Subgroups — C₁₃×#23615 #15709954

Order 3328.

1054 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×C₁₃×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2316	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2310	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2068	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2066	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1735	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#428	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₁₃×#424	—	2	4	no	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
22	C₁₃×#419	—	2	4	no	—
23	C₂×C₁₃×#103	—	2	4	no	—
24	C₂×C₁₃×#103	C₂²	1	4	yes	—
25	C₂×C₁₃×#103	C₂²	1	4	yes	—
26	C₁₃×#391	—	2	2	no	—
27	C₁₃×#391	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	2	yes	—
29	C₁₃×#389	—	2	2	no	—
30	C₁₃×#389	C₂²	1	4	yes	—
31	C₁₃×#381	—	2	2	no	—
32	C₁₃×#380	—	2	2	no	—
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	—	2	1	no	—
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	2	no	—
41	C₂²×Q₈×C₁₃	Q₈	1	4	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×#117	—	2	2	no	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#106	—	2	4	no	—
77	C₁₃×C₄⋊C₈	—	2	8	no	—
78	C₁₃×#103	—	2	8	no	—
79	C₁₃×#103	—	2	8	no	—
80	C₁₃×#95	—	2	4	no	—
81	C₁₃×#95	—	2	4	no	—
82	C₁₃×#95	—	2	4	no	—
83	#23615	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	—	2	4	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	8	no	—
88	C₂×Q₈×C₁₃	—	2	8	no	—
89	C₂×Q₈×C₁₃	—	2	2	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	—	4	2	no	—
94	C₂×Q₈×C₁₃	—	4	2	no	—
95	C₂×Q₈×C₁₃	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	4	4	no	—
97	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	8	2	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₁₃	#41	1	2	yes	—
114	C₂²×C₄×C₁₃	#41	1	2	yes	—
115	C₂²×C₄×C₁₃	#41	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×M₁₆	—	2	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	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	4	4	no	—
124	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	8	4	no	—
135	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
136	C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₂×#428	C₂×C₁₃	1	1	yes	characteristic
144	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
145	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
146	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic
147	#2316	C₂×C₁₃	1	1	yes	characteristic
148	#2310	C₂×C₁₃	1	1	yes	characteristic
149	#2068	C₂×C₁₃	1	4	yes	complemented
150	#2066	C₂×C₁₃	1	4	yes	complemented
151	#1735	C₂×C₁₃	1	1	yes	characteristic
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	#121	1	2	yes	—
155	C₂³×C₁₃	#121	1	2	yes	—
156	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
157	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	Q₈×C₁₃	—	4	8	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	8	4	no	—
180	C₂×C₄×C₁₃	#121	1	4	yes	—
181	C₂×C₄×C₁₃	#121	1	2	yes	—
182	C₂×C₄×C₁₃	#121	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
185	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₃	#126	1	4	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₈×C₁₃	—	2	4	no	—
194	C₈×C₁₃	—	4	2	no	—
195	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
197	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
202	#428	—	2	4	no	—
203	C₂×#107	C₂²×C₁₃	1	2	yes	—
204	C₂×#106	C₂²×C₁₃	1	2	yes	—
205	#424	—	2	4	no	—
206	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
207	#419	—	2	4	no	—
208	C₂×#103	—	2	4	no	—
209	C₂×#103	C₂²×C₁₃	1	4	yes	—
210	C₂×#103	C₂²×C₁₃	1	4	yes	—
211	#391	—	2	2	no	—
212	#391	C₂²×C₁₃	1	2	yes	—
213	#391	C₂²×C₁₃	1	2	yes	—
214	#389	—	2	2	no	—
215	#389	C₂²×C₁₃	1	4	yes	—
216	#381	—	2	2	no	—
217	#380	—	2	2	no	—
218	#340	C₂²×C₁₃	1	2	yes	—
219	#340	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₁₃	—	2	4	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	#396	1	4	yes	—
225	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
228	C₂²×C₁₃	#577	1	2	yes	—
229	C₂²×C₁₃	#578	1	2	yes	—
230	C₄×C₁₃	—	4	4	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	#396	1	4	yes	—
237	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
238	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
239	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
240	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	2	2	no	—
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	2	2	no	—
247	C₂²×Q₈	Q₈×C₁₃	1	4	yes	—
248	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
259	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
270	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
281	#107	—	2	4	no	—
282	#106	—	2	4	no	—
283	C₄⋊C₈	—	2	8	no	—
284	#103	—	2	8	no	—
285	#103	—	2	8	no	—
286	#95	—	2	4	no	—
287	#95	—	2	4	no	—
288	#95	—	2	4	no	—
289	C₂×C₁₃	—	2	4	no	—
290	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
291	C₂×C₁₃	#3042	1	1	yes	characteristic
292	C₂×C₁₃	#3044	1	1	yes	characteristic
293	C₂×C₁₃	#3063	1	2	yes	—
294	C₂×C₁₃	#3082	1	2	yes	—
295	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	2	8	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	—	4	4	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	8	2	no	—
319	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
324	C₂²×C₄	C₁₃×#41	1	2	yes	—
325	C₂²×C₄	C₁₃×#41	1	2	yes	—
326	C₂²×C₄	C₁₃×#41	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
328	M₁₆	—	2	8	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	4	no	—
335	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	8	4	no	—
346	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	2	no	—
353	C₄²	—	4	2	no	—
354	C₁₃	#23615	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	C₁₃×#121	1	2	yes	—
358	C₂³	C₁₃×#121	1	2	yes	—
359	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
360	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	2	4	no	—
363	Q₈	—	4	8	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	4	no	—
383	C₂×C₄	C₁₃×#121	1	2	yes	—
384	C₂×C₄	C₁₃×#121	1	2	yes	—
385	C₂×C₄	C₁₃×#121	1	4	yes	—
386	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
387	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
388	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
389	C₂×C₄	C₁₃×#126	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
394	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
396	C₈	—	2	4	no	—
397	C₈	—	4	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	C₁₃×#396	1	4	yes	—
403	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
404	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
405	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
406	C₂²	C₁₃×#577	1	2	yes	—
407	C₂²	C₁₃×#578	1	2	yes	—
408	C₄	—	4	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	—	8	2	no	—
414	C₄	C₁₃×#396	1	4	yes	—
415	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
416	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
417	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
418	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
419	C₂	—	2	4	no	—
420	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
421	C₂	C₁₃×#3042	1	1	yes	characteristic
422	C₂	C₁₃×#3044	1	1	yes	characteristic
423	C₂	C₁₃×#3063	1	2	yes	—
424	C₂	C₁₃×#3082	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2066	C₂	semidirect
83. #23615	C₁₃	direct (N × H)
149. #2068	C₂×C₁₃	semidirect
150. #2066	C₂×C₁₃	semidirect
354. C₁₃	#23615	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×#428	2
C₂×C₁₃×#424	2
C₂×C₁₃×#419	2
C₂²×C₁₃×#103	2
C₁₃×#2316	2
C₁₃×#2310	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#1735	2
#23615	13

Subgroups — C13×#23615 #15709954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23615 #15709954