Subgroups — C₁₃×#34232 #15720571

Order 3328.

2606 conjugacy classes of subgroups.

The subgroup lattice has 528 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×#2366	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2365	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2363	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2353	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2341	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2333	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#124	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₁₃×#532	C₄	1	16	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	4	yes	—
29	C₁₃×#390	C₂²	1	4	yes	—
30	C₁₃×#390	C₂²	1	4	yes	—
31	C₁₃×#390	C₂²	1	8	yes	—
32	C₁₃×#389	C₂²	1	4	yes	—
33	C₁₃×#388	C₂²	1	8	yes	—
34	C₁₃×#388	C₂²	1	8	yes	—
35	C₁₃×#387	C₂²	1	8	yes	—
36	C₁₃×#386	C₂²	1	8	yes	—
37	C₁₃×#386	C₂²	1	8	yes	—
38	C₁₃×#383	C₂²	1	2	yes	—
39	C₁₃×#382	C₂²	1	2	yes	—
40	C₁₃×#381	C₂²	1	2	yes	—
41	C₁₃×#381	C₂²	1	4	yes	—
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₁₃×#380	C₂²	1	4	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
56	C₁₃×#376	C₂²	1	2	yes	—
57	C₁₃×#376	C₂²	1	2	yes	—
58	C₂×C₁₃×#95	C₂²	1	4	yes	—
59	C₄³×C₁₃	C₂²	1	2	yes	—
60	C₂×C₁₃×#41	—	4	8	no	—
61	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
73	C₁₃×#127	C₂×C₄	1	8	yes	—
74	C₁₃×#124	C₂×C₄	1	16	yes	complemented
75	C₁₃×#121	C₂×C₄	1	16	yes	complemented
76	C₁₃×#121	C₂×C₄	1	16	yes	complemented
77	C₄×Q₈×C₁₃	—	4	8	no	—
78	C₄×D₄×C₁₃	—	2	16	no	—
79	C₄×D₄×C₁₃	—	4	8	no	—
80	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
81	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
82	C₁₃×#117	—	2	8	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
99	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#95	C₂³	1	2	yes	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	2	yes	—
112	C₁₃×#95	C₂³	1	4	yes	—
113	C₁₃×#95	C₂³	1	2	yes	—
114	C₁₃×#95	C₂³	1	4	yes	—
115	C₁₃×#95	C₂³	1	8	yes	—
116	C₁₃×#95	C₂³	1	8	yes	—
117	C₁₃×#95	C₂³	1	4	yes	—
118	C₁₃×#95	C₂³	1	2	yes	—
119	#34232	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
122	C₁₃×#41	—	4	32	no	—
123	C₂×Q₈×C₁₃	—	2	8	no	—
124	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	4	2	no	—
129	C₂×D₄×C₁₃	—	4	8	no	—
130	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
131	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
132	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
133	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	16	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	—	4	1	no	—
139	C₂²×C₄×C₁₃	—	4	8	no	—
140	C₂²×C₄×C₁₃	—	4	8	no	—
141	C₂²×C₄×C₁₃	—	4	8	no	—
142	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	4	8	no	—
161	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
162	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
163	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	16	no	—
166	C₁₃×C₂²⋊C₄	—	4	8	no	—
167	C₁₃×C₂²⋊C₄	—	4	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	2	no	—
169	C₁₃×C₂²⋊C₄	—	4	8	no	—
170	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
171	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	—	2	8	no	—
174	C₄²×C₁₃	—	2	8	no	—
175	C₄²×C₁₃	—	4	2	no	—
176	C₄²×C₁₃	—	4	2	no	—
177	C₄²×C₁₃	—	4	8	no	—
178	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
179	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
180	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
181	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
182	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
183	#2366	C₂×C₁₃	1	2	yes	complemented
184	#2365	C₂×C₁₃	1	2	yes	complemented
185	#2363	C₂×C₁₃	1	4	yes	complemented
186	#2353	C₂×C₁₃	1	4	yes	complemented
187	#2341	C₂×C₁₃	1	2	yes	complemented
188	#2339	C₂×C₁₃	1	2	yes	complemented
189	#2333	C₂×C₁₃	1	4	yes	complemented
190	#2319	C₂×C₁₃	1	2	yes	complemented
191	C₄×#124	C₂×C₁₃	1	4	yes	complemented
192	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#2275	C₂×C₁₃	1	2	yes	complemented
194	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	8	no	—
197	C₂³×C₁₃	—	2	8	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	4	no	—
203	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
204	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
205	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
206	Q₈×C₁₃	—	2	16	no	—
207	D₄×C₁₃	—	2	16	no	—
208	D₄×C₁₃	—	2	16	no	—
209	D₄×C₁₃	—	4	8	no	—
