Subgroups — C₁₃×#23684 #15710023

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#440	—	2	8	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#97	C₂²	1	2	yes	—
26	C₁₃×#391	C₂²	1	1	yes	characteristic
27	C₁₃×#391	C₂²	1	1	yes	characteristic
28	C₁₃×#390	—	2	1	no	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#389	C₂²	1	1	yes	characteristic
33	C₁₃×#387	—	2	1	no	—
34	C₁₃×#387	—	2	1	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
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×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	4	no	—
51	C₂×C₁₃×SD₁₆	—	2	4	no	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×#127	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	4	4	no	—
60	C₄×D₄×C₁₃	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#107	—	2	4	no	—
83	C₁₃×C₄⋊C₈	—	2	4	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×#102	—	2	4	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₁₃×#102	—	2	4	no	—
88	C₁₃×#97	—	2	4	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	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	1	no	—
96	#23684	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	#41	1	4	yes	—
114	C₂²×C₄×C₁₃	—	2	1	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	—	4	4	no	—
120	C₂²×C₄×C₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₃	—	4	4	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×SD₁₆	—	2	16	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	#41	1	4	yes	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	—	4	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₄²×C₁₃	—	2	4	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	4	1	no	—
157	C₄²×C₁₃	—	4	2	no	—
158	C₄²×C₁₃	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃	#41	1	2	yes	—
160	C₂×#440	C₂×C₁₃	1	2	yes	complemented
161	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
162	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2083	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2067	C₂×C₁₃	1	2	yes	complemented
166	#2055	C₂×C₁₃	1	2	yes	complemented
167	#2041	C₂×C₁₃	1	1	yes	characteristic
168	#2014	C₂×C₁₃	1	1	yes	characteristic
169	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1762	C₂×C₁₃	1	2	yes	complemented
171	C₂³×C₁₃	—	2	4	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	4	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	4	no	—
183	D₄×C₁₃	—	4	8	no	—
184	D₄×C₁₃	—	4	8	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	8	8	no	—
216	C₂×C₄×C₁₃	#121	1	2	yes	—
217	C₂×C₄×C₁₃	#121	1	2	yes	—
218	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₁₃	#137	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₈×C₁₃	—	2	4	no	—
226	C₈×C₁₃	—	4	2	no	—
227	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
228	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
233	#440	—	2	8	no	—
234	C₂×#107	C₂²×C₁₃	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#102	C₂²×C₁₃	1	2	yes	—
238	C₂×#102	C₂²×C₁₃	1	2	yes	—
239	C₂×#102	C₂²×C₁₃	1	2	yes	—
240	C₂×#97	C₂²×C₁₃	1	2	yes	—
241	#391	C₂²×C₁₃	1	1	yes	characteristic
242	#391	C₂²×C₁₃	1	1	yes	characteristic
243	#390	—	2	1	no	—
244	#390	—	2	1	no	—
245	#390	C₂²×C₁₃	1	2	yes	—
246	#389	C₂²×C₁₃	1	1	yes	characteristic
247	#389	C₂²×C₁₃	1	1	yes	characteristic
248	#387	—	2	1	no	—
249	#387	—	2	1	no	—
250	#384	C₂²×C₁₃	1	1	yes	characteristic
251	C₄×C₄⋊C₄	—	2	1	no	—
252	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	#376	—	2	1	no	—
254	C₄³	C₂²×C₁₃	1	1	yes	characteristic
255	#340	C₂²×C₁₃	1	2	yes	—
256	#340	C₂²×C₁₃	1	2	yes	—
257	#336	C₂²×C₁₃	1	1	yes	characteristic
258	#336	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	8	2	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
267	C₂²×C₁₃	#525	1	1	yes	characteristic
268	C₂²×C₁₃	#532	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
272	C₂²×C₁₃	#575	1	1	yes	characteristic
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	8	1	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	—	8	2	no	—
284	C₄×C₁₃	#525	1	2	yes	—
285	C₄×C₁₃	#529	1	2	yes	—
286	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
290	C₂³×C₄	—	2	2	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
296	#127	—	2	4	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	D₄×C₁₃	1	4	yes	complemented
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	4	4	no	—
302	C₄×D₄	—	4	4	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
324	#107	—	2	4	no	—
325	C₄⋊C₈	—	2	4	no	—
326	#103	—	2	4	no	—
327	#102	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	—	2	4	no	—
330	#97	—	2	4	no	—
331	#95	—	2	1	no	—
332	#95	—	2	1	no	—
333	#95	—	2	1	no	—
334	#95	—	2	1	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	C₂×C₁₃	—	8	4	no	—
339	C₂×C₁₃	#2392	1	1	yes	characteristic
340	C₂×C₁₃	#3037	1	1	yes	characteristic
341	C₂×C₁₃	#3038	1	1	yes	characteristic
342	C₂×C₁₃	#3110	1	1	yes	characteristic
343	C₂×C₁₃	#3114	1	1	yes	characteristic
344	C₂×C₁₃	#3180	1	1	yes	characteristic
345	C₂×C₁₃	#3182	1	1	yes	characteristic
346	C₂⁴	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	C₁₃×#41	1	4	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
378	SD₁₆	—	2	16	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	C₁₃×#41	1	4	yes	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	4	1	no	—
406	C₄²	—	4	2	no	—
407	C₄²	C₂×D₄×C₁₃	1	2	yes	—
408	C₄²	C₁₃×#41	1	2	yes	—
409	C₁₃	#23684	1	1	yes	characteristic, direct product factor, Sylow
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	4	2	no	—
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	8	no	—
423	D₄	—	4	8	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	8	8	no	—
455	C₂×C₄	C₁₃×#121	1	2	yes	—
456	C₂×C₄	C₁₃×#121	1	2	yes	—
457	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
458	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
459	C₂×C₄	C₁₃×#137	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
462	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
463	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
474	C₂²	C₁₃×#525	1	1	yes	characteristic
475	C₂²	C₁₃×#532	1	1	yes	characteristic
476	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
477	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
479	C₂²	C₁₃×#575	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	C₁₃×#525	1	2	yes	—
492	C₄	C₁₃×#529	1	2	yes	—
493	C₂	—	8	4	no	—
494	C₂	C₁₃×#2392	1	1	yes	characteristic
495	C₂	C₁₃×#3037	1	1	yes	characteristic
496	C₂	C₁₃×#3038	1	1	yes	characteristic
497	C₂	C₁₃×#3110	1	1	yes	characteristic
498	C₂	C₁₃×#3114	1	1	yes	characteristic
499	C₂	C₁₃×#3180	1	1	yes	characteristic
500	C₂	C₁₃×#3182	1	1	yes	characteristic

