Subgroups — C₁₃×#32960 #15719299

Order 3328.

1288 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	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1805	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
15	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃	—	2	1	no	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#479	—	2	8	no	—
24	C₂×C₁₃×#107	C₂²	1	2	yes	—
25	C₂×C₁₃×#106	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#387	—	2	1	no	—
37	C₁₃×#385	—	2	1	no	—
38	C₁₃×#385	—	2	1	no	—
39	C₁₃×#382	C₂²	1	1	yes	characteristic
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	—	2	4	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	Q₈	1	4	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#125	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	8	no	—
60	C₄×Q₈×C₁₃	—	2	8	no	—
61	C₄×Q₈×C₁₃	—	2	4	no	—
62	C₄×Q₈×C₁₃	—	2	4	no	—
63	C₄×Q₈×C₁₃	—	2	4	no	—
64	C₄×Q₈×C₁₃	D₄	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	2	8	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#107	—	2	4	no	—
90	C₁₃×#106	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	4	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#103	—	2	4	no	—
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	#32960	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	16	no	—
108	C₂×Q₈×C₁₃	—	2	4	no	—
109	C₂×Q₈×C₁₃	—	2	16	no	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
115	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
116	C₂×Q₈×C₁₃	#41	1	4	yes	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	4	1	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₁₃	#41	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	—	4	2	no	—
161	C₁₃×C₄⋊C₄	—	4	2	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₂²⋊C₄	—	4	2	no	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₄²×C₁₃	—	2	8	no	—
167	C₄²×C₁₃	—	2	8	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
173	C₂×#479	C₂×C₁₃	1	2	yes	complemented
174	#2851	C₂×C₁₃	1	1	yes	characteristic
175	#1865	C₂×C₁₃	1	2	yes	complemented
176	#1863	C₂×C₁₃	1	2	yes	complemented
177	#1853	C₂×C₁₃	1	1	yes	characteristic
178	#1852	C₂×C₁₃	1	1	yes	characteristic
179	#1805	C₂×C₁₃	1	2	yes	complemented
180	#1797	C₂×C₁₃	1	1	yes	characteristic
181	#1787	C₂×C₁₃	1	1	yes	characteristic
182	#1787	C₂×C₁₃	1	1	yes	characteristic
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
188	C₂³×C₁₃	#135	1	2	yes	—
189	C₂³×C₁₃	#137	1	2	yes	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	16	no	—
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	2	4	no	—
194	Q₈×C₁₃	—	2	4	no	—
195	Q₈×C₁₃	C₂²⋊Q₈	1	8	yes	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	16	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	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	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	8	no	—
217	C₂×C₄×C₁₃	—	4	2	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	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	#120	1	2	yes	—
232	C₂×C₄×C₁₃	#120	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
234	C₂×C₄×C₁₃	#137	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
238	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
239	C₈×C₁₃	—	4	2	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄×Q₈	—	2	8	no	—
244	C₂×C₄×Q₈	—	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	2	yes	—
248	C₂²×C₄⋊C₄	—	2	1	no	—
249	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₄²	—	2	1	no	—
251	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
252	#479	—	2	8	no	—
253	C₂×#107	C₂²×C₁₃	1	2	yes	—
254	C₂×#106	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
256	C₂×#103	C₂²×C₁₃	1	2	yes	—
257	C₂×#103	C₂²×C₁₃	1	2	yes	—
258	C₂×#103	C₂²×C₁₃	1	2	yes	—
259	C₂×#103	C₂²×C₁₃	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
262	#389	C₂²×C₁₃	1	1	yes	characteristic
263	#389	C₂²×C₁₃	1	1	yes	characteristic
264	#387	—	2	1	no	—
265	#387	—	2	1	no	—
266	#385	—	2	1	no	—
267	#385	—	2	1	no	—
268	#382	C₂²×C₁₃	1	1	yes	characteristic
269	#380	C₂²×C₁₃	1	1	yes	characteristic
270	#380	C₂²×C₁₃	1	1	yes	characteristic
271	#340	C₂²×C₁₃	1	2	yes	—
272	#340	C₂²×C₁₃	1	2	yes	—
273	#336	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	#479	1	4	yes	complemented
281	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
282	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
283	C₂²×C₁₃	#525	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
285	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
