Subgroups — C₂×C₁₃×#2544 #15721225

Order 3328.

4174 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2544	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×#127	—	2	8	no	—
17	C₂×C₁₃×#127	C₂²	1	8	yes	—
18	C₂×C₁₃×#124	—	2	8	no	—
19	C₂×C₁₃×#124	—	2	8	no	—
20	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
22	C₂×C₄×D₄×C₁₃	—	2	8	no	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	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	4	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#394	C₂²	1	32	yes	complemented
35	C₁₃×#391	C₂²	1	8	yes	complemented
36	C₁₃×#390	C₂²	1	8	yes	complemented
37	C₁₃×#386	C₂²	1	32	yes	complemented
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	4	yes	—
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	4	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
47	C₂²×D₄×C₁₃	—	2	16	no	—
48	C₂²×D₄×C₁₃	—	2	4	no	—
49	C₂²×D₄×C₁₃	—	2	4	no	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	—	2	16	no	—
53	C₂²×D₄×C₁₃	—	2	4	no	—
54	C₂²×D₄×C₁₃	—	4	8	no	—
55	C₂²×D₄×C₁₃	D₄	1	8	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	—	2	8	no	—
60	C₂³×C₄×C₁₃	—	4	8	no	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	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	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#127	—	2	32	no	—
70	C₁₃×#124	—	2	32	no	—
71	C₁₃×#124	—	2	32	no	—
72	C₄×D₄×C₁₃	—	2	32	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	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	16	yes	—
87	C₂×C₄²×C₁₃	—	2	4	no	—
88	C₂×C₄²×C₁₃	—	2	4	no	—
89	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
90	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₁₃×#95	C₂³	1	8	yes	—
94	C₁₃×#95	C₂³	1	16	yes	—
95	C₂×#2544	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	2	4	no	—
97	C₂⁴×C₁₃	—	2	4	no	—
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	8	no	—
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	—	2	4	no	—
102	C₂⁴×C₁₃	—	2	4	no	—
103	C₂⁴×C₁₃	—	2	8	no	—
104	C₂⁴×C₁₃	—	2	8	no	—
105	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
106	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
107	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×Q₈×C₁₃	—	2	8	no	—
110	C₂×Q₈×C₁₃	—	2	8	no	—
111	C₂×Q₈×C₁₃	—	2	8	no	—
112	C₂×Q₈×C₁₃	—	4	16	no	—
113	C₂×D₄×C₁₃	—	2	32	no	—
114	C₂×D₄×C₁₃	—	2	32	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	32	no	—
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	4	16	no	—
122	C₂×D₄×C₁₃	—	4	64	no	—
123	C₂×D₄×C₁₃	—	4	16	no	—
124	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	16	no	—
138	C₂²×C₄×C₁₃	—	4	16	no	—
139	C₂²×C₄×C₁₃	—	4	32	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	#41	1	8	yes	—
145	C₂²×C₄×C₁₃	#41	1	4	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	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	16	no	—
155	C₁₃×C₂²⋊C₄	—	2	32	no	—
156	C₁₃×C₂²⋊C₄	—	2	16	no	—
157	C₁₃×C₂²⋊C₄	—	2	16	no	—
158	C₁₃×C₂²⋊C₄	—	2	16	no	—
159	C₁₃×C₂²⋊C₄	—	4	16	no	—
160	C₄²×C₁₃	—	2	8	no	—
161	C₄²×C₁₃	—	2	8	no	—
162	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
163	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic
164	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2544	C₂×C₁₃	1	16	yes	direct product factor
168	C₂×#394	C₂×C₁₃	1	4	yes	complemented
169	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂×#386	C₂×C₁₃	1	4	yes	complemented
172	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	16	no	—
174	C₂³×C₁₃	—	2	32	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	8	no	—
178	C₂³×C₁₃	—	2	8	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	2	8	no	—
183	C₂³×C₁₃	—	2	8	no	—
184	C₂³×C₁₃	—	4	8	no	—
185	C₂³×C₁₃	—	4	8	no	—
186	C₂³×C₁₃	—	4	16	no	—
187	C₂³×C₁₃	—	4	8	no	—
188	C₂³×C₁₃	—	4	8	no	—
189	C₂³×C₁₃	—	4	8	no	—
190	C₂³×C₁₃	—	4	16	no	—
191	C₂³×C₁₃	—	4	16	no	—
192	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
193	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
194	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
195	C₂³×C₁₃	C₂×#41	1	2	yes	—
196	C₂³×C₁₃	C₂×#41	1	4	yes	—
197	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
198	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
199	Q₈×C₁₃	—	4	16	no	—
200	D₄×C₁₃	—	2	32	no	—
201	D₄×C₁₃	—	4	64	no	—
202	D₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	16	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	4	32	no	—
