Subgroups — C₁₃×#23797 #15710136

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal
3	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2097	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2015	C₂	1	2	yes	maximal
10	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×Q₁₆	—	2	8	no	—
20	C₄×C₁₃×SD₁₆	—	2	8	no	—
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×#106	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	2	yes	—
29	C₁₃×#391	C₂²	1	1	yes	characteristic
30	C₁₃×#390	C₂²	1	1	yes	characteristic
31	C₁₃×#389	—	2	2	no	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
36	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
37	C₄³×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂×C₁₃×Q₁₆	—	2	4	no	—
46	C₂×C₁₃×Q₁₆	—	2	4	no	—
47	C₂×C₁₃×Q₁₆	—	2	4	no	—
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	4	no	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×#124	—	2	2	no	—
55	C₁₃×#124	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#107	—	2	4	no	—
78	C₁₃×#106	—	2	4	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₄×C₈×C₁₃	D₄	1	8	yes	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	4	no	—
87	#23797	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×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	—	2	2	no	—
97	C₂×Q₈×C₁₃	#41	1	2	yes	—
98	C₂×Q₈×C₁₃	#41	1	4	yes	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	#41	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	2	16	no	—
116	C₁₃×SD₁₆	—	2	16	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
122	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
123	C₁₃×C₄⋊C₄	—	2	8	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₂²⋊C₄	—	2	8	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₄²×C₁₃	—	2	4	no	—
135	C₄²×C₁₃	—	2	4	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	4	2	no	—
140	C₄²×C₁₃	—	4	4	no	—
141	C₄²×C₁₃	C₂×D₄	1	4	yes	—
142	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
143	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	—
144	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
146	#2097	C₂×C₁₃	1	2	yes	complemented
147	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2093	C₂×C₁₃	1	1	yes	characteristic
149	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2015	C₂×C₁₃	1	2	yes	—
151	#2013	C₂×C₁₃	1	1	yes	characteristic
152	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	2	4	no	—
161	Q₈×C₁₃	—	2	4	no	—
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	2	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	8	4	no	—
186	C₂×C₄×C₁₃	#127	1	2	yes	—
187	C₂×C₄×C₁₃	#127	1	2	yes	—
188	C₂×C₄×C₁₃	#135	1	4	yes	—
189	C₂×C₄×C₁₃	#137	1	4	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₈×C₁₃	—	2	4	no	—
195	C₈×C₁₃	—	2	4	no	—
196	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
197	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×Q₁₆	—	2	8	no	—
204	C₄×SD₁₆	—	2	8	no	—
205	C₂×#107	C₂²×C₁₃	1	2	yes	—
206	C₂×#106	C₂²×C₁₃	1	2	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×#103	C₂²×C₁₃	1	2	yes	—
209	C₂×#103	C₂²×C₁₃	1	2	yes	—
210	C₂×#102	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
212	#391	C₂²×C₁₃	1	2	yes	—
213	#391	C₂²×C₁₃	1	1	yes	characteristic
214	#390	C₂²×C₁₃	1	1	yes	characteristic
215	#389	—	2	2	no	—
216	#388	—	2	2	no	—
217	#384	C₂²×C₁₃	1	1	yes	characteristic
218	#382	C₂²×C₁₃	1	1	yes	characteristic
219	C₄×C₄⋊C₄	—	2	2	no	—
220	C₄×C₂²⋊C₄	—	2	2	no	—
221	C₄³	C₂²×C₁₃	1	1	yes	characteristic
222	#336	C₂²×C₁₃	1	1	yes	characteristic
223	#336	C₂²×C₁₃	1	1	yes	characteristic
224	#336	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₁₃	—	4	4	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	1	no	—
