Subgroups — C₁₃×#25878 #15712217

Order 3328.

1346 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	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×#2641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2037	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1792	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
11	C₁₃×#550	—	2	2	no	—
12	D₄²×C₁₃	—	2	4	no	—
13	D₄²×C₁₃	—	2	2	no	—
14	C₁₃×#535	—	2	2	no	—
15	C₁₃×#535	C₂²	1	2	yes	—
16	C₁₃×#532	—	2	1	no	—
17	C₁₃×#532	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#127	—	2	1	no	—
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
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	complemented
28	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#104	C₂²	1	2	yes	—
30	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
31	C₁₃×#417	C₂²	1	2	yes	—
32	C₁₃×#417	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#100	C₂²	1	4	yes	complemented
34	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#394	—	2	4	no	—
36	C₁₃×#390	C₂²	1	4	yes	complemented
37	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#339	C₂²	1	2	yes	complemented
39	C₁₃×H(5,𝔽₂)	—	2	8	no	—
40	C₁₃×H(5,𝔽₂)	—	4	4	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	C₂³	1	2	yes	—
44	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	4	no	—
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	D₄	1	4	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₃×#127	—	2	4	no	—
55	C₁₃×#127	—	2	2	no	—
56	C₁₃×#127	—	2	1	no	—
57	C₁₃×#127	—	2	1	no	—
58	C₁₃×#127	—	2	2	no	—
59	C₁₃×#127	D₄	1	1	yes	characteristic
60	C₁₃×#125	—	2	2	no	—
61	C₁₃×#125	—	2	1	no	—
62	C₁₃×#125	—	2	1	no	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#124	D₄	1	2	yes	—
65	C₁₃×#121	—	2	4	no	—
66	C₁₃×#121	—	2	8	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#120	—	2	8	no	—
70	C₁₃×#120	—	2	4	no	—
71	C₄×Q₈×C₁₃	D₄	1	2	yes	—
72	C₄×D₄×C₁₃	—	2	4	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₄×D₄×C₁₃	D₄	1	2	yes	—
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×#117	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#107	—	2	2	no	—
85	C₁₃×#106	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×#104	—	2	4	no	—
88	C₁₃×#104	—	4	4	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#103	—	2	4	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₁₃×#100	—	4	4	no	—
94	C₁₃×#97	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	C₁₃×#95	—	2	2	no	—
97	#25878	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	4	no	—
99	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	4	no	—
102	C₁₃×#41	—	2	4	no	—
103	C₁₃×#41	—	4	8	no	—
104	C₁₃×#41	—	4	4	no	—
105	C₁₃×#41	—	4	4	no	—
106	C₁₃×#41	#41	1	4	yes	—
107	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	4	8	no	—
122	C₂×D₄×C₁₃	—	4	16	no	—
123	C₂×D₄×C₁₃	—	4	4	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	8	8	no	—
126	C₂×D₄×C₁₃	—	8	4	no	—
127	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×M₁₆	—	2	2	no	—
138	C₁₃×M₁₆	—	2	2	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₁₃×C₂²⋊C₄	—	2	8	no	—
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₁₃×C₂²⋊C₄	—	8	8	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	#3498	C₂×C₁₃	1	1	yes	characteristic
162	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2641	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2037	C₂×C₁₃	1	4	yes	complemented
166	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1963	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1792	C₂×C₁₃	1	4	yes	complemented
169	#1759	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	4	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	8	no	—
174	C₂³×C₁₃	—	4	8	no	—
175	C₂³×C₁₃	—	4	8	no	—
176	C₂³×C₁₃	—	8	8	no	—
177	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₃	—	2	1	no	—
179	Q₈×C₁₃	—	2	4	no	—
180	Q₈×C₁₃	#124	1	2	yes	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	1	no	—
183	D₄×C₁₃	—	2	4	no	—
184	D₄×C₁₃	—	4	8	no	—
185	D₄×C₁₃	—	4	8	no	—
186	D₄×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	4	8	no	—
188	D₄×C₁₃	—	4	4	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	4	no	—
192	D₄×C₁₃	—	8	4	no	—
193	D₄×C₁₃	—	8	8	no	—
194	D₄×C₁₃	#124	1	2	yes	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	#120	1	2	yes	—
209	C₂×C₄×C₁₃	#120	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₁₃	—	4	2	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
217	#550	—	2	2	no	—
218	D₄²	—	2	4	no	—
219	D₄²	—	2	2	no	—
220	#535	—	2	2	no	—
221	#535	C₂²×C₁₃	1	2	yes	—
222	#532	—	2	1	no	—
223	#532	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#127	—	2	1	no	—
225	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
227	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
228	#491	—	2	1	no	—
229	#490	—	2	1	no	—
230	#488	—	2	2	no	—
231	#479	—	2	2	no	—
232	#478	—	2	2	no	—
233	#428	C₂²×C₁₃	1	2	yes	complemented
234	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#104	C₂²×C₁₃	1	2	yes	—
236	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
237	#417	C₂²×C₁₃	1	2	yes	—
238	#417	C₂²×C₁₃	1	4	yes	complemented
239	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
240	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	#394	—	2	4	no	—
