Subgroups — C₂×C₁₃×#2420 #15721035

Order 3328.

3438 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2420	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#381	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	—	2	8	no	—
18	C₂×C₁₃×#121	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₁₃	—	2	8	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#397	C₂²	1	16	yes	complemented
35	C₁₃×#394	C₂²	1	16	yes	complemented
36	C₁₃×#390	C₂²	1	8	yes	complemented
37	C₁₃×#389	C₂²	1	8	yes	complemented
38	C₁₃×#386	C₂²	1	16	yes	complemented
39	C₁₃×#382	C₂²	1	8	yes	complemented
40	C₁₃×#381	C₂²	1	16	yes	complemented
41	C₁₃×#380	C₂²	1	8	yes	complemented
42	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	8	no	—
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	4	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	4	4	no	—
56	C₂²×D₄×C₁₃	D₄	1	8	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	—	2	8	no	—
60	C₂³×C₄×C₁₃	—	2	4	no	—
61	C₂³×C₄×C₁₃	—	2	8	no	—
62	C₂³×C₄×C₁₃	—	2	4	no	—
63	C₂³×C₄×C₁₃	—	2	4	no	—
64	C₂³×C₄×C₁₃	—	4	4	no	—
65	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#121	—	2	32	no	—
77	C₄×D₄×C₁₃	—	2	32	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₄²×C₁₃	—	2	4	no	—
101	C₂×C₄²×C₁₃	—	2	4	no	—
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	C₁₃×#95	C₂³	1	8	yes	—
108	C₁₃×#95	C₂³	1	8	yes	—
109	C₁₃×#95	C₂³	1	8	yes	—
110	C₂×#2420	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	2	2	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	2	4	no	—
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	2	4	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	2	no	—
123	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
124	C₂⁴×C₁₃	#41	1	4	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₂×D₄×C₁₃	—	2	16	no	—
129	C₂×D₄×C₁₃	—	2	16	no	—
130	C₂×D₄×C₁₃	—	2	32	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	8	no	—
133	C₂×D₄×C₁₃	—	4	8	no	—
134	C₂×D₄×C₁₃	—	4	32	no	—
135	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	16	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
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	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	8	no	—
161	C₂²×C₄×C₁₃	—	2	16	no	—
162	C₂²×C₄×C₁₃	—	2	8	no	—
163	C₂²×C₄×C₁₃	—	2	8	no	—
164	C₂²×C₄×C₁₃	—	4	8	no	—
165	C₂²×C₄×C₁₃	—	4	32	no	—
166	C₂²×C₄×C₁₃	—	4	16	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₃	#41	1	4	yes	—
169	C₂²×C₄×C₁₃	#41	1	4	yes	—
170	C₂²×C₄×C₁₃	#41	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	4	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	16	no	—
185	C₁₃×C₂²⋊C₄	—	2	16	no	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	4	8	no	—
189	C₁₃×C₂²⋊C₄	—	4	8	no	—
190	C₁₃×C₂²⋊C₄	—	4	8	no	—
191	C₄²×C₁₃	—	2	8	no	—
192	C₄²×C₁₃	—	2	8	no	—
193	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
194	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2420	C₂×C₁₃	1	16	yes	direct product factor
196	C₂×#397	C₂×C₁₃	1	2	yes	complemented
197	C₂×#394	C₂×C₁₃	1	2	yes	complemented
198	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#386	C₂×C₁₃	1	2	yes	complemented
201	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#381	C₂×C₁₃	1	2	yes	complemented
203	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	16	no	—
206	C₂³×C₁₃	—	2	8	no	—
207	C₂³×C₁₃	—	2	16	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	16	no	—
210	C₂³×C₁₃	—	2	8	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	2	2	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	4	4	no	—
224	C₂³×C₁₃	—	4	8	no	—
225	C₂³×C₁₃	—	4	4	no	—
