Subgroups — C₁₃×#23676 #15710015

Order 3328.

1092 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2054	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2011	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₄×C₁₃×D₈	—	2	8	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	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×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#390	—	2	1	no	—
28	C₁₃×#390	—	2	1	no	—
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#390	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#388	—	2	1	no	—
35	C₁₃×#388	—	2	1	no	—
36	C₁₃×#384	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₂²⋊C₄	—	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×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	4	no	—
52	C₂×C₁₃×D₈	—	2	4	no	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#127	—	2	4	no	—
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	4	4	no	—
60	C₄×D₄×C₁₃	—	4	4	no	—
61	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
62	C₁₃×#117	—	4	4	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	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#107	—	2	4	no	—
88	C₁₃×C₄⋊C₈	—	2	4	no	—
89	C₁₃×#102	—	2	4	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₄×C₈×C₁₃	—	2	4	no	—
94	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	1	no	—
96	C₁₃×#95	—	2	1	no	—
97	#23676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	1	no	—
99	C₂⁴×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	4	no	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	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	1	no	—
109	C₂×D₄×C₁₃	—	2	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	—	4	2	no	—
114	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₃	#41	1	4	yes	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	4	4	no	—
124	C₂²×C₄×C₁₃	—	4	4	no	—
125	C₂²×C₄×C₁₃	—	4	4	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×D₈	—	2	16	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	#41	1	4	yes	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	1	no	—
163	C₄²×C₁₃	—	4	2	no	—
164	C₄²×C₁₃	D₈	1	4	yes	complemented
165	C₄²×C₁₃	C₂×D₄	1	2	yes	—
166	C₄²×C₁₃	#41	1	2	yes	—
167	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
168	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#2083	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2067	C₂×C₁₃	1	2	yes	complemented
173	#2054	C₂×C₁₃	1	2	yes	complemented
174	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2011	C₂×C₁₃	1	1	yes	characteristic
176	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₄×#102	C₂×C₁₃	1	2	yes	complemented
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	D₄×C₁₃	—	2	4	no	—
194	D₄×C₁₃	—	2	4	no	—
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	—	4	8	no	—
197	D₄×C₁₃	—	4	8	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	8	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	8	8	no	—
226	C₂×C₄×C₁₃	#121	1	2	yes	—
227	C₂×C₄×C₁₃	#121	1	2	yes	—
228	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
231	C₂×C₄×C₁₃	#135	1	2	yes	—
232	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₃	—	2	4	no	—
238	C₈×C₁₃	—	4	2	no	—
239	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
240	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×D₄	—	2	1	no	—
242	C₂×C₄×D₄	—	2	1	no	—
243	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#117	—	2	1	no	—
246	C₄×D₈	—	2	8	no	—
247	C₂×#107	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	2	yes	—
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	C₂×#102	C₂²×C₁₃	1	2	yes	—
252	C₂×#102	C₂²×C₁₃	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
254	#390	—	2	1	no	—
255	#390	—	2	1	no	—
256	#390	C₂²×C₁₃	1	2	yes	—
257	#390	C₂²×C₁₃	1	1	yes	characteristic
258	#390	C₂²×C₁₃	1	1	yes	characteristic
259	#389	C₂²×C₁₃	1	1	yes	characteristic
260	#389	C₂²×C₁₃	1	1	yes	characteristic
261	#388	—	2	1	no	—
262	#388	—	2	1	no	—
263	#384	C₂²×C₁₃	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	—	2	1	no	—
266	C₄³	C₂²×C₁₃	1	1	yes	characteristic
267	#340	C₂²×C₁₃	1	2	yes	—
268	#340	C₂²×C₁₃	1	2	yes	—
269	#336	C₂²×C₁₃	1	1	yes	characteristic
270	#336	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	—	8	1	no	—
279	C₂²×C₁₃	—	8	1	no	—
280	C₂²×C₁₃	—	8	2	no	—
281	C₂²×C₁₃	—	8	2	no	—
282	C₂²×C₁₃	—	8	1	no	—
283	C₂²×C₁₃	—	8	2	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
286	C₂²×C₁₃	#525	1	1	yes	characteristic
287	C₂²×C₁₃	#532	1	1	yes	characteristic
288	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