242	#390	C₂²×C₁₃	1	4	yes	complemented
243	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
244	#339	C₂²×C₁₃	1	2	yes	complemented
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	4	8	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	8	8	no	—
253	C₂²×C₁₃	—	16	8	no	—
254	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
255	C₂²×C₁₃	#546	1	2	yes	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	—	8	2	no	—
263	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
264	C₄×C₁₃	#535	1	1	yes	characteristic
265	C₄×C₁₃	#546	1	2	yes	—
266	H(5,𝔽₂)	—	2	8	no	—
267	H(5,𝔽₂)	—	4	4	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	C₂³×C₁₃	1	2	yes	—
271	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×D₄	—	2	4	no	—
273	C₂²×D₄	—	2	4	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	D₄×C₁₃	1	4	yes	—
277	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
278	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
279	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
280	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
281	#127	—	2	4	no	—
282	#127	—	2	2	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	2	no	—
286	#127	D₄×C₁₃	1	1	yes	characteristic
287	#125	—	2	2	no	—
288	#125	—	2	1	no	—
289	#125	—	2	1	no	—
290	#124	—	2	2	no	—
291	#124	D₄×C₁₃	1	2	yes	—
292	#121	—	2	4	no	—
293	#121	—	2	8	no	—
294	#121	—	2	2	no	—
295	#121	—	2	4	no	—
296	#120	—	2	8	no	—
297	#120	—	2	4	no	—
298	C₄×Q₈	D₄×C₁₃	1	2	yes	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₁₃	1	2	yes	—
303	#117	—	2	1	no	—
304	#117	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	8	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	#107	—	2	2	no	—
312	#106	—	2	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	#104	—	2	4	no	—
315	#104	—	4	4	no	—
316	#103	—	2	2	no	—
317	#103	—	2	4	no	—
318	#102	—	2	2	no	—
319	#102	—	2	4	no	—
320	#100	—	4	4	no	—
321	#97	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	#95	—	2	2	no	—
324	C₂×C₁₃	—	2	2	no	—
325	C₂×C₁₃	—	4	2	no	—
326	C₂×C₁₃	—	8	4	no	—
327	C₂×C₁₃	—	8	2	no	—
328	C₂×C₁₃	#2435	1	1	yes	characteristic
329	C₂×C₁₃	#3019	1	2	yes	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
332	#41	—	2	2	no	—
333	#41	—	2	4	no	—
334	#41	—	2	4	no	—
335	#41	—	4	8	no	—
336	#41	—	4	4	no	—
337	#41	—	4	4	no	—
338	#41	C₁₃×#41	1	4	yes	—
339	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
340	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	—	4	16	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	8	8	no	—
358	C₂×D₄	—	8	4	no	—
359	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	4	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	8	8	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₃	1	2	yes	—
393	C₁₃	#25878	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	8	8	no	—
401	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	Q₈	—	2	1	no	—
403	Q₈	—	2	4	no	—
404	Q₈	C₁₃×#124	1	2	yes	—
405	D₄	—	2	4	no	—
406	D₄	—	2	1	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	8	4	no	—
417	D₄	—	8	8	no	—
418	D₄	C₁₃×#124	1	2	yes	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	C₁₃×#120	1	2	yes	—
433	C₂×C₄	C₁₃×#120	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
437	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	8	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	8	8	no	—
448	C₂²	—	16	8	no	—
449	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
450	C₂²	C₁₃×#546	1	2	yes	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	2	no	—
458	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
459	C₄	C₁₃×#535	1	1	yes	characteristic
460	C₄	C₁₃×#546	1	2	yes	—
461	C₂	—	2	2	no	—
462	C₂	—	4	2	no	—
463	C₂	—	8	4	no	—
464	C₂	—	8	2	no	—
465	C₂	C₁₃×#2435	1	1	yes	characteristic
466	C₂	C₁₃×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3498	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×#2641	C₂	semidirect
5. C₁₃×#2037	C₂	semidirect
6. C₁₃×#1965	C₂	semidirect
7. C₁₃×#1963	C₂	semidirect
8. C₁₃×#1792	C₂	semidirect
9. C₁₃×#1759	C₂	semidirect
20. C₂×C₁₃×#125	C₂²	semidirect
27. C₁₃×#428	C₂²	semidirect
28. C₁₃×#423	C₂²	semidirect
30. C₂×C₁₃×#104	C₂²	semidirect
32. C₁₃×#417	C₂²	semidirect
33. C₂×C₁₃×#100	C₂²	semidirect
34. C₄×C₁₃×M₁₆	C₂²	semidirect
36. C₁₃×#390	C₂²	semidirect
37. C₁₃×#376	C₂²	semidirect
38. C₁₃×#339	C₂²	semidirect
97. #25878	C₁₃	direct (N × H)
162. #3142	C₂×C₁₃	semidirect
163. #3080	C₂×C₁₃	semidirect
164. #2641	C₂×C₁₃	semidirect
165. #2037	C₂×C₁₃	semidirect
166. #1965	C₂×C₁₃	semidirect
167. #1963	C₂×C₁₃	semidirect
168. #1792	C₂×C₁₃	semidirect
169. #1759	C₂×C₁₃	semidirect
226. C₂×#125	C₂²×C₁₃	semidirect
233. #428	C₂²×C₁₃	semidirect
234. #423	C₂²×C₁₃	semidirect
236. C₂×#104	C₂²×C₁₃	semidirect
238. #417	C₂²×C₁₃	semidirect
239. C₂×#100	C₂²×C₁₃	semidirect
240. C₄×M₁₆	C₂²×C₁₃	semidirect
242. #390	C₂²×C₁₃	semidirect
243. #376	C₂²×C₁₃	semidirect
244. #339	C₂²×C₁₃	semidirect
393. C₁₃	#25878	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×#3498	2
C₁₃×#3142	2
C₁₃×#3080	2
C₁₃×#2641	2
C₁₃×#2037	2
C₁₃×#1965	2
C₁₃×#1963	2
C₁₃×#1792	2
C₁₃×#1759	2
#25878	13

Subgroups — C13×#25878 #15712217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25878 #15712217