226	C₂³×C₁₃	—	4	8	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	—	4	8	no	—
229	C₂³×C₁₃	—	4	4	no	—
230	C₂³×C₁₃	—	4	8	no	—
231	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
232	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₃	C₂×#41	1	4	yes	—
234	C₂³×C₁₃	C₂×#41	1	2	yes	—
235	C₂³×C₁₃	C₂×#41	1	2	yes	—
236	C₂³×C₁₃	C₂×#41	1	2	yes	—
237	C₂³×C₁₃	C₂×#41	1	2	yes	—
238	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
239	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
240	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
241	D₄×C₁₃	—	2	32	no	—
242	D₄×C₁₃	—	4	32	no	—
243	C₂×C₄×C₁₃	—	2	8	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	4	32	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	—	4	4	no	—
271	C₂×C₄×C₁₃	—	4	8	no	—
272	C₂×C₄×C₁₃	—	4	8	no	—
273	C₂×C₄×C₁₃	—	4	4	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	16	no	—
276	C₂×C₄×C₁₃	#123	1	16	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
279	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
280	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
281	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
282	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
285	C₂×#121	—	2	8	no	—
286	C₂×#121	C₂²×C₁₃	1	8	yes	—
287	C₂×C₄×D₄	—	2	8	no	—
288	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
289	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
293	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
295	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
300	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
302	#397	C₂²×C₁₃	1	16	yes	complemented
303	#394	C₂²×C₁₃	1	16	yes	complemented
304	#390	C₂²×C₁₃	1	8	yes	complemented
305	#389	C₂²×C₁₃	1	8	yes	complemented
306	#386	C₂²×C₁₃	1	16	yes	complemented
307	#382	C₂²×C₁₃	1	8	yes	complemented
308	#381	C₂²×C₁₃	1	16	yes	complemented
309	#380	C₂²×C₁₃	1	8	yes	complemented
310	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
311	C₂×#95	C₂²×C₁₃	1	2	yes	—
312	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#95	C₂²×C₁₃	1	2	yes	—
314	C₂×#95	C₂²×C₁₃	1	2	yes	—
315	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#95	C₂²×C₁₃	1	2	yes	—
317	C₂²×C₁₃	—	2	8	no	—
318	C₂²×C₁₃	—	2	4	no	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	2	4	no	—
321	C₂²×C₁₃	—	2	8	no	—
322	C₂²×C₁₃	—	2	4	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	32	no	—
326	C₂²×C₁₃	—	4	16	no	—
327	C₂²×C₁₃	—	4	2	no	—
328	C₂²×C₁₃	—	4	4	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	C₂×#123	1	4	yes	—
334	C₂²×C₁₃	#529	1	4	yes	—
335	C₂²×C₁₃	#540	1	4	yes	—
336	C₂²×C₁₃	#546	1	4	yes	—
337	C₂²×C₁₃	#546	1	4	yes	—
338	C₂²×C₁₃	#553	1	4	yes	—
339	C₂²×C₁₃	#555	1	4	yes	—
340	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
341	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
344	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₄×C₁₃	—	2	4	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	4	no	—
350	C₄×C₁₃	—	4	2	no	—
351	C₄×C₁₃	—	4	4	no	—
352	C₄×C₁₃	—	4	4	no	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	C₂×#123	1	8	yes	—
356	C₂⁵	C₂³×C₁₃	1	2	yes	—
357	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×D₄	—	2	8	no	—
359	C₂²×D₄	—	2	8	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	4	no	—
362	C₂²×D₄	—	4	4	no	—
363	C₂²×D₄	D₄×C₁₃	1	8	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
365	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
366	C₂³×C₄	—	2	8	no	—
367	C₂³×C₄	—	2	4	no	—
368	C₂³×C₄	—	2	8	no	—
369	C₂³×C₄	—	2	4	no	—
370	C₂³×C₄	—	2	4	no	—
371	C₂³×C₄	—	4	4	no	—
