Subgroups — C₁₃×#34226 #15720565

Order 3328.

2706 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2367	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2363	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2349	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2341	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2324	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#127	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₁₃×#532	C₄	1	16	yes	complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
24	C₂×C₄×D₄×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×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	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×#390	C₂²	1	4	yes	—
34	C₁₃×#390	C₂²	1	4	yes	—
35	C₁₃×#390	C₂²	1	8	yes	—
36	C₁₃×#389	C₂²	1	4	yes	—
37	C₁₃×#389	C₂²	1	4	yes	—
38	C₁₃×#388	C₂²	1	8	yes	—
39	C₁₃×#388	C₂²	1	8	yes	—
40	C₁₃×#386	C₂²	1	8	yes	—
41	C₁₃×#385	C₂²	1	8	yes	—
42	C₁₃×#384	C₂²	1	2	yes	—
43	C₁₃×#382	C₂²	1	2	yes	—
44	C₁₃×#381	C₂²	1	4	yes	—
45	C₁₃×#380	C₂²	1	2	yes	—
46	C₁₃×#380	C₂²	1	2	yes	—
47	C₁₃×#380	C₂²	1	4	yes	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
60	C₁₃×#376	C₂²	1	1	yes	characteristic
61	C₁₃×#376	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#95	C₂²	1	4	yes	—
63	C₄³×C₁₃	C₂²	1	2	yes	—
64	C₂×C₁₃×#41	—	4	8	no	—
65	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
66	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
77	C₁₃×#127	C₂×C₄	1	8	yes	—
78	C₁₃×#124	C₂×C₄	1	16	yes	complemented
79	C₁₃×#121	C₂×C₄	1	16	yes	complemented
80	C₁₃×#121	C₂×C₄	1	16	yes	complemented
81	C₄×Q₈×C₁₃	—	4	8	no	—
82	C₄×D₄×C₁₃	—	2	16	no	—
83	C₄×D₄×C₁₃	—	4	8	no	—
84	C₄×D₄×C₁₃	—	4	8	no	—
85	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
86	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
87	C₁₃×#117	—	2	8	no	—
88	C₁₃×#117	—	4	4	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
106	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₁₃×#95	C₂³	1	1	yes	characteristic
119	C₁₃×#95	C₂³	1	2	yes	—
120	C₁₃×#95	C₂³	1	1	yes	characteristic
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	1	yes	characteristic
123	C₁₃×#95	C₂³	1	8	yes	—
124	C₁₃×#95	C₂³	1	2	yes	—
125	C₁₃×#95	C₂³	1	1	yes	characteristic
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	8	yes	—
128	#34226	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
131	C₁₃×#41	—	4	32	no	—
132	C₂×Q₈×C₁₃	—	2	8	no	—
133	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	8	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	4	8	no	—
139	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
140	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
141	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	16	no	—
148	C₂²×C₄×C₁₃	—	4	8	no	—
149	C₂²×C₄×C₁₃	—	4	8	no	—
150	C₂²×C₄×C₁₃	—	4	8	no	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	8	no	—
172	C₁₃×C₄⋊C₄	—	4	8	no	—
173	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
174	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
175	C₁₃×C₂²⋊C₄	—	2	4	no	—
176	C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₁₃×C₂²⋊C₄	—	2	16	no	—
178	C₁₃×C₂²⋊C₄	—	4	4	no	—
179	C₁₃×C₂²⋊C₄	—	4	8	no	—
180	C₁₃×C₂²⋊C₄	—	4	8	no	—
181	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
182	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
183	C₄²×C₁₃	—	2	4	no	—
184	C₄²×C₁₃	—	2	4	no	—
185	C₄²×C₁₃	—	2	4	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	—	2	4	no	—
188	C₄²×C₁₃	—	4	4	no	—
189	C₄²×C₁₃	—	4	8	no	—
190	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
191	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
192	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
193	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
194	C₄²×C₁₃	#41	1	8	yes	complemented
195	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
196	#2367	C₂×C₁₃	1	4	yes	complemented
197	#2363	C₂×C₁₃	1	4	yes	complemented
198	#2357	C₂×C₁₃	1	2	yes	complemented
199	#2349	C₂×C₁₃	1	2	yes	complemented
200	#2341	C₂×C₁₃	1	2	yes	complemented
201	#2339	C₂×C₁₃	1	2	yes	complemented
202	#2324	C₂×C₁₃	1	4	yes	complemented
203	#2319	C₂×C₁₃	1	2	yes	complemented
204	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
205	C₄×#127	C₂×C₁₃	1	2	yes	complemented
206	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2275	C₂×C₁₃	1	2	yes	complemented
208	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	8	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
218	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
219	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	16	no	—
221	D₄×C₁₃	—	2	16	no	—
222	D₄×C₁₃	—	2	16	no	—
223	D₄×C₁₃	—	2	16	no	—
224	D₄×C₁₃	—	4	16	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	8	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	8	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	4	16	no	—
247	C₂×C₄×C₁₃	—	8	16	no	—
