Subgroups — C₁₃×#34081 #15720420

Order 3328.

2202 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2335	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2334	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2333	C₂	1	2	yes	maximal
7	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2298	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2293	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#117	C₂	1	2	yes	maximal, complemented
16	C₁₃×#529	C₄	1	16	yes	complemented
17	C₂×C₁₃×#126	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	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	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#391	C₂²	1	4	yes	—
32	C₁₃×#390	C₂²	1	4	yes	—
33	C₁₃×#389	C₂²	1	4	yes	—
34	C₁₃×#389	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#388	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	4	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	4	yes	—
41	C₁₃×#387	C₂²	1	4	yes	—
42	C₁₃×#387	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	—
44	C₁₃×#387	C₂²	1	4	yes	—
45	C₁₃×#387	C₂²	1	4	yes	—
46	C₁₃×#387	C₂²	1	4	yes	—
47	C₁₃×#386	C₂²	1	4	yes	—
48	C₁₃×#386	C₂²	1	4	yes	—
49	C₁₃×#385	C₂²	1	4	yes	—
50	C₁₃×#385	C₂²	1	4	yes	—
51	C₁₃×#383	C₂²	1	2	yes	—
52	C₁₃×#382	C₂²	1	2	yes	—
53	C₁₃×#381	C₂²	1	2	yes	—
54	C₁₃×#380	C₂²	1	2	yes	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₁₃×#376	C₂²	1	2	yes	—
71	C₁₃×#376	C₂²	1	2	yes	—
72	C₁₃×#376	C₂²	1	2	yes	—
73	C₄³×C₁₃	C₂²	1	1	yes	characteristic
74	C₄³×C₁₃	C₂²	1	2	yes	—
75	C₄³×C₁₃	C₂²	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#126	C₂×C₄	1	16	yes	complemented
85	C₁₃×#125	C₂×C₄	1	8	yes	complemented
86	C₁₃×#124	C₂×C₄	1	8	yes	—
87	C₁₃×#123	C₂×C₄	1	16	yes	complemented
88	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
89	C₁₃×#121	C₂×C₄	1	8	yes	—
90	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
91	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
92	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
93	C₁₃×#117	—	2	8	no	—
94	C₁₃×#117	—	2	8	no	—
95	C₁₃×#117	C₂×C₄	1	16	yes	complemented
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	—	2	8	no	—
119	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	2	yes	—
143	C₁₃×#95	C₂³	1	2	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	#34081	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
152	C₂×Q₈×C₁₃	—	4	2	no	—
153	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	2	no	—
156	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
157	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	4	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
168	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	—	2	8	no	—
184	C₁₃×C₄⋊C₄	—	2	8	no	—
185	C₁₃×C₄⋊C₄	—	4	4	no	—
186	C₁₃×C₄⋊C₄	—	4	4	no	—
187	C₁₃×C₄⋊C₄	—	4	4	no	—
188	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
189	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
191	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₁₃×C₂²⋊C₄	—	4	2	no	—
197	C₁₃×C₂²⋊C₄	—	4	4	no	—
198	C₁₃×C₂²⋊C₄	—	4	4	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
201	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
202	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
203	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
204	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
205	C₄²×C₁₃	—	2	8	no	—
206	C₄²×C₁₃	—	2	4	no	—
207	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	4	2	no	—
210	C₄²×C₁₃	—	4	2	no	—
211	C₄²×C₁₃	—	4	4	no	—
212	C₄²×C₁₃	—	4	4	no	—
213	C₄²×C₁₃	—	4	2	no	—
214	C₄²×C₁₃	—	4	2	no	—
215	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
216	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
217	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
218	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
219	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
220	C₄²×C₁₃	#41	1	8	yes	—
221	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
222	#2337	C₂×C₁₃	1	2	yes	complemented
223	#2336	C₂×C₁₃	1	2	yes	complemented
224	#2335	C₂×C₁₃	1	4	yes	complemented
225	#2334	C₂×C₁₃	1	4	yes	complemented
226	#2333	C₂×C₁₃	1	2	yes	—
227	#2332	C₂×C₁₃	1	2	yes	complemented
228	#2298	C₂×C₁₃	1	2	yes	complemented
229	#2295	C₂×C₁₃	1	2	yes	complemented
230	#2293	C₂×C₁₃	1	2	yes	complemented
231	#2290	C₂×C₁₃	1	2	yes	complemented
232	#2290	C₂×C₁₃	1	2	yes	complemented
233	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₄×#117	C₂×C₁₃	1	2	yes	complemented
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
244	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
245	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
