Subgroups — C₂×#13128471 #16770802

Order 3328.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88251	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128471	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719511	C₂	1	8	yes	maximal, complemented
4	C₂×D₄×C₂²⋊D₁₃	C₂	1	8	yes	maximal, complemented
5	C₂×#11719510	C₂	1	2	yes	maximal, complemented
6	C₂×#11719509	C₂	1	4	yes	maximal, complemented
7	C₂×#11719496	C₂	1	2	yes	maximal, complemented
8	C₂²×#88207	C₂	1	4	yes	maximal, complemented
9	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₁₃	C₂²	1	2	yes	complemented
12	C₂³×D₄×C₁₃	—	2	16	no	—
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	8	yes	complemented
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₁₃	C₂²	1	16	yes	complemented
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
20	C₂³×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
21	C₂×#88251	—	2	16	no	—
22	C₂×#88251	C₂²	1	16	yes	complemented
23	C₂²×#6129	C₂²	1	4	yes	complemented
24	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
25	C₂²×#6127	C₂²	1	2	yes	complemented
26	C₂×#88207	C₂²	1	4	yes	complemented
27	C₂×#88207	C₂²	1	16	yes	complemented
28	C₂×#88207	C₂²	1	8	yes	complemented
29	C₂×#88207	C₂²	1	64	yes	complemented
30	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
31	C₂²×C₂²⋊Dic₁₃	C₂²	1	8	yes	complemented
32	#11719511	C₂²	1	128	yes	complemented
33	#11719510	C₂²	1	32	yes	complemented
34	#11719509	C₂²	1	64	yes	complemented
35	C₂×#88194	C₂²	1	4	yes	complemented
36	C₂×#88193	C₂²	1	16	yes	complemented
37	D₄×C₂²⋊D₁₃	C₂²	1	128	yes	complemented
38	C₂×#88192	C₂²	1	8	yes	complemented
39	C₂×#88191	C₂²	1	8	yes	complemented
40	#11719503	C₂²	1	16	yes	complemented
41	C₂×#88190	C₂²	1	4	yes	complemented
42	C₂×#88189	C₂²	1	8	yes	complemented
43	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
44	#11719496	C₂²	1	32	yes	complemented
45	C₂×#88184	C₂²	1	4	yes	complemented
46	C₂×#88183	C₂²	1	4	yes	complemented
47	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
48	C₂×#88180	C₂²	1	2	yes	complemented
49	C₂×#88178	C₂²	1	4	yes	complemented
50	C₂⁵×C₁₃	—	2	16	no	—
51	C₂⁵×C₁₃	—	4	16	no	—
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₃	C₂³	1	8	yes	—
54	C₂⁵×C₁₃	C₂³	1	2	yes	—
55	C₂⁵×C₁₃	C₂³	1	2	yes	—
56	C₂⁵×C₁₃	C₂³	1	16	yes	complemented
57	C₂⁴×D₁₃	C₂³	1	4	yes	complemented
58	C₂²×D₄×C₁₃	—	2	16	no	—
59	C₂²×D₄×C₁₃	—	2	64	no	—
60	C₂²×D₄×C₁₃	—	2	128	no	—
61	C₂²×D₄×C₁₃	—	2	8	no	—
62	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
68	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
69	C₂²×D₄×C₁₃	C₂³	1	8	yes	complemented
70	C₂³×C₄×C₁₃	—	2	8	no	—
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
75	C₂²×C₂²⋊D₁₃	—	2	32	no	—
76	C₂²×C₂²⋊D₁₃	—	4	32	no	—
77	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
78	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