248	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
249	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
250	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
252	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
256	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
258	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
259	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
260	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
261	C₂²×#41	C₂²×C₁₃	1	2	yes	—
262	#532	C₄×C₁₃	1	16	yes	complemented
263	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#124	C₂²×C₁₃	1	2	yes	—
266	C₂×#121	C₂²×C₁₃	1	2	yes	—
267	C₂×#121	C₂²×C₁₃	1	2	yes	—
268	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
269	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
270	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
272	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
274	C₂×#117	C₂²×C₁₃	1	2	yes	—
275	C₂×#117	C₂²×C₁₃	1	2	yes	—
276	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
277	#391	C₂²×C₁₃	1	4	yes	—
278	#390	C₂²×C₁₃	1	4	yes	—
279	#390	C₂²×C₁₃	1	4	yes	—
280	#390	C₂²×C₁₃	1	4	yes	—
281	#390	C₂²×C₁₃	1	8	yes	—
282	#389	C₂²×C₁₃	1	4	yes	—
283	#389	C₂²×C₁₃	1	4	yes	—
284	#388	C₂²×C₁₃	1	8	yes	—
285	#388	C₂²×C₁₃	1	8	yes	—
286	#386	C₂²×C₁₃	1	8	yes	—
287	#385	C₂²×C₁₃	1	8	yes	—
288	#384	C₂²×C₁₃	1	2	yes	—
289	#382	C₂²×C₁₃	1	2	yes	—
290	#381	C₂²×C₁₃	1	4	yes	—
291	#380	C₂²×C₁₃	1	4	yes	—
292	#380	C₂²×C₁₃	1	2	yes	—
293	#380	C₂²×C₁₃	1	2	yes	—
294	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
295	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
296	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
305	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
306	#376	C₂²×C₁₃	1	1	yes	characteristic
307	#376	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#95	C₂²×C₁₃	1	4	yes	—
309	C₄³	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	8	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	8	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	8	no	—
316	C₂²×C₁₃	—	4	8	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	8	no	—
320	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
321	C₂²×C₁₃	C₂²×#41	1	2	yes	—
322	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	8	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	4	no	—
330	C₄×C₁₃	—	2	4	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	—	4	8	no	—
333	C₄×C₁₃	—	4	2	no	—
334	C₄×C₁₃	C₄×#41	1	4	yes	—
335	C₄×C₁₃	#518	1	4	yes	—
336	C₄×C₁₃	#520	1	4	yes	—
337	C₂×#41	—	4	8	no	—
338	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
339	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
341	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
342	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
343	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
349	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
350	#127	C₂×C₄×C₁₃	1	8	yes	—
351	#124	C₂×C₄×C₁₃	1	16	yes	complemented
352	#121	C₂×C₄×C₁₃	1	16	yes	complemented
353	#121	C₂×C₄×C₁₃	1	16	yes	complemented
354	C₄×Q₈	—	4	8	no	—
355	C₄×D₄	—	2	16	no	—
356	C₄×D₄	—	4	8	no	—
357	C₄×D₄	—	4	8	no	—
358	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
359	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
360	#117	—	2	8	no	—
361	#117	—	4	4	no	—
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	2	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	8	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	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	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
379	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
382	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
385	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
391	#95	C₂³×C₁₃	1	1	yes	characteristic
392	#95	C₂³×C₁₃	1	4	yes	—
393	#95	C₂³×C₁₃	1	8	yes	—
394	#95	C₂³×C₁₃	1	1	yes	characteristic
395	#95	C₂³×C₁₃	1	2	yes	—
396	#95	C₂³×C₁₃	1	1	yes	characteristic
397	#95	C₂³×C₁₃	1	1	yes	characteristic
398	#95	C₂³×C₁₃	1	2	yes	—
399	#95	C₂³×C₁₃	1	4	yes	—
400	#95	C₂³×C₁₃	1	8	yes	—
401	C₂×C₁₃	—	4	2	no	—
402	C₂×C₁₃	—	4	8	no	—
403	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
404	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
405	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
406	C₂×C₁₃	#3508	1	2	yes	—
407	C₂×C₁₃	#3511	1	2	yes	—
408	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
409	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
410	#41	—	4	32	no	—
411	C₂×Q₈	—	2	8	no	—
412	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
419	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
420	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
421	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	16	no	—
427	C₂²×C₄	—	4	8	no	—
428	C₂²×C₄	—	4	8	no	—
429	C₂²×C₄	—	4	8	no	—
