C₂	semidirect
6. C₁₃×#1980	C₂	semidirect
7. C₁₃×#1793	C₂	semidirect
8. C₁₃×#1793	C₂	semidirect
9. C₄×C₁₃×#101	C₂	semidirect
92. #25873	C₁₃	direct (N × H)
150. #3142	C₂×C₁₃	semidirect
151. #2565	C₂×C₁₃	semidirect
152. #2040	C₂×C₁₃	semidirect
153. #2039	C₂×C₁₃	semidirect
154. #1980	C₂×C₁₃	semidirect
155. #1793	C₂×C₁₃	semidirect
156. #1793	C₂×C₁₃	semidirect
157. C₄×#101	C₂×C₁₃	semidirect
363. C₁₃	#25873	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×#3497	2
C₁₃×#3142	2
C₁₃×#2565	2
C₁₃×#2040	2
C₁₃×#2039	2
C₁₃×#1980	2
C₁₃×#1793	2
C₄×C₁₃×#101	2
#25873	13

Subgroups — C13×#25873 #15712212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25873 #15712212