Subgroups — C₂²×D₁₃×#121 #16769552

Order 3328.

19998 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂³×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88149	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88184	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88138	C₂	1	2	yes	maximal, complemented
7	C₂²×#88193	C₂	1	2	yes	maximal, complemented
8	C₂²×#88192	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₁₃×#121	C₂	1	48	yes	maximal, direct product factor
10	C₂²×C₄⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₁₃	C₂²	1	2	yes	—
14	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
19	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
20	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
21	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×D₁₃	—	2	32	no	—
23	C₂²×D₄×D₁₃	—	2	16	no	—
24	C₂²×D₄×D₁₃	C₂²	1	48	yes	complemented
25	C₂²×D₄×D₁₃	C₂²	1	24	yes	complemented
26	C₂³×D₅₂	C₂²	1	2	yes	complemented
27	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₄×D₁₃	—	2	16	no	—
29	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
31	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
32	C₂³×C₄×D₁₃	C₂²	1	24	yes	complemented
33	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
39	C₂×#88193	C₂²	1	48	yes	complemented
40	C₂×#88192	C₂²	1	24	yes	complemented
41	C₂×#88184	C₂²	1	24	yes	complemented
42	C₂²×#6103	C₂²	1	2	yes	complemented
43	C₂²×#6103	C₂²	1	2	yes	complemented
44	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#6101	C₂²	1	2	yes	complemented
46	D₁₃×#121	C₂²	1	256	yes	direct product factor
47	C₂×#88149	C₂²	1	24	yes	complemented
48	C₂×C₄⋊C₄×D₁₃	C₂²	1	24	yes	complemented
49	C₂×#88138	C₂²	1	48	yes	complemented
50	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	complemented
51	C₂⁵×C₁₃	C₂³	1	2	yes	—
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂⁴×D₁₃	—	2	8	no	—
54	C₂⁴×D₁₃	—	2	8	no	—
55	C₂⁴×D₁₃	—	2	16	no	—
56	C₂⁴×D₁₃	—	2	16	no	—
57	C₂⁴×D₁₃	—	2	16	no	—
58	C₂⁴×D₁₃	D₄	1	16	yes	complemented
59	C₂⁴×D₁₃	C₂³	1	24	yes	—
60	C₂⁴×D₁₃	C₂³	1	2	yes	—
61	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
62	C₂⁴×D₁₃	C₂³	1	12	yes	—
63	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	—	2	16	no	—
65	C₂²×D₄×C₁₃	—	2	8	no	—
66	C₂²×D₄×C₁₃	C₂³	1	12	yes	complemented
67	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
68	C₂³×C₄×C₁₃	—	2	8	no	—
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
73	C₂²×C₂²⋊D₁₃	—	2	16	no	—
74	C₂²×C₂²⋊D₁₃	—	2	16	no	—
75	C₂²×C₂²⋊D₁₃	—	2	16	no	—
76	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
77	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
78	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	complemented
79	C₂³×Dic₁₃	—	2	8	no	—
80	C₂³×Dic₁₃	C₂³	1	2	yes	—
81	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
83	C₂³×Dic₁₃	C₂³	1	12	yes	complemented
84	C₂×D₄×D₁₃	—	2	384	no	—
85	C₂×D₄×D₁₃	—	2	192	no	—
86	C₂×D₄×D₁₃	C₂³	1	128	yes	complemented
