Subgroups — C₁₃×#24129 #15710468

Order 3328.

1204 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1999	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1875	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₁₃×#555	—	2	4	no	—
14	C₁₃×#555	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#124	—	2	2	no	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	—	2	1	no	—
24	C₂×C₁₃×#117	C₂²	1	2	yes	—
25	C₁₃×#474	—	2	4	no	—
26	C₁₃×#442	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	2	yes	—
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₁₃×#397	—	2	1	no	—
38	C₁₃×#392	—	2	1	no	—
39	C₁₃×#386	—	2	2	no	—
40	C₁₃×#382	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	D₄	1	4	yes	complemented
62	C₁₃×#124	—	2	16	no	—
63	C₁₃×#121	—	2	8	no	—
64	C₁₃×#121	—	2	4	no	—
65	C₁₃×#121	—	2	4	no	—
66	C₁₃×#121	—	2	4	no	—
67	C₁₃×#121	—	4	2	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
74	C₁₃×#117	—	2	8	no	—
75	C₁₃×#117	—	2	4	no	—
76	C₁₃×#117	—	2	4	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
90	C₂×C₄²×C₁₃	—	2	2	no	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#107	—	2	4	no	—
93	C₁₃×#106	—	2	2	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	4	no	—
98	C₁₃×#102	—	4	2	no	—
99	C₁₃×C₂²⋊C₈	—	2	4	no	—
100	C₁₃×C₂²⋊C₈	—	4	2	no	—
101	C₁₃×#97	—	2	2	no	—
102	C₁₃×#95	—	2	2	no	—
103	C₁₃×#95	—	2	1	no	—
104	C₁₃×#95	—	2	1	no	—
105	#24129	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂⁴×C₁₃	—	2	1	no	—
108	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	8	2	no	—
111	C₂×D₄×C₁₃	—	2	8	no	—
112	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	8	2	no	—
127	C₂×D₄×C₁₃	—	8	2	no	—
128	C₂×D₄×C₁₃	—	8	2	no	—
129	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₃	#41	1	2	yes	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	—	4	2	no	—
144	C₂²×C₄×C₁₃	—	8	2	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×D₈	—	2	8	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	#41	1	2	yes	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	4	4	no	—
174	C₁₃×C₂²⋊C₄	—	4	2	no	—
175	C₁₃×C₂²⋊C₄	—	8	2	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₄²×C₁₃	C₂×D₄	1	2	yes	—
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2535	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2033	C₂×C₁₃	1	2	yes	complemented
184	#1999	C₂×C₁₃	1	2	yes	complemented
185	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#1955	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1875	C₂×C₁₃	1	2	yes	complemented
188	#1854	C₂×C₁₃	1	2	yes	complemented
189	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	—	4	2	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	—	4	2	no	—
207	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₃	—	8	4	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	2	2	no	—
213	D₄×C₁₃	—	4	4	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	1	no	—
216	D₄×C₁₃	—	4	1	no	—
217	D₄×C₁₃	—	4	1	no	—
218	D₄×C₁₃	—	8	8	no	—
219	D₄×C₁₃	—	8	8	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	4	8	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	8	4	no	—
241	C₂×C₄×C₁₃	#120	1	2	yes	—
242	C₂×C₄×C₁₃	#120	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
249	C₈×C₁₃	—	2	2	no	—
250	C₈×C₁₃	—	4	1	no	—
251	C₈×C₁₃	—	4	2	no	—
252	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
253	#555	—	2	4	no	—
254	#555	—	2	4	no	—
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#124	—	2	2	no	—
257	C₂×#121	—	2	1	no	—
258	C₂×#121	C₂²×C₁₃	1	2	yes	—
259	C₂×#121	C₂²×C₁₃	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#117	—	2	1	no	—
264	C₂×#117	C₂²×C₁₃	1	2	yes	—
265	#474	—	2	4	no	—
266	#442	—	2	4	no	—
267	C₂×#107	C₂²×C₁₃	1	2	yes	—
268	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#102	C₂²×C₁₃	1	2	yes	—
272	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#102	C₂²×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
276	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
277	#397	—	2	1	no	—
278	#392	—	2	1	no	—
279	#386	—	2	2	no	—
280	#382	C₂²×C₁₃	1	1	yes	characteristic
281	#380	C₂²×C₁₃	1	2	yes	—
282	#340	C₂²×C₁₃	1	2	yes	—
283	#340	C₂²×C₁₃	1	2	yes	—
284	#340	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	2	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	8	2	no	—
298	C₂²×C₁₃	—	8	2	no	—
299	C₂²×C₁₃	—	8	1	no	—
300	C₂²×C₁₃	—	8	1	no	—
