Subgroups — C₁₃×#34268 #15720607

Order 3328.

2946 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2367	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2365	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2359	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2323	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#536	C₄	1	16	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#124	C₂²	1	2	yes	—
18	C₂×C₁₃×#123	C₂²	1	4	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₁₃×#519	—	2	8	no	—
21	C₄×C₁₃×#41	—	2	8	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	4	yes	—
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	4	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#390	C₂²	1	2	yes	—
40	C₁₃×#389	C₂²	1	2	yes	—
41	C₁₃×#389	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	8	yes	—
43	C₁₃×#388	C₂²	1	8	yes	—
44	C₁₃×#388	C₂²	1	8	yes	—
45	C₁₃×#387	C₂²	1	8	yes	—
46	C₁₃×#387	C₂²	1	8	yes	—
47	C₁₃×#386	C₂²	1	4	yes	—
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₁₃×#385	C₂²	1	8	yes	—
50	C₁₃×#380	C₂²	1	4	yes	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
57	C₂×C₁₃×#95	C₂²	1	4	yes	—
58	C₂×C₁₃×#41	—	2	4	no	—
59	C₂×C₁₃×#41	—	2	4	no	—
60	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
61	C₂²×Q₈×C₁₃	—	2	4	no	—
62	C₂²×Q₈×C₁₃	—	2	4	no	—
63	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
76	C₁₃×#124	C₂×C₄	1	16	yes	complemented
77	C₁₃×#123	C₂×C₄	1	32	yes	complemented
78	C₁₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
79	C₄×Q₈×C₁₃	—	2	8	no	—
80	C₄×Q₈×C₁₃	—	2	16	no	—
81	C₄×Q₈×C₁₃	—	2	16	no	—
82	C₄×D₄×C₁₃	—	2	8	no	—
83	C₄×D₄×C₁₃	—	2	16	no	—
84	C₁₃×#117	—	2	4	no	—
85	C₁₃×#117	—	2	16	no	—
86	C₁₃×#117	—	2	8	no	—
87	C₁₃×#117	C₂×C₄	1	8	yes	complemented
88	C₁₃×#117	D₄	1	8	yes	—
89	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	—	2	4	no	—
107	C₂×C₄²×C₁₃	—	2	8	no	—
108	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
117	C₁₃×#95	C₂³	1	4	yes	—
118	C₁₃×#95	C₂³	1	8	yes	—
119	C₁₃×#95	C₂³	1	8	yes	—
120	C₁₃×#95	C₂³	1	8	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	8	yes	—
123	#34268	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×#41	—	2	32	no	—
127	C₂×Q₈×C₁₃	—	2	32	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
135	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
136	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
156	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	#41	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	16	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	4	4	no	—
177	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
178	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	4	8	no	—
183	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
184	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
185	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
186	C₄²×C₁₃	—	2	2	no	—
187	C₄²×C₁₃	—	2	2	no	—
188	C₄²×C₁₃	—	2	8	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	2	16	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	—	4	8	no	—
193	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
194	C₄²×C₁₃	C₂×D₄	1	8	yes	—
195	C₂×#536	C₂×C₁₃	1	1	yes	characteristic
196	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
198	#2367	C₂×C₁₃	1	4	yes	complemented
199	#2365	C₂×C₁₃	1	4	yes	complemented
200	#2359	C₂×C₁₃	1	8	yes	complemented
201	#2323	C₂×C₁₃	1	4	yes	complemented
202	#2311	C₂×C₁₃	1	1	yes	characteristic
203	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
204	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
214	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₁₃	C₂×#41	1	2	yes	—
217	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
218	Q₈×C₁₃	—	2	16	no	—
219	Q₈×C₁₃	—	2	16	no	—
220	Q₈×C₁₃	—	2	8	no	—
221	D₄×C₁₃	—	2	16	no	—
222	D₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	16	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	16	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	16	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	8	4	no	—
246	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	—
247	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
248	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
249	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
250	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
256	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
257	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
258	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
259	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	#536	C₄×C₁₃	1	16	yes	complemented
261	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
262	C₂×#124	C₂²×C₁₃	1	2	yes	—
263	C₂×#123	C₂²×C₁₃	1	4	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
265	#519	—	2	8	no	—
266	C₄×#41	—	2	8	no	—
267	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
268	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
269	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
270	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
272	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#117	C₂²×C₁₃	1	2	yes	—
274	C₂×#117	C₂²×C₁₃	1	4	yes	—
275	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
278	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
279	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
280	#391	C₂²×C₁₃	1	2	yes	—
281	#391	C₂²×C₁₃	1	2	yes	—
282	#391	C₂²×C₁₃	1	4	yes	—
283	#391	C₂²×C₁₃	1	2	yes	—
284	#390	C₂²×C₁₃	1	2	yes	—
285	#389	C₂²×C₁₃	1	2	yes	—
286	#389	C₂²×C₁₃	1	8	yes	—
287	#389	C₂²×C₁₃	1	2	yes	—
288	#388	C₂²×C₁₃	1	8	yes	—
289	#388	C₂²×C₁₃	1	8	yes	—
290	#387	C₂²×C₁₃	1	8	yes	—
291	#387	C₂²×C₁₃	1	8	yes	—
292	#386	C₂²×C₁₃	1	4	yes	—
293	#385	C₂²×C₁₃	1	4	yes	—
294	#385	C₂²×C₁₃	1	8	yes	—
295	#380	C₂²×C₁₃	1	4	yes	—
296	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
298	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
300	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
302	C₂×#95	C₂²×C₁₃	1	4	yes	—
303	C₂²×C₁₃	—	2	4	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	8	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
313	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
314	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
315	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
316	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