219	C₂×C₄×C₁₃	—	4	8	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	#121	1	16	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
228	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
229	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
232	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
234	C₂×#127	—	2	8	no	—
235	C₂×#127	C₂²×C₁₃	1	8	yes	—
236	C₂×#124	—	2	8	no	—
237	C₂×#124	—	2	8	no	—
238	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
239	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
240	C₂×C₄×D₄	—	2	8	no	—
241	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
242	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
247	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
249	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
252	#394	C₂²×C₁₃	1	32	yes	complemented
253	#391	C₂²×C₁₃	1	8	yes	complemented
254	#390	C₂²×C₁₃	1	8	yes	complemented
255	#386	C₂²×C₁₃	1	32	yes	complemented
256	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
257	C₂×#95	C₂²×C₁₃	1	4	yes	—
258	C₂×#95	C₂²×C₁₃	1	2	yes	—
259	C₂²×C₁₃	—	2	8	no	—
260	C₂²×C₁₃	—	2	16	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	4	8	no	—
264	C₂²×C₁₃	—	4	32	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	4	8	no	—
269	C₂²×C₁₃	—	4	8	no	—
270	C₂²×C₁₃	—	8	16	no	—
271	C₂²×C₁₃	C₂×#121	1	4	yes	—
272	C₂²×C₁₃	#532	1	4	yes	—
273	C₂²×C₁₃	#535	1	4	yes	—
274	C₂²×C₁₃	#546	1	8	yes	—
275	C₂²×C₁₃	#559	1	8	yes	—
276	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
277	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₁₃	C₂²×#41	1	2	yes	—
280	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
281	C₄×C₁₃	—	2	4	no	—
282	C₄×C₁₃	—	2	4	no	—
283	C₄×C₁₃	—	2	8	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	—	4	4	no	—
286	C₄×C₁₃	—	4	4	no	—
287	C₄×C₁₃	C₂×#121	1	8	yes	—
288	C₂⁵	C₂³×C₁₃	1	2	yes	—
289	C₂⁵	C₂³×C₁₃	1	2	yes	—
290	C₂²×Q₈	—	2	4	no	—
291	C₂²×Q₈	—	2	4	no	—
292	C₂²×Q₈	—	2	4	no	—
293	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
294	C₂²×D₄	—	2	16	no	—
295	C₂²×D₄	—	2	4	no	—
296	C₂²×D₄	—	2	4	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	—	2	16	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	4	8	no	—
302	C₂²×D₄	D₄×C₁₃	1	8	yes	—
303	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
304	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
305	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
306	C₂³×C₄	—	2	8	no	—
307	C₂³×C₄	—	4	8	no	—
308	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
309	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
310	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
316	#127	—	2	32	no	—
317	#124	—	2	32	no	—
318	#124	—	2	32	no	—
319	C₄×D₄	—	2	32	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	8	no	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
324	C₂×C₂²⋊C₄	—	2	16	no	—
325	C₂×C₂²⋊C₄	—	2	8	no	—
326	C₂×C₂²⋊C₄	—	2	8	no	—
327	C₂×C₂²⋊C₄	—	2	8	no	—
328	C₂×C₂²⋊C₄	—	4	8	no	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	2	4	no	—
336	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
337	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
338	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
340	#95	C₂³×C₁₃	1	8	yes	—
341	#95	C₂³×C₁₃	1	16	yes	—
342	C₂×C₁₃	—	4	8	no	—
343	C₂×C₁₃	—	8	4	no	—
344	C₂×C₁₃	#2544	1	8	yes	direct product factor
345	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
346	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
348	C₂×C₁₃	C₂×#546	1	2	yes	—
349	C₂×C₁₃	C₂×#559	1	2	yes	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	8	no	—
353	C₂⁴	—	2	8	no	—
354	C₂⁴	—	2	4	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	2	8	no	—
359	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
360	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
361	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
362	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
363	C₂×Q₈	—	2	8	no	—
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	—	2	8	no	—
366	C₂×Q₈	—	4	16	no	—
367	C₂×D₄	—	2	32	no	—
368	C₂×D₄	—	2	32	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	32	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	4	16	no	—
376	C₂×D₄	—	4	64	no	—
377	C₂×D₄	—	4	16	no	—
378	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	16	no	—
392	C₂²×C₄	—	4	16	no	—
