Subgroups — C₁₃×#26263 #15712602

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2448	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#495	—	2	4	no	—
18	C₁₃×#441	—	2	4	no	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#399	—	2	2	no	—
30	C₁₃×#397	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#388	—	2	2	no	—
36	C₁₃×#388	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂×C₁₃×Q₁₆	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
46	C₂×C₁₃×SD₁₆	—	2	4	no	—
47	C₂×C₁₃×SD₁₆	—	2	4	no	—
48	C₂×C₁₃×SD₁₆	—	4	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#124	—	2	4	no	—
57	C₁₃×#124	—	4	2	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	4	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#106	—	2	2	no	—
76	C₁₃×#106	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#103	—	2	4	no	—
79	C₁₃×#103	—	4	2	no	—
80	C₁₃×#102	—	4	2	no	—
81	C₁₃×#102	—	4	2	no	—
82	C₁₃×#97	—	2	2	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	D₄	1	2	yes	—
89	#26263	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	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×D₄	1	4	yes	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
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	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₁₃×Q₁₆	—	2	8	no	—
112	C₁₃×SD₁₆	—	4	8	no	—
113	C₁₃×D₈	—	4	4	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₃	#41	1	2	yes	—
124	C₂×C₈×C₁₃	#41	1	2	yes	—
125	C₂×C₈×C₁₃	#41	1	2	yes	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	8	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₁₃×C₂²⋊C₄	—	4	4	no	—
135	C₁₃×C₂²⋊C₄	—	4	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	8	2	no	—
138	C₁₃×C₂²⋊C₄	—	8	2	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	4	4	no	—
146	C₂×#495	C₂×C₁₃	1	1	yes	characteristic
147	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2448	C₂×C₁₃	1	2	yes	complemented
149	#2055	C₂×C₁₃	1	2	yes	complemented
150	#2042	C₂×C₁₃	1	2	yes	complemented
151	#1972	C₂×C₁₃	1	1	yes	characteristic
152	#1972	C₂×C₁₃	1	1	yes	characteristic
153	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1880	C₂×C₁₃	1	2	yes	complemented
156	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	2	4	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	—	4	1	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₈×C₁₃	#123	1	4	yes	—
202	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
204	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#124	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
207	#495	—	2	4	no	—
208	#441	—	2	4	no	—
209	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#103	C₂²×C₁₃	1	2	yes	—
213	C₂×#103	C₂²×C₁₃	1	2	yes	—
214	C₂×#102	C₂²×C₁₃	1	2	yes	—
215	C₂×#102	C₂²×C₁₃	1	2	yes	—
216	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#399	—	2	2	no	—
220	#397	—	2	2	no	—
221	#391	C₂²×C₁₃	1	2	yes	—
222	#390	C₂²×C₁₃	1	2	yes	—
223	#390	C₂²×C₁₃	1	2	yes	—
224	#389	C₂²×C₁₃	1	2	yes	—
225	#388	—	2	2	no	—
226	#388	—	2	2	no	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
228	#340	C₂²×C₁₃	1	2	yes	—
229	#336	C₂²×C₁₃	1	1	yes	characteristic
230	#336	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	—	8	2	no	—
233	C₂²×C₁₃	—	8	2	no	—
234	C₂²×C₁₃	—	8	2	no	—
235	C₂²×C₁₃	—	8	2	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	#532	1	1	yes	characteristic
239	C₂²×C₁₃	D₄²	1	1	yes	characteristic
240	C₂²×C₁₃	#550	1	1	yes	characteristic
241	C₂²×C₁₃	#575	1	2	yes	—
242	C₂²×C₁₃	#577	1	2	yes	—
243	C₄×C₁₃	—	4	1	no	—
244	C₄×C₁₃	—	4	1	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	8	2	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
251	C₄×C₁₃	#540	1	1	yes	characteristic
252	C₄×C₁₃	#546	1	1	yes	characteristic
253	C₄×C₁₃	#559	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
255	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	4	2	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	2	2	no	—
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	#124	—	2	4	no	—
270	#124	—	4	2	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₄×Q₈	—	4	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
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	#106	—	2	2	no	—
289	#106	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	#103	—	2	4	no	—
292	#103	—	4	2	no	—
293	#102	—	4	2	no	—
294	#102	—	4	2	no	—
295	#97	—	2	2	no	—
296	#97	—	2	2	no	—
297	C₄×C₈	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	D₄×C₁₃	1	2	yes	—
302	C₂×C₁₃	—	16	2	no	—
303	C₂×C₁₃	#2445	1	1	yes	characteristic
304	C₂×C₁₃	#3173	1	1	yes	characteristic
305	C₂×C₁₃	#3183	1	1	yes	characteristic
306	C₂×C₁₃	#3271	1	2	yes	—
307	C₂×C₁₃	#3401	1	2	yes	—
308	C₂⁴	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
329	Q₁₆	—	2	8	no	—
330	SD₁₆	—	4	8	no	—
331	D₈	—	4	4	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
341	C₂×C₈	C₁₃×#41	1	2	yes	—
342	C₂×C₈	C₁₃×#41	1	2	yes	—
343	C₂×C₈	C₁₃×#41	1	2	yes	—
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	—	4	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	8	2	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	8	2	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	4	4	no	—
364	C₁₃	#26263	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
402	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
403	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
404	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	C₁₃×#123	1	4	yes	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₁₃×#532	1	1	yes	characteristic
418	C₂²	D₄²×C₁₃	1	1	yes	characteristic
419	C₂²	C₁₃×#550	1	1	yes	characteristic
420	C₂²	C₁₃×#575	1	2	yes	—
421	C₂²	C₁₃×#577	1	2	yes	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
430	C₄	C₁₃×#540	1	1	yes	characteristic
431	C₄	C₁₃×#546	1	1	yes	characteristic
432	C₄	C₁₃×#559	1	1	yes	characteristic
433	C₂	—	16	2	no	—
434	C₂	C₁₃×#2445	1	1	yes	characteristic
435	C₂	C₁₃×#3173	1	1	yes	characteristic
436	C₂	C₁₃×#3183	1	1	yes	characteristic
437	C₂	C₁₃×#3271	1	2	yes	—
438	C₂	C₁₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#441	C₂	semidirect
3. C₁₃×#2448	C₂	semidirect
4. C₁₃×#2055	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
8. C₁₃×#1971	C₂	semidirect
9. C₁₃×#1941	C₂	semidirect
10. C₁₃×#1880	C₂	semidirect
11. C₁₃×#1771	C₂	semidirect
89. #26263	C₁₃	direct (N × H)
147. C₂×#441	C₂×C₁₃	semidirect
148. #2448	C₂×C₁₃	semidirect
149. #2055	C₂×C₁₃	semidirect
150. #2042	C₂×C₁₃	semidirect
153. #1971	C₂×C₁₃	semidirect
154. #1941	C₂×C₁₃	semidirect
155. #1880	C₂×C₁₃	semidirect
156. #1771	C₂×C₁₃	semidirect
364. C₁₃	#26263	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#495	2
C₂×C₁₃×#441	2
C₁₃×#2448	2
C₁₃×#2055	2
C₁₃×#2042	2
C₁₃×#1972	2
C₁₃×#1971	2
C₁₃×#1941	2
C₁₃×#1880	2
C₁₃×#1771	2
#26263	13

Subgroups — C13×#26263 #15712602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26263 #15712602