230	C₂²×C₁₃	#525	1	1	yes	characteristic
231	C₂²×C₁₃	#525	1	1	yes	characteristic
232	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
233	C₂²×C₁₃	C₂×#135	1	2	yes	—
234	C₂²×C₁₃	C₂×#137	1	2	yes	—
235	C₄×C₁₃	—	2	4	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	4	no	—
240	C₄×C₁₃	—	8	1	no	—
241	C₄×C₁₃	—	8	2	no	—
242	C₄×C₁₃	—	8	1	no	—
243	C₄×C₁₃	#497	1	4	yes	—
244	C₄×C₁₃	#525	1	2	yes	—
245	C₄×C₁₃	#525	1	2	yes	—
246	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
249	C₂³×C₄	—	2	1	no	—
250	C₂×Q₁₆	—	2	4	no	—
251	C₂×Q₁₆	—	2	4	no	—
252	C₂×Q₁₆	—	2	4	no	—
253	C₂×SD₁₆	—	2	4	no	—
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
258	C₄⋊Q₈	—	2	4	no	—
259	#124	—	2	2	no	—
260	#124	—	2	2	no	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	D₄×C₁₃	1	2	yes	—
278	C₂×C₄²	D₄×C₁₃	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
282	#107	—	2	4	no	—
283	#106	—	2	4	no	—
284	#103	—	2	4	no	—
285	#103	—	2	4	no	—
286	#103	—	2	4	no	—
287	#102	—	2	4	no	—
288	C₄×C₈	D₄×C₁₃	1	8	yes	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	4	no	—
292	C₂×C₁₃	—	8	2	no	—
293	C₂×C₁₃	#2397	1	1	yes	characteristic
294	C₂×C₁₃	#3107	1	2	yes	—
295	C₂×C₁₃	#3108	1	2	yes	—
296	C₂×C₁₃	#3147	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#497	1	1	yes	characteristic
298	C₂⁴	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	C₁₃×#41	1	2	yes	—
308	C₂×Q₈	C₁₃×#41	1	4	yes	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	C₁₃×#41	1	2	yes	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
325	Q₁₆	—	2	16	no	—
326	SD₁₆	—	2	16	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
332	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	2	no	—
350	C₄²	—	4	4	no	—
351	C₄²	C₂×D₄×C₁₃	1	4	yes	—
352	C₁₃	#23797	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	2	4	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	C₁₃×#127	1	2	yes	—
387	C₂×C₄	C₁₃×#127	1	2	yes	—
388	C₂×C₄	C₁₃×#135	1	4	yes	—
389	C₂×C₄	C₁₃×#137	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
391	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
392	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
393	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
394	C₈	—	2	4	no	—
395	C₈	—	2	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₁₃×#525	1	1	yes	characteristic
402	C₂²	C₁₃×#525	1	1	yes	characteristic
403	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
404	C₂²	C₂×C₁₃×#135	1	2	yes	—
405	C₂²	C₂×C₁₃×#137	1	2	yes	—
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	C₁₃×#497	1	4	yes	—
415	C₄	C₁₃×#525	1	2	yes	—
416	C₄	C₁₃×#525	1	2	yes	—
417	C₂	—	8	2	no	—
418	C₂	C₁₃×#2397	1	1	yes	characteristic
419	C₂	C₁₃×#3107	1	2	yes	—
420	C₂	C₁₃×#3108	1	2	yes	—
421	C₂	C₁₃×#3147	1	1	yes	characteristic
422	C₂	C₂×C₁₃×#497	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
3. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
5. C₁₃×#2097	C₂	semidirect
6. C₁₃×#2096	C₂	semidirect
8. C₁₃×#2016	C₂	semidirect
11. C₁₃×#1744	C₂	semidirect
87. #23797	C₁₃	direct (N × H)
142. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
144. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
146. #2097	C₂×C₁₃	semidirect
147. #2096	C₂×C₁₃	semidirect
149. #2016	C₂×C₁₃	semidirect
152. #1744	C₂×C₁₃	semidirect
352. C₁₃	#23797	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×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×SD₁₆	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₁₃×#2097	2
C₁₃×#2096	2
C₁₃×#2093	2
C₁₃×#2016	2
C₁₃×#2015	2
C₁₃×#2013	2
C₁₃×#1744	2
#23797	13

Subgroups — C13×#23797 #15710136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23797 #15710136