Subgroups — C₁₃×#34256 #15720595

Order 3328.

5898 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2339	C₂	1	8	yes	maximal, complemented
5	D₄×C₁₃×C₂²⋊C₄	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2311	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2308	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	8	no	—
11	C₂×C₁₃×H(5,𝔽₂)	—	2	8	no	—
12	C₂×C₁₃×H(5,𝔽₂)	C₄	1	16	yes	complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂²×C₁₃×#41	C₂²	1	4	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
16	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
19	C₁₃×#518	—	2	8	no	—
20	C₂×C₄×D₄×C₁₃	—	2	8	no	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
22	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#391	C₂²	1	4	yes	complemented
30	C₁₃×#391	C₂²	1	4	yes	complemented
31	C₁₃×#390	C₂²	1	4	yes	complemented
32	C₁₃×#390	C₂²	1	4	yes	complemented
33	C₁₃×#386	C₂²	1	4	yes	complemented
34	C₁₃×#386	C₂²	1	8	yes	complemented
35	C₁₃×#386	C₂²	1	16	yes	complemented
36	C₁₃×#386	C₂²	1	4	yes	complemented
37	C₁₃×#386	C₂²	1	16	yes	complemented
38	C₁₃×#381	C₂²	1	8	yes	complemented
39	C₁₃×#380	C₂²	1	8	yes	complemented
40	C₁₃×#379	C₂²	1	8	yes	complemented
41	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
42	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₃	C₂³	1	4	yes	—
44	C₂⁵×C₁₃	C₂³	1	2	yes	—
45	C₁₃×H(5,𝔽₂)	—	2	128	no	—
46	C₂×C₁₃×#41	—	2	16	no	—
47	C₂×C₁₃×#41	—	2	16	no	—
48	C₂×C₁₃×#41	—	2	8	no	—
49	C₂×C₁₃×#41	—	2	8	no	—
50	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
51	C₂×C₁₃×#41	C₂×C₄	1	32	yes	complemented
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃	—	2	16	no	—
54	C₂²×D₄×C₁₃	—	2	16	no	—
55	C₂²×D₄×C₁₃	—	2	16	no	—
56	C₂²×D₄×C₁₃	—	2	16	no	—
57	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
58	C₂²×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
59	C₂²×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
60	C₂²×D₄×C₁₃	D₄	1	8	yes	—
61	C₂²×D₄×C₁₃	D₄	1	8	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	—	2	8	no	—
67	C₂³×C₄×C₁₃	—	4	8	no	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₁₃	—	2	32	no	—
77	C₄×D₄×C₁₃	—	2	32	no	—
78	C₁₃×#117	—	2	8	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	4	16	no	—
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	8	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
91	C₂×C₄²×C₁₃	—	2	4	no	—
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
94	C₁₃×#95	C₂³	1	8	yes	—
95	C₁₃×#95	C₂³	1	8	yes	—
96	C₁₃×#95	C₂³	1	16	yes	—
97	#34256	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	8	no	—
100	C₂⁴×C₁₃	—	4	4	no	—
101	C₂⁴×C₁₃	—	4	4	no	—
102	C₂⁴×C₁₃	—	4	8	no	—
103	C₂⁴×C₁₃	—	4	8	no	—
104	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
105	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	complemented
106	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
107	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
111	C₁₃×#41	—	2	128	no	—
112	C₁₃×#41	—	2	64	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	complemented
116	C₂×D₄×C₁₃	—	2	128	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	16	no	—
120	C₂×D₄×C₁₃	—	2	16	no	—
121	C₂×D₄×C₁₃	—	2	128	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	C₂²⋊C₄	1	64	yes	complemented
125	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
126	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
127	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
128	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	complemented
129	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
130	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	16	no	—
140	C₂²×C₄×C₁₃	—	2	16	no	—
141	C₂²×C₄×C₁₃	—	2	16	no	—
142	C₂²×C₄×C₁₃	—	4	8	no	—
143	C₂²×C₄×C₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₃	—	4	2	no	—
145	C₂²×C₄×C₁₃	—	4	8	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	—	4	32	no	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	complemented
150	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	complemented
151	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	16	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	2	16	no	—
165	C₁₃×C₂²⋊C₄	—	4	16	no	—
166	C₁₃×C₂²⋊C₄	—	4	8	no	—
167	C₄²×C₁₃	—	2	8	no	—
168	C₄²×C₁₃	—	2	8	no	—
169	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic
170	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2339	C₂×C₁₃	1	8	yes	complemented
173	D₄×C₂²⋊C₄	C₂×C₁₃	1	8	yes	complemented
174	#2311	C₂×C₁₃	1	2	yes	complemented
175	#2308	C₂×C₁₃	1	4	yes	complemented
176	#2297	C₂×C₁₃	1	2	yes	complemented
177	C₂×#386	C₂×C₁₃	1	4	yes	complemented
