Subgroups — C₁₃×#34194 #15720533

Order 3328.

3014 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2354	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2352	C₂	1	4	yes	maximal, complemented
4	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2345	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2342	C₂	1	4	yes	maximal, complemented
7	D₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
8	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2318	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2280	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#380	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₄	1	16	yes	complemented
18	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	4	yes	—
33	C₁₃×#389	C₂²	1	4	yes	complemented
34	C₁₃×#388	C₂²	1	8	yes	complemented
35	C₁₃×#388	C₂²	1	8	yes	complemented
36	C₁₃×#387	C₂²	1	8	yes	complemented
37	C₁₃×#386	C₂²	1	8	yes	—
38	C₁₃×#385	C₂²	1	8	yes	complemented
39	C₁₃×#384	C₂²	1	2	yes	complemented
40	C₁₃×#383	C₂²	1	2	yes	complemented
41	C₁₃×#382	C₂²	1	2	yes	complemented
42	C₁₃×#382	C₂²	1	2	yes	complemented
43	C₁₃×#381	C₂²	1	2	yes	—
44	C₁₃×#381	C₂²	1	4	yes	complemented
45	C₁₃×#380	C₂²	1	1	yes	characteristic
46	C₁₃×#380	C₂²	1	2	yes	—
47	C₁₃×#380	C₂²	1	4	yes	—
48	C₁₃×#380	C₂²	1	1	yes	characteristic
49	C₁₃×#380	C₂²	1	2	yes	—
50	C₁₃×#380	C₂²	1	4	yes	complemented
51	C₁₃×#380	C₂²	1	4	yes	complemented
52	C₁₃×#380	C₂²	1	4	yes	complemented
53	C₁₃×#379	C₂²	1	4	yes	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
62	C₁₃×#376	C₂²	1	2	yes	complemented
63	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
64	C₂⁵×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	—	2	8	no	—
66	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	4	8	no	—
71	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₄×D₄×C₁₃	—	2	16	no	—
82	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
83	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
84	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
85	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
86	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
87	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
88	C₁₃×#117	—	4	4	no	—
89	C₁₃×#117	—	4	8	no	—
90	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
102	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
114	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#95	C₂³	1	8	yes	—
122	C₁₃×#95	C₂³	1	4	yes	—
123	C₁₃×#95	C₂³	1	2	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	4	yes	—
126	C₁₃×#95	C₂³	1	8	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	2	yes	—
130	#34194	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	8	no	—
132	C₂⁴×C₁₃	—	2	4	no	—
133	C₂⁴×C₁₃	—	2	4	no	—
134	C₂⁴×C₁₃	—	4	4	no	—
135	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
137	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	32	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
143	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
144	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
145	C₂×D₄×C₁₃	#41	1	8	yes	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	16	no	—
153	C₂²×C₄×C₁₃	—	4	32	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	4	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	—	4	8	no	—
158	C₂²×C₄×C₁₃	—	4	8	no	—
159	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
163	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
164	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
165	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	4	8	no	—
183	C₁₃×C₄⋊C₄	—	4	4	no	—
184	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
185	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
186	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
187	C₁₃×C₂²⋊C₄	—	2	16	no	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	4	8	no	—
192	C₁₃×C₂²⋊C₄	—	4	8	no	—
193	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
194	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
195	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
196	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
197	C₄²×C₁₃	—	2	8	no	—
198	C₄²×C₁₃	—	4	4	no	—
199	C₄²×C₁₃	—	4	8	no	—
200	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
201	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
202	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
203	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
205	#2354	C₂×C₁₃	1	2	yes	complemented
206	#2352	C₂×C₁₃	1	4	yes	complemented
207	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
208	#2345	C₂×C₁₃	1	2	yes	complemented
