Subgroups — C₁₃×#24329 #15710668

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2058	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	2	yes	maximal
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1880	C₂	1	2	yes	maximal
10	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	Q₈²×C₁₃	—	2	4	no	—
14	Q₈²×C₁₃	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	—	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×#476	—	2	4	no	—
26	C₄×C₁₃×SD₁₆	—	2	4	no	—
27	C₂×C₁₃×#106	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×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#396	—	2	2	no	—
36	C₁₃×#390	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#384	C₂²	1	1	yes	characteristic
39	C₁₃×#380	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
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	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
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	16	no	—
58	C₁₃×C₄⋊Q₈	—	2	8	no	—
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×C₂²⋊Q₈	—	4	4	no	—
64	C₄×Q₈×C₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	D₄	1	4	yes	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×#106	—	2	2	no	—
94	C₁₃×#106	—	2	4	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×#103	—	2	2	no	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	2	4	no	—
100	C₄×C₈×C₁₃	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	#24329	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	8	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	8	1	no	—
112	C₂×Q₈×C₁₃	—	8	1	no	—
113	C₂×Q₈×C₁₃	—	8	2	no	—
114	C₂×Q₈×C₁₃	—	8	2	no	—
115	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
116	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
124	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×SD₁₆	—	2	8	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	4	2	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	—	8	1	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
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×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
176	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
177	#2538	C₂×C₁₃	1	1	yes	characteristic
178	#2058	C₂×C₁₃	1	2	yes	complemented
179	#2023	C₂×C₁₃	1	2	yes	—
180	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1880	C₂×C₁₃	1	2	yes	—
183	#1865	C₂×C₁₃	1	2	yes	complemented
184	#1803	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	1	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₃	—	2	2	no	—
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	2	2	no	—
196	Q₈×C₁₃	—	2	8	no	—
197	Q₈×C₁₃	—	8	4	no	—
198	Q₈×C₁₃	—	8	8	no	—
199	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
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	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	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	1	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	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	8	4	no	—
227	C₂×C₄×C₁₃	#120	1	2	yes	—
228	C₂×C₄×C₁₃	#120	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
230	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	#137	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	2₋¹⁺⁴	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	1	yes	characteristic
242	Q₈²	—	2	4	no	—
243	Q₈²	—	2	4	no	—
244	C₂×C₄⋊Q₈	—	2	1	no	—
245	C₂×C₄⋊Q₈	—	2	2	no	—
246	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₄×Q₈	—	2	1	no	—
250	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
254	#476	—	2	4	no	—
255	C₄×SD₁₆	—	2	4	no	—
256	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#106	C₂²×C₁₃	1	2	yes	—
258	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#103	C₂²×C₁₃	1	2	yes	—
260	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#102	C₂²×C₁₃	1	2	yes	—
262	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
264	#396	—	2	2	no	—
265	#390	C₂²×C₁₃	1	2	yes	—
266	#389	C₂²×C₁₃	1	2	yes	—
267	#384	C₂²×C₁₃	1	1	yes	characteristic
268	#380	—	2	1	no	—
269	#340	C₂²×C₁₃	1	2	yes	—
270	#340	C₂²×C₁₃	1	2	yes	—
271	#340	C₂²×C₁₃	1	2	yes	—
272	#336	C₂²×C₁₃	1	2	yes	—
273	#336	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₁₃	—	4	2	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	1	no	—
281	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
282	C₂²×C₁₃	#548	1	1	yes	characteristic
283	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
284	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
285	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
286	C₂²×C₁₃	#576	1	1	yes	characteristic
287	C₂²×C₁₃	#577	1	1	yes	characteristic
288	C₄×C₁₃	—	2	4	no	—
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	4	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	8	2	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	#448	1	4	yes	—
297	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
298	C₄×C₁₃	#536	1	1	yes	characteristic
299	C₄×C₁₃	#548	1	1	yes	characteristic
300	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
304	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
310	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₄⋊Q₈	—	2	16	no	—
314	C₄⋊Q₈	—	2	8	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	4	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
319	C₂²⋊Q₈	—	4	4	no	—
320	C₄×Q₈	—	2	8	no	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	D₄×C₁₃	1	4	yes	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
348	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	#106	—	2	2	no	—
350	#106	—	2	4	no	—
351	C₄⋊C₈	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	2	4	no	—
354	#102	—	2	2	no	—
355	#102	—	2	4	no	—
356	C₄×C₈	—	2	2	no	—
357	#95	—	2	2	no	—
358	C₂×C₁₃	—	8	2	no	—
359	C₂×C₁₃	#2409	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
361	C₂×C₁₃	#3012	1	1	yes	characteristic
362	C₂×C₁₃	#3362	1	1	yes	characteristic
363	C₂×C₁₃	#3369	1	1	yes	characteristic
364	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
365	C₂×C₁₃	#3385	1	1	yes	characteristic
366	C₂⁴	—	2	1	no	—
367	C₂×Q₈	—	2	8	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	8	1	no	—
375	C₂×Q₈	—	8	1	no	—
376	C₂×Q₈	—	8	2	no	—
377	C₂×Q₈	—	8	2	no	—
378	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	complemented
379	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
380	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
381	C₂×Q₈	C₁₃×#41	1	2	yes	—
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×Q₈×C₁₃	1	2	yes	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
401	SD₁₆	—	2	8	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	4	no	—
425	C₄⋊C₄	—	8	1	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
427	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	8	2	no	—
431	C₄²	—	2	8	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	C₂×D₄×C₁₃	1	2	yes	—
436	C₄²	C₂×D₄×C₁₃	1	2	yes	—
437	C₁₃	#24329	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	Q₈	—	2	8	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	2	2	no	—
450	Q₈	—	8	4	no	—
451	Q₈	—	8	8	no	—
452	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	C₁₃×#120	1	2	yes	—
481	C₂×C₄	C₁₃×#120	1	2	yes	—
482	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
483	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
484	C₂×C₄	C₁₃×#137	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
489	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
490	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
502	C₂²	C₁₃×#548	1	1	yes	characteristic
503	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
504	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
505	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
506	C₂²	C₁₃×#576	1	1	yes	characteristic
507	C₂²	C₁₃×#577	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	2	no	—
515	C₄	—	8	1	no	—
516	C₄	C₁₃×#448	1	4	yes	—
517	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
518	C₄	C₁₃×#536	1	1	yes	characteristic
519	C₄	C₁₃×#548	1	1	yes	characteristic
520	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
521	C₂	—	8	2	no	—
522	C₂	C₁₃×#2409	1	1	yes	characteristic
523	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
524	C₂	C₁₃×#3012	1	1	yes	characteristic
525	C₂	C₁₃×#3362	1	1	yes	characteristic
526	C₂	C₁₃×#3369	1	1	yes	characteristic
527	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
528	C₂	C₁₃×#3385	1	1	yes	characteristic