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	8	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	8	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	2	8	no	—
185	C₂³×C₁₃	—	2	8	no	—
186	C₂³×C₁₃	—	2	32	no	—
187	C₂³×C₁₃	—	4	8	no	—
188	C₂³×C₁₃	—	4	16	no	—
189	C₂³×C₁₃	—	4	8	no	—
190	C₂³×C₁₃	—	4	16	no	—
191	C₂³×C₁₃	—	4	32	no	—
192	C₂³×C₁₃	—	8	8	no	—
193	C₂³×C₁₃	—	8	8	no	—
194	C₂³×C₁₃	—	8	16	no	—
195	C₂³×C₁₃	C₂×C₂²⋊C₄	1	32	yes	complemented
196	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
197	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
198	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
199	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
200	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
201	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
202	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	16	no	—
205	D₄×C₁₃	—	2	32	no	—
206	D₄×C₁₃	—	2	64	no	—
207	D₄×C₁₃	—	2	16	no	—
208	D₄×C₁₃	C₂×C₂²⋊C₄	1	64	yes	complemented
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	32	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	32	no	—
216	C₂×C₄×C₁₃	—	2	2	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	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	4	32	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	8	no	—
226	C₂×C₄×C₁₃	—	8	16	no	—
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	16	yes	complemented
228	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
229	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
233	C₂×H(5,𝔽₂)	—	2	8	no	—
234	C₂×H(5,𝔽₂)	—	2	8	no	—
235	C₂×H(5,𝔽₂)	C₄×C₁₃	1	16	yes	complemented
236	C₂²×#41	C₂²×C₁₃	1	2	yes	—
237	C₂²×#41	C₂²×C₁₃	1	4	yes	—
238	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
239	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
240	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
242	#518	—	2	8	no	—
243	C₂×C₄×D₄	—	2	8	no	—
244	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
245	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
246	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
249	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
250	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
251	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
252	#391	C₂²×C₁₃	1	4	yes	complemented
253	#391	C₂²×C₁₃	1	4	yes	complemented
254	#390	C₂²×C₁₃	1	4	yes	complemented
255	#390	C₂²×C₁₃	1	4	yes	complemented
256	#386	C₂²×C₁₃	1	4	yes	complemented
257	#386	C₂²×C₁₃	1	8	yes	complemented
258	#386	C₂²×C₁₃	1	16	yes	complemented
259	#386	C₂²×C₁₃	1	16	yes	complemented
260	#386	C₂²×C₁₃	1	4	yes	complemented
261	#381	C₂²×C₁₃	1	8	yes	complemented
262	#380	C₂²×C₁₃	1	8	yes	complemented
263	#379	C₂²×C₁₃	1	8	yes	complemented
264	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
265	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
266	C₂²×C₁₃	—	2	4	no	—
267	C₂²×C₁₃	—	2	16	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	8	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	2	8	no	—
272	C₂²×C₁₃	—	2	16	no	—
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	2	8	no	—
275	C₂²×C₁₃	—	2	16	no	—
276	C₂²×C₁₃	—	4	32	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	—	4	8	no	—
280	C₂²×C₁₃	—	8	32	no	—
281	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	16	yes	—
282	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
283	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
284	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
285	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
286	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₁₃	#585	1	2	yes	—
288	C₄×C₁₃	—	2	8	no	—
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	4	4	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	8	no	—
293	C₄×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
294	C₂⁵	C₂³×C₁₃	1	4	yes	—
295	C₂⁵	C₂³×C₁₃	1	2	yes	—
296	H(5,𝔽₂)	—	2	128	no	—
297	C₂×#41	—	2	16	no	—
298	C₂×#41	—	2	16	no	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	2	8	no	—
301	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
302	C₂×#41	C₂×C₄×C₁₃	1	32	yes	complemented
303	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	—	2	16	no	—
305	C₂²×D₄	—	2	16	no	—
306	C₂²×D₄	—	2	16	no	—
307	C₂²×D₄	—	2	16	no	—
308	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
309	C₂²×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
310	C₂²×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
311	C₂²×D₄	D₄×C₁₃	1	8	yes	—
312	C₂²×D₄	D₄×C₁₃	1	8	yes	—
313	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