79	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
80	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
81	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
82	C₂²×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
83	C₂³×Dic₁₃	C₂³	1	4	yes	complemented
84	C₂³×Dic₁₃	C₂³	1	8	yes	complemented
85	#88251	—	2	128	no	—
86	C₂×#6129	—	2	32	no	—
87	C₂×#6129	C₂³	1	32	yes	complemented
88	C₂×D₄×D₁₃	—	2	32	no	—
89	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
90	C₂×#6127	—	2	16	no	—
91	C₂×#6127	C₂³	1	16	yes	complemented
92	C₂²×D₅₂	C₂³	1	2	yes	complemented
93	C₂²×C₄×D₁₃	C₂³	1	4	yes	complemented
94	C₂²×Dic₂₆	C₂³	1	2	yes	complemented
95	#88207	C₂³	1	32	yes	complemented
96	#88207	C₂³	1	128	yes	complemented
97	#88207	C₂³	1	64	yes	complemented
98	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
99	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
101	C₂×C₂²⋊Dic₁₃	C₂³	1	64	yes	complemented
102	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	complemented
103	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	complemented
104	#88194	C₂³	1	32	yes	complemented
105	#88193	C₂³	1	128	yes	complemented
106	#88192	C₂³	1	64	yes	complemented
107	#88191	C₂³	1	64	yes	complemented
108	#88190	C₂³	1	32	yes	complemented
109	#88189	C₂³	1	64	yes	complemented
110	D₄×Dic₁₃	C₂³	1	64	yes	complemented
111	#88184	C₂³	1	32	yes	complemented
112	#88183	C₂³	1	32	yes	complemented
113	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
114	C₂×#6103	C₂³	1	8	yes	complemented
115	#88180	C₂³	1	16	yes	complemented
116	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
117	#88178	C₂³	1	32	yes	complemented
118	C₂×#6101	C₂³	1	8	yes	complemented
119	C₂×C₄×Dic₁₃	C₂³	1	4	yes	complemented
120	C₂×#3484	—	13	1	no	maximal, Sylow
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	8	no	—
123	C₂⁴×C₁₃	—	2	32	no	—
124	C₂⁴×C₁₃	—	2	8	no	—
125	C₂⁴×C₁₃	—	2	64	no	—
126	C₂⁴×C₁₃	—	2	32	no	—
127	C₂⁴×C₁₃	—	4	8	no	—
128	C₂⁴×C₁₃	—	4	16	no	—
129	C₂⁴×C₁₃	—	4	8	no	—
130	C₂⁴×C₁₃	—	4	64	no	—
131	C₂⁴×C₁₃	—	4	128	no	—
132	C₂⁴×C₁₃	C₂×D₄	1	16	yes	complemented
133	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₃	C₂⁴	1	32	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
138	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
139	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
140	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
141	C₂³×D₁₃	—	2	16	no	—
142	C₂³×D₁₃	—	4	16	no	—
143	C₂³×D₁₃	C₂⁴	1	4	yes	—
144	C₂³×D₁₃	C₂⁴	1	16	yes	complemented
145	C₂×D₄×C₁₃	—	2	32	no	—
146	C₂×D₄×C₁₃	—	2	64	no	—
147	C₂×D₄×C₁₃	—	2	256	no	—
148	C₂×D₄×C₁₃	—	2	16	no	—
149	C₂×D₄×C₁₃	—	2	32	no	—
150	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	complemented
151	C₂×D₄×C₁₃	C₂×D₄	1	64	yes	complemented
152	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	16	no	—