210	D₄×C₁₃	—	4	16	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	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	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	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	16	no	—
233	C₂×C₄×C₁₃	—	8	16	no	—
234	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
239	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
242	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
243	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
244	C₂²×#41	C₂²×C₁₃	1	2	yes	—
245	#532	C₄×C₁₃	1	16	yes	complemented
246	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#124	C₂²×C₁₃	1	2	yes	—
249	C₂×#121	C₂²×C₁₃	1	2	yes	—
250	C₂×#121	C₂²×C₁₃	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
252	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
253	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
254	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
256	C₂×#117	C₂²×C₁₃	1	2	yes	—
257	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
258	#391	C₂²×C₁₃	1	4	yes	—
259	#390	C₂²×C₁₃	1	4	yes	—
260	#390	C₂²×C₁₃	1	8	yes	—
261	#390	C₂²×C₁₃	1	4	yes	—
262	#389	C₂²×C₁₃	1	4	yes	—
263	#388	C₂²×C₁₃	1	8	yes	—
264	#388	C₂²×C₁₃	1	8	yes	—
265	#387	C₂²×C₁₃	1	8	yes	—
266	#386	C₂²×C₁₃	1	8	yes	—
267	#386	C₂²×C₁₃	1	8	yes	—
268	#383	C₂²×C₁₃	1	2	yes	—
269	#382	C₂²×C₁₃	1	2	yes	—
270	#381	C₂²×C₁₃	1	4	yes	—
271	#381	C₂²×C₁₃	1	2	yes	—
272	#380	C₂²×C₁₃	1	4	yes	—
273	#380	C₂²×C₁₃	1	1	yes	characteristic
274	#380	C₂²×C₁₃	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
277	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
278	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
279	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
283	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
284	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
285	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
286	#376	C₂²×C₁₃	1	2	yes	—
287	#376	C₂²×C₁₃	1	2	yes	—
288	C₂×#95	C₂²×C₁₃	1	4	yes	—
289	C₄³	C₂²×C₁₃	1	2	yes	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	8	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	8	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	8	no	—
296	C₂²×C₁₃	—	4	8	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	8	no	—
300	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
301	C₂²×C₁₃	C₂²×#41	1	2	yes	—
302	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
303	C₂²×C₁₃	#585	1	1	yes	characteristic
304	C₂²×C₁₃	#585	1	1	yes	characteristic
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	2	8	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	8	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	C₄×#41	1	4	yes	—
315	C₄×C₁₃	#518	1	4	yes	—
316	C₂×#41	—	4	8	no	—
317	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
318	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
319	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
322	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
329	#127	C₂×C₄×C₁₃	1	8	yes	—
330	#124	C₂×C₄×C₁₃	1	16	yes	complemented
331	#121	C₂×C₄×C₁₃	1	16	yes	complemented
332	#121	C₂×C₄×C₁₃	1	16	yes	complemented
333	C₄×Q₈	—	4	8	no	—
334	C₄×D₄	—	2	16	no	—
335	C₄×D₄	—	4	8	no	—
336	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
337	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
338	#117	—	2	8	no	—
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
355	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
358	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
359	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
360	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
365	#95	C₂³×C₁₃	1	2	yes	—
366	#95	C₂³×C₁₃	1	2	yes	—
367	#95	C₂³×C₁₃	1	8	yes	—
368	#95	C₂³×C₁₃	1	2	yes	—
369	#95	C₂³×C₁₃	1	4	yes	—
370	#95	C₂³×C₁₃	1	2	yes	—
371	#95	C₂³×C₁₃	1	4	yes	—
372	#95	C₂³×C₁₃	1	4	yes	—
373	#95	C₂³×C₁₃	1	8	yes	—
374	#95	C₂³×C₁₃	1	4	yes	—
375	C₂×C₁₃	—	4	2	no	—
376	C₂×C₁₃	—	4	8	no	—
377	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
379	C₂×C₁₃	#3428	1	1	yes	characteristic
380	C₂×C₁₃	#3514	1	2	yes	—
381	C₂×C₁₃	#3517	1	2	yes	—
382	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
384	#41	—	4	32	no	—
385	C₂×Q₈	—	2	8	no	—
386	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
393	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
394	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
