Subgroups — C₁₃×#34222 #15720561

Order 3328.

2650 conjugacy classes of subgroups.

The subgroup lattice has 482 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×#2372	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2364	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2353	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2339	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2331	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2328	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₁₃×#532	C₄	1	16	yes	complemented
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	8	yes	—
27	C₁₃×#390	C₂²	1	4	yes	—
28	C₁₃×#389	C₂²	1	4	yes	—
29	C₁₃×#388	C₂²	1	8	yes	—
30	C₁₃×#388	C₂²	1	8	yes	—
31	C₁₃×#387	C₂²	1	8	yes	—
32	C₁₃×#386	C₂²	1	8	yes	—
33	C₁₃×#386	C₂²	1	8	yes	—
34	C₁₃×#386	C₂²	1	8	yes	—
35	C₁₃×#383	C₂²	1	2	yes	—
36	C₁₃×#382	C₂²	1	2	yes	—
37	C₁₃×#381	C₂²	1	2	yes	—
38	C₁₃×#381	C₂²	1	4	yes	—
39	C₁₃×#380	C₂²	1	2	yes	—
40	C₁₃×#380	C₂²	1	4	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
43	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
44	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
47	C₁₃×#376	C₂²	1	1	yes	characteristic
48	C₁₃×#376	C₂²	1	1	yes	characteristic
49	C₁₃×#376	C₂²	1	2	yes	—
50	C₁₃×#376	C₂²	1	2	yes	—
51	C₁₃×#376	C₂²	1	2	yes	—
52	C₁₃×#376	C₂²	1	2	yes	—
53	C₂×C₁₃×#95	C₂²	1	2	yes	—
54	C₂×C₁₃×#95	C₂²	1	2	yes	—
55	C₂×C₁₃×#95	C₂²	1	4	yes	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
70	C₁₃×#127	C₂×C₄	1	8	yes	complemented
71	C₁₃×#124	C₂×C₄	1	16	yes	complemented
72	C₁₃×#121	C₂×C₄	1	16	yes	complemented
73	C₁₃×#121	C₂×C₄	1	16	yes	complemented
74	C₄×D₄×C₁₃	—	2	16	no	—
75	C₄×D₄×C₁₃	—	4	16	no	—
76	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
77	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	—	2	8	no	—
89	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
90	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
99	C₁₃×#95	C₂³	1	2	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	2	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	2	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	2	yes	—
111	#34222	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×#41	—	4	32	no	—
115	C₂×Q₈×C₁₃	—	4	4	no	—
116	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₁₃	—	2	16	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	4	4	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
124	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	2	16	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	4	8	no	—
133	C₂²×C₄×C₁₃	—	4	8	no	—
134	C₂²×C₄×C₁₃	—	4	8	no	—
135	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	4	8	no	—
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₁₃×C₂²⋊C₄	—	2	16	no	—
155	C₁₃×C₂²⋊C₄	—	4	8	no	—
156	C₁₃×C₂²⋊C₄	—	4	8	no	—
157	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
158	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
159	C₄²×C₁₃	—	2	8	no	—
160	C₄²×C₁₃	—	2	4	no	—
161	C₄²×C₁₃	—	4	4	no	—
162	C₄²×C₁₃	—	4	8	no	—
163	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
164	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
165	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
166	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
167	C₄²×C₁₃	#41	1	8	yes	complemented
168	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
169	#2372	C₂×C₁₃	1	4	yes	complemented
170	#2364	C₂×C₁₃	1	4	yes	complemented
171	#2353	C₂×C₁₃	1	4	yes	complemented
172	#2339	C₂×C₁₃	1	4	yes	complemented
173	#2331	C₂×C₁₃	1	2	yes	complemented
174	#2328	C₂×C₁₃	1	2	yes	complemented
175	#2319	C₂×C₁₃	1	2	yes	complemented
176	C₄×#121	C₂×C₁₃	1	4	yes	complemented
177	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2275	C₂×C₁₃	1	2	yes	complemented
179	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	8	no	—
183	C₂³×C₁₃	—	2	8	no	—
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
187	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
188	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
189	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
190	Q₈×C₁₃	—	4	8	no	—
191	D₄×C₁₃	—	2	32	no	—
192	D₄×C₁₃	—	2	16	no	—
193	D₄×C₁₃	—	4	8	no	—
