Subgroups — C₁₃×#25879 #15712218

Order 3328.

1178 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2642	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1793	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
11	D₄×Q₈×C₁₃	—	2	2	no	—
12	C₁₃×#547	—	2	2	no	—
13	C₁₃×#547	—	2	4	no	—
14	C₁₃×#536	—	2	2	no	—
15	C₁₃×#536	C₂²	1	2	yes	—
16	C₁₃×#532	—	2	1	no	—
17	C₁₃×#532	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₁₃×#491	—	2	1	no	—
23	C₁₃×#490	—	2	1	no	—
24	C₁₃×#488	—	2	2	no	—
25	C₁₃×#479	—	2	2	no	—
26	C₁₃×#478	—	2	2	no	—
27	C₁₃×#428	C₂²	1	2	yes	—
28	C₁₃×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#104	C₂²	1	2	yes	—
30	C₂×C₁₃×#104	C₂²	1	4	yes	—
31	C₁₃×#417	C₂²	1	4	yes	—
32	C₁₃×#417	C₂²	1	2	yes	—
33	C₂×C₁₃×#101	C₂²	1	4	yes	—
34	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₁₃×#400	—	2	4	no	—
36	C₁₃×#391	C₂²	1	4	yes	—
37	C₁₃×#376	C₂²	1	1	yes	characteristic
38	C₁₃×#339	C₂²	1	2	yes	—
39	C₁₃×2₋¹⁺⁴	—	2	8	no	—
40	C₁₃×2₋¹⁺⁴	—	4	4	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	C₂³	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	2	4	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₃×#127	D₄	1	1	yes	characteristic
58	C₁₃×#125	—	2	2	no	—
59	C₁₃×#125	—	2	1	no	—
60	C₁₃×#125	—	2	1	no	—
61	C₁₃×#124	—	2	2	no	—
62	C₁₃×#124	D₄	1	2	yes	—
63	C₁₃×#123	—	2	8	no	—
64	C₁₃×#123	—	2	4	no	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×#121	—	2	4	no	—
68	C₁₃×#121	—	2	2	no	—
69	C₄×Q₈×C₁₃	D₄	1	2	yes	—
70	C₄×D₄×C₁₃	—	2	4	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	D₄	1	2	yes	—
74	C₁₃×#117	—	2	1	no	—
75	C₁₃×#117	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#107	—	2	2	no	—
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×#104	—	2	4	no	—
87	C₁₃×#104	—	4	4	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#101	—	4	4	no	—
93	C₁₃×#97	—	2	1	no	—
94	C₄×C₈×C₁₃	—	2	1	no	—
95	C₁₃×#95	—	2	8	no	—
96	C₁₃×#95	—	2	2	no	—
97	#25879	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₁₃×#41	—	2	2	no	—
99	C₁₃×#41	—	2	4	no	—
100	C₁₃×#41	—	2	4	no	—
101	C₁₃×#41	—	4	8	no	—
102	C₁₃×#41	—	4	16	no	—
103	C₁₃×#41	—	4	4	no	—
104	C₁₃×#41	—	4	4	no	—
105	C₁₃×#41	#41	1	4	yes	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	4	8	no	—
112	C₂×Q₈×C₁₃	—	4	4	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×M₁₆	—	2	2	no	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₁₃×M₁₆	—	2	4	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₁₃×C₂²⋊C₄	—	2	8	no	—
148	C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	2	yes	—
158	#3499	C₂×C₁₃	1	1	yes	characteristic
159	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2642	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2038	C₂×C₁₃	1	4	yes	complemented
163	#1966	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1963	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1793	C₂×C₁₃	1	4	yes	complemented
166	#1759	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	1	no	—
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	—	4	8	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	4	4	no	—
176	Q₈×C₁₃	#124	1	2	yes	—
177	D₄×C₁₃	—	2	4	no	—
178	D₄×C₁₃	—	2	1	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	4	4	no	—
181	D₄×C₁₃	—	4	8	no	—
182	D₄×C₁₃	—	4	4	no	—
183	D₄×C₁₃	#124	1	2	yes	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	4	no	—
192	C₂×C₄×C₁₃	—	4	8	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	4	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	#120	1	2	yes	—
201	C₂×C₄×C₁₃	#120	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
205	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
209	D₄×Q₈	—	2	2	no	—
210	#547	—	2	2	no	—
211	#547	—	2	4	no	—
212	#536	—	2	2	no	—
213	#536	C₂²×C₁₃	1	2	yes	—
214	#532	—	2	1	no	—
215	#532	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	—	2	1	no	—
217	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
219	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