317	C₂²×C₁₃	#585	1	2	yes	—
318	C₄×C₁₃	—	2	4	no	—
319	C₄×C₁₃	—	2	8	no	—
320	C₄×C₁₃	—	2	8	no	—
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	2	8	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
327	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
328	C₂×#41	—	2	4	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
331	C₂²×Q₈	—	2	4	no	—
332	C₂²×Q₈	—	2	4	no	—
333	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
334	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
335	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
336	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
346	#124	C₂×C₄×C₁₃	1	16	yes	complemented
347	#123	C₂×C₄×C₁₃	1	32	yes	complemented
348	C₂²⋊Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
349	C₄×Q₈	—	2	8	no	—
350	C₄×Q₈	—	2	16	no	—
351	C₄×Q₈	—	2	16	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	16	no	—
354	#117	—	2	4	no	—
355	#117	—	2	16	no	—
356	#117	—	2	8	no	—
357	#117	C₂×C₄×C₁₃	1	8	yes	complemented
358	#117	D₄×C₁₃	1	8	yes	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₄²	—	2	4	no	—
377	C₂×C₄²	—	2	8	no	—
378	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
382	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
385	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
386	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
387	#95	C₂³×C₁₃	1	8	yes	—
388	#95	C₂³×C₁₃	1	8	yes	—
389	#95	C₂³×C₁₃	1	4	yes	—
390	#95	C₂³×C₁₃	1	8	yes	—
391	#95	C₂³×C₁₃	1	8	yes	—
392	#95	C₂³×C₁₃	1	4	yes	—
393	C₂×C₁₃	—	2	4	no	—
394	C₂×C₁₃	—	4	4	no	—
395	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
396	C₂×C₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
397	C₂×C₁₃	#3489	1	2	yes	—
398	C₂×C₁₃	#3509	1	1	yes	characteristic
399	C₂×C₁₃	#3510	1	1	yes	characteristic
400	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
401	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
402	#41	—	2	32	no	—
403	C₂×Q₈	—	2	32	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
411	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
412	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
418	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
432	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
433	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
434	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
435	C₂²×C₄	C₁₃×#41	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	16	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
454	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
455	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	4	8	no	—
459	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
460	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
461	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	8	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	16	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	4	8	no	—
469	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
470	C₄²	C₂×D₄×C₁₃	1	8	yes	—
471	C₁₃	#34268	1	1	yes	characteristic, direct product factor, Sylow
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
479	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
480	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂³	C₂×C₁₃×#41	1	2	yes	—
482	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
483	Q₈	—	2	16	no	—
484	Q₈	—	2	16	no	—
485	Q₈	—	2	8	no	—
486	D₄	—	2	16	no	—
487	D₄	—	2	8	no	—
488	C₂×C₄	—	2	16	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	16	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	16	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	—
512	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
513	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
514	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
515	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
516	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
520	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
521	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
522	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
533	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
534	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
535	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
536	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
537	C₂²	C₁₃×#585	1	2	yes	—
538	C₄	—	2	4	no	—
539	C₄	—	2	8	no	—
540	C₄	—	2	8	no	—
541	C₄	—	2	4	no	—
542	C₄	—	2	8	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
547	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	4	4	no	—
550	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
551	C₂	C₄×C₁₃×2₋¹⁺⁴	1	2	yes	—
552	C₂	C₁₃×#3489	1	2	yes	—
553	C₂	C₁₃×#3509	1	1	yes	characteristic
554	C₂	C₁₃×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#519	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2365	C₂	semidirect
6. C₁₃×#2359	C₂	semidirect
7. C₁₃×#2323	C₂	semidirect
9. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
10. C₁₃×#2296	C₂	semidirect
11. C₂×C₁₃×#391	C₂	semidirect
12. C₁₃×#2274	C₂	semidirect
15. C₁₃×#536	C₄	semidirect
63. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
75. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
76. C₁₃×#124	C₂×C₄	semidirect
77. C₁₃×#123	C₂×C₄	semidirect
78. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
87. C₁₃×#117	C₂×C₄	semidirect
123. #34268	C₁₃	direct (N × H)
196. C₂×#519	C₂×C₁₃	semidirect
198. #2367	C₂×C₁₃	semidirect
199. #2365	C₂×C₁₃	semidirect
200. #2359	C₂×C₁₃	semidirect
201. #2323	C₂×C₁₃	semidirect
203. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
204. #2296	C₂×C₁₃	semidirect
205. C₂×#391	C₂×C₁₃	semidirect
206. #2274	C₂×C₁₃	semidirect
260. #536	C₄×C₁₃	semidirect
333. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
345. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
346. #124	C₂×C₄×C₁₃	semidirect
347. #123	C₂×C₄×C₁₃	semidirect
348. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
357. #117	C₂×C₄×C₁₃	semidirect
471. C₁₃	#34268	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×#536	2
C₂×C₁₃×#519	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2367	2
C₁₃×#2365	2
C₁₃×#2359	2
C₁₃×#2323	2
C₁₃×#2311	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2296	2
C₂×C₁₃×#391	2
C₁₃×#2274	2
#34268	13

Subgroups — C13×#34268 #15720607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34268 #15720607