290	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₂²×C₁₃	#575	1	1	yes	characteristic
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	2	no	—
298	C₄×C₁₃	—	8	1	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	—	8	2	no	—
301	C₄×C₁₃	#459	1	4	yes	—
302	C₄×C₁₃	#525	1	2	yes	—
303	C₄×C₁₃	#529	1	2	yes	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	2	no	—
310	C₂×D₈	—	2	4	no	—
311	C₂×D₈	—	2	4	no	—
312	C₂×D₈	—	2	4	no	—
313	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
314	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
315	#127	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	4	4	no	—
320	C₄×D₄	—	4	4	no	—
321	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
322	#117	—	4	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
347	#107	—	2	4	no	—
348	C₄⋊C₈	—	2	4	no	—
349	#102	—	2	4	no	—
350	#102	—	2	4	no	—
351	#102	—	2	4	no	—
352	#102	—	2	4	no	—
353	C₄×C₈	—	2	4	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	C₂×C₁₃	—	8	4	no	—
358	C₂×C₁₃	—	8	2	no	—
359	C₂×C₁₃	#2392	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
361	C₂×C₁₃	#3035	1	1	yes	characteristic
362	C₂×C₁₃	#3100	1	1	yes	characteristic
363	C₂×C₁₃	#3105	1	1	yes	characteristic
364	C₂×C₁₃	#3169	1	1	yes	characteristic
365	C₂×C₁₃	#3171	1	1	yes	characteristic
366	C₂⁴	—	2	1	no	—
367	C₂⁴	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂×D₄	C₁₃×#41	1	4	yes	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
401	D₈	—	2	16	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	C₁₃×#41	1	4	yes	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	2	no	—
432	C₄²	C₁₃×D₈	1	4	yes	complemented
433	C₄²	C₂×D₄×C₁₃	1	2	yes	—
434	C₄²	C₁₃×#41	1	2	yes	—
435	C₁₃	#23676	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	2	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	D₄	—	2	4	no	—
452	D₄	—	2	4	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	8	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	8	8	no	—
484	C₂×C₄	C₁₃×#121	1	2	yes	—
485	C₂×C₄	C₁₃×#121	1	2	yes	—
486	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
487	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
488	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
489	C₂×C₄	C₁₃×#135	1	2	yes	—
490	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
493	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
494	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
495	C₈	—	2	4	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	1	no	—
511	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
512	C₂²	C₁₃×#525	1	1	yes	characteristic
513	C₂²	C₁₃×#532	1	1	yes	characteristic
514	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
515	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
516	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₂²	C₁₃×#575	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	1	no	—
526	C₄	—	8	1	no	—
527	C₄	C₁₃×#459	1	4	yes	—
528	C₄	C₁₃×#525	1	2	yes	—
529	C₄	C₁₃×#529	1	2	yes	—
530	C₂	—	8	2	no	—
531	C₂	—	8	4	no	—
532	C₂	C₁₃×#2392	1	1	yes	characteristic
533	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
534	C₂	C₁₃×#3035	1	1	yes	characteristic
535	C₂	C₁₃×#3100	1	1	yes	characteristic
536	C₂	C₁₃×#3105	1	1	yes	characteristic
537	C₂	C₁₃×#3169	1	1	yes	characteristic
538	C₂	C₁₃×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₁₃×#2011	C₂
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
1. C₂×C₄×C₁₃×D₈	C₂	semidirect
2. C₄×C₁₃×#127	C₂	semidirect
3. C₁₃×#2293	C₂	semidirect
4. C₁₃×#2083	C₂	semidirect
5. C₁₃×#2071	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2054	C₂	semidirect
8. C₁₃×#2041	C₂	semidirect
10. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
11. C₄×C₁₃×#102	C₂	semidirect
61. C₄×D₄×C₁₃	D₄	semidirect
97. #23676	C₁₃	direct (N × H)
164. C₄²×C₁₃	D₈	semidirect
167. C₂×C₄×D₈	C₂×C₁₃	semidirect
168. C₄×#127	C₂×C₁₃	semidirect
169. #2293	C₂×C₁₃	semidirect
170. #2083	C₂×C₁₃	semidirect
171. #2071	C₂×C₁₃	semidirect
172. #2067	C₂×C₁₃	semidirect
173. #2054	C₂×C₁₃	semidirect
174. #2041	C₂×C₁₃	semidirect
176. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
177. C₄×#102	C₂×C₁₃	semidirect
321. C₄×D₄	D₄×C₁₃	semidirect
432. C₄²	C₁₃×D₈	semidirect
435. C₁₃	#23676	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×D₈	2
C₄×C₁₃×#127	2
C₁₃×#2293	2
C₁₃×#2083	2
C₁₃×#2071	2
C₁₃×#2067	2
C₁₃×#2054	2
C₁₃×#2041	2
C₁₃×#2011	2
C₄×C₁₃×C₄⋊C₈	2
C₄×C₁₃×#102	2
#23676	13

Subgroups — C13×#23676 #15710015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23676 #15710015