209	#2342	C₂×C₁₃	1	4	yes	complemented
210	D₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
211	#2319	C₂×C₁₃	1	2	yes	complemented
212	#2318	C₂×C₁₃	1	4	yes	complemented
213	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2280	C₂×C₁₃	1	2	yes	complemented
216	C₂×#380	C₂×C₁₃	1	2	yes	complemented
217	#2275	C₂×C₁₃	1	2	yes	complemented
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	16	no	—
224	C₂³×C₁₃	—	2	16	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	4	8	no	—
230	C₂³×C₁₃	—	4	16	no	—
231	C₂³×C₁₃	—	4	16	no	—
232	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
233	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
234	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
235	C₂³×C₁₃	C₂×#41	1	8	yes	—
236	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
238	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
239	D₄×C₁₃	—	2	16	no	—
240	D₄×C₁₃	—	2	8	no	—
241	D₄×C₁₃	#117	1	16	yes	complemented
242	C₂×C₄×C₁₃	—	2	8	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	8	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	16	no	—
254	C₂×C₄×C₁₃	—	2	16	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	8	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	8	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	4	8	no	—
265	C₂×C₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	—	4	8	no	—
267	C₂×C₄×C₁₃	—	8	16	no	—
268	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
274	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
277	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
278	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
280	C₂×C₄×D₄	C₄×C₁₃	1	16	yes	complemented
281	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
282	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₃	1	2	yes	—
289	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
290	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
292	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
293	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
294	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
295	#390	C₂²×C₁₃	1	4	yes	—
296	#389	C₂²×C₁₃	1	4	yes	complemented
297	#388	C₂²×C₁₃	1	8	yes	complemented
298	#388	C₂²×C₁₃	1	8	yes	complemented
299	#387	C₂²×C₁₃	1	8	yes	complemented
300	#386	C₂²×C₁₃	1	8	yes	—
301	#385	C₂²×C₁₃	1	8	yes	complemented
302	#384	C₂²×C₁₃	1	2	yes	complemented
303	#383	C₂²×C₁₃	1	2	yes	complemented
304	#382	C₂²×C₁₃	1	2	yes	complemented
305	#382	C₂²×C₁₃	1	2	yes	complemented
306	#381	C₂²×C₁₃	1	2	yes	—
307	#381	C₂²×C₁₃	1	4	yes	complemented
308	#380	C₂²×C₁₃	1	2	yes	—
309	#380	C₂²×C₁₃	1	4	yes	—
310	#380	C₂²×C₁₃	1	1	yes	characteristic
311	#380	C₂²×C₁₃	1	2	yes	—
312	#380	C₂²×C₁₃	1	1	yes	characteristic
313	#380	C₂²×C₁₃	1	4	yes	complemented
314	#380	C₂²×C₁₃	1	4	yes	complemented
315	#380	C₂²×C₁₃	1	4	yes	complemented
316	#379	C₂²×C₁₃	1	4	yes	—
317	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
318	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
319	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
320	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
321	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
323	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
324	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
325	#376	C₂²×C₁₃	1	2	yes	complemented
326	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	2	8	no	—
332	C₂²×C₁₃	—	2	4	no	—
333	C₂²×C₁₃	—	2	4	no	—
334	C₂²×C₁₃	—	2	8	no	—
335	C₂²×C₁₃	—	2	4	no	—
336	C₂²×C₁₃	—	2	4	no	—
337	C₂²×C₁₃	—	2	4	no	—
338	C₂²×C₁₃	—	4	32	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	4	no	—
341	C₂²×C₁₃	C₂×#117	1	8	yes	—
342	C₂²×C₁₃	#520	1	4	yes	—
343	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
344	C₂²×C₁₃	C₂²×#41	1	2	yes	—
345	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
346	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	4	no	—
351	C₄×C₁₃	—	2	4	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	4	8	no	—
355	C₄×C₁₃	—	4	4	no	—
356	C₄×C₁₃	—	4	4	no	—
357	C₄×C₁₃	C₂×#117	1	4	yes	—
358	C₄×C₁₃	#518	1	4	yes	—
359	C₂⁵	C₂³×C₁₃	1	2	yes	—
360	C₂²×D₄	—	2	8	no	—
361	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
362	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
363	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂³×C₄	—	4	8	no	—
366	C₂³×C₄	C₂×C₄×C₁₃	1	16	yes	complemented
367	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
370	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
371	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
375	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
376	C₄×D₄	—	2	16	no	—