87	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
88	C₂²×D₅₂	—	2	16	no	—
89	C₂²×D₅₂	—	2	8	no	—
90	C₂²×D₅₂	C₂³	1	24	yes	complemented
91	C₂²×D₅₂	C₂³	1	12	yes	complemented
92	C₂²×C₄×D₁₃	—	2	8	no	—
93	C₂²×C₄×D₁₃	—	2	16	no	—
94	C₂²×C₄×D₁₃	—	2	8	no	—
95	C₂²×C₄×D₁₃	—	2	8	no	—
96	C₂²×C₄×D₁₃	—	2	192	no	—
97	C₂²×C₄×D₁₃	D₄	1	16	yes	complemented
98	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
99	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
100	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
101	C₂²×C₄×D₁₃	C₂³	1	64	yes	complemented
102	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
103	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
104	C₁₃×#121	C₂³	1	64	yes	complemented
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
107	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
108	#88193	C₂³	1	128	yes	complemented
109	#88192	C₂³	1	64	yes	complemented
110	#88184	C₂³	1	64	yes	complemented
111	C₂×#6103	C₂³	1	24	yes	complemented
112	C₂×#6103	C₂³	1	24	yes	complemented
113	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
114	C₂×#6101	C₂³	1	24	yes	complemented
115	#88149	C₂³	1	64	yes	complemented
116	C₄⋊C₄×D₁₃	C₂³	1	64	yes	complemented
117	#88138	C₂³	1	128	yes	complemented
118	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	complemented
119	C₂³×#121	—	13	1	no	maximal, Sylow
120	C₂⁴×C₁₃	—	2	4	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	8	no	—
123	C₂⁴×C₁₃	—	2	8	no	—
124	C₂⁴×C₁₃	—	2	8	no	—
125	C₂⁴×C₁₃	C₂×D₄	1	8	yes	complemented
126	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂³×D₁₃	—	2	4	no	—
130	C₂³×D₁₃	—	2	4	no	—
131	C₂³×D₁₃	—	2	128	no	—
132	C₂³×D₁₃	—	2	48	no	—
133	C₂³×D₁₃	—	2	48	no	—
134	C₂³×D₁₃	—	2	8	no	—
135	C₂³×D₁₃	—	2	8	no	—
136	C₂³×D₁₃	—	2	8	no	—
137	C₂³×D₁₃	—	2	96	no	—
138	C₂³×D₁₃	—	2	96	no	—
139	C₂³×D₁₃	—	2	96	no	—
140	C₂³×D₁₃	—	4	128	no	—
141	C₂³×D₁₃	C₂×D₄	1	8	yes	—
142	C₂³×D₁₃	C₂×D₄	1	8	yes	—
143	C₂³×D₁₃	C₂×D₄	1	96	yes	complemented
144	C₂³×D₁₃	C₂×D₄	1	8	yes	complemented
145	C₂³×D₁₃	#41	1	8	yes	—
146	C₂³×D₁₃	C₂⁴	1	32	yes	—
147	C₂³×D₁₃	C₂⁴	1	12	yes	—
148	C₂³×D₁₃	C₂⁴	1	6	yes	—
149	C₂³×D₁₃	C₂⁴	1	16	yes	—
150	C₂³×D₁₃	C₂⁴	1	6	yes	—
151	C₂×D₄×C₁₃	—	2	96	no	—
152	C₂×D₄×C₁₃	—	2	48	no	—
153	C₂×D₄×C₁₃	C₂⁴	1	16	yes	complemented
154	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	8	no	—
157	C₂²×C₄×C₁₃	—	2	48	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
159	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
163	C₂×C₂²⋊D₁₃	—	2	96	no	—
164	C₂×C₂²⋊D₁₃	—	2	96	no	—
165	C₂×C₂²⋊D₁₃	—	2	96	no	—
166	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
167	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
168	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
169	C₂²×Dic₁₃	—	2	4	no	—
170	C₂²×Dic₁₃	—	2	8	no	—
171	C₂²×Dic₁₃	—	2	48	no	—
172	C₂²×Dic₁₃	C₂×D₄	1	8	yes	complemented
173	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
174	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
175	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
