Subgroups — C₁₃×#34240 #15720579

Order 3328.

2682 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2372	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2367	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2342	C₂	1	4	yes	maximal, complemented
5	Q₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
7	C₁₃×#2337	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2312	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#124	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2273	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₄	1	16	yes	complemented
16	C₂×C₁₃×#124	C₂²	1	2	yes	—
17	C₂×C₁₃×#124	C₂²	1	2	yes	—
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₁₃×#117	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#391	C₂²	1	4	yes	complemented
28	C₁₃×#391	C₂²	1	8	yes	complemented
29	C₁₃×#390	C₂²	1	4	yes	—
30	C₁₃×#388	C₂²	1	8	yes	complemented
31	C₁₃×#388	C₂²	1	8	yes	complemented
32	C₁₃×#388	C₂²	1	8	yes	complemented
33	C₁₃×#388	C₂²	1	8	yes	complemented
34	C₁₃×#386	C₂²	1	8	yes	—
35	C₁₃×#385	C₂²	1	8	yes	complemented
36	C₁₃×#383	C₂²	1	2	yes	complemented
37	C₁₃×#382	C₂²	1	2	yes	complemented
38	C₁₃×#381	C₂²	1	2	yes	—
39	C₁₃×#380	C₂²	1	2	yes	—
40	C₁₃×#380	C₂²	1	4	yes	—
41	C₁₃×#379	C₂²	1	4	yes	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
53	C₁₃×#376	C₂²	1	2	yes	complemented
54	C₁₃×#376	C₂²	1	2	yes	complemented
55	C₄³×C₁₃	C₂²	1	2	yes	complemented
56	C₂⁵×C₁₃	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	—	4	4	no	—
58	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	—	4	4	no	—
62	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₁₃×#124	C₂×C₄	1	16	yes	complemented
71	C₁₃×#124	C₂×C₄	1	16	yes	complemented
72	C₁₃×#124	C₂×C₄	1	16	yes	complemented
73	C₁₃×#124	C₂×C₄	1	16	yes	complemented
74	C₄×Q₈×C₁₃	—	4	8	no	—
75	C₄×D₄×C₁₃	—	4	8	no	—
76	C₁₃×#117	—	2	8	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
82	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
94	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₁₃×#95	C₂³	1	2	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	2	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	8	yes	—
111	C₁₃×#95	C₂³	1	4	yes	—
112	C₁₃×#95	C₂³	1	4	yes	—
113	#34240	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	8	no	—
115	C₂⁴×C₁₃	—	4	4	no	—
116	C₂⁴×C₁₃	—	4	4	no	—
117	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	4	4	no	—
122	C₂×Q₈×C₁₃	—	4	16	no	—
123	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
124	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	4	16	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
129	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	16	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	4	4	no	—
135	C₂²×C₄×C₁₃	—	4	8	no	—
136	C₂²×C₄×C₁₃	—	4	8	no	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	4	8	no	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	2	16	no	—
157	C₁₃×C₂²⋊C₄	—	4	8	no	—
158	C₁₃×C₂²⋊C₄	—	4	8	no	—
159	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
160	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
161	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
162	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
163	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
164	C₄²×C₁₃	—	2	8	no	—
165	C₄²×C₁₃	—	2	8	no	—
166	C₄²×C₁₃	—	4	2	no	—
167	C₄²×C₁₃	—	4	2	no	—
168	C₄²×C₁₃	—	4	4	no	—
169	C₄²×C₁₃	—	4	8	no	—
170	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
171	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
172	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
173	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
175	#2372	C₂×C₁₃	1	4	yes	complemented
176	#2367	C₂×C₁₃	1	4	yes	complemented
177	#2342	C₂×C₁₃	1	4	yes	complemented
178	Q₈×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
179	D₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
180	#2337	C₂×C₁₃	1	4	yes	complemented
181	#2312	C₂×C₁₃	1	2	yes	complemented
182	C₄×#124	C₂×C₁₃	1	4	yes	complemented
183	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#2273	C₂×C₁₃	1	2	yes	complemented
185	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	16	no	—
193	C₂³×C₁₃	—	4	8	no	—
194	C₂³×C₁₃	—	4	8	no	—
195	C₂³×C₁₃	—	8	16	no	—
196	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
197	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
198	C₂³×C₁₃	C₂×#41	1	4	yes	—
199	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	16	no	—
201	Q₈×C₁₃	—	4	8	no	—
202	D₄×C₁₃	—	2	16	no	—
203	D₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	8	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	8	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	—	8	16	no	—
223	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
229	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
231	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
232	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#124	C₄×C₁₃	1	16	yes	complemented