246	Q₈×C₁₃	—	4	4	no	—
247	D₄×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	4	8	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	16	no	—
261	C₂×C₄×C₁₃	—	2	8	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	4	no	—
273	C₂×C₄×C₁₃	—	4	16	no	—
274	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
279	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
280	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
281	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
282	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
284	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
285	#529	C₄×C₁₃	1	16	yes	complemented
286	C₂×#126	C₂²×C₁₃	1	2	yes	—
287	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#123	C₂²×C₁₃	1	2	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
295	C₂×#117	C₂²×C₁₃	1	2	yes	—
296	C₂×#117	C₂²×C₁₃	1	2	yes	—
297	C₂×#117	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
300	#391	C₂²×C₁₃	1	4	yes	—
301	#390	C₂²×C₁₃	1	4	yes	—
302	#389	C₂²×C₁₃	1	4	yes	—
303	#389	C₂²×C₁₃	1	4	yes	—
304	#388	C₂²×C₁₃	1	4	yes	—
305	#388	C₂²×C₁₃	1	4	yes	—
306	#388	C₂²×C₁₃	1	4	yes	—
307	#388	C₂²×C₁₃	1	4	yes	—
308	#388	C₂²×C₁₃	1	4	yes	—
309	#388	C₂²×C₁₃	1	4	yes	—
310	#387	C₂²×C₁₃	1	4	yes	—
311	#387	C₂²×C₁₃	1	4	yes	—
312	#387	C₂²×C₁₃	1	4	yes	—
313	#387	C₂²×C₁₃	1	4	yes	—
314	#387	C₂²×C₁₃	1	4	yes	—
315	#387	C₂²×C₁₃	1	4	yes	—
316	#386	C₂²×C₁₃	1	4	yes	—
317	#386	C₂²×C₁₃	1	4	yes	—
318	#385	C₂²×C₁₃	1	4	yes	—
319	#385	C₂²×C₁₃	1	4	yes	—
320	#383	C₂²×C₁₃	1	2	yes	—
321	#382	C₂²×C₁₃	1	2	yes	—
322	#381	C₂²×C₁₃	1	2	yes	—
323	#380	C₂²×C₁₃	1	2	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
325	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
332	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
334	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
336	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
337	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
338	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
339	#376	C₂²×C₁₃	1	2	yes	—
340	#376	C₂²×C₁₃	1	2	yes	—
341	#376	C₂²×C₁₃	1	2	yes	—
342	C₄³	C₂²×C₁₃	1	1	yes	characteristic
343	C₄³	C₂²×C₁₃	1	2	yes	—
344	C₄³	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	4	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	4	no	—
350	C₂²×C₁₃	—	2	4	no	—
351	C₂²×C₁₃	—	4	4	no	—
352	C₂²×C₁₃	—	4	4	no	—
353	C₂²×C₁₃	—	4	4	no	—
354	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
355	C₂²×C₁₃	C₂²×#41	1	2	yes	—
356	C₂²×C₁₃	#585	1	2	yes	—
357	C₂²×C₁₃	#585	1	2	yes	—
358	C₄×C₁₃	—	2	4	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	2	4	no	—
365	C₄×C₁₃	—	2	4	no	—
366	C₄×C₁₃	—	2	8	no	—
367	C₄×C₁₃	—	4	4	no	—
368	C₄×C₁₃	—	4	4	no	—
369	C₄×C₁₃	—	4	4	no	—
370	C₄×C₁₃	C₄×#41	1	4	yes	—
371	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
373	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
377	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	#126	C₂×C₄×C₁₃	1	16	yes	complemented
380	#125	C₂×C₄×C₁₃	1	8	yes	complemented
381	#124	C₂×C₄×C₁₃	1	8	yes	—
382	#123	C₂×C₄×C₁₃	1	16	yes	complemented
383	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
384	#121	C₂×C₄×C₁₃	1	8	yes	—
385	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
386	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
387	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
388	#117	—	2	8	no	—
389	#117	—	2	8	no	—
390	#117	C₂×C₄×C₁₃	1	16	yes	complemented
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₄²	—	2	8	no	—
414	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
415	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
416	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
419	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
431	#95	C₂³×C₁₃	1	4	yes	—
432	#95	C₂³×C₁₃	1	4	yes	—
433	#95	C₂³×C₁₃	1	4	yes	—
434	#95	C₂³×C₁₃	1	4	yes	—
435	#95	C₂³×C₁₃	1	4	yes	—
436	#95	C₂³×C₁₃	1	4	yes	—
437	#95	C₂³×C₁₃	1	2	yes	—
438	#95	C₂³×C₁₃	1	2	yes	—
439	#95	C₂³×C₁₃	1	4	yes	—
440	#95	C₂³×C₁₃	1	4	yes	—
441	#95	C₂³×C₁₃	1	4	yes	—
442	#95	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	4	yes	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	4	4	no	—
446	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
447	C₂×C₁₃	#3428	1	1	yes	characteristic
448	C₂×C₁₃	#3428	1	1	yes	characteristic
449	C₂×C₁₃	#3455	1	4	yes	—
450	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
457	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
468	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
469	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
483	C₄⋊C₄	—	2	8	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	4	4	no	—