176	C₂²×Dic₁₃	C₂⁴	1	16	yes	complemented
177	D₄×D₁₃	—	2	512	no	—
178	D₄×D₁₃	—	2	256	no	—
179	C₂×D₅₂	—	2	96	no	—
180	C₂×D₅₂	—	2	48	no	—
181	C₂×D₅₂	C₂⁴	1	32	yes	complemented
182	C₂×D₅₂	C₂⁴	1	16	yes	complemented
183	C₂×C₄×D₁₃	—	2	48	no	—
184	C₂×C₄×D₁₃	—	2	96	no	—
185	C₂×C₄×D₁₃	—	2	48	no	—
186	C₂×C₄×D₁₃	—	2	48	no	—
187	C₂×C₄×D₁₃	—	2	256	no	—
188	C₂×C₄×D₁₃	C₂×D₄	1	96	yes	complemented
189	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
190	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
191	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
192	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
193	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
194	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
195	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
196	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
197	#6103	C₂⁴	1	32	yes	complemented
198	#6103	C₂⁴	1	32	yes	complemented
199	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
200	#6101	C₂⁴	1	32	yes	complemented
201	C₂⁴×D₄	—	13	1	no	—
202	C₂⁴×D₄	—	13	2	no	—
203	C₂⁵×C₄	—	13	1	no	—
204	C₂²×#121	—	13	1	no	—
205	C₂²×#121	—	13	2	no	—
206	C₂²×#121	—	13	1	no	—
207	C₂²×#121	—	13	48	no	—
208	C₂²×#121	—	13	1	no	—
209	C₂²×#121	—	13	2	no	—
210	C₂²×#121	D₁₃	1	1	yes	characteristic, direct product factor
211	C₂³×C₄⋊C₄	—	13	1	no	—
212	C₂³×C₂²⋊C₄	—	13	2	no	—
213	C₂³×C₁₃	—	2	32	no	—
214	C₂³×C₁₃	—	2	12	no	—
215	C₂³×C₁₃	—	2	12	no	—
216	C₂³×C₁₃	—	2	24	no	—
217	C₂³×C₁₃	—	2	24	no	—
218	C₂³×C₁₃	—	2	24	no	—
219	C₂³×C₁₃	—	4	32	no	—
220	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
221	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
222	C₂³×C₁₃	C₂²×D₄	1	24	yes	complemented
223	C₂³×C₁₃	C₂×#41	1	4	yes	—
224	C₂³×C₁₃	C₂⁵	1	8	yes	—
225	C₂³×C₁₃	C₂⁵	1	4	yes	—
226	C₂³×C₁₃	C₂⁵	1	3	yes	—
227	C₂²×D₁₃	—	2	32	no	—
228	C₂²×D₁₃	—	2	12	no	—
229	C₂²×D₁₃	—	2	12	no	—
230	C₂²×D₁₃	—	2	384	no	—
231	C₂²×D₁₃	—	2	32	no	—
232	C₂²×D₁₃	—	2	32	no	—
233	C₂²×D₁₃	—	2	24	no	—
234	C₂²×D₁₃	—	2	24	no	—
235	C₂²×D₁₃	—	2	24	no	—
236	C₂²×D₁₃	—	2	64	no	—
237	C₂²×D₁₃	—	2	64	no	—
238	C₂²×D₁₃	—	2	64	no	—
239	C₂²×D₁₃	—	4	32	no	—
240	C₂²×D₁₃	—	4	384	no	—
241	C₂²×D₁₃	#121	1	64	yes	direct product factor
242	C₂²×D₁₃	C₂²×D₄	1	24	yes	—
243	C₂²×D₁₃	C₂²×D₄	1	24	yes	—
244	C₂²×D₁₃	C₂²×D₄	1	64	yes	complemented
245	C₂²×D₁₃	C₂²×D₄	1	24	yes	complemented
246	C₂²×D₁₃	C₂×#41	1	24	yes	—
247	C₂²×D₁₃	C₂⁵	1	8	yes	—
248	C₂²×D₁₃	C₂⁵	1	4	yes	—
249	C₂²×D₁₃	C₂⁵	1	4	yes	—
250	D₄×C₁₃	—	2	64	no	—
251	D₄×C₁₃	—	2	32	no	—
252	C₂×C₄×C₁₃	—	2	12	no	—
253	C₂×C₄×C₁₃	—	2	24	no	—
254	C₂×C₄×C₁₃	—	2	32	no	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	complemented
256	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
257	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
259	C₂²⋊D₁₃	—	2	64	no	—
260	C₂²⋊D₁₃	—	2	64	no	—
261	C₂²⋊D₁₃	—	2	64	no	—
262	C₂×Dic₁₃	—	2	12	no	—
263	C₂×Dic₁₃	—	2	24	no	—
264	C₂×Dic₁₃	—	2	32	no	—