157	C₂²×C₄×C₁₃	—	2	32	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂×C₂²⋊D₁₃	—	2	16	no	—
165	C₂×C₂²⋊D₁₃	—	2	32	no	—
166	C₂×C₂²⋊D₁₃	—	2	128	no	—
167	C₂×C₂²⋊D₁₃	—	2	32	no	—
168	C₂×C₂²⋊D₁₃	—	4	32	no	—
169	C₂×C₂²⋊D₁₃	—	4	128	no	—
170	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
171	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
172	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
173	C₂×C₂²⋊D₁₃	C₂⁴	1	64	yes	complemented
174	C₂²×Dic₁₃	—	2	16	no	—
175	C₂²×Dic₁₃	—	4	16	no	—
176	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
177	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
178	C₂²×Dic₁₃	C₂⁴	1	16	yes	complemented
179	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
180	#6129	—	2	128	no	—
181	D₄×D₁₃	—	2	128	no	—
182	#6127	—	2	64	no	—
183	C₂×D₅₂	—	2	8	no	—
184	C₂×D₅₂	C₂⁴	1	8	yes	complemented
185	C₂×C₄×D₁₃	—	2	16	no	—
186	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
187	C₂×Dic₂₆	—	2	8	no	—
188	C₂×Dic₂₆	C₂⁴	1	8	yes	complemented
189	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
190	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
191	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
192	C₂²⋊Dic₁₃	C₂⁴	1	64	yes	complemented
193	#6103	C₂⁴	1	32	yes	complemented
194	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
195	#6101	C₂⁴	1	32	yes	complemented
196	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
197	C₂²×H(5,𝔽₂)	—	13	1	no	—
198	C₂⁴×D₄	D₁₃	1	1	yes	characteristic, complemented
199	#3484	—	13	32	no	—
200	C₂×#546	—	13	8	no	—
201	C₂×D₄²	—	13	8	no	—
202	C₂×#535	—	13	2	no	—
203	C₂×#534	—	13	4	no	—
204	C₂×#525	—	13	2	no	—
205	C₂²×#120	—	13	4	no	—
206	C₂×#518	—	13	1	no	—
207	C₂³×C₁₃	—	2	32	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	16	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	16	no	—
214	C₂³×C₁₃	—	2	64	no	—
215	C₂³×C₁₃	—	2	16	no	—
216	C₂³×C₁₃	—	2	8	no	—
217	C₂³×C₁₃	—	2	16	no	—
218	C₂³×C₁₃	—	2	64	no	—
219	C₂³×C₁₃	—	4	32	no	—
220	C₂³×C₁₃	—	4	16	no	—
221	C₂³×C₁₃	—	4	32	no	—
222	C₂³×C₁₃	—	4	16	no	—
223	C₂³×C₁₃	—	4	128	no	—
224	C₂³×C₁₃	—	4	256	no	—
225	C₂³×C₁₃	—	4	32	no	—
226	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
227	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
228	C₂³×C₁₃	C₂²×D₄	1	32	yes	complemented
229	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	complemented
230	C₂³×C₁₃	C₂⁵	1	8	yes	—
231	C₂³×C₁₃	C₂⁵	1	2	yes	—
232	C₂³×C₁₃	C₂⁵	1	8	yes	—
233	C₂³×C₁₃	C₂⁵	1	4	yes	—
234	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
235	C₂²×D₁₃	—	2	8	no	—
236	C₂²×D₁₃	—	2	16	no	—
237	C₂²×D₁₃	—	2	32	no	—
238	C₂²×D₁₃	—	4	32	no	—
239	C₂²×D₁₃	—	8	32	no	—
240	C₂²×D₁₃	C₂⁵	1	8	yes	—
241	D₄×C₁₃	—	2	64	no	—
242	D₄×C₁₃	—	2	32	no	—
243	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	32	no	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	complemented
