Subgroups — C₁₃×#25932 #15712271

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2023	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1880	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
11	Q₈²×C₁₃	—	2	4	no	—
12	Q₈²×C₁₃	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#486	—	2	4	no	—
24	C₁₃×#460	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#394	—	2	2	no	—
31	C₁₃×#390	—	2	1	no	—
32	C₁₃×#390	C₂²	1	4	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂×C₁₃×SD₁₆	—	2	4	no	—
45	C₂×C₁₃×SD₁₆	—	2	8	no	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×C₄⋊Q₈	—	2	16	no	—
49	C₁₃×C₄⋊Q₈	—	2	8	no	—
50	C₁₃×C₄⋊Q₈	—	2	4	no	—
51	C₁₃×C₄⋊Q₈	—	2	4	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
54	C₁₃×#127	—	2	2	no	—
55	C₁₃×#127	—	2	2	no	—
56	C₁₃×#124	—	4	4	no	—
57	C₄×Q₈×C₁₃	—	2	8	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	4	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	D₄	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	8	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	#25932	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	8	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	8	2	no	—
95	C₂×Q₈×C₁₃	—	8	4	no	—
96	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
97	C₂×Q₈×C₁₃	C₂×D₄	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	4	no	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	8	2	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×SD₁₆	—	4	8	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	—	2	4	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	8	no	—
124	C₁₃×C₄⋊C₄	—	2	8	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
134	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
135	C₁₃×C₂²⋊C₄	—	4	8	no	—
136	C₁₃×C₂²⋊C₄	—	8	4	no	—
137	C₄²×C₁₃	—	2	8	no	—
138	C₄²×C₁₃	—	2	4	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂×#486	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
147	#2548	C₂×C₁₃	1	1	yes	characteristic
148	#2023	C₂×C₁₃	1	4	yes	complemented
149	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1880	C₂×C₁₃	1	4	yes	complemented
152	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	4	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	—	4	4	no	—
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	2	no	—
160	Q₈×C₁₃	—	2	4	no	—
161	Q₈×C₁₃	—	2	8	no	—
162	Q₈×C₁₃	—	8	4	no	—
163	Q₈×C₁₃	—	8	8	no	—
164	Q₈×C₁₃	#124	1	4	yes	complemented
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	4	no	—
168	D₄×C₁₃	—	8	4	no	—
169	D₄×C₁₃	—	8	4	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	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	#120	1	2	yes	—
185	C₂×C₄×C₁₃	#120	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
187	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
188	C₂×C₄×C₁₃	#137	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
193	C₈×C₁₃	—	4	2	no	—
194	C₈×C₁₃	—	4	2	no	—
195	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
196	Q₈²	—	2	4	no	—
197	Q₈²	—	2	4	no	—
198	C₂×C₄⋊Q₈	—	2	1	no	—
199	C₂×C₄⋊Q₈	—	2	2	no	—
200	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#124	—	2	1	no	—
204	C₂×C₄×Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	#486	—	2	4	no	—
209	#460	—	2	4	no	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#103	C₂²×C₁₃	1	2	yes	—
212	C₂×#102	C₂²×C₁₃	1	4	yes	—
213	C₂×#102	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
215	#394	—	2	2	no	—
216	#390	—	2	1	no	—
217	#390	C₂²×C₁₃	1	4	yes	—
218	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	#340	C₂²×C₁₃	1	4	yes	—
220	#340	C₂²×C₁₃	1	2	yes	—
221	#336	C₂²×C₁₃	1	4	yes	—
222	C₂²×C₁₃	—	8	4	no	—
223	C₂²×C₁₃	—	8	4	no	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	—	8	2	no	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
228	C₂²×C₁₃	#548	1	2	yes	—
229	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
231	C₂²×C₁₃	#576	1	2	yes	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	#448	1	4	yes	—
240	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
241	C₄×C₁₃	#536	1	1	yes	characteristic
242	C₄×C₁₃	#548	1	2	yes	—
243	C₂²×Q₈	—	2	2	no	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
246	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×SD₁₆	—	2	8	no	—
252	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
253	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
254	C₄⋊Q₈	—	2	16	no	—
255	C₄⋊Q₈	—	2	8	no	—
256	C₄⋊Q₈	—	2	4	no	—
257	C₄⋊Q₈	—	2	4	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
260	#127	—	2	2	no	—
261	#127	—	2	2	no	—
262	#124	—	4	4	no	—
263	C₄×Q₈	—	2	8	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	D₄×C₁₃	1	4	yes	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	C₄⋊C₈	—	2	2	no	—
287	#103	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	8	no	—
290	C₄×C₈	—	2	2	no	—
291	#95	—	2	1	no	—
292	C₂×C₁₃	—	16	2	no	—
293	C₂×C₁₃	#2436	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
295	C₂×C₁₃	#3008	1	1	yes	characteristic
296	C₂×C₁₃	#3362	1	2	yes	—
297	C₂×C₁₃	#3375	1	2	yes	—
298	C₂⁴	—	2	2	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	8	2	no	—
306	C₂×Q₈	—	8	4	no	—
307	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	complemented
308	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
309	C₂×Q₈	C₁₃×#41	1	4	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	8	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
328	SD₁₆	—	4	8	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²⋊C₄	—	4	8	no	—
347	C₂²⋊C₄	—	8	4	no	—
348	C₄²	—	2	8	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂×D₄×C₁₃	1	2	yes	—
354	C₄²	C₂×D₄×C₁₃	1	2	yes	—
355	C₁₃	#25932	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	4	2	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
362	Q₈	—	2	8	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	8	4	no	—
366	Q₈	—	8	8	no	—
367	Q₈	C₁₃×#124	1	4	yes	complemented
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	4	no	—
371	D₄	—	8	4	no	—
372	D₄	—	8	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	C₁₃×#120	1	2	yes	—
388	C₂×C₄	C₁₃×#120	1	2	yes	—
389	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
390	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
391	C₂×C₄	C₁₃×#137	1	2	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
395	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
404	C₂²	C₁₃×#548	1	2	yes	—
405	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
406	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
407	C₂²	C₁₃×#576	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₁₃×#448	1	4	yes	—
416	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
417	C₄	C₁₃×#536	1	1	yes	characteristic
418	C₄	C₁₃×#548	1	2	yes	—
419	C₂	—	16	2	no	—
420	C₂	C₁₃×#2436	1	1	yes	characteristic
421	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
422	C₂	C₁₃×#3008	1	1	yes	characteristic
423	C₂	C₁₃×#3362	1	2	yes	—
424	C₂	C₁₃×#3375	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈²×C₁₃	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
8. C₁₃×#1880	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
86. #25932	C₁₃	direct (N × H)
96. C₂×Q₈×C₁₃	SD₁₆	semidirect
144. C₂×Q₈²	C₂×C₁₃	semidirect
148. #2023	C₂×C₁₃	semidirect
149. #1987	C₂×C₁₃	semidirect
150. #1984	C₂×C₁₃	semidirect
151. #1880	C₂×C₁₃	semidirect
152. C₄×#103	C₂×C₁₃	semidirect
164. Q₈×C₁₃	#124	semidirect
307. C₂×Q₈	C₁₃×SD₁₆	semidirect
355. C₁₃	#25932	direct (N × H)
367. Q₈	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₁₃	2
C₂×C₁₃×#486	2
C₂×C₁₃×#460	2
C₁₃×#2548	2
C₁₃×#2023	2
C₁₃×#1987	2
C₁₃×#1984	2
C₁₃×#1880	2
C₄×C₁₃×#103	2
#25932	13

Subgroups — C13×#25932 #15712271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25932 #15712271