286	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
287	C₂²×C₁₃	#575	1	1	yes	characteristic
288	C₄×C₁₃	—	2	8	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	1	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	—	8	1	no	—
297	C₄×C₁₃	—	8	1	no	—
298	C₄×C₁₃	—	8	1	no	—
299	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
300	C₄×C₁₃	#525	1	2	yes	—
301	C₂²×Q₈	—	2	4	no	—
302	C₂²×Q₈	—	2	4	no	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×Q₈	—	2	2	no	—
305	C₂²×Q₈	Q₈×C₁₃	1	4	yes	—
306	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
313	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
314	#125	—	2	4	no	—
315	C₄×Q₈	—	2	8	no	—
316	C₄×Q₈	—	2	8	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	—	2	4	no	—
320	C₄×Q₈	D₄×C₁₃	1	8	yes	—
321	C₂×C₄⋊C₄	—	2	8	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	8	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	4	no	—
341	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
345	#107	—	2	4	no	—
346	#106	—	2	4	no	—
347	C₄⋊C₈	—	2	4	no	—
348	#103	—	2	4	no	—
349	#103	—	2	4	no	—
350	#103	—	2	4	no	—
351	#103	—	2	4	no	—
352	C₂²⋊C₈	—	2	2	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	C₂×C₁₃	—	2	4	no	—
361	C₂×C₁₃	#2848	1	1	yes	characteristic
362	C₂×C₁₃	#3002	1	1	yes	characteristic
363	C₂×C₁₃	#3004	1	1	yes	characteristic
364	C₂×C₁₃	C₂×#479	1	1	yes	characteristic
365	C₂×C₁₃	#3078	1	1	yes	characteristic
366	C₂×C₁₃	#3108	1	1	yes	characteristic
367	C₂×C₁₃	#3117	1	1	yes	characteristic
368	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	16	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	16	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
378	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
379	C₂×Q₈	C₁₃×#41	1	4	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
406	C₂²×C₄	C₁₃×#41	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	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	—	4	2	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₄²	—	2	8	no	—
430	C₄²	—	2	8	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂×D₄×C₁₃	1	4	yes	—
435	C₁₃	#32960	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
441	C₂³	C₁₃×#135	1	2	yes	—
442	C₂³	C₁₃×#137	1	2	yes	—
443	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	Q₈	—	2	16	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	C₁₃×C₂²⋊Q₈	1	8	yes	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	16	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	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	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	C₁₃×#120	1	2	yes	—
485	C₂×C₄	C₁₃×#120	1	2	yes	—
486	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
487	C₂×C₄	C₁₃×#137	1	2	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
489	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
491	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
492	C₈	—	4	2	no	—
493	C₈	—	4	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	C₁₃×#479	1	4	yes	complemented
501	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
502	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
503	C₂²	C₁₃×#525	1	1	yes	characteristic
504	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
505	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
506	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
507	C₂²	C₁₃×#575	1	1	yes	characteristic
508	C₄	—	2	8	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	4	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
520	C₄	C₁₃×#525	1	2	yes	—
521	C₂	—	2	4	no	—
522	C₂	C₁₃×#2848	1	1	yes	characteristic
523	C₂	C₁₃×#3002	1	1	yes	characteristic
524	C₂	C₁₃×#3004	1	1	yes	characteristic
525	C₂	C₂×C₁₃×#479	1	1	yes	characteristic
526	C₂	C₁₃×#3078	1	1	yes	characteristic
527	C₂	C₁₃×#3108	1	1	yes	characteristic
528	C₂	C₁₃×#3117	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#479	C₂	semidirect
4. C₁₃×#1865	C₂	semidirect
5. C₁₃×#1863	C₂	semidirect
8. C₁₃×#1805	C₂	semidirect
104. #32960	C₁₃	direct (N × H)
173. C₂×#479	C₂×C₁₃	semidirect
175. #1865	C₂×C₁₃	semidirect
176. #1863	C₂×C₁₃	semidirect
179. #1805	C₂×C₁₃	semidirect
280. C₂²×C₁₃	#479	semidirect
435. C₁₃	#32960	direct (N × H)
500. C₂²	C₁₃×#479	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₃	2
C₂×C₁₃×#479	2
C₁₃×#2851	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1853	2
C₁₃×#1852	2
C₁₃×#1805	2
C₁₃×#1797	2
C₁₃×#1787	2
#32960	13

Subgroups — C13×#32960 #15719299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32960 #15719299