265	C₂×Dic₁₃	C₂²×D₄	1	24	yes	complemented
266	C₂×Dic₁₃	C₂⁵	1	8	yes	—
267	C₂×Dic₁₃	C₂⁵	1	4	yes	—
268	C₂×Dic₁₃	C₂⁵	1	4	yes	—
269	D₅₂	—	2	64	no	—
270	D₅₂	—	2	32	no	—
271	C₄×D₁₃	—	2	32	no	—
272	C₄×D₁₃	—	2	64	no	—
273	C₄×D₁₃	—	2	32	no	—
274	C₄×D₁₃	—	2	32	no	—
275	C₄×D₁₃	C₂²×D₄	1	64	yes	complemented
276	C₂⁶	—	13	1	no	—
277	C₂⁶	—	13	2	no	—
278	C₂³×D₄	—	13	2	no	—
279	C₂³×D₄	—	13	2	no	—
280	C₂³×D₄	—	13	2	no	—
281	C₂³×D₄	—	13	24	no	—
282	C₂³×D₄	—	13	48	no	—
283	C₂³×D₄	—	13	2	no	—
284	C₂³×D₄	—	13	1	no	—
285	C₂³×D₄	—	26	16	no	—
286	C₂³×D₄	—	26	32	no	—
287	C₂³×D₄	C₂×D₁₃	1	2	yes	complemented
288	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
289	C₂⁴×C₄	—	13	1	no	—
290	C₂⁴×C₄	—	13	1	no	—
291	C₂⁴×C₄	—	13	1	no	—
292	C₂⁴×C₄	—	13	1	no	—
293	C₂⁴×C₄	—	13	1	no	—
294	C₂⁴×C₄	—	13	2	no	—
295	C₂⁴×C₄	—	13	24	no	—
296	C₂⁴×C₄	—	26	16	no	—
297	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
298	C₂×#121	—	13	24	no	—
299	C₂×#121	—	13	48	no	—
300	C₂×#121	—	13	24	no	—
301	C₂×#121	—	13	256	no	—
302	C₂×#121	—	13	24	no	—
303	C₂×#121	—	13	48	no	—
304	C₂×#121	C₂×D₁₃	1	24	yes	direct product factor
305	C₂²×C₄⋊C₄	—	13	2	no	—
306	C₂²×C₄⋊C₄	—	13	1	no	—
307	C₂²×C₄⋊C₄	—	13	24	no	—
308	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
309	C₂²×C₂²⋊C₄	—	13	2	no	—
310	C₂²×C₂²⋊C₄	—	13	2	no	—
311	C₂²×C₂²⋊C₄	—	13	2	no	—
312	C₂²×C₂²⋊C₄	—	13	48	no	—
313	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
314	C₂²×C₁₃	—	2	4	no	—
315	C₂²×C₁₃	—	2	4	no	—
316	C₂²×C₁₃	—	2	48	no	—
317	C₂²×C₁₃	—	2	8	no	—
318	C₂²×C₁₃	—	2	8	no	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	4	48	no	—
321	C₂²×C₁₃	C₂×#121	1	16	yes	complemented
322	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
323	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
324	C₂²×C₁₃	C₂³×D₄	1	8	yes	complemented
325	C₂²×C₁₃	C₂²×#41	1	6	yes	—
326	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
327	C₂×D₁₃	—	2	4	no	—
328	C₂×D₁₃	—	2	4	no	—
329	C₂×D₁₃	—	2	48	no	—
330	C₂×D₁₃	—	2	128	no	—
331	C₂×D₁₃	—	2	8	no	—
332	C₂×D₁₃	—	2	8	no	—
333	C₂×D₁₃	—	2	8	no	—
334	C₂×D₁₃	—	4	48	no	—
335	C₂×D₁₃	—	4	128	no	—
336	C₂×D₁₃	C₂×#121	1	96	yes	direct product factor
337	C₂×D₁₃	C₂³×D₄	1	8	yes	—
338	C₂×D₁₃	C₂³×D₄	1	8	yes	—
339	C₂×D₁₃	C₂³×D₄	1	8	yes	complemented
340	C₂×D₁₃	C₂²×#41	1	8	yes	—
341	C₄×C₁₃	—	2	4	no	—
342	C₄×C₁₃	—	2	8	no	—
343	C₄×C₁₃	C₂³×D₄	1	8	yes	complemented
344	Dic₁₃	—	2	4	no	—
345	Dic₁₃	—	2	8	no	—
346	Dic₁₃	C₂³×D₄	1	8	yes	complemented
347	C₂⁵	—	13	1	no	—
348	C₂⁵	—	13	16	no	—
349	C₂⁵	—	13	12	no	—
350	C₂⁵	—	13	1	no	—
351	C₂⁵	—	13	24	no	—
352	C₂⁵	—	13	2	no	—
353	C₂⁵	—	26	8	no	—
354	C₂⁵	—	26	8	no	—
355	C₂⁵	—	26	16	no	—
356	C₂⁵	—	26	16	no	—
357	C₂⁵	—	26	16	no	—
358	C₂⁵	C₂²×D₁₃	1	2	yes	—
359	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
360	C₂²×D₄	—	2	16	no	—
361	C₂²×D₄	—	2	8	no	—
362	C₂²×D₄	—	13	24	no	—
363	C₂²×D₄	—	13	24	no	—
364	C₂²×D₄	—	13	24	no	—
365	C₂²×D₄	—	13	64	no	—
366	C₂²×D₄	—	13	128	no	—
367	C₂²×D₄	—	13	24	no	—
368	C₂²×D₄	—	13	12	no	—