220	#491	—	2	1	no	—
221	#490	—	2	1	no	—
222	#488	—	2	2	no	—
223	#479	—	2	2	no	—
224	#478	—	2	2	no	—
225	#428	C₂²×C₁₃	1	2	yes	—
226	#423	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#104	C₂²×C₁₃	1	2	yes	—
228	C₂×#104	C₂²×C₁₃	1	4	yes	—
229	#417	C₂²×C₁₃	1	2	yes	—
230	#417	C₂²×C₁₃	1	4	yes	—
231	C₂×#101	C₂²×C₁₃	1	4	yes	—
232	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	#400	—	2	4	no	—
234	#391	C₂²×C₁₃	1	4	yes	—
235	#376	C₂²×C₁₃	1	1	yes	characteristic
236	#339	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
243	C₂²×C₁₃	#546	1	2	yes	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
253	C₄×C₁₃	#535	1	1	yes	characteristic
254	C₄×C₁₃	#546	1	2	yes	—
255	2₋¹⁺⁴	—	2	8	no	—
256	2₋¹⁺⁴	—	4	4	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	C₂³×C₁₃	1	2	yes	—
261	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
265	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
266	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
273	#127	D₄×C₁₃	1	1	yes	characteristic
274	#125	—	2	2	no	—
275	#125	—	2	1	no	—
276	#125	—	2	1	no	—
277	#124	—	2	2	no	—
278	#124	D₄×C₁₃	1	2	yes	—
279	#123	—	2	8	no	—
280	#123	—	2	4	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	#121	—	2	4	no	—
284	#121	—	2	2	no	—
285	C₄×Q₈	D₄×C₁₃	1	2	yes	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	D₄×C₁₃	1	2	yes	—
290	#117	—	2	1	no	—
291	#117	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	#107	—	2	2	no	—
300	#106	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	#104	—	2	4	no	—
303	#104	—	4	4	no	—
304	#103	—	2	2	no	—
305	#103	—	2	4	no	—
306	#102	—	2	2	no	—
307	#102	—	2	4	no	—
308	#101	—	4	4	no	—
309	#97	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	#95	—	2	2	no	—
312	#95	—	2	8	no	—
313	C₂×C₁₃	—	2	2	no	—
314	C₂×C₁₃	—	4	2	no	—
315	C₂×C₁₃	—	8	2	no	—
316	C₂×C₁₃	#2435	1	1	yes	characteristic
317	C₂×C₁₃	#3020	1	2	yes	—
318	#41	—	2	2	no	—
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	4	8	no	—
322	#41	—	4	16	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	#41	C₁₃×#41	1	4	yes	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	4	8	no	—
332	C₂×Q₈	—	4	4	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	4	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₁₃	1	2	yes	—
378	C₁₃	#25879	1	1	yes	characteristic, direct product factor, Sylow
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	4	8	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	4	no	—
388	Q₈	C₁₃×#124	1	2	yes	—
389	D₄	—	2	4	no	—
390	D₄	—	2	1	no	—
391	D₄	—	2	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	4	no	—
395	D₄	C₁₃×#124	1	2	yes	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	C₁₃×#120	1	2	yes	—
413	C₂×C₄	C₁₃×#120	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
417	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
426	C₂²	C₁₃×#546	1	2	yes	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
436	C₄	C₁₃×#535	1	1	yes	characteristic
437	C₄	C₁₃×#546	1	2	yes	—
438	C₂	—	2	2	no	—
439	C₂	—	4	2	no	—
440	C₂	—	8	2	no	—
441	C₂	C₁₃×#2435	1	1	yes	characteristic
442	C₂	C₁₃×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3499	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×#3080	C₂	semidirect
4. C₁₃×#2642	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
6. C₁₃×#1966	C₂	semidirect
7. C₁₃×#1963	C₂	semidirect
8. C₁₃×#1793	C₂	semidirect
9. C₁₃×#1759	C₂	semidirect
97. #25879	C₁₃	direct (N × H)
159. #3142	C₂×C₁₃	semidirect
160. #3080	C₂×C₁₃	semidirect
161. #2642	C₂×C₁₃	semidirect
162. #2038	C₂×C₁₃	semidirect
163. #1966	C₂×C₁₃	semidirect
164. #1963	C₂×C₁₃	semidirect
165. #1793	C₂×C₁₃	semidirect
166. #1759	C₂×C₁₃	semidirect
378. C₁₃	#25879	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×#3499	2
C₁₃×#3142	2
C₁₃×#3080	2
C₁₃×#2642	2
C₁₃×#2038	2
C₁₃×#1966	2
C₁₃×#1963	2
C₁₃×#1793	2
C₁₃×#1759	2
#25879	13

Subgroups — C13×#25879 #15712218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25879 #15712218