Subgroups — C₁₃×#24199 #15710538

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2580	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2043	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2013	C₂	1	2	yes	maximal
7	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1880	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₁₃×#557	—	2	4	no	—
15	C₁₃×#557	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	—	2	2	no	—
19	C₂×C₁₃×#125	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#461	—	2	4	no	—
26	C₁₃×#440	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₁₃×#399	—	2	1	no	—
37	C₁₃×#393	—	2	1	no	—
38	C₁₃×#390	C₂²	1	2	yes	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#385	—	2	2	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	4	no	—
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	4	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
63	C₁₃×#125	—	2	16	no	—
64	C₁₃×#125	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	8	no	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	D₄	1	4	yes	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	—	2	2	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#107	—	2	2	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	2	4	no	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#103	—	4	2	no	—
99	C₁₃×#103	—	4	2	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#97	—	2	2	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	C₁₃×#95	—	2	2	no	—
105	#24199	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	#41	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	8	2	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×SD₁₆	—	2	8	no	—
140	C₁₃×SD₁₆	—	4	8	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	#41	1	2	yes	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	8	2	no	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	4	no	—
167	C₁₃×C₂²⋊C₄	—	8	2	no	—
168	C₄²×C₁₃	—	2	8	no	—
169	C₄²×C₁₃	—	2	4	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
176	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
177	#2580	C₂×C₁₃	1	1	yes	characteristic
178	#2043	C₂×C₁₃	1	2	yes	complemented
179	#2013	C₂×C₁₃	1	2	yes	—
180	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1960	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1880	C₂×C₁₃	1	2	yes	—
183	#1863	C₂×C₁₃	1	2	yes	complemented
184	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	8	no	—
192	Q₈×C₁₃	—	2	2	no	—
193	Q₈×C₁₃	—	2	2	no	—
194	Q₈×C₁₃	—	2	4	no	—
195	Q₈×C₁₃	—	2	4	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	Q₈×C₁₃	—	4	1	no	—
199	Q₈×C₁₃	—	4	1	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	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	4	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	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	1	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	2	no	—
224	C₂×C₄×C₁₃	—	8	4	no	—
225	C₂×C₄×C₁₃	#120	1	2	yes	—
226	C₂×C₄×C₁₃	#120	1	2	yes	—
227	C₂×C₄×C₁₃	#137	1	4	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	4	1	no	—
236	C₈×C₁₃	—	4	2	no	—
237	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
239	#557	—	2	4	no	—
240	#557	—	2	4	no	—
241	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#125	—	2	2	no	—
244	C₂×#125	—	2	1	no	—
245	C₂×C₄×Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
250	#461	—	2	4	no	—
251	#440	—	2	4	no	—
252	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#103	C₂²×C₁₃	1	2	yes	—
255	C₂×#103	C₂²×C₁₃	1	2	yes	—
256	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₁₃	1	2	yes	—
258	C₂×#103	C₂²×C₁₃	1	2	yes	—
259	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
261	#399	—	2	1	no	—
262	#393	—	2	1	no	—
263	#390	C₂²×C₁₃	1	2	yes	—
264	#389	C₂²×C₁₃	1	2	yes	—
265	#385	—	2	2	no	—
266	#382	C₂²×C₁₃	1	1	yes	characteristic
267	#340	C₂²×C₁₃	1	2	yes	—
268	#336	C₂²×C₁₃	1	2	yes	—