369	C₂²×D₄	—	26	16	no	—
370	C₂²×D₄	—	26	192	no	—
371	C₂²×D₄	—	26	16	no	—
372	C₂²×D₄	—	26	384	no	—
373	C₂²×D₄	—	26	16	no	—
374	C₂²×D₄	—	26	16	no	—
375	C₂²×D₄	—	26	8	no	—
376	C₂²×D₄	C₂²×D₁₃	1	24	yes	complemented
377	C₂²×D₄	C₂²×D₁₃	1	12	yes	complemented
378	C₂³×C₄	—	2	8	no	—
379	C₂³×C₄	—	13	1	no	—
380	C₂³×C₄	—	13	16	no	—
381	C₂³×C₄	—	13	12	no	—
382	C₂³×C₄	—	13	12	no	—
383	C₂³×C₄	—	13	1	no	—
384	C₂³×C₄	—	13	2	no	—
385	C₂³×C₄	—	13	12	no	—
386	C₂³×C₄	—	13	24	no	—
387	C₂³×C₄	—	13	12	no	—
388	C₂³×C₄	—	13	12	no	—
389	C₂³×C₄	—	13	64	no	—
390	C₂³×C₄	—	26	8	no	—
391	C₂³×C₄	—	26	192	no	—
392	C₂³×C₄	—	26	8	no	—
393	C₂³×C₄	—	26	16	no	—
394	C₂³×C₄	—	26	8	no	—
395	C₂³×C₄	—	26	8	no	—
396	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
397	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
398	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
399	C₂³×C₄	C₂²×D₁₃	1	12	yes	complemented
400	#121	—	13	64	no	—
401	#121	—	13	128	no	—
402	#121	—	13	64	no	—
403	#121	—	13	64	no	—
404	#121	—	13	128	no	—
405	#121	C₂²×D₁₃	1	64	yes	direct product factor
406	C₂×C₄⋊C₄	—	13	24	no	—
407	C₂×C₄⋊C₄	—	13	12	no	—
408	C₂×C₄⋊C₄	—	13	64	no	—
409	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
410	C₂×C₂²⋊C₄	—	13	24	no	—
411	C₂×C₂²⋊C₄	—	13	24	no	—
412	C₂×C₂²⋊C₄	—	13	24	no	—
413	C₂×C₂²⋊C₄	—	13	128	no	—
414	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	complemented
415	C₂×C₁₃	—	2	8	no	—
416	C₂×C₁₃	—	4	8	no	—
417	C₂×C₁₃	C₂²×#121	1	12	yes	complemented
418	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
419	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
420	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
421	D₁₃	—	2	8	no	—
422	D₁₃	—	4	8	no	—
423	D₁₃	C₂²×#121	1	16	yes	direct product factor
424	C₂⁴	—	2	4	no	—
425	C₂⁴	—	2	4	no	—
426	C₂⁴	—	2	8	no	—
427	C₂⁴	—	2	8	no	—
428	C₂⁴	—	2	8	no	—
429	C₂⁴	—	13	8	no	—
430	C₂⁴	—	13	8	no	—
431	C₂⁴	—	13	8	no	—
432	C₂⁴	—	13	6	no	—
433	C₂⁴	—	13	8	no	—
434	C₂⁴	—	13	96	no	—
435	C₂⁴	—	13	16	no	—
436	C₂⁴	—	13	6	no	—
437	C₂⁴	—	13	32	no	—
438	C₂⁴	—	13	12	no	—
439	C₂⁴	—	26	48	no	—
440	C₂⁴	—	26	128	no	—
441	C₂⁴	—	26	48	no	—
442	C₂⁴	—	26	96	no	—
443	C₂⁴	—	26	96	no	—
444	C₂⁴	—	26	96	no	—
445	C₂⁴	—	26	4	no	—
446	C₂⁴	—	26	4	no	—
447	C₂⁴	—	26	8	no	—
448	C₂⁴	—	26	8	no	—
449	C₂⁴	—	26	8	no	—
450	C₂⁴	—	52	128	no	—
451	C₂⁴	D₄×D₁₃	1	8	yes	complemented
452	C₂⁴	C₂³×D₁₃	1	12	yes	—
453	C₂⁴	C₂³×D₁₃	1	6	yes	—
454	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
455	C₂×D₄	—	2	96	no	—
456	C₂×D₄	—	2	48	no	—
457	C₂×D₄	—	13	32	no	—
458	C₂×D₄	—	13	32	no	—
459	C₂×D₄	—	13	32	no	—
460	C₂×D₄	—	13	32	no	—
461	C₂×D₄	—	13	16	no	—
462	C₂×D₄	—	26	96	no	—
463	C₂×D₄	—	26	256	no	—
464	C₂×D₄	—	26	96	no	—
465	C₂×D₄	—	26	512	no	—
466	C₂×D₄	—	26	96	no	—
467	C₂×D₄	—	26	96	no	—
468	C₂×D₄	—	26	48	no	—
469	C₂×D₄	C₂³×D₁₃	1	32	yes	complemented
470	C₂×D₄	C₂³×D₁₃	1	16	yes	complemented
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	48	no	—
474	C₂²×C₄	—	13	8	no	—
475	C₂²×C₄	—	13	6	no	—