372	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
377	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
379	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
380	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
381	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
383	#121	—	2	32	no	—
384	C₄×D₄	—	2	32	no	—
385	C₂×C₄⋊C₄	—	2	4	no	—
386	C₂×C₄⋊C₄	—	2	4	no	—
387	C₂×C₄⋊C₄	—	2	4	no	—
388	C₂×C₄⋊C₄	—	4	4	no	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
393	C₂×C₂²⋊C₄	—	2	8	no	—
394	C₂×C₂²⋊C₄	—	2	8	no	—
395	C₂×C₂²⋊C₄	—	2	4	no	—
396	C₂×C₂²⋊C₄	—	2	4	no	—
397	C₂×C₂²⋊C₄	—	4	4	no	—
398	C₂×C₂²⋊C₄	—	4	4	no	—
399	C₂×C₂²⋊C₄	—	4	4	no	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
407	C₂×C₄²	—	2	4	no	—
408	C₂×C₄²	—	2	4	no	—
409	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
410	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
411	#95	C₂³×C₁₃	1	4	yes	—
412	#95	C₂³×C₁₃	1	4	yes	—
413	#95	C₂³×C₁₃	1	8	yes	—
414	#95	C₂³×C₁₃	1	8	yes	—
415	#95	C₂³×C₁₃	1	8	yes	—
416	#95	C₂³×C₁₃	1	8	yes	—
417	C₂×C₁₃	—	4	8	no	—
418	C₂×C₁₃	—	4	4	no	—
419	C₂×C₁₃	#2420	1	8	yes	direct product factor
420	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
421	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
422	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
424	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
425	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
426	C₂×C₁₃	C₂×#555	1	1	yes	characteristic
427	C₂⁴	—	2	2	no	—
428	C₂⁴	—	2	2	no	—
429	C₂⁴	—	2	2	no	—
430	C₂⁴	—	2	4	no	—
431	C₂⁴	—	2	2	no	—
432	C₂⁴	—	2	4	no	—
433	C₂⁴	—	2	4	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	2	4	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
440	C₂⁴	C₁₃×#41	1	4	yes	—
441	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
442	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
443	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	2	16	no	—
446	C₂×D₄	—	2	32	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	4	8	no	—
450	C₂×D₄	—	4	32	no	—
451	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	16	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	16	no	—
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	32	no	—
482	C₂²×C₄	—	4	16	no	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
484	C₂²×C₄	C₁₃×#41	1	4	yes	—
485	C₂²×C₄	C₁₃×#41	1	4	yes	—
486	C₂²×C₄	C₁₃×#41	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₄⋊C₄	—	2	8	no	—
497	C₄⋊C₄	—	2	8	no	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	4	8	no	—
500	C₂²⋊C₄	—	2	16	no	—
501	C₂²⋊C₄	—	2	16	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	4	8	no	—
505	C₂²⋊C₄	—	4	8	no	—
506	C₂²⋊C₄	—	4	8	no	—
507	C₄²	—	2	8	no	—
508	C₄²	—	2	8	no	—
509	C₁₃	C₂×#2420	1	1	yes	characteristic, direct product factor, Sylow
510	C₂³	—	2	16	no	—
511	C₂³	—	2	8	no	—
512	C₂³	—	2	16	no	—
513	C₂³	—	2	8	no	—
514	C₂³	—	2	16	no	—
515	C₂³	—	2	8	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	4	4	no	—
529	C₂³	—	4	8	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	8	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	4	8	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	8	no	—
536	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
537	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
538	C₂³	C₂×C₁₃×#41	1	4	yes	—
539	C₂³	C₂×C₁₃×#41	1	2	yes	—
540	C₂³	C₂×C₁₃×#41	1	2	yes	—
541	C₂³	C₂×C₁₃×#41	1	2	yes	—
542	C₂³	C₂×C₁₃×#41	1	2	yes	—
543	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
544	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
545	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