486	C₄⋊C₄	—	4	4	no	—
487	C₄⋊C₄	—	4	4	no	—
488	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
489	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
490	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
491	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
492	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
493	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	2	8	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	4	4	no	—
498	C₂²⋊C₄	—	4	4	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
501	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
502	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
503	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
504	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
505	C₄²	—	2	8	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	—	2	4	no	—
509	C₄²	—	4	2	no	—
510	C₄²	—	4	2	no	—
511	C₄²	—	4	4	no	—
512	C₄²	—	4	4	no	—
513	C₄²	—	4	2	no	—
514	C₄²	—	4	2	no	—
515	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
516	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
517	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
518	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
519	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
520	C₄²	C₁₃×#41	1	8	yes	—
521	C₁₃	#34081	1	1	yes	characteristic, direct product factor, Sylow
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
530	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
531	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
532	Q₈	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	8	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	16	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	16	no	—
560	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
561	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
562	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
563	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
564	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
566	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
567	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
568	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
570	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
581	C₂²	C₂²×C₁₃×#41	1	2	yes	—
582	C₂²	C₁₃×#585	1	2	yes	—
583	C₂²	C₁₃×#585	1	2	yes	—
584	C₄	—	2	4	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	4	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	8	no	—
593	C₄	—	4	4	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	4	no	—
596	C₄	C₄×C₁₃×#41	1	4	yes	—
597	C₂	—	4	2	no	—
598	C₂	—	4	4	no	—
599	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
600	C₂	C₁₃×#3428	1	1	yes	characteristic
601	C₂	C₁₃×#3428	1	1	yes	characteristic
602	C₂	C₁₃×#3455	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2337	C₂	semidirect
3. C₁₃×#2336	C₂	semidirect
4. C₁₃×#2335	C₂	semidirect
5. C₁₃×#2334	C₂	semidirect
7. C₁₃×#2332	C₂	semidirect
8. C₁₃×#2298	C₂	semidirect
9. C₁₃×#2295	C₂	semidirect
10. C₁₃×#2293	C₂	semidirect
11. C₁₃×#2290	C₂	semidirect
12. C₁₃×#2290	C₂	semidirect
13. C₁₃×#2283	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
15. C₄×C₁₃×#117	C₂	semidirect
16. C₁₃×#529	C₄	semidirect
84. C₁₃×#126	C₂×C₄	semidirect
85. C₁₃×#125	C₂×C₄	semidirect
87. C₁₃×#123	C₂×C₄	semidirect
88. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
90. C₄×Q₈×C₁₃	C₂×C₄	semidirect
92. C₄×D₄×C₁₃	C₂×C₄	semidirect
95. C₁₃×#117	C₂×C₄	semidirect
119. C₂×C₄²×C₁₃	C₂×C₄	semidirect
149. #34081	C₁₃	direct (N × H)
222. #2337	C₂×C₁₃	semidirect
223. #2336	C₂×C₁₃	semidirect
224. #2335	C₂×C₁₃	semidirect
225. #2334	C₂×C₁₃	semidirect
227. #2332	C₂×C₁₃	semidirect
228. #2298	C₂×C₁₃	semidirect
229. #2295	C₂×C₁₃	semidirect
230. #2293	C₂×C₁₃	semidirect
231. #2290	C₂×C₁₃	semidirect
232. #2290	C₂×C₁₃	semidirect
233. #2283	C₂×C₁₃	semidirect
234. C₄×#117	C₂×C₁₃	semidirect
235. C₄×#117	C₂×C₁₃	semidirect
285. #529	C₄×C₁₃	semidirect
379. #126	C₂×C₄×C₁₃	semidirect
380. #125	C₂×C₄×C₁₃	semidirect
382. #123	C₂×C₄×C₁₃	semidirect
383. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
385. C₄×Q₈	C₂×C₄×C₁₃	semidirect
387. C₄×D₄	C₂×C₄×C₁₃	semidirect
390. #117	C₂×C₄×C₁₃	semidirect
414. C₂×C₄²	C₂×C₄×C₁₃	semidirect
521. C₁₃	#34081	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×#529	2
C₁₃×#2337	2
C₁₃×#2336	2
C₁₃×#2335	2
C₁₃×#2334	2
C₁₃×#2333	2
C₁₃×#2332	2
C₁₃×#2298	2
C₁₃×#2295	2
C₁₃×#2293	2
C₁₃×#2290	2
C₁₃×#2283	2
C₄×C₁₃×#117	2
#34081	13

Subgroups — C13×#34081 #15720420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34081 #15720420