269	#336	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	8	2	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	—	8	1	no	—
275	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
276	C₂²×C₁₃	#548	1	1	yes	characteristic
277	C₂²×C₁₃	#550	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×#137	1	2	yes	—
279	C₂²×C₁₃	#577	1	2	yes	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	4	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	8	2	no	—
288	C₄×C₁₃	—	8	1	no	—
289	C₄×C₁₃	#525	1	1	yes	characteristic
290	C₄×C₁₃	#537	1	1	yes	characteristic
291	C₄×C₁₃	#546	1	1	yes	characteristic
292	C₄×C₁₃	#547	1	1	yes	characteristic
293	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
295	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	4	2	no	—
304	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₄⋊Q₈	—	2	4	no	—
308	C₄⋊Q₈	—	2	4	no	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
311	#125	—	2	16	no	—
312	#125	—	2	8	no	—
313	C₄×Q₈	—	2	8	no	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	D₄×C₁₃	1	4	yes	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	C₄⋊C₈	—	2	2	no	—
343	#103	—	2	2	no	—
344	#103	—	2	4	no	—
345	#103	—	2	4	no	—
346	#103	—	4	2	no	—
347	#103	—	4	2	no	—
348	#102	—	2	2	no	—
349	#97	—	2	2	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	2	no	—
353	C₂×C₁₃	—	8	2	no	—
354	C₂×C₁₃	#2407	1	1	yes	characteristic
355	C₂×C₁₃	#3004	1	1	yes	characteristic
356	C₂×C₁₃	#3010	1	1	yes	characteristic
357	C₂×C₁₃	#3372	1	2	yes	—
358	C₂×C₁₃	#3400	1	2	yes	—
359	C₂⁴	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
373	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	C₁₃×#41	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	SD₁₆	—	2	8	no	—
393	SD₁₆	—	4	8	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	C₁₃×#41	1	2	yes	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	8	2	no	—
417	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	8	2	no	—
421	C₄²	—	2	8	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	C₂×D₄×C₁₃	1	2	yes	—
426	C₄²	C₂×D₄×C₁₃	1	2	yes	—
427	C₁₃	#24199	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	2	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
434	Q₈	—	2	8	no	—
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	2	4	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	4	no	—
468	C₂×C₄	C₁₃×#120	1	2	yes	—
469	C₂×C₄	C₁₃×#120	1	2	yes	—
470	C₂×C₄	C₁₃×#137	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
475	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	1	no	—
485	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
486	C₂²	C₁₃×#548	1	1	yes	characteristic
487	C₂²	C₁₃×#550	1	1	yes	characteristic
488	C₂²	C₂×C₁₃×#137	1	2	yes	—
489	C₂²	C₁₃×#577	1	2	yes	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	4	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	4	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	2	no	—
499	C₄	C₁₃×#525	1	1	yes	characteristic
500	C₄	C₁₃×#537	1	1	yes	characteristic
501	C₄	C₁₃×#546	1	1	yes	characteristic
502	C₄	C₁₃×#547	1	1	yes	characteristic
503	C₂	—	8	2	no	—
504	C₂	C₁₃×#2407	1	1	yes	characteristic
505	C₂	C₁₃×#3004	1	1	yes	characteristic
506	C₂	C₁₃×#3010	1	1	yes	characteristic
507	C₂	C₁₃×#3372	1	2	yes	—
508	C₂	C₁₃×#3400	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#557	C₂	semidirect
5. C₁₃×#2043	C₂	semidirect
7. C₁₃×#1985	C₂	semidirect
8. C₁₃×#1960	C₂	semidirect
10. C₁₃×#1863	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
105. #24199	C₁₃	direct (N × H)
174. C₂×#557	C₂×C₁₃	semidirect
178. #2043	C₂×C₁₃	semidirect
180. #1985	C₂×C₁₃	semidirect
181. #1960	C₂×C₁₃	semidirect
183. #1863	C₂×C₁₃	semidirect
184. #1805	C₂×C₁₃	semidirect
427. C₁₃	#24199	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×#557	2
C₂×C₁₃×#461	2
C₂×C₁₃×#440	2
C₁₃×#2580	2
C₁₃×#2043	2
C₁₃×#2013	2
C₁₃×#1985	2
C₁₃×#1960	2
C₁₃×#1880	2
C₁₃×#1863	2
C₁₃×#1805	2
#24199	13

Subgroups — C13×#24199 #15710538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24199 #15710538