194	D₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	8	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	16	no	—
213	C₂×C₄×C₁₃	—	4	16	no	—
214	C₂×C₄×C₁₃	—	8	16	no	—
215	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
218	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
223	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
224	C₂²×#41	C₂²×C₁₃	1	2	yes	—
225	#532	C₄×C₁₃	1	16	yes	complemented
226	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#124	C₂²×C₁₃	1	2	yes	—
229	C₂×#121	C₂²×C₁₃	1	2	yes	—
230	C₂×#121	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
232	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
233	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
237	#391	C₂²×C₁₃	1	8	yes	—
238	#390	C₂²×C₁₃	1	4	yes	—
239	#389	C₂²×C₁₃	1	4	yes	—
240	#388	C₂²×C₁₃	1	8	yes	—
241	#388	C₂²×C₁₃	1	8	yes	—
242	#387	C₂²×C₁₃	1	8	yes	—
243	#386	C₂²×C₁₃	1	8	yes	—
244	#386	C₂²×C₁₃	1	8	yes	—
245	#386	C₂²×C₁₃	1	8	yes	—
246	#383	C₂²×C₁₃	1	2	yes	—
247	#382	C₂²×C₁₃	1	2	yes	—
248	#381	C₂²×C₁₃	1	4	yes	—
249	#381	C₂²×C₁₃	1	2	yes	—
250	#380	C₂²×C₁₃	1	4	yes	—
251	#380	C₂²×C₁₃	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
254	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
255	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
256	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
258	#376	C₂²×C₁₃	1	1	yes	characteristic
259	#376	C₂²×C₁₃	1	2	yes	—
260	#376	C₂²×C₁₃	1	2	yes	—
261	#376	C₂²×C₁₃	1	2	yes	—
262	#376	C₂²×C₁₃	1	2	yes	—
263	#376	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#95	C₂²×C₁₃	1	2	yes	—
265	C₂×#95	C₂²×C₁₃	1	4	yes	—
266	C₂×#95	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	8	no	—
270	C₂²×C₁₃	—	2	8	no	—
271	C₂²×C₁₃	—	2	8	no	—
272	C₂²×C₁₃	—	2	8	no	—
273	C₂²×C₁₃	—	4	8	no	—
274	C₂²×C₁₃	—	4	8	no	—
275	C₂²×C₁₃	#518	1	4	yes	—
276	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
277	C₂²×C₁₃	C₂²×#41	1	2	yes	—
278	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
279	C₂²×C₁₃	#585	1	2	yes	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	8	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	2	8	no	—
287	C₄×C₁₃	—	4	4	no	—
288	C₄×C₁₃	—	4	8	no	—
289	C₄×C₁₃	C₄×#41	1	4	yes	—
290	C₂×#41	—	4	8	no	—
291	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
292	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
293	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
294	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
295	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
296	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
301	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
302	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
304	#127	C₂×C₄×C₁₃	1	8	yes	complemented
305	#124	C₂×C₄×C₁₃	1	16	yes	complemented
306	#121	C₂×C₄×C₁₃	1	16	yes	complemented
307	#121	C₂×C₄×C₁₃	1	16	yes	complemented
308	C₄×D₄	—	2	16	no	—
309	C₄×D₄	—	4	16	no	—
310	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
311	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₂×C₄²	—	2	8	no	—
323	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
324	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
325	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
327	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
333	#95	C₂³×C₁₃	1	2	yes	—
334	#95	C₂³×C₁₃	1	2	yes	—
335	#95	C₂³×C₁₃	1	2	yes	—
336	#95	C₂³×C₁₃	1	4	yes	—
337	#95	C₂³×C₁₃	1	4	yes	—
338	#95	C₂³×C₁₃	1	2	yes	—
339	#95	C₂³×C₁₃	1	4	yes	—
340	#95	C₂³×C₁₃	1	8	yes	—
341	#95	C₂³×C₁₃	1	4	yes	—
342	#95	C₂³×C₁₃	1	4	yes	—
343	#95	C₂³×C₁₃	1	8	yes	—
344	#95	C₂³×C₁₃	1	4	yes	—
345	C₂×C₁₃	—	2	4	no	—
346	C₂×C₁₃	—	4	8	no	—
347	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
348	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
349	C₂×C₁₃	#3428	1	1	yes	characteristic
350	C₂×C₁₃	#3494	1	4	yes	—
351	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
352	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
353	#41	—	4	32	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
356	C₂×D₄	—	2	16	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
361	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
362	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
