Subgroups — C₁₃×#23679 #15710018

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 454 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
2	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2068	C₂	1	2	yes	maximal
7	C₁₃×#2056	C₂	1	2	yes	maximal
8	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#103	C₂	1	2	yes	maximal
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×Q₁₆	—	2	8	no	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
24	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	2	yes	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	—	2	1	no	—
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#387	—	2	1	no	—
32	C₁₃×#387	—	2	1	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#376	—	2	1	no	—
39	C₄³×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₁₃×#336	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
46	C₂×C₁₃×Q₁₆	—	2	4	no	—
47	C₂×C₁₃×Q₁₆	—	2	4	no	—
48	C₂×C₁₃×Q₁₆	—	2	4	no	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	2	4	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	—	2	4	no	—
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	D₄	1	4	yes	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₄×C₈×C₁₃	—	2	4	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	#23679	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₁₃	#41	1	4	yes	—
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	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×Q₁₆	—	2	16	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	—	2	2	no	—
124	C₂×C₈×C₁₃	#41	1	4	yes	—
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	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	4	1	no	—
145	C₄²×C₁₃	—	4	4	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₄²×C₁₃	Q₁₆	1	4	yes	complemented
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₄²×C₁₃	#41	1	2	yes	—
150	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	—
151	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
152	#2295	C₂×C₁₃	1	1	yes	characteristic
153	#2083	C₂×C₁₃	1	1	yes	characteristic
154	#2072	C₂×C₁₃	1	1	yes	characteristic
155	#2068	C₂×C₁₃	1	2	yes	—
156	#2056	C₂×C₁₃	1	2	yes	—
157	#2043	C₂×C₁₃	1	1	yes	characteristic
158	#2016	C₂×C₁₃	1	1	yes	characteristic
159	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
160	C₄×#103	C₂×C₁₃	1	2	yes	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	4	no	—
163	Q₈×C₁₃	—	2	4	no	—
164	Q₈×C₁₃	—	2	4	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	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	2	no	—
197	C₂×C₄×C₁₃	#121	1	2	yes	—
198	C₂×C₄×C₁₃	#121	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
202	C₂×C₄×C₁₃	#135	1	2	yes	—
203	C₂×C₄×C₁₃	#137	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₃	—	2	4	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×Q₁₆	—	2	8	no	—
215	C₂×#107	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
217	C₂×#103	C₂²×C₁₃	1	2	yes	—
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
222	#391	C₂²×C₁₃	1	2	yes	—
223	#391	C₂²×C₁₃	1	1	yes	characteristic
224	#391	C₂²×C₁₃	1	1	yes	characteristic
225	#389	—	2	1	no	—
226	#389	—	2	1	no	—
227	#389	C₂²×C₁₃	1	1	yes	characteristic
228	#389	C₂²×C₁₃	1	1	yes	characteristic
229	#387	—	2	1	no	—
230	#387	—	2	1	no	—
231	#384	C₂²×C₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	—	2	1	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	#376	—	2	1	no	—
237	C₄³	C₂²×C₁₃	1	1	yes	characteristic
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#336	C₂²×C₁₃	1	1	yes	characteristic
241	#336	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
243	C₂²×C₁₃	#525	1	1	yes	characteristic
244	C₂²×C₁₃	#532	1	1	yes	characteristic
245	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
248	C₂²×C₁₃	#575	1	1	yes	characteristic
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	8	1	no	—
258	C₄×C₁₃	—	8	1	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	#462	1	4	yes	—
261	C₄×C₁₃	#525	1	2	yes	—
262	C₄×C₁₃	#529	1	2	yes	—
263	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
265	C₂×Q₁₆	—	2	4	no	—
266	C₂×Q₁₆	—	2	4	no	—
267	C₂×Q₁₆	—	2	4	no	—
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	4	no	—
274	C₄×Q₈	D₄×C₁₃	1	4	yes	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	#107	—	2	4	no	—
298	C₄⋊C₈	—	2	4	no	—
299	#103	—	2	4	no	—
300	#103	—	2	4	no	—
301	#103	—	2	4	no	—
302	#103	—	2	4	no	—
303	C₄×C₈	—	2	4	no	—
304	#95	—	2	1	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	1	no	—
308	#95	—	2	1	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	C₂×C₁₃	#2392	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
315	C₂×C₁₃	#3035	1	1	yes	characteristic
316	C₂×C₁₃	#3104	1	1	yes	characteristic
317	C₂×C₁₃	#3108	1	1	yes	characteristic
318	C₂×C₁₃	#3170	1	1	yes	characteristic
319	C₂×C₁₃	#3172	1	1	yes	characteristic
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
329	C₂×Q₈	C₁₃×#41	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
343	Q₁₆	—	2	16	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	C₁₃×#41	1	4	yes	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	1	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	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₁₃×Q₁₆	1	4	yes	complemented
373	C₄²	C₂×D₄×C₁₃	1	2	yes	—
374	C₄²	C₁₃×#41	1	2	yes	—
375	C₁₃	#23679	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	C₁₃×#121	1	2	yes	—
413	C₂×C₄	C₁₃×#121	1	2	yes	—
414	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
415	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
416	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
417	C₂×C₄	C₁₃×#135	1	2	yes	—
418	C₂×C₄	C₁₃×#137	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
421	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
426	C₂²	C₁₃×#525	1	1	yes	characteristic
427	C₂²	C₁₃×#532	1	1	yes	characteristic
428	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
429	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
430	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
431	C₂²	C₁₃×#575	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₁₃×#462	1	4	yes	—
444	C₄	C₁₃×#525	1	2	yes	—
445	C₄	C₁₃×#529	1	2	yes	—
446	C₂	C₁₃×#2392	1	1	yes	characteristic
447	C₂	C₂×C₁₃×#462	1	1	yes	characteristic
448	C₂	C₁₃×#3035	1	1	yes	characteristic
449	C₂	C₁₃×#3104	1	1	yes	characteristic
450	C₂	C₁₃×#3108	1	1	yes	characteristic
451	C₂	C₁₃×#3170	1	1	yes	characteristic
452	C₂	C₁₃×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×D₄
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
94. #23679	C₁₃	direct (N × H)
147. C₄²×C₁₃	Q₁₆	semidirect
372. C₄²	C₁₃×Q₁₆	semidirect
375. C₁₃	#23679	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
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2295	2
C₁₃×#2083	2
C₁₃×#2072	2
C₁₃×#2068	2
C₁₃×#2056	2
C₁₃×#2043	2
C₁₃×#2016	2
C₄×C₁₃×C₄⋊C₈	2
C₄×C₁₃×#103	2
#23679	13

Subgroups — C13×#23679 #15710018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23679 #15710018