377	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
378	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
379	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
380	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
381	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
382	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
383	#117	—	4	4	no	—
384	#117	—	4	8	no	—
385	C₂×C₄⋊C₄	—	4	8	no	—
386	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	—	4	8	no	—
397	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
398	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	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	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
409	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
410	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
411	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	#95	C₂³×C₁₃	1	2	yes	—
417	#95	C₂³×C₁₃	1	4	yes	—
418	#95	C₂³×C₁₃	1	8	yes	—
419	#95	C₂³×C₁₃	1	2	yes	—
420	#95	C₂³×C₁₃	1	4	yes	—
421	#95	C₂³×C₁₃	1	8	yes	—
422	#95	C₂³×C₁₃	1	4	yes	—
423	#95	C₂³×C₁₃	1	4	yes	—
424	#95	C₂³×C₁₃	1	4	yes	—
425	C₂×C₁₃	—	2	4	no	—
426	C₂×C₁₃	—	2	8	no	—
427	C₂×C₁₃	—	4	4	no	—
428	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
429	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
430	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
431	C₂×C₁₃	#3519	1	2	yes	—
432	C₂×C₁₃	#3520	1	2	yes	—
433	C₂⁴	—	2	8	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	4	no	—
436	C₂⁴	—	4	4	no	—
437	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
438	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
439	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
440	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	32	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
445	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
446	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
447	C₂×D₄	C₁₃×#41	1	8	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	16	no	—
455	C₂²×C₄	—	4	32	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	4	8	no	—
460	C₂²×C₄	—	4	8	no	—
461	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
463	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
465	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
466	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
467	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
468	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	4	8	no	—
485	C₄⋊C₄	—	4	4	no	—
486	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
487	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
488	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
489	C₂²⋊C₄	—	2	16	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	4	8	no	—
494	C₂²⋊C₄	—	4	8	no	—
495	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
496	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
497	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
498	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
499	C₄²	—	2	8	no	—
500	C₄²	—	4	4	no	—
501	C₄²	—	4	8	no	—
502	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
503	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
504	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
505	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
506	C₁₃	#34194	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	16	no	—
513	C₂³	—	2	16	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	16	no	—
520	C₂³	—	4	16	no	—
521	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
522	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
523	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
524	C₂³	C₂×C₁₃×#41	1	8	yes	—
525	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
526	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
527	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
528	D₄	—	2	16	no	—
529	D₄	—	2	8	no	—
530	D₄	C₁₃×#117	1	16	yes	complemented
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	16	no	—
543	C₂×C₄	—	2	16	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	8	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	4	8	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	8	16	no	—
557	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
558	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
559	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
560	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
561	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
562	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
563	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