	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#440	C₂	semidirect
3. C₁₃×#2295	C₂	semidirect
4. C₁₃×#2083	C₂	semidirect
5. C₁₃×#2072	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2055	C₂	semidirect
10. C₁₃×#1767	C₂	semidirect
11. C₁₃×#1762	C₂	semidirect
56. C₄×Q₈×C₁₃	D₄	semidirect
96. #23684	C₁₃	direct (N × H)
160. C₂×#440	C₂×C₁₃	semidirect
162. #2295	C₂×C₁₃	semidirect
163. #2083	C₂×C₁₃	semidirect
164. #2072	C₂×C₁₃	semidirect
165. #2067	C₂×C₁₃	semidirect
166. #2055	C₂×C₁₃	semidirect
169. #1767	C₂×C₁₃	semidirect
170. #1762	C₂×C₁₃	semidirect
298. C₄×Q₈	D₄×C₁₃	semidirect
409. C₁₃	#23684	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×#440	2
C₄×C₁₃×#127	2
C₁₃×#2295	2
C₁₃×#2083	2
C₁₃×#2072	2
C₁₃×#2067	2
C₁₃×#2055	2
C₁₃×#2041	2
C₁₃×#2014	2
C₁₃×#1767	2
C₁₃×#1762	2
#23684	13

Subgroups — C13×#23684 #15710023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23684 #15710023