476	C₂²×C₄	—	13	96	no	—
477	C₂²×C₄	—	13	16	no	—
478	C₂²×C₄	—	13	6	no	—
479	C₂²×C₄	—	13	12	no	—
480	C₂²×C₄	—	13	16	no	—
481	C₂²×C₄	—	13	16	no	—
482	C₂²×C₄	—	13	32	no	—
483	C₂²×C₄	—	13	16	no	—
484	C₂²×C₄	—	13	16	no	—
485	C₂²×C₄	—	26	48	no	—
486	C₂²×C₄	—	26	256	no	—
487	C₂²×C₄	—	26	48	no	—
488	C₂²×C₄	—	26	96	no	—
489	C₂²×C₄	—	26	48	no	—
490	C₂²×C₄	—	26	4	no	—
491	C₂²×C₄	—	26	8	no	—
492	C₂²×C₄	—	26	48	no	—
493	C₂²×C₄	D₄×D₁₃	1	8	yes	complemented
494	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
495	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
496	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
497	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
498	C₄⋊C₄	—	13	32	no	—
499	C₄⋊C₄	—	13	16	no	—
500	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
501	C₂²⋊C₄	—	13	32	no	—
502	C₂²⋊C₄	—	13	32	no	—
503	C₂²⋊C₄	—	13	32	no	—
504	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	complemented
505	C₁₃	C₂³×#121	1	1	yes	characteristic, complemented, Sylow
506	C₂³	—	2	32	no	—
507	C₂³	—	2	12	no	—
508	C₂³	—	2	12	no	—
509	C₂³	—	2	24	no	—
510	C₂³	—	2	24	no	—
511	C₂³	—	2	24	no	—
512	C₂³	—	4	32	no	—
513	C₂³	—	13	64	no	—
514	C₂³	—	13	24	no	—
515	C₂³	—	13	24	no	—
516	C₂³	—	13	24	no	—
517	C₂³	—	13	4	no	—
518	C₂³	—	13	24	no	—
519	C₂³	—	13	64	no	—
520	C₂³	—	13	4	no	—
521	C₂³	—	13	8	no	—
522	C₂³	—	26	32	no	—
523	C₂³	—	26	384	no	—
524	C₂³	—	26	32	no	—
525	C₂³	—	26	64	no	—
526	C₂³	—	26	64	no	—
527	C₂³	—	26	64	no	—
528	C₂³	—	26	32	no	—
529	C₂³	—	26	12	no	—
530	C₂³	—	26	12	no	—
531	C₂³	—	26	24	no	—
532	C₂³	—	26	24	no	—
533	C₂³	—	26	24	no	—
534	C₂³	—	52	384	no	—
535	C₂³	—	52	32	no	—
536	C₂³	C₂×D₄×D₁₃	1	4	yes	—
537	C₂³	C₂×D₄×D₁₃	1	4	yes	—
538	C₂³	C₂×D₄×D₁₃	1	24	yes	complemented
539	C₂³	#41×D₁₃	1	4	yes	—
540	C₂³	C₂⁴×D₁₃	1	8	yes	—
541	C₂³	C₂⁴×D₁₃	1	4	yes	—
542	C₂³	C₂⁴×D₁₃	1	3	yes	—
543	D₄	—	2	64	no	—
544	D₄	—	2	32	no	—
545	D₄	—	26	64	no	—
546	D₄	—	26	64	no	—
547	D₄	—	26	64	no	—
548	D₄	—	26	64	no	—
549	D₄	—	26	32	no	—
550	C₂×C₄	—	2	12	no	—
551	C₂×C₄	—	2	24	no	—
552	C₂×C₄	—	2	32	no	—
553	C₂×C₄	—	13	24	no	—
554	C₂×C₄	—	13	4	no	—
555	C₂×C₄	—	13	64	no	—
556	C₂×C₄	—	13	4	no	—
557	C₂×C₄	—	13	8	no	—
558	C₂×C₄	—	26	32	no	—
559	C₂×C₄	—	26	32	no	—
560	C₂×C₄	—	26	64	no	—
561	C₂×C₄	—	26	32	no	—
562	C₂×C₄	—	26	12	no	—
563	C₂×C₄	—	26	24	no	—
564	C₂×C₄	—	26	32	no	—
565	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	complemented
566	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
567	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
568	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
569	C₂²	—	2	48	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	4	48	no	—
576	C₂²	—	13	96	no	—
577	C₂²	—	13	8	no	—
578	C₂²	—	13	8	no	—
579	C₂²	—	13	8	no	—
580	C₂²	—	13	8	no	—
581	C₂²	—	26	128	no	—
582	C₂²	—	26	48	no	—
583	C₂²	—	26	4	no	—
584	C₂²	—	26	4	no	—
585	C₂²	—	26	8	no	—
586	C₂²	—	26	8	no	—
587	C₂²	—	26	8	no	—
588	C₂²	—	52	128	no	—
589	C₂²	—	52	48	no	—