235	C₂×#124	C₂²×C₁₃	1	2	yes	—
236	C₂×#124	C₂²×C₁₃	1	2	yes	—
237	C₂×#124	C₂²×C₁₃	1	2	yes	—
238	C₂×#124	C₂²×C₁₃	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
240	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
241	C₂×#117	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
246	#391	C₂²×C₁₃	1	8	yes	complemented
247	#391	C₂²×C₁₃	1	4	yes	complemented
248	#390	C₂²×C₁₃	1	4	yes	—
249	#388	C₂²×C₁₃	1	8	yes	complemented
250	#388	C₂²×C₁₃	1	8	yes	complemented
251	#388	C₂²×C₁₃	1	8	yes	complemented
252	#388	C₂²×C₁₃	1	8	yes	complemented
253	#386	C₂²×C₁₃	1	8	yes	—
254	#385	C₂²×C₁₃	1	8	yes	complemented
255	#383	C₂²×C₁₃	1	2	yes	complemented
256	#382	C₂²×C₁₃	1	2	yes	complemented
257	#381	C₂²×C₁₃	1	2	yes	—
258	#380	C₂²×C₁₃	1	4	yes	—
259	#380	C₂²×C₁₃	1	2	yes	—
260	#379	C₂²×C₁₃	1	4	yes	—
261	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
262	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
263	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
264	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
266	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
267	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
270	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
271	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
272	#376	C₂²×C₁₃	1	2	yes	complemented
273	#376	C₂²×C₁₃	1	2	yes	complemented
274	C₄³	C₂²×C₁₃	1	2	yes	complemented
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	8	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	8	no	—
280	C₂²×C₁₃	—	2	8	no	—
281	C₂²×C₁₃	—	4	8	no	—
282	C₂²×C₁₃	—	4	8	no	—
283	C₂²×C₁₃	—	8	16	no	—
284	C₂²×C₁₃	C₄×#41	1	4	yes	—
285	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
286	C₂²×C₁₃	C₂²×#41	1	2	yes	—
287	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
288	C₂²×C₁₃	#585	1	2	yes	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	8	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	8	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	—	4	8	no	—
298	C₄×C₁₃	#518	1	4	yes	—
299	C₂⁵	C₂³×C₁₃	1	2	yes	—
300	C₂²×Q₈	—	4	4	no	—
301	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
302	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
306	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
307	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
311	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
313	#124	C₂×C₄×C₁₃	1	16	yes	complemented
314	#124	C₂×C₄×C₁₃	1	16	yes	complemented
315	#124	C₂×C₄×C₁₃	1	16	yes	complemented
316	#124	C₂×C₄×C₁₃	1	16	yes	complemented
317	C₄×Q₈	—	4	8	no	—
318	C₄×D₄	—	4	8	no	—
319	#117	—	2	8	no	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
323	C₂×C₂²⋊C₄	—	2	16	no	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
325	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
326	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
337	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
338	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
340	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
341	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
342	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
347	#95	C₂³×C₁₃	1	2	yes	—
348	#95	C₂³×C₁₃	1	4	yes	—
349	#95	C₂³×C₁₃	1	2	yes	—
350	#95	C₂³×C₁₃	1	4	yes	—
351	#95	C₂³×C₁₃	1	4	yes	—
352	#95	C₂³×C₁₃	1	4	yes	—
353	#95	C₂³×C₁₃	1	8	yes	—
354	#95	C₂³×C₁₃	1	8	yes	—
355	#95	C₂³×C₁₃	1	4	yes	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	—	4	8	no	—
358	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
360	C₂×C₁₃	#3428	1	1	yes	characteristic
361	C₂×C₁₃	#3514	1	4	yes	—
362	C₂⁴	—	2	8	no	—
363	C₂⁴	—	4	4	no	—
364	C₂⁴	—	4	4	no	—
365	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
366	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
367	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	4	4	no	—
370	C₂×Q₈	—	4	16	no	—
371	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
372	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	4	16	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
377	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	16	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	8	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
389	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
390	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	16	no	—
405	C₂²⋊C₄	—	4	8	no	—
406	C₂²⋊C₄	—	4	8	no	—
407	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
408	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
409	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
410	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
411	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
412	C₄²	—	2	8	no	—
413	C₄²	—	2	8	no	—
414	C₄²	—	4	8	no	—
415	C₄²	—	4	2	no	—
416	C₄²	—	4	2	no	—
417	C₄²	—	4	4	no	—
418	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
419	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
420	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