393	C₂²×C₄	—	4	32	no	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
398	C₂²×C₄	C₁₃×#41	1	8	yes	—
399	C₂²×C₄	C₁₃×#41	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	16	no	—
409	C₂²⋊C₄	—	2	32	no	—
410	C₂²⋊C₄	—	2	16	no	—
411	C₂²⋊C₄	—	2	16	no	—
412	C₂²⋊C₄	—	2	16	no	—
413	C₂²⋊C₄	—	4	16	no	—
414	C₄²	—	2	8	no	—
415	C₄²	—	2	8	no	—
416	C₄²	C₂×D₄×C₁₃	1	16	yes	complemented
417	C₁₃	C₂×#2544	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	16	no	—
419	C₂³	—	2	32	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	16	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	8	no	—
435	C₂³	—	4	16	no	—
436	C₂³	—	4	16	no	—
437	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
438	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
439	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
440	C₂³	C₂×C₁₃×#41	1	2	yes	—
441	C₂³	C₂×C₁₃×#41	1	4	yes	—
442	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
443	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
444	Q₈	—	4	16	no	—
445	D₄	—	2	32	no	—
446	D₄	—	4	64	no	—
447	D₄	—	4	16	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	16	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	4	32	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	C₁₃×#121	1	16	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
472	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
473	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	16	no	—
476	C₂²	—	4	32	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	8	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	8	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	8	16	no	—
486	C₂²	C₂×C₁₃×#121	1	4	yes	—
487	C₂²	C₁₃×#532	1	4	yes	—
488	C₂²	C₁₃×#535	1	4	yes	—
489	C₂²	C₁₃×#546	1	8	yes	—
490	C₂²	C₁₃×#559	1	8	yes	—
491	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
492	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
493	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
494	C₂²	C₂²×C₁₃×#41	1	2	yes	—
495	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
496	C₄	—	2	4	no	—
497	C₄	—	2	4	no	—
498	C₄	—	2	8	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	C₂×C₁₃×#121	1	8	yes	—
503	C₂	—	4	8	no	—
504	C₂	—	8	4	no	—
505	C₂	C₁₃×#2544	1	8	yes	direct product factor
506	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
507	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
508	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
509	C₂	C₂×C₁₃×#546	1	2	yes	—
510	C₂	C₂×C₁₃×#559	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#127	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×C₁₃×#124	C₂	semidirect
3. C₂²×C₁₃×#124	C₂	semidirect
4. C₂²×C₄×D₄×C₁₃	C₂	semidirect
5. C₁₃×#2544	C₂	direct (N × H)
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#391	C₂	semidirect
8. C₂×C₁₃×#390	C₂	semidirect
9. C₂×C₁₃×#386	C₂	semidirect
10. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
20. C₂×C₁₃×#124	C₂²	semidirect
21. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₁₃×#394	C₂²	semidirect
35. C₁₃×#391	C₂²	semidirect
36. C₁₃×#390	C₂²	semidirect
37. C₁₃×#386	C₂²	semidirect
38. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
89. C₂×C₄²×C₁₃	D₄	semidirect
95. C₂×#2544	C₁₃	direct (N × H)
162. C₄²×C₁₃	C₂×D₄	semidirect
164. C₂²×#124	C₂×C₁₃	semidirect
165. C₂²×#124	C₂×C₁₃	semidirect
166. C₂²×C₄×D₄	C₂×C₁₃	semidirect
167. #2544	C₂×C₁₃	direct (N × H)
168. C₂×#394	C₂×C₁₃	semidirect
169. C₂×#391	C₂×C₁₃	semidirect
170. C₂×#390	C₂×C₁₃	semidirect
171. C₂×#386	C₂×C₁₃	semidirect
172. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
238. C₂×#124	C₂²×C₁₃	semidirect
239. C₂×#124	C₂²×C₁₃	semidirect
241. C₂×C₄×D₄	C₂²×C₁₃	semidirect
252. #394	C₂²×C₁₃	semidirect
253. #391	C₂²×C₁₃	semidirect
254. #390	C₂²×C₁₃	semidirect
255. #386	C₂²×C₁₃	semidirect
256. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
336. C₂×C₄²	D₄×C₁₃	semidirect
344. C₂×C₁₃	#2544	direct (N × H)
416. C₄²	C₂×D₄×C₁₃	semidirect
417. C₁₃	C₂×#2544	direct (N × H)
505. C₂	C₁₃×#2544	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×#127	2
C₂²×C₁₃×#124	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2544	2
C₂×C₁₃×#394	2
C₂×C₁₃×#391	2
C₂×C₁₃×#390	2
C₂×C₁₃×#386	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2544	13

Subgroups — C2×C13×#2544 #15721225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2544 #15721225