301	C₂²×C₁₃	—	8	2	no	—
302	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
303	C₂²×C₁₃	#546	1	1	yes	characteristic
304	C₂²×C₁₃	#547	1	1	yes	characteristic
305	C₂²×C₁₃	#575	1	2	yes	—
306	C₂²×C₁₃	#576	1	2	yes	—
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	—	8	1	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	#525	1	1	yes	characteristic
315	C₄×C₁₃	#537	1	1	yes	characteristic
316	C₄×C₁₃	#548	1	1	yes	characteristic
317	C₄×C₁₃	#550	1	1	yes	characteristic
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	2	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	D₄×C₁₃	1	4	yes	complemented
335	#124	—	2	16	no	—
336	#121	—	2	8	no	—
337	#121	—	2	4	no	—
338	#121	—	2	4	no	—
339	#121	—	2	4	no	—
340	#121	—	4	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
347	#117	—	2	8	no	—
348	#117	—	2	4	no	—
349	#117	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
365	#107	—	2	4	no	—
366	#106	—	2	2	no	—
367	C₄⋊C₈	—	2	2	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	2	4	no	—
371	#102	—	4	2	no	—
372	C₂²⋊C₈	—	2	4	no	—
373	C₂²⋊C₈	—	4	2	no	—
374	#97	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	C₂×C₁₃	—	8	2	no	—
379	C₂×C₁₃	—	8	2	no	—
380	C₂×C₁₃	—	8	2	no	—
381	C₂×C₁₃	#2407	1	1	yes	characteristic
382	C₂×C₁₃	#3005	1	1	yes	characteristic
383	C₂×C₁₃	#3008	1	1	yes	characteristic
384	C₂×C₁₃	#3319	1	2	yes	—
385	C₂×C₁₃	#3347	1	2	yes	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	—	2	1	no	—
388	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	8	2	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	—	8	2	no	—
409	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂×D₄	C₁₃×#41	1	2	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	8	2	no	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
429	D₈	—	2	8	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	C₁₃×#41	1	2	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	8	2	no	—
456	C₄²	—	2	8	no	—
457	C₄²	C₂×D₄×C₁₃	1	2	yes	—
458	C₄²	C₂×D₄×C₁₃	1	2	yes	—
459	C₁₃	#24129	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	Q₈	—	8	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	1	no	—
488	D₄	—	8	8	no	—
489	D₄	—	8	8	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	C₁₃×#120	1	2	yes	—
512	C₂×C₄	C₁₃×#120	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
516	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
517	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
519	C₈	—	2	2	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	1	no	—
539	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
540	C₂²	C₁₃×#546	1	1	yes	characteristic
541	C₂²	C₁₃×#547	1	1	yes	characteristic
542	C₂²	C₁₃×#575	1	2	yes	—
543	C₂²	C₁₃×#576	1	2	yes	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	2	no	—
551	C₄	C₁₃×#525	1	1	yes	characteristic
552	C₄	C₁₃×#537	1	1	yes	characteristic
553	C₄	C₁₃×#548	1	1	yes	characteristic
554	C₄	C₁₃×#550	1	1	yes	characteristic
555	C₂	—	8	2	no	—
556	C₂	—	8	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₁₃×#2407	1	1	yes	characteristic
559	C₂	C₁₃×#3005	1	1	yes	characteristic
560	C₂	C₁₃×#3008	1	1	yes	characteristic
561	C₂	C₁₃×#3319	1	2	yes	—
562	C₂	C₁₃×#3347	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#555	C₂	semidirect
2. C₂×C₁₃×#474	C₂	semidirect
3. C₂×C₁₃×#442	C₂	semidirect
4. C₁₃×#2535	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#1999	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1955	C₂	semidirect
9. C₁₃×#1875	C₂	semidirect
10. C₁₃×#1854	C₂	semidirect
11. C₁₃×#1804	C₂	semidirect
61. C₁₃×C₄⋊Q₈	D₄	semidirect
73. C₄×D₄×C₁₃	D₄	semidirect
105. #24129	C₁₃	direct (N × H)
179. C₂×#555	C₂×C₁₃	semidirect
180. C₂×#474	C₂×C₁₃	semidirect
181. C₂×#442	C₂×C₁₃	semidirect
182. #2535	C₂×C₁₃	semidirect
183. #2033	C₂×C₁₃	semidirect
184. #1999	C₂×C₁₃	semidirect
185. #1993	C₂×C₁₃	semidirect
186. #1955	C₂×C₁₃	semidirect
187. #1875	C₂×C₁₃	semidirect
188. #1854	C₂×C₁₃	semidirect
189. #1804	C₂×C₁₃	semidirect
334. C₄⋊Q₈	D₄×C₁₃	semidirect
346. C₄×D₄	D₄×C₁₃	semidirect
459. C₁₃	#24129	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×#555	2
C₂×C₁₃×#474	2
C₂×C₁₃×#442	2
C₁₃×#2535	2
C₁₃×#2033	2
C₁₃×#1999	2
C₁₃×#1993	2
C₁₃×#1955	2
C₁₃×#1875	2
C₁₃×#1854	2
C₁₃×#1804	2
#24129	13

Subgroups — C13×#24129 #15710468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24129 #15710468