430	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
432	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
433	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	4	8	no	—
452	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
453	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	16	no	—
457	C₂²⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	4	8	no	—
459	C₂²⋊C₄	—	4	8	no	—
460	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
461	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	4	4	no	—
468	C₄²	—	4	8	no	—
469	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
470	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
471	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
472	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
473	C₄²	C₁₃×#41	1	8	yes	complemented
474	C₁₃	#34226	1	1	yes	characteristic, direct product factor, Sylow
475	C₂³	—	2	2	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	4	no	—
483	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
484	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
485	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
486	Q₈	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	16	no	—
489	D₄	—	2	16	no	—
490	D₄	—	4	16	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	16	no	—
513	C₂×C₄	—	8	16	no	—
514	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
515	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
516	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
517	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
518	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
519	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
520	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
521	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
522	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
523	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
524	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
525	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	8	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	4	8	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	8	no	—
537	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
538	C₂²	C₂²×C₁₃×#41	1	2	yes	—
539	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
540	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	8	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	4	no	—
547	C₄	—	2	4	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	8	no	—
550	C₄	—	4	2	no	—
551	C₄	C₄×C₁₃×#41	1	4	yes	—
552	C₄	C₁₃×#518	1	4	yes	—
553	C₄	C₁₃×#520	1	4	yes	—
554	C₂	—	4	2	no	—
555	C₂	—	4	8	no	—
556	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
557	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
558	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
559	C₂	C₁₃×#3508	1	2	yes	—
560	C₂	C₁₃×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
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×#2367	C₂	semidirect
3. C₁₃×#2363	C₂	semidirect
4. C₁₃×#2357	C₂	semidirect
5. C₁₃×#2349	C₂	semidirect
6. C₁₃×#2341	C₂	semidirect
7. C₁₃×#2339	C₂	semidirect
8. C₁₃×#2324	C₂	semidirect
9. C₁₃×#2319	C₂	semidirect
10. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
11. C₄×C₁₃×#127	C₂	semidirect
12. C₁₃×#2285	C₂	semidirect
13. C₁₃×#2275	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
16. C₁₃×#532	C₄	semidirect
65. C₂×C₁₃×#41	C₂×C₄	semidirect
76. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
78. C₁₃×#124	C₂×C₄	semidirect
79. C₁₃×#121	C₂×C₄	semidirect
80. C₁₃×#121	C₂×C₄	semidirect
85. C₄×D₄×C₁₃	C₂×C₄	semidirect
86. C₄×D₄×C₁₃	C₂×C₄	semidirect
105. C₂×C₄²×C₁₃	C₂×C₄	semidirect
128. #34226	C₁₃	direct (N × H)
194. C₄²×C₁₃	#41	semidirect
196. #2367	C₂×C₁₃	semidirect
197. #2363	C₂×C₁₃	semidirect
198. #2357	C₂×C₁₃	semidirect
199. #2349	C₂×C₁₃	semidirect
200. #2341	C₂×C₁₃	semidirect
201. #2339	C₂×C₁₃	semidirect
202. #2324	C₂×C₁₃	semidirect
203. #2319	C₂×C₁₃	semidirect
204. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
205. C₄×#127	C₂×C₁₃	semidirect
206. #2285	C₂×C₁₃	semidirect
207. #2275	C₂×C₁₃	semidirect
208. C₄×#117	C₂×C₁₃	semidirect
262. #532	C₄×C₁₃	semidirect
338. C₂×#41	C₂×C₄×C₁₃	semidirect
349. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
351. #124	C₂×C₄×C₁₃	semidirect
352. #121	C₂×C₄×C₁₃	semidirect
353. #121	C₂×C₄×C₁₃	semidirect
358. C₄×D₄	C₂×C₄×C₁₃	semidirect
359. C₄×D₄	C₂×C₄×C₁₃	semidirect
378. C₂×C₄²	C₂×C₄×C₁₃	semidirect
473. C₄²	C₁₃×#41	semidirect
474. C₁₃	#34226	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×#532	2
C₁₃×#2367	2
C₁₃×#2363	2
C₁₃×#2357	2
C₁₃×#2349	2
C₁₃×#2341	2
C₁₃×#2339	2
C₁₃×#2324	2
C₁₃×#2319	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#127	2
C₁₃×#2285	2
C₁₃×#2275	2
C₄×C₁₃×#117	2
#34226	13

Subgroups — C13×#34226 #15720565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34226 #15720565