395	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	16	no	—
399	C₂²×C₄	—	4	8	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	8	no	—
404	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
406	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	4	8	no	—
423	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
424	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
425	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	16	no	—
428	C₂²⋊C₄	—	4	8	no	—
429	C₂²⋊C₄	—	4	8	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
433	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
434	C₄²	—	2	8	no	—
435	C₄²	—	2	8	no	—
436	C₄²	—	2	8	no	—
437	C₄²	—	4	8	no	—
438	C₄²	—	4	2	no	—
439	C₄²	—	4	2	no	—
440	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
441	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
442	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
443	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
444	C₁₃	#34232	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³	—	2	2	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
454	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
455	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
456	Q₈	—	2	16	no	—
457	D₄	—	2	16	no	—
458	D₄	—	2	16	no	—
459	D₄	—	4	8	no	—
460	D₄	—	4	16	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	16	no	—
483	C₂×C₄	—	8	16	no	—
484	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
486	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
487	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
488	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
489	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
491	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
492	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
493	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	8	no	—
500	C₂²	—	4	8	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	8	no	—
504	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
505	C₂²	C₂²×C₁₃×#41	1	2	yes	—
506	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
507	C₂²	C₁₃×#585	1	1	yes	characteristic
508	C₂²	C₁₃×#585	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	8	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	8	no	—
515	C₄	—	4	4	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	4	no	—
518	C₄	C₄×C₁₃×#41	1	4	yes	—
519	C₄	C₁₃×#518	1	4	yes	—
520	C₂	—	4	2	no	—
521	C₂	—	4	8	no	—
522	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
523	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
524	C₂	C₁₃×#3428	1	1	yes	characteristic
525	C₂	C₁₃×#3514	1	2	yes	—
526	C₂	C₁₃×#3517	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×#2366	C₂	semidirect
3. C₁₃×#2365	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2353	C₂	semidirect
6. C₁₃×#2341	C₂	semidirect
7. C₁₃×#2339	C₂	semidirect
8. C₁₃×#2333	C₂	semidirect
9. C₁₃×#2319	C₂	semidirect
10. C₄×C₁₃×#124	C₂	semidirect
11. C₁₃×#2283	C₂	semidirect
12. C₁₃×#2275	C₂	semidirect
13. C₄×C₁₃×#117	C₂	semidirect
15. C₁₃×#532	C₄	semidirect
61. C₂×C₁₃×#41	C₂×C₄	semidirect
72. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
74. C₁₃×#124	C₂×C₄	semidirect
75. C₁₃×#121	C₂×C₄	semidirect
76. C₁₃×#121	C₂×C₄	semidirect
80. C₄×D₄×C₁₃	C₂×C₄	semidirect
81. C₄×D₄×C₁₃	C₂×C₄	semidirect
98. C₂×C₄²×C₁₃	C₂×C₄	semidirect
119. #34232	C₁₃	direct (N × H)
163. C₁₃×C₄⋊C₄	#41	semidirect
183. #2366	C₂×C₁₃	semidirect
184. #2365	C₂×C₁₃	semidirect
185. #2363	C₂×C₁₃	semidirect
186. #2353	C₂×C₁₃	semidirect
187. #2341	C₂×C₁₃	semidirect
188. #2339	C₂×C₁₃	semidirect
189. #2333	C₂×C₁₃	semidirect
190. #2319	C₂×C₁₃	semidirect
191. C₄×#124	C₂×C₁₃	semidirect
192. #2283	C₂×C₁₃	semidirect
193. #2275	C₂×C₁₃	semidirect
194. C₄×#117	C₂×C₁₃	semidirect
245. #532	C₄×C₁₃	semidirect
317. C₂×#41	C₂×C₄×C₁₃	semidirect
328. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
330. #124	C₂×C₄×C₁₃	semidirect
331. #121	C₂×C₄×C₁₃	semidirect
332. #121	C₂×C₄×C₁₃	semidirect
336. C₄×D₄	C₂×C₄×C₁₃	semidirect
337. C₄×D₄	C₂×C₄×C₁₃	semidirect
354. C₂×C₄²	C₂×C₄×C₁₃	semidirect
425. C₄⋊C₄	C₁₃×#41	semidirect
444. C₁₃	#34232	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×#2366	2
C₁₃×#2365	2
C₁₃×#2363	2
C₁₃×#2353	2
C₁₃×#2341	2
C₁₃×#2339	2
C₁₃×#2333	2
C₁₃×#2319	2
C₄×C₁₃×#124	2
C₁₃×#2283	2
C₁₃×#2275	2
C₄×C₁₃×#117	2
#34232	13

Subgroups — C13×#34232 #15720571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34232 #15720571