Subgroups — C₁₃×#23736 #15710075

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 474 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×#427	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×#2097	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2097	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2096	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2095	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#428	—	2	4	no	—
20	C₁₃×#427	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	2	yes	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	2	yes	—
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₁₃×#419	—	2	4	no	—
28	C₂×C₁₃×#103	—	2	4	no	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₁₃×#391	—	2	2	no	—
34	C₁₃×#391	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#385	—	2	2	no	—
38	C₁₃×#384	C₂²	1	2	yes	—
39	C₁₃×#382	C₂²	1	2	yes	—
40	C₁₃×#381	—	2	2	no	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	2	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	Q₈	1	4	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	D₄	1	4	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#117	—	2	2	no	—
64	C₁₃×#117	—	2	2	no	—
65	C₁₃×#117	—	2	2	no	—
66	C₁₃×#117	—	2	2	no	—
67	C₁₃×#117	—	2	2	no	—
68	C₁₃×#117	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₁₃×#107	—	2	2	no	—
86	C₁₃×#107	—	2	2	no	—
87	C₁₃×#107	—	2	4	no	—
88	C₁₃×#106	—	2	2	no	—
89	C₁₃×#106	—	2	2	no	—
90	C₁₃×#106	—	2	4	no	—
91	C₁₃×#103	—	2	4	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#95	—	2	4	no	—
96	C₁₃×#95	—	2	4	no	—
97	C₁₃×#95	—	2	4	no	—
98	#23736	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₃	—	2	4	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	8	no	—
103	C₂×Q₈×C₁₃	—	2	8	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×Q₈×C₁₃	—	4	4	no	—
110	C₂×Q₈×C₁₃	—	4	4	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	8	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₁₃	#41	1	2	yes	—
130	C₂²×C₄×C₁₃	#41	1	2	yes	—
131	C₂²×C₄×C₁₃	#41	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×M₁₆	—	2	8	no	—
134	C₂×C₈×C₁₃	—	2	8	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	—	8	4	no	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	2	no	—
163	C₄²×C₁₃	—	4	2	no	—
164	C₂×#428	C₂×C₁₃	1	1	yes	characteristic
165	C₂×#427	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
167	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic
168	#2317	C₂×C₁₃	1	1	yes	characteristic
169	#2310	C₂×C₁₃	1	1	yes	characteristic
170	#2097	C₂×C₁₃	1	2	yes	complemented
171	#2097	C₂×C₁₃	1	2	yes	complemented
172	#2096	C₂×C₁₃	1	2	yes	complemented
173	#2095	C₂×C₁₃	1	2	yes	complemented
174	#1729	C₂×C₁₃	1	1	yes	characteristic
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
178	C₂³×C₁₃	#123	1	2	yes	—
179	C₂³×C₁₃	#127	1	2	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	4	no	—
182	Q₈×C₁₃	—	2	4	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	8	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	8	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	8	4	no	—
204	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₁₃	#123	1	4	yes	—
208	C₂×C₄×C₁₃	#123	1	4	yes	—
209	C₂×C₄×C₁₃	#123	1	2	yes	—
210	C₂×C₄×C₁₃	#127	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₈×C₁₃	—	2	2	no	—
218	C₈×C₁₃	—	2	2	no	—
219	C₈×C₁₃	—	2	4	no	—
220	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	#428	—	2	4	no	—
228	#427	—	2	4	no	—
229	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#107	C₂²×C₁₃	1	2	yes	—
231	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#106	C₂²×C₁₃	1	2	yes	—
234	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
235	#419	—	2	4	no	—
236	C₂×#103	—	2	4	no	—
237	C₂×#103	C₂²×C₁₃	1	2	yes	—
238	C₂×#103	C₂²×C₁₃	1	2	yes	—
239	C₂×#103	C₂²×C₁₃	1	2	yes	—
240	C₂×#103	C₂²×C₁₃	1	2	yes	—
241	#391	—	2	2	no	—
242	#391	C₂²×C₁₃	1	2	yes	—
243	#391	C₂²×C₁₃	1	2	yes	—
244	#389	—	2	2	no	—
245	#385	—	2	2	no	—
246	#384	C₂²×C₁₃	1	2	yes	—
247	#382	C₂²×C₁₃	1	2	yes	—
248	#381	—	2	2	no	—
