Subgroups — C₁₃×#24627 #15710966

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2012	C₂	1	2	yes	maximal
7	C₁₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1928	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₁₃×#461	—	2	4	no	—
20	C₄×C₁₃×D₈	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#397	—	2	2	no	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#388	—	2	2	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#380	—	2	1	no	—
37	C₁₃×#380	—	2	1	no	—
38	C₁₃×#380	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	4	2	no	—
50	C₂×C₁₃×SD₁₆	—	4	2	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	2	no	—
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×#124	—	2	4	no	—
60	C₁₃×#124	—	4	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	D₄	1	4	yes	—
65	C₁₃×#117	—	4	4	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#107	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	4	2	no	—
87	C₁₃×#103	—	2	4	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	4	2	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	4	2	no	—
93	C₄×C₈×C₁₃	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	D₄	1	2	yes	—
98	#24627	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂⁴×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₁₃	#41	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×SD₁₆	—	4	8	no	—
135	C₁₃×D₈	—	2	8	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	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	#41	1	2	yes	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	—	4	2	no	—
155	C₁₃×C₄⋊C₄	—	8	1	no	—
156	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₁₃×C₂²⋊C₄	—	4	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₁₃×C₂²⋊C₄	—	4	2	no	—
162	C₁₃×C₂²⋊C₄	—	8	2	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	4	4	no	—
166	C₄²×C₁₃	C₂×D₄	1	2	yes	—
167	C₄²×C₁₃	#41	1	2	yes	—
168	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
170	#2547	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2055	C₂×C₁₃	1	2	yes	complemented
173	#2012	C₂×C₁₃	1	2	yes	—
174	#1983	C₂×C₁₃	1	2	yes	complemented
175	#1956	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1928	C₂×C₁₃	1	2	yes	complemented
178	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₃	—	4	2	no	—
195	Q₈×C₁₃	—	4	2	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	2	2	no	—
199	D₄×C₁₃	—	2	2	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	2	2	no	—
202	D₄×C₁₃	—	4	1	no	—
203	D₄×C₁₃	—	4	1	no	—
204	D₄×C₁₃	—	4	1	no	—
205	D₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	8	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	8	4	no	—
228	C₂×C₄×C₁₃	#121	1	2	yes	—
229	C₂×C₄×C₁₃	#121	1	2	yes	—
230	C₂×C₄×C₁₃	#135	1	2	yes	—
231	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	4	1	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
242	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#124	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#117	—	2	1	no	—
248	#461	—	2	4	no	—
249	C₄×D₈	—	2	4	no	—
250	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
253	C₂×#103	C₂²×C₁₃	1	2	yes	—
254	C₂×#103	C₂²×C₁₃	1	2	yes	—
255	C₂×#103	C₂²×C₁₃	1	2	yes	—
256	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#102	C₂²×C₁₃	1	2	yes	—
259	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
260	#397	—	2	2	no	—
261	#391	C₂²×C₁₃	1	2	yes	—
262	#390	C₂²×C₁₃	1	2	yes	—
263	#388	—	2	2	no	—
264	#384	C₂²×C₁₃	1	1	yes	characteristic
265	#380	—	2	1	no	—
266	#380	—	2	1	no	—
267	#380	—	2	1	no	—
268	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
270	#340	C₂²×C₁₃	1	2	yes	—
271	#336	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	2	no	—
278	C₂²×C₁₃	—	8	1	no	—
279	C₂²×C₁₃	—	8	1	no	—
280	C₂²×C₁₃	—	8	1	no	—
281	C₂²×C₁₃	—	8	1	no	—
282	C₂²×C₁₃	—	8	1	no	—
283	C₂²×C₁₃	—	8	1	no	—
284	C₂²×C₁₃	—	8	1	no	—
285	C₂²×C₁₃	—	8	1	no	—
286	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
287	C₂²×C₁₃	#546	1	1	yes	characteristic
288	C₂²×C₁₃	#550	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	#577	1	1	yes	characteristic
292	C₂²×C₁₃	#578	1	1	yes	characteristic