363	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	16	no	—
369	C₂²×C₄	—	4	8	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
375	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
391	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	16	no	—
394	C₂²⋊C₄	—	4	8	no	—
395	C₂²⋊C₄	—	4	8	no	—
396	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
397	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	4	8	no	—
401	C₄²	—	4	4	no	—
402	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
403	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
404	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
405	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
406	C₄²	C₁₃×#41	1	8	yes	complemented
407	C₁₃	#34222	1	1	yes	characteristic, direct product factor, Sylow
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	8	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
415	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
416	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
417	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
418	Q₈	—	4	8	no	—
419	D₄	—	2	32	no	—
420	D₄	—	2	16	no	—
421	D₄	—	4	8	no	—
422	D₄	—	4	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	16	no	—
442	C₂×C₄	—	8	16	no	—
443	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
445	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
446	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
447	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
448	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
449	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
450	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
451	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	8	no	—
455	C₂²	—	2	8	no	—
456	C₂²	—	2	8	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	4	8	no	—
460	C₂²	C₁₃×#518	1	4	yes	—
461	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
462	C₂²	C₂²×C₁₃×#41	1	2	yes	—
463	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
464	C₂²	C₁₃×#585	1	2	yes	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	8	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	8	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	8	no	—
474	C₄	C₄×C₁₃×#41	1	4	yes	—
475	C₂	—	2	4	no	—
476	C₂	—	4	8	no	—
477	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
478	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
479	C₂	C₁₃×#3428	1	1	yes	characteristic
480	C₂	C₁₃×#3494	1	4	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×#2372	C₂	semidirect
3. C₁₃×#2364	C₂	semidirect
4. C₁₃×#2353	C₂	semidirect
5. C₁₃×#2339	C₂	semidirect
6. C₁₃×#2331	C₂	semidirect
7. C₁₃×#2328	C₂	semidirect
8. C₁₃×#2319	C₂	semidirect
9. C₄×C₁₃×#121	C₂	semidirect
10. C₁₃×#2283	C₂	semidirect
11. C₁₃×#2275	C₂	semidirect
12. C₂×C₁₃×#376	C₂	semidirect
14. C₁₃×#532	C₄	semidirect
57. C₂×C₁₃×#41	C₂×C₄	semidirect
69. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
70. C₁₃×#127	C₂×C₄	semidirect
71. C₁₃×#124	C₂×C₄	semidirect
72. C₁₃×#121	C₂×C₄	semidirect
73. C₁₃×#121	C₂×C₄	semidirect
76. C₄×D₄×C₁₃	C₂×C₄	semidirect
77. C₄×D₄×C₁₃	C₂×C₄	semidirect
89. C₂×C₄²×C₁₃	C₂×C₄	semidirect
111. #34222	C₁₃	direct (N × H)
167. C₄²×C₁₃	#41	semidirect
169. #2372	C₂×C₁₃	semidirect
170. #2364	C₂×C₁₃	semidirect
171. #2353	C₂×C₁₃	semidirect
172. #2339	C₂×C₁₃	semidirect
173. #2331	C₂×C₁₃	semidirect
174. #2328	C₂×C₁₃	semidirect
175. #2319	C₂×C₁₃	semidirect
176. C₄×#121	C₂×C₁₃	semidirect
177. #2283	C₂×C₁₃	semidirect
178. #2275	C₂×C₁₃	semidirect
179. C₂×#376	C₂×C₁₃	semidirect
225. #532	C₄×C₁₃	semidirect
291. C₂×#41	C₂×C₄×C₁₃	semidirect
303. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
304. #127	C₂×C₄×C₁₃	semidirect
305. #124	C₂×C₄×C₁₃	semidirect
306. #121	C₂×C₄×C₁₃	semidirect
307. #121	C₂×C₄×C₁₃	semidirect
310. C₄×D₄	C₂×C₄×C₁₃	semidirect
311. C₄×D₄	C₂×C₄×C₁₃	semidirect
323. C₂×C₄²	C₂×C₄×C₁₃	semidirect
406. C₄²	C₁₃×#41	semidirect
407. C₁₃	#34222	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×#2372	2
C₁₃×#2364	2
C₁₃×#2353	2
C₁₃×#2339	2
C₁₃×#2331	2
C₁₃×#2328	2
C₁₃×#2319	2
C₄×C₁₃×#121	2
C₁₃×#2283	2
C₁₃×#2275	2
C₂×C₁₃×#376	2
#34222	13

Subgroups — C13×#34222 #15720561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34222 #15720561