546	D₄	—	2	32	no	—
547	D₄	—	4	32	no	—
548	C₂×C₄	—	2	8	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	4	32	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	—	4	8	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	16	no	—
581	C₂×C₄	C₁₃×#123	1	16	yes	—
582	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
583	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
584	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
585	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	8	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	32	no	—
595	C₂²	—	4	16	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	C₂×C₁₃×#123	1	4	yes	—
603	C₂²	C₁₃×#529	1	4	yes	—
604	C₂²	C₁₃×#540	1	4	yes	—
605	C₂²	C₁₃×#546	1	4	yes	—
606	C₂²	C₁₃×#546	1	4	yes	—
607	C₂²	C₁₃×#553	1	4	yes	—
608	C₂²	C₁₃×#555	1	4	yes	—
609	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
610	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
611	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
612	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
613	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
614	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
616	C₄	—	2	4	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	4	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	C₂×C₁₃×#123	1	8	yes	—
625	C₂	—	4	8	no	—
626	C₂	—	4	4	no	—
627	C₂	C₁₃×#2420	1	8	yes	direct product factor
628	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
629	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
630	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
631	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
632	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
633	C₂	C₂×C₁₃×#553	1	1	yes	characteristic
634	C₂	C₂×C₁₃×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2420	C₂	direct (N × H)
4. C₂×C₁₃×#397	C₂	semidirect
5. C₂×C₁₃×#394	C₂	semidirect
6. C₂×C₁₃×#390	C₂	semidirect
7. C₂×C₁₃×#389	C₂	semidirect
8. C₂×C₁₃×#386	C₂	semidirect
9. C₂×C₁₃×#382	C₂	semidirect
10. C₂×C₁₃×#381	C₂	semidirect
11. C₂×C₁₃×#380	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₁₃×#397	C₂²	semidirect
35. C₁₃×#394	C₂²	semidirect
36. C₁₃×#390	C₂²	semidirect
37. C₁₃×#389	C₂²	semidirect
38. C₁₃×#386	C₂²	semidirect
39. C₁₃×#382	C₂²	semidirect
40. C₁₃×#381	C₂²	semidirect
41. C₁₃×#380	C₂²	semidirect
42. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
110. C₂×#2420	C₁₃	direct (N × H)
194. C₂²×C₄×D₄	C₂×C₁₃	semidirect
195. #2420	C₂×C₁₃	direct (N × H)
196. C₂×#397	C₂×C₁₃	semidirect
197. C₂×#394	C₂×C₁₃	semidirect
198. C₂×#390	C₂×C₁₃	semidirect
199. C₂×#389	C₂×C₁₃	semidirect
200. C₂×#386	C₂×C₁₃	semidirect
201. C₂×#382	C₂×C₁₃	semidirect
202. C₂×#381	C₂×C₁₃	semidirect
203. C₂×#380	C₂×C₁₃	semidirect
204. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
288. C₂×C₄×D₄	C₂²×C₁₃	semidirect
302. #397	C₂²×C₁₃	semidirect
303. #394	C₂²×C₁₃	semidirect
304. #390	C₂²×C₁₃	semidirect
305. #389	C₂²×C₁₃	semidirect
306. #386	C₂²×C₁₃	semidirect
307. #382	C₂²×C₁₃	semidirect
308. #381	C₂²×C₁₃	semidirect
309. #380	C₂²×C₁₃	semidirect
310. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
419. C₂×C₁₃	#2420	direct (N × H)
509. C₁₃	C₂×#2420	direct (N × H)
627. C₂	C₁₃×#2420	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2420	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#390	2
C₂×C₁₃×#389	2
C₂×C₁₃×#386	2
C₂×C₁₃×#382	2
C₂×C₁₃×#381	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2420	13

Subgroups — C2×C13×#2420 #15721035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2420 #15721035