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	8	2	no	—
298	C₄×C₁₃	—	8	2	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	#463	1	4	yes	—
301	C₄×C₁₃	#525	1	1	yes	characteristic
302	C₄×C₁₃	#535	1	1	yes	characteristic
303	C₄×C₁₃	#553	1	1	yes	characteristic
304	C₄×C₁₃	#555	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
306	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	1	no	—
310	C₂×SD₁₆	—	2	4	no	—
311	C₂×SD₁₆	—	4	2	no	—
312	C₂×SD₁₆	—	4	2	no	—
313	C₂×D₈	—	2	2	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	2	no	—
316	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
317	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	#124	—	2	4	no	—
322	#124	—	4	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	D₄×C₁₃	1	4	yes	—
327	#117	—	4	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	#107	—	2	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	4	2	no	—
349	#103	—	2	4	no	—
350	#103	—	2	4	no	—
351	#103	—	4	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	4	2	no	—
355	C₄×C₈	—	2	2	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	#95	D₄×C₁₃	1	2	yes	—
360	C₂×C₁₃	—	8	2	no	—
361	C₂×C₁₃	—	8	2	no	—
362	C₂×C₁₃	#2414	1	1	yes	characteristic
363	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
364	C₂×C₁₃	#3046	1	1	yes	characteristic
365	C₂×C₁₃	#3303	1	1	yes	characteristic
366	C₂×C₁₃	#3330	1	1	yes	characteristic
367	C₂×C₁₃	#3393	1	1	yes	characteristic
368	C₂×C₁₃	#3397	1	1	yes	characteristic
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂×D₄	C₁₃×#41	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	SD₁₆	—	4	8	no	—
405	D₈	—	2	8	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	C₁₃×#41	1	2	yes	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	8	1	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	8	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	4	4	no	—
436	C₄²	C₂×D₄×C₁₃	1	2	yes	—
437	C₄²	C₁₃×#41	1	2	yes	—
438	C₁₃	#24627	1	1	yes	characteristic, direct product factor, Sylow
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	C₁₃×#121	1	2	yes	—
489	C₂×C₄	C₁₃×#121	1	2	yes	—
490	C₂×C₄	C₁₃×#135	1	2	yes	—
491	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
494	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
496	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
516	C₂²	C₁₃×#546	1	1	yes	characteristic
517	C₂²	C₁₃×#550	1	1	yes	characteristic
518	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
519	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
520	C₂²	C₁₃×#577	1	1	yes	characteristic
521	C₂²	C₁₃×#578	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₄	C₁₃×#463	1	4	yes	—
530	C₄	C₁₃×#525	1	1	yes	characteristic
531	C₄	C₁₃×#535	1	1	yes	characteristic
532	C₄	C₁₃×#553	1	1	yes	characteristic
533	C₄	C₁₃×#555	1	1	yes	characteristic
534	C₂	—	8	2	no	—
535	C₂	—	8	2	no	—
536	C₂	C₁₃×#2414	1	1	yes	characteristic
537	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
538	C₂	C₁₃×#3046	1	1	yes	characteristic
539	C₂	C₁₃×#3303	1	1	yes	characteristic
540	C₂	C₁₃×#3330	1	1	yes	characteristic
541	C₂	C₁₃×#3393	1	1	yes	characteristic
542	C₂	C₁₃×#3397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#461	C₂	semidirect
3. C₁₃×#2547	C₂	semidirect
4. C₁₃×#2354	C₂	semidirect
5. C₁₃×#2055	C₂	semidirect
7. C₁₃×#1983	C₂	semidirect
8. C₁₃×#1956	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1928	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
98. #24627	C₁₃	direct (N × H)
168. C₂×#461	C₂×C₁₃	semidirect
170. #2547	C₂×C₁₃	semidirect
171. #2354	C₂×C₁₃	semidirect
172. #2055	C₂×C₁₃	semidirect
174. #1983	C₂×C₁₃	semidirect
175. #1956	C₂×C₁₃	semidirect
176. #1939	C₂×C₁₃	semidirect
177. #1928	C₂×C₁₃	semidirect
178. #1802	C₂×C₁₃	semidirect
438. C₁₃	#24627	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×#461	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2547	2
C₁₃×#2354	2
C₁₃×#2055	2
C₁₃×#2012	2
C₁₃×#1983	2
C₁₃×#1956	2
C₁₃×#1939	2
C₁₃×#1928	2
C₁₃×#1802	2
#24627	13

Subgroups — C13×#24627 #15710966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24627 #15710966