421	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
422	C₁₃	#34240	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	16	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	8	16	no	—
433	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
434	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
435	C₂³	C₂×C₁₃×#41	1	4	yes	—
436	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
437	Q₈	—	2	16	no	—
438	Q₈	—	4	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	4	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	8	16	no	—
460	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
461	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
464	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
465	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
466	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
467	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
468	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	8	16	no	—
478	C₂²	C₄×C₁₃×#41	1	4	yes	—
479	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
480	C₂²	C₂²×C₁₃×#41	1	2	yes	—
481	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
482	C₂²	C₁₃×#585	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	8	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	8	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	8	no	—
492	C₄	C₁₃×#518	1	4	yes	—
493	C₂	—	2	4	no	—
494	C₂	—	4	8	no	—
495	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
496	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
497	C₂	C₁₃×#3428	1	1	yes	characteristic
498	C₂	C₁₃×#3514	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	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. C₁₃×#2372	C₂	semidirect
3. C₁₃×#2367	C₂	semidirect
4. C₁₃×#2342	C₂	semidirect
5. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₁₃×#2337	C₂	semidirect
8. C₁₃×#2312	C₂	semidirect
9. C₄×C₁₃×#124	C₂	semidirect
10. C₁₃×#2283	C₂	semidirect
11. C₁₃×#2273	C₂	semidirect
12. C₄×C₁₃×#117	C₂	semidirect
15. C₂×C₁₃×#124	C₄	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
27. C₁₃×#391	C₂²	semidirect
28. C₁₃×#391	C₂²	semidirect
30. C₁₃×#388	C₂²	semidirect
31. C₁₃×#388	C₂²	semidirect
32. C₁₃×#388	C₂²	semidirect
33. C₁₃×#388	C₂²	semidirect
35. C₁₃×#385	C₂²	semidirect
36. C₁₃×#383	C₂²	semidirect
37. C₁₃×#382	C₂²	semidirect
42. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
44. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
50. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
51. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
52. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
53. C₁₃×#376	C₂²	semidirect
54. C₁₃×#376	C₂²	semidirect
55. C₄³×C₁₃	C₂²	semidirect
58. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
70. C₁₃×#124	C₂×C₄	semidirect
71. C₁₃×#124	C₂×C₄	semidirect
72. C₁₃×#124	C₂×C₄	semidirect
73. C₁₃×#124	C₂×C₄	semidirect
81. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
82. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
93. C₂×C₄²×C₁₃	C₂×C₄	semidirect
113. #34240	C₁₃	direct (N × H)
175. #2372	C₂×C₁₃	semidirect
176. #2367	C₂×C₁₃	semidirect
177. #2342	C₂×C₁₃	semidirect
178. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
180. #2337	C₂×C₁₃	semidirect
181. #2312	C₂×C₁₃	semidirect
182. C₄×#124	C₂×C₁₃	semidirect
183. #2283	C₂×C₁₃	semidirect
184. #2273	C₂×C₁₃	semidirect
185. C₄×#117	C₂×C₁₃	semidirect
234. C₂×#124	C₄×C₁₃	semidirect
239. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
246. #391	C₂²×C₁₃	semidirect
247. #391	C₂²×C₁₃	semidirect
249. #388	C₂²×C₁₃	semidirect
250. #388	C₂²×C₁₃	semidirect
251. #388	C₂²×C₁₃	semidirect
252. #388	C₂²×C₁₃	semidirect
254. #385	C₂²×C₁₃	semidirect
255. #383	C₂²×C₁₃	semidirect
256. #382	C₂²×C₁₃	semidirect
261. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
262. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
263. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
269. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
270. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
271. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
272. #376	C₂²×C₁₃	semidirect
273. #376	C₂²×C₁₃	semidirect
274. C₄³	C₂²×C₁₃	semidirect
301. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
313. #124	C₂×C₄×C₁₃	semidirect
314. #124	C₂×C₄×C₁₃	semidirect
315. #124	C₂×C₄×C₁₃	semidirect
316. #124	C₂×C₄×C₁₃	semidirect
324. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
325. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
336. C₂×C₄²	C₂×C₄×C₁₃	semidirect
422. C₁₃	#34240	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#124	2
C₁₃×#2372	2
C₁₃×#2367	2
C₁₃×#2342	2
Q₈×C₁₃×C₂²⋊C₄	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2337	2
C₁₃×#2312	2
C₄×C₁₃×#124	2
C₁₃×#2283	2
C₁₃×#2273	2
C₄×C₁₃×#117	2
#34240	13

Subgroups — C13×#34240 #15720579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34240 #15720579