Subgroups — C₁₃×#23613 #15709952

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#427	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×#2317	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×#1736	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×#427	—	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	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₁₃×#419	—	2	4	no	—
24	C₂×C₁₃×#103	—	2	4	no	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₁₃×#391	—	2	1	no	—
29	C₁₃×#391	—	2	1	no	—
30	C₁₃×#391	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#385	—	2	2	no	—
33	C₁₃×#384	—	2	1	no	—
34	C₁₃×#382	—	2	1	no	—
35	C₁₃×#381	—	2	2	no	—
36	C₁₃×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	1	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	—	2	2	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	Q₈	1	4	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	D₄	1	4	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	—	2	2	no	—
60	C₁₃×#117	—	2	2	no	—
61	C₁₃×#117	—	2	2	no	—
62	C₁₃×#117	D₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×#106	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	8	no	—
85	C₁₃×#95	—	2	4	no	—
86	C₁₃×#95	—	2	4	no	—
87	C₁₃×#95	—	2	4	no	—
88	#23613	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	8	no	—
93	C₂×Q₈×C₁₃	—	2	8	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	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	4	no	—
101	C₂×Q₈×C₁₃	—	4	4	no	—
102	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	8	2	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₃	#41	1	2	yes	—
119	C₂²×C₄×C₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×M₁₆	—	4	4	no	—
123	C₂×C₈×C₁₃	—	2	8	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	8	4	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₁₃×C₂²⋊C₄	—	2	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₄²×C₁₃	—	2	4	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	4	2	no	—
150	C₂×#427	C₂×C₁₃	1	1	yes	characteristic
151	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
152	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
153	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic
154	#2317	C₂×C₁₃	1	1	yes	characteristic
155	#2310	C₂×C₁₃	1	1	yes	characteristic
156	#2068	C₂×C₁₃	1	4	yes	complemented
157	#2066	C₂×C₁₃	1	4	yes	complemented
158	#1736	C₂×C₁₃	1	1	yes	characteristic
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	#121	1	2	yes	—
162	C₂³×C₁₃	#121	1	2	yes	—
163	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
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	Q₈×C₁₃	—	4	8	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	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	8	no	—
181	C₂×C₄×C₁₃	—	4	2	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	—	4	2	no	—
186	C₂×C₄×C₁₃	—	8	4	no	—
187	C₂×C₄×C₁₃	#121	1	4	yes	—
188	C₂×C₄×C₁₃	#121	1	2	yes	—
189	C₂×C₄×C₁₃	#121	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
191	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
192	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₁₃	#126	1	4	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	4	2	no	—
203	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
210	#427	—	2	4	no	—
211	C₂×#107	C₂²×C₁₃	1	2	yes	—
212	C₂×#106	C₂²×C₁₃	1	2	yes	—
213	#424	—	2	4	no	—
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
216	#419	—	2	4	no	—
217	C₂×#103	—	2	4	no	—
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	4	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	#391	—	2	1	no	—
222	#391	—	2	1	no	—
223	#391	C₂²×C₁₃	1	4	yes	—
224	#389	C₂²×C₁₃	1	4	yes	—
225	#385	—	2	2	no	—
226	#384	—	2	1	no	—
227	#382	—	2	1	no	—
228	#381	—	2	2	no	—
229	#340	C₂²×C₁₃	1	4	yes	—
230	C₂²×C₁₃	—	2	4	no	—
231	C₂²×C₁₃	—	2	4	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	#396	1	4	yes	—
235	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
236	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
237	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₂²×C₁₃	#577	1	2	yes	—
239	C₂²×C₁₃	#578	1	2	yes	—
240	C₄×C₁₃	—	4	4	no	—
241	C₄×C₁₃	—	4	4	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	—	8	2	no	—
246	C₄×C₁₃	#396	1	4	yes	—
247	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
248	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
250	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	Q₈×C₁₃	1	4	yes	—
258	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	D₄×C₁₃	1	4	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	#117	D₄×C₁₃	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
292	#107	—	2	4	no	—
293	#106	—	2	4	no	—
294	C₄⋊C₈	—	2	4	no	—
295	C₄⋊C₈	—	2	4	no	—
296	#103	—	2	4	no	—
297	#103	—	2	4	no	—
298	#103	—	2	8	no	—
299	#95	—	2	4	no	—
300	#95	—	2	4	no	—
301	#95	—	2	4	no	—
302	C₂×C₁₃	—	2	4	no	—
303	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
304	C₂×C₁₃	#3046	1	2	yes	—
305	C₂×C₁₃	#3057	1	1	yes	characteristic
306	C₂×C₁₃	#3059	1	1	yes	characteristic
307	C₂×C₁₃	#3082	1	2	yes	—
308	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	2	no	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
337	C₂²×C₄	C₁₃×#41	1	2	yes	—
338	C₂²×C₄	C₁₃×#41	1	2	yes	—
339	C₂²×C₄	C₁₃×#41	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
341	M₁₆	—	4	4	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	8	4	no	—
361	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₁₃	#23613	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	C₁₃×#121	1	2	yes	—
373	C₂³	C₁₃×#121	1	2	yes	—
374	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
375	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
376	Q₈	—	2	4	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	4	8	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	4	no	—
398	C₂×C₄	C₁₃×#121	1	2	yes	—
399	C₂×C₄	C₁₃×#121	1	2	yes	—
400	C₂×C₄	C₁₃×#121	1	4	yes	—
401	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
402	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
403	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
404	C₂×C₄	C₁₃×#126	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
409	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	C₁₃×#396	1	4	yes	—
419	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
420	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
421	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
422	C₂²	C₁₃×#577	1	2	yes	—
423	C₂²	C₁₃×#578	1	2	yes	—
424	C₄	—	4	4	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₁₃×#396	1	4	yes	—
431	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
432	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
433	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
434	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
435	C₂	—	2	4	no	—
436	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
437	C₂	C₁₃×#3046	1	2	yes	—
438	C₂	C₁₃×#3057	1	1	yes	characteristic
439	C₂	C₁₃×#3059	1	1	yes	characteristic
440	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
88. #23613	C₁₃	direct (N × H)
156. #2068	C₂×C₁₃	semidirect
157. #2066	C₂×C₁₃	semidirect
369. C₁₃	#23613	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×#427	2
C₂×C₁₃×#424	2
C₂×C₁₃×#419	2
C₂²×C₁₃×#103	2
C₁₃×#2317	2
C₁₃×#2310	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#1736	2
#23613	13

Subgroups — C13×#23613 #15709952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23613 #15709952