314	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
315	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
316	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
317	C₂³×C₄	—	2	8	no	—
318	C₂³×C₄	—	4	8	no	—
319	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
321	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
322	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₄×D₄	—	2	32	no	—
328	C₄×D₄	—	2	32	no	—
329	#117	—	2	8	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	16	no	—
335	C₂×C₂²⋊C₄	—	4	16	no	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
344	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
345	#95	C₂³×C₁₃	1	8	yes	—
346	#95	C₂³×C₁₃	1	16	yes	—
347	#95	C₂³×C₁₃	1	8	yes	—
348	C₂×C₁₃	—	2	4	no	—
349	C₂×C₁₃	—	2	16	no	—
350	C₂×C₁₃	—	4	8	no	—
351	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
353	C₂×C₁₃	#3484	1	1	yes	characteristic
354	C₂×C₁₃	#3485	1	1	yes	characteristic
355	C₂×C₁₃	#3496	1	2	yes	—
356	C₂⁴	—	2	8	no	—
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	—	4	4	no	—
360	C₂⁴	—	4	8	no	—
361	C₂⁴	—	4	8	no	—
362	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
363	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	complemented
364	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
365	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
366	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
367	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
368	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
369	#41	—	2	128	no	—
370	#41	—	2	64	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	complemented
374	C₂×D₄	—	2	128	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	16	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	2	128	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	C₁₃×C₂²⋊C₄	1	64	yes	complemented
383	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
384	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
385	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	complemented
386	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	complemented
387	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
388	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	16	no	—
398	C₂²×C₄	—	2	16	no	—
399	C₂²×C₄	—	2	16	no	—
400	C₂²×C₄	—	4	8	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	8	no	—
404	C₂²×C₄	—	4	8	no	—
405	C₂²×C₄	—	4	32	no	—
406	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
408	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
409	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	16	no	—
421	C₂²⋊C₄	—	2	16	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₂²⋊C₄	—	4	16	no	—
424	C₂²⋊C₄	—	4	8	no	—
425	C₄²	—	2	8	no	—
426	C₄²	—	2	8	no	—
427	C₁₃	#34256	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	2	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	32	no	—
437	C₂³	—	4	8	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	16	no	—
441	C₂³	—	4	32	no	—
442	C₂³	—	8	8	no	—
443	C₂³	—	8	8	no	—
444	C₂³	—	8	16	no	—
445	C₂³	C₂×C₁₃×C₂²⋊C₄	1	32	yes	complemented
446	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
447	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
448	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
449	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
450	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
451	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
452	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
453	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
454	Q₈	—	2	16	no	—
455	D₄	—	2	32	no	—
456	D₄	—	2	64	no	—
457	D₄	—	2	16	no	—
458	D₄	C₂×C₁₃×C₂²⋊C₄	1	64	yes	complemented
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	32	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	32	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	4	32	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	8	16	no	—
477	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	16	yes	complemented
478	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
479	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
482	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
483	C₂²	—	2	4	no	—
484	C₂²	—	2	16	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	8	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	16	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	16	no	—
493	C₂²	—	4	32	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	8	no	—
497	C₂²	—	8	32	no	—
498	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	16	yes	—
499	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	4	yes	—