590	C₂²	D₁₃×#121	1	16	yes	direct product factor
591	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
592	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
593	C₂²	C₂²×D₄×D₁₃	1	8	yes	complemented
594	C₂²	C₂×#41×D₁₃	1	6	yes	—
595	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
596	C₄	—	2	4	no	—
597	C₄	—	2	8	no	—
598	C₄	—	13	8	no	—
599	C₄	—	26	4	no	—
600	C₄	—	26	8	no	—
601	C₄	C₂²×D₄×D₁₃	1	8	yes	complemented
602	C₂	—	2	8	no	—
603	C₂	—	4	8	no	—
604	C₂	—	13	16	no	—
605	C₂	—	26	8	no	—
606	C₂	—	52	8	no	—
607	C₂	C₂×D₁₃×#121	1	12	yes	direct product factor
608	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
609	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
610	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#121	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×#121	D₁₃
hypocenter	C₁₃	C₂³×#121
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₁₃	C₂	semidirect
2. C₂³×D₄×D₁₃	C₂	semidirect
3. C₂⁴×C₄×D₁₃	C₂	semidirect
4. C₂²×#88149	C₂	semidirect
5. C₂²×#88184	C₂	semidirect
6. C₂²×#88138	C₂	semidirect
7. C₂²×#88193	C₂	semidirect
8. C₂²×#88192	C₂	semidirect
9. C₂×D₁₃×#121	C₂	direct (N × H)
10. C₂²×C₄⋊C₄×D₁₃	C₂	semidirect
11. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
12. C₂²×C₁₃×#121	C₂	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂⁴×C₄×C₁₃	C₂²	semidirect
18. C₂³×C₂²⋊D₁₃	C₂²	semidirect
19. C₂³×C₂²⋊D₁₃	C₂²	semidirect
20. C₂³×C₂²⋊D₁₃	C₂²	semidirect
21. C₂⁴×Dic₁₃	C₂²	semidirect
24. C₂²×D₄×D₁₃	C₂²	semidirect
25. C₂²×D₄×D₁₃	C₂²	semidirect
26. C₂³×D₅₂	C₂²	semidirect
27. C₂³×D₅₂	C₂²	semidirect
32. C₂³×C₄×D₁₃	C₂²	semidirect
33. C₂³×C₄×D₁₃	C₂²	semidirect
34. C₂³×C₄×D₁₃	C₂²	semidirect
35. C₂×C₁₃×#121	C₂²	semidirect
36. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
37. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
38. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
39. C₂×#88193	C₂²	semidirect
40. C₂×#88192	C₂²	semidirect
41. C₂×#88184	C₂²	semidirect
42. C₂²×#6103	C₂²	semidirect
43. C₂²×#6103	C₂²	semidirect
44. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
45. C₂²×#6101	C₂²	semidirect
46. D₁₃×#121	C₂²	direct (N × H)
47. C₂×#88149	C₂²	semidirect
48. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
49. C₂×#88138	C₂²	semidirect
50. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
58. C₂⁴×D₁₃	D₄	semidirect
66. C₂²×D₄×C₁₃	C₂³	semidirect
67. C₂²×D₄×C₁₃	C₂³	semidirect
72. C₂³×C₄×C₁₃	C₂³	semidirect
76. C₂²×C₂²⋊D₁₃	C₂³	semidirect
77. C₂²×C₂²⋊D₁₃	C₂³	semidirect
78. C₂²×C₂²⋊D₁₃	C₂³	semidirect
83. C₂³×Dic₁₃	C₂³	semidirect
86. C₂×D₄×D₁₃	C₂³	semidirect
87. C₂×D₄×D₁₃	C₂³	semidirect
90. C₂²×D₅₂	C₂³	semidirect
91. C₂²×D₅₂	C₂³	semidirect
97. C₂²×C₄×D₁₃	D₄	semidirect
101. C₂²×C₄×D₁₃	C₂³	semidirect
102. C₂²×C₄×D₁₃	C₂³	semidirect
103. C₂²×C₄×D₁₃	C₂³	semidirect
104. C₁₃×#121	C₂³	semidirect
105. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
106. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
107. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
108. #88193	C₂³	semidirect
109. #88192	C₂³	semidirect
110. #88184	C₂³	semidirect
111. C₂×#6103	C₂³	semidirect
112. C₂×#6103	C₂³	semidirect
113. C₂×C₄⋊Dic₁₃	C₂³	semidirect
114. C₂×#6101	C₂³	semidirect
115. #88149	C₂³	semidirect
116. C₄⋊C₄×D₁₃	C₂³	semidirect
117. #88138	C₂³	semidirect
118. C₂²⋊C₄×D₁₃	C₂³	semidirect
125. C₂⁴×C₁₃	C₂×D₄	semidirect
143. C₂³×D₁₃	C₂×D₄	semidirect
144. C₂³×D₁₃	C₂×D₄	semidirect
153. C₂×D₄×C₁₃	C₂⁴	semidirect
154. C₂×D₄×C₁₃	C₂⁴	semidirect
158. C₂²×C₄×C₁₃	C₂×D₄	semidirect
162. C₂²×C₄×C₁₃	C₂⁴	semidirect
166. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
167. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
168. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
172. C₂²×Dic₁₃	C₂×D₄	semidirect
176. C₂²×Dic₁₃	C₂⁴	semidirect
181. C₂×D₅₂	C₂⁴	semidirect
182. C₂×D₅₂	C₂⁴	semidirect
188. C₂×C₄×D₁₃	C₂×D₄	semidirect
192. C₂×C₄×D₁₃	C₂⁴	semidirect
193. C₂×C₄×D₁₃	C₂⁴	semidirect
194. C₁₃×C₄⋊C₄	C₂⁴	semidirect
195. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
196. C₂²⋊Dic₁₃	C₂⁴	semidirect
197. #6103	C₂⁴	semidirect
198. #6103	C₂⁴	semidirect
199. C₄⋊Dic₁₃	C₂⁴	semidirect
200. #6101	C₂⁴	semidirect
210. C₂²×#121	D₁₃	direct (N × H)
222. C₂³×C₁₃	C₂²×D₄	semidirect
241. C₂²×D₁₃	#121	direct (N × H)
244. C₂²×D₁₃	C₂²×D₄	semidirect
245. C₂²×D₁₃	C₂²×D₄	semidirect
255. C₂×C₄×C₁₃	C₂²×D₄	semidirect
265. C₂×Dic₁₃	C₂²×D₄	semidirect
275. C₄×D₁₃	C₂²×D₄	semidirect
287. C₂³×D₄	C₂×D₁₃	semidirect
288. C₂³×D₄	C₂×D₁₃	semidirect
297. C₂⁴×C₄	C₂×D₁₃	semidirect
304. C₂×#121	C₂×D₁₃	direct (N × H)
308. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
313. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
321. C₂²×C₁₃	C₂×#121	semidirect
324. C₂²×C₁₃	C₂³×D₄	semidirect
336. C₂×D₁₃	C₂×#121	direct (N × H)
339. C₂×D₁₃	C₂³×D₄	semidirect
343. C₄×C₁₃	C₂³×D₄	semidirect
346. Dic₁₃	C₂³×D₄	semidirect
376. C₂²×D₄	C₂²×D₁₃	semidirect
377. C₂²×D₄	C₂²×D₁₃	semidirect
399. C₂³×C₄	C₂²×D₁₃	semidirect
405. #121	C₂²×D₁₃	direct (N × H)
409. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
414. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
417. C₂×C₁₃	C₂²×#121	semidirect
423. D₁₃	C₂²×#121	direct (N × H)
451. C₂⁴	D₄×D₁₃	semidirect
469. C₂×D₄	C₂³×D₁₃	semidirect
470. C₂×D₄	C₂³×D₁₃	semidirect
493. C₂²×C₄	D₄×D₁₃	semidirect
497. C₂²×C₄	C₂³×D₁₃	semidirect
500. C₄⋊C₄	C₂³×D₁₃	semidirect
504. C₂²⋊C₄	C₂³×D₁₃	semidirect
505. C₁₃	C₂³×#121	semidirect
538. C₂³	C₂×D₄×D₁₃	semidirect
565. C₂×C₄	C₂×D₄×D₁₃	semidirect
590. C₂²	D₁₃×#121	direct (N × H)
593. C₂²	C₂²×D₄×D₁₃	semidirect
601. C₄	C₂²×D₄×D₁₃	semidirect
607. C₂	C₂×D₁₃×#121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₁₃	2
C₂⁴×C₄×D₁₃	2
C₂²×#88149	2
C₂²×#88184	2
C₂²×#88138	2
C₂²×#88193	2
C₂²×#88192	2
C₂×D₁₃×#121	2
C₂²×C₄⋊C₄×D₁₃	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×#121	2
C₂³×#121	13

Subgroups — C22×D13×#121 #16769552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₁₃×#121 #16769552