	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×Q₈²×C₁₃	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1984	C₂	semidirect
10. C₁₃×#1865	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
53. C₂×C₁₃×SD₁₆	Q₈	semidirect
102. #24329	C₁₃	direct (N × H)
115. C₂×Q₈×C₁₃	SD₁₆	semidirect
174. C₂×Q₈²	C₂×C₁₃	semidirect
178. #2058	C₂×C₁₃	semidirect
180. #1990	C₂×C₁₃	semidirect
181. #1984	C₂×C₁₃	semidirect
183. #1865	C₂×C₁₃	semidirect
184. #1803	C₂×C₁₃	semidirect
199. Q₈×C₁₃	C₂²⋊Q₈	semidirect
309. C₂×SD₁₆	Q₈×C₁₃	semidirect
378. C₂×Q₈	C₁₃×SD₁₆	semidirect
437. C₁₃	#24329	direct (N × H)
452. Q₈	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Q₈²×C₁₃	2
C₂×C₁₃×#476	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2538	2
C₁₃×#2058	2
C₁₃×#2023	2
C₁₃×#1990	2
C₁₃×#1984	2
C₁₃×#1880	2
C₁₃×#1865	2
C₁₃×#1803	2
#24329	13

Subgroups — C13×#24329 #15710668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24329 #15710668