249	#336	C₂²×C₁₃	1	2	yes	—
250	#336	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	2	4	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	#399	1	4	yes	—
256	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
259	C₂²×C₁₃	#577	1	2	yes	—
260	C₂²×C₁₃	#578	1	2	yes	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	—	8	1	no	—
265	C₄×C₁₃	—	8	2	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	#399	1	4	yes	—
269	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
270	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
271	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
272	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	—	2	2	no	—
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×Q₈	Q₈×C₁₃	1	4	yes	—
280	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	D₄×C₁₃	1	4	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
293	#117	—	2	2	no	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
315	#107	—	2	2	no	—
316	#107	—	2	2	no	—
317	#107	—	2	4	no	—
318	#106	—	2	2	no	—
319	#106	—	2	2	no	—
320	#106	—	2	4	no	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#95	—	2	4	no	—
326	#95	—	2	4	no	—
327	#95	—	2	4	no	—
328	C₂×C₁₃	—	2	4	no	—
329	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
330	C₂×C₁₃	#3082	1	2	yes	—
331	C₂×C₁₃	#3097	1	2	yes	—
332	C₂×C₁₃	#3154	1	1	yes	characteristic
333	C₂×C₁₃	#3156	1	1	yes	characteristic
334	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	2	8	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	8	2	no	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
364	C₂²×C₄	C₁₃×#41	1	2	yes	—
365	C₂²×C₄	C₁₃×#41	1	2	yes	—
366	C₂²×C₄	C₁₃×#41	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
368	M₁₆	—	2	8	no	—
369	C₂×C₈	—	2	8	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
377	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
378	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	8	4	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	2	no	—
398	C₄²	—	4	2	no	—
399	C₁₃	#23736	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
403	C₂³	C₁₃×#123	1	2	yes	—
404	C₂³	C₁₃×#127	1	2	yes	—
405	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	8	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	4	no	—
429	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
430	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
431	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
432	C₂×C₄	C₁₃×#123	1	2	yes	—
433	C₂×C₄	C₁₃×#123	1	4	yes	—
434	C₂×C₄	C₁₃×#123	1	4	yes	—
435	C₂×C₄	C₁₃×#127	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
441	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	C₁₃×#399	1	4	yes	—
450	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
451	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
452	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
453	C₂²	C₁₃×#577	1	2	yes	—
454	C₂²	C₁₃×#578	1	2	yes	—
455	C₄	—	4	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₁₃×#399	1	4	yes	—
463	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
464	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
465	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
466	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
467	C₂	—	2	4	no	—
468	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
469	C₂	C₁₃×#3082	1	2	yes	—
470	C₂	C₁₃×#3097	1	2	yes	—
471	C₂	C₁₃×#3154	1	1	yes	characteristic
472	C₂	C₁₃×#3156	1	1	yes	characteristic

	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×#2097	C₂	semidirect
8. C₁₃×#2097	C₂	semidirect
9. C₁₃×#2096	C₂	semidirect
10. C₁₃×#2095	C₂	semidirect
98. #23736	C₁₃	direct (N × H)
170. #2097	C₂×C₁₃	semidirect
171. #2097	C₂×C₁₃	semidirect
172. #2096	C₂×C₁₃	semidirect
173. #2095	C₂×C₁₃	semidirect
399. C₁₃	#23736	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×#427	2
C₂×C₁₃×#419	2
C₂²×C₁₃×#103	2
C₁₃×#2317	2
C₁₃×#2310	2
C₁₃×#2097	2
C₁₃×#2096	2
C₁₃×#2095	2
C₁₃×#1729	2
#23736	13

Subgroups — C13×#23736 #15710075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23736 #15710075