564	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
566	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	32	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	C₂×C₁₃×#117	1	8	yes	—
582	C₂²	C₁₃×#520	1	4	yes	—
583	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
584	C₂²	C₂²×C₁₃×#41	1	2	yes	—
585	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
587	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	4	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	8	no	—
595	C₄	—	4	4	no	—
596	C₄	—	4	4	no	—
597	C₄	C₂×C₁₃×#117	1	4	yes	—
598	C₄	C₁₃×#518	1	4	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	2	8	no	—
601	C₂	—	4	4	no	—
602	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
603	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
604	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
605	C₂	C₁₃×#3519	1	2	yes	—
606	C₂	C₁₃×#3520	1	2	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×#2354	C₂	semidirect
3. C₁₃×#2352	C₂	semidirect
4. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2345	C₂	semidirect
6. C₁₃×#2342	C₂	semidirect
8. C₁₃×#2319	C₂	semidirect
9. C₁₃×#2318	C₂	semidirect
10. C₁₃×#2285	C₂	semidirect
11. C₁₃×#2283	C₂	semidirect
12. C₁₃×#2280	C₂	semidirect
13. C₂×C₁₃×#380	C₂	semidirect
14. C₁₃×#2275	C₂	semidirect
17. C₂×C₄×D₄×C₁₃	C₄	semidirect
26. C₂×C₁₃×#117	C₂²	semidirect
28. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#388	C₂²	semidirect
35. C₁₃×#388	C₂²	semidirect
36. C₁₃×#387	C₂²	semidirect
38. C₁₃×#385	C₂²	semidirect
39. C₁₃×#384	C₂²	semidirect
40. C₁₃×#383	C₂²	semidirect
41. C₁₃×#382	C₂²	semidirect
42. C₁₃×#382	C₂²	semidirect
44. C₁₃×#381	C₂²	semidirect
50. C₁₃×#380	C₂²	semidirect
51. C₁₃×#380	C₂²	semidirect
52. C₁₃×#380	C₂²	semidirect
54. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
55. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
56. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
57. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
60. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
61. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
62. C₁₃×#376	C₂²	semidirect
63. C₂×C₁₃×#95	C₂²	semidirect
71. C₂³×C₄×C₁₃	C₂×C₄	semidirect
84. C₄×D₄×C₁₃	C₂×C₄	semidirect
85. C₄×D₄×C₁₃	C₂×C₄	semidirect
86. C₄×D₄×C₁₃	C₂×C₄	semidirect
87. C₄×D₄×C₁₃	C₂×C₄	semidirect
91. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
102. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
113. C₂×C₄²×C₁₃	C₂×C₄	semidirect
130. #34194	C₁₃	direct (N × H)
205. #2354	C₂×C₁₃	semidirect
206. #2352	C₂×C₁₃	semidirect
207. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
208. #2345	C₂×C₁₃	semidirect
209. #2342	C₂×C₁₃	semidirect
211. #2319	C₂×C₁₃	semidirect
212. #2318	C₂×C₁₃	semidirect
213. #2285	C₂×C₁₃	semidirect
214. #2283	C₂×C₁₃	semidirect
215. #2280	C₂×C₁₃	semidirect
216. C₂×#380	C₂×C₁₃	semidirect
217. #2275	C₂×C₁₃	semidirect
241. D₄×C₁₃	#117	semidirect
280. C₂×C₄×D₄	C₄×C₁₃	semidirect
289. C₂×#117	C₂²×C₁₃	semidirect
291. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
296. #389	C₂²×C₁₃	semidirect
297. #388	C₂²×C₁₃	semidirect
298. #388	C₂²×C₁₃	semidirect
299. #387	C₂²×C₁₃	semidirect
301. #385	C₂²×C₁₃	semidirect
302. #384	C₂²×C₁₃	semidirect
303. #383	C₂²×C₁₃	semidirect
304. #382	C₂²×C₁₃	semidirect
305. #382	C₂²×C₁₃	semidirect
307. #381	C₂²×C₁₃	semidirect
313. #380	C₂²×C₁₃	semidirect
314. #380	C₂²×C₁₃	semidirect
315. #380	C₂²×C₁₃	semidirect
317. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
318. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
319. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
320. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
323. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
324. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
325. #376	C₂²×C₁₃	semidirect
326. C₂×#95	C₂²×C₁₃	semidirect
366. C₂³×C₄	C₂×C₄×C₁₃	semidirect
379. C₄×D₄	C₂×C₄×C₁₃	semidirect
380. C₄×D₄	C₂×C₄×C₁₃	semidirect
381. C₄×D₄	C₂×C₄×C₁₃	semidirect
382. C₄×D₄	C₂×C₄×C₁₃	semidirect
386. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
397. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
408. C₂×C₄²	C₂×C₄×C₁₃	semidirect
506. C₁₃	#34194	direct (N × H)
530. D₄	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2354	2
C₁₃×#2352	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2345	2
C₁₃×#2342	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2319	2
C₁₃×#2318	2
C₁₃×#2285	2
C₁₃×#2283	2
C₁₃×#2280	2
C₂×C₁₃×#380	2
C₁₃×#2275	2
#34194	13

Subgroups — C13×#34194 #15720533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34194 #15720533