500	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
501	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
502	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
503	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
504	C₂²	C₁₃×#585	1	2	yes	—
505	C₄	—	2	8	no	—
506	C₄	—	2	4	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	8	no	—
510	C₄	C₂²×C₁₃×C₂²⋊C₄	1	8	yes	—
511	C₂	—	2	4	no	—
512	C₂	—	2	16	no	—
513	C₂	—	4	8	no	—
514	C₂	C₂³×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
515	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
516	C₂	C₁₃×#3484	1	1	yes	characteristic
517	C₂	C₁₃×#3485	1	1	yes	characteristic
518	C₂	C₁₃×#3496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×H(5,𝔽₂)	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. C₂×C₁₃×#518	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2339	C₂	semidirect
5. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
6. C₁₃×#2311	C₂	semidirect
7. C₁₃×#2308	C₂	semidirect
8. C₁₃×#2297	C₂	semidirect
9. C₂×C₁₃×#386	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₄	semidirect
18. C₂⁴×C₄×C₁₃	C₂²	semidirect
21. C₂×C₄×D₄×C₁₃	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
23. C₂×C₁₃×#117	C₂²	semidirect
24. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
25. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
26. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₂²×C₄²×C₁₃	C₂²	semidirect
29. C₁₃×#391	C₂²	semidirect
30. C₁₃×#391	C₂²	semidirect
31. C₁₃×#390	C₂²	semidirect
32. C₁₃×#390	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#386	C₂²	semidirect
35. C₁₃×#386	C₂²	semidirect
36. C₁₃×#386	C₂²	semidirect
37. C₁₃×#386	C₂²	semidirect
38. C₁₃×#381	C₂²	semidirect
39. C₁₃×#380	C₂²	semidirect
40. C₁₃×#379	C₂²	semidirect
41. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₁₃×#95	C₂²	semidirect
50. C₂×C₁₃×#41	C₂×C₄	semidirect
51. C₂×C₁₃×#41	C₂×C₄	semidirect
58. C₂²×D₄×C₁₃	C₂×C₄	semidirect
59. C₂²×D₄×C₁₃	C₂×C₄	semidirect
97. #34256	C₁₃	direct (N × H)
105. C₂⁴×C₁₃	C₂²×C₄	semidirect
115. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
124. C₂×D₄×C₁₃	C₂²⋊C₄	semidirect
127. C₂×D₄×C₁₃	C₂²×C₄	semidirect
128. C₂×D₄×C₁₃	C₂²×C₄	semidirect
149. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
150. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
170. C₂×#518	C₂×C₁₃	semidirect
171. C₂²×C₄×D₄	C₂×C₁₃	semidirect
172. #2339	C₂×C₁₃	semidirect
173. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
174. #2311	C₂×C₁₃	semidirect
175. #2308	C₂×C₁₃	semidirect
176. #2297	C₂×C₁₃	semidirect
177. C₂×#386	C₂×C₁₃	semidirect
195. C₂³×C₁₃	C₂×C₂²⋊C₄	semidirect
208. D₄×C₁₃	C₂×C₂²⋊C₄	semidirect
227. C₂×C₄×C₁₃	C₂×C₂²⋊C₄	semidirect
232. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
235. C₂×H(5,𝔽₂)	C₄×C₁₃	semidirect
241. C₂⁴×C₄	C₂²×C₁₃	semidirect
244. C₂×C₄×D₄	C₂²×C₁₃	semidirect
245. C₂×C₄×D₄	C₂²×C₁₃	semidirect
246. C₂×#117	C₂²×C₁₃	semidirect
247. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
248. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
249. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
250. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
251. C₂²×C₄²	C₂²×C₁₃	semidirect
252. #391	C₂²×C₁₃	semidirect
253. #391	C₂²×C₁₃	semidirect
254. #390	C₂²×C₁₃	semidirect
255. #390	C₂²×C₁₃	semidirect
256. #386	C₂²×C₁₃	semidirect
257. #386	C₂²×C₁₃	semidirect
258. #386	C₂²×C₁₃	semidirect
259. #386	C₂²×C₁₃	semidirect
260. #386	C₂²×C₁₃	semidirect
261. #381	C₂²×C₁₃	semidirect
262. #380	C₂²×C₁₃	semidirect
263. #379	C₂²×C₁₃	semidirect
264. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
265. C₂×#95	C₂²×C₁₃	semidirect
301. C₂×#41	C₂×C₄×C₁₃	semidirect
302. C₂×#41	C₂×C₄×C₁₃	semidirect
309. C₂²×D₄	C₂×C₄×C₁₃	semidirect
310. C₂²×D₄	C₂×C₄×C₁₃	semidirect
363. C₂⁴	C₂²×C₄×C₁₃	semidirect
373. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
382. C₂×D₄	C₁₃×C₂²⋊C₄	semidirect
385. C₂×D₄	C₂²×C₄×C₁₃	semidirect
386. C₂×D₄	C₂²×C₄×C₁₃	semidirect
407. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
408. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
427. C₁₃	#34256	direct (N × H)
445. C₂³	C₂×C₁₃×C₂²⋊C₄	semidirect
458. D₄	C₂×C₁₃×C₂²⋊C₄	semidirect
477. C₂×C₄	C₂×C₁₃×C₂²⋊C₄	semidirect
482. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×H(5,𝔽₂)	2
C₂×C₁₃×#518	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2339	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2311	2
C₁₃×#2308	2
C₁₃×#2297	2
C₂×C₁₃×#386	2
#34256	13

Subgroups — C13×#34256 #15720595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34256 #15720595