249	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
250	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
251	C₂²⋊D₁₃	—	2	32	no	—
252	C₂²⋊D₁₃	—	2	64	no	—
253	C₂²⋊D₁₃	—	2	64	no	—
254	C₂²⋊D₁₃	—	4	64	no	—
255	C₂×Dic₁₃	—	2	8	no	—
256	C₂×Dic₁₃	—	2	32	no	—
257	C₂×Dic₁₃	—	2	16	no	—
258	C₂×Dic₁₃	—	4	32	no	—
259	C₂×Dic₁₃	C₂⁵	1	16	yes	—
260	C₂×Dic₁₃	C₂⁵	1	8	yes	—
261	D₅₂	—	2	16	no	—
262	C₄×D₁₃	—	2	32	no	—
263	Dic₂₆	—	2	16	no	—
264	C₂⁶	C₂×D₁₃	1	2	yes	complemented
265	C₂×H(5,𝔽₂)	—	13	16	no	—
266	C₂×H(5,𝔽₂)	—	26	16	no	—
267	C₂²×#41	—	13	4	no	—
268	C₂²×#41	—	13	2	no	—
269	C₂³×D₄	—	2	16	no	—
270	C₂³×D₄	—	13	4	no	—
271	C₂³×D₄	—	13	8	no	—
272	C₂³×D₄	—	13	4	no	—
273	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
274	C₂³×D₄	C₂×D₁₃	1	2	yes	complemented
275	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
276	C₂³×D₄	C₂×D₁₃	1	8	yes	complemented
277	C₂³×D₄	C₂×D₁₃	1	16	yes	complemented
278	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
279	#546	—	13	128	no	—
280	D₄²	—	13	128	no	—
281	#535	—	13	32	no	—
282	#534	—	13	64	no	—
283	C₂×#127	—	13	4	no	—
284	C₂×#124	—	13	4	no	—
285	#525	—	13	32	no	—
286	C₂×#123	—	13	8	no	—
287	C₂×#123	—	13	4	no	—
288	C₂×C₂²⋊Q₈	—	13	4	no	—
289	C₂×#121	—	13	8	no	—
290	C₂×#121	—	13	16	no	—
291	C₂×#121	—	13	4	no	—
292	C₂×#120	—	13	4	no	—
293	C₂×#120	—	13	8	no	—
294	C₂×#120	—	13	16	no	—
295	C₂×#120	—	13	64	no	—
296	C₂×#120	—	13	8	no	—
297	#518	—	13	16	no	—
298	C₂×C₄×D₄	—	13	8	no	—
299	C₂×C₄×D₄	—	13	8	no	—
300	C₂×#117	—	13	2	no	—
301	C₂²×C₂²⋊C₄	—	13	4	no	—
302	C₂²×C₂²⋊C₄	—	13	8	no	—
303	C₂²×C₁₃	—	2	32	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	16	no	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	32	no	—
309	C₂²×C₁₃	—	2	8	no	—
310	C₂²×C₁₃	—	2	16	no	—
311	C₂²×C₁₃	—	2	8	no	—
312	C₂²×C₁₃	—	2	16	no	—
313	C₂²×C₁₃	—	4	32	no	—
314	C₂²×C₁₃	—	4	128	no	—
315	C₂²×C₁₃	—	4	32	no	—
316	C₂²×C₁₃	—	4	16	no	—
317	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
318	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
319	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
320	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
321	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
322	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
323	C₂×D₁₃	—	2	8	no	—
324	C₂×D₁₃	—	2	16	no	—
325	C₂×D₁₃	—	4	16	no	—
326	C₂×D₁₃	—	8	32	no	—
327	C₄×C₁₃	—	2	4	no	—
328	C₄×C₁₃	C₂³×D₄	1	8	yes	—
329	Dic₁₃	—	2	8	no	—
330	Dic₁₃	—	2	16	no	—
331	C₂⁵	—	2	16	no	—
332	C₂⁵	—	4	16	no	—
333	C₂⁵	—	13	4	no	—
334	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
335	C₂⁵	C₂²×D₁₃	1	8	yes	—
336	C₂⁵	C₂²×D₁₃	1	2	yes	—
337	C₂⁵	C₂²×D₁₃	1	2	yes	—
338	C₂⁵	C₂²×D₁₃	1	16	yes	complemented
339	H(5,𝔽₂)	—	26	128	no	—
340	C₂×#41	—	13	32	no	—
341	C₂×#41	—	13	16	no	—
342	C₂×#41	—	26	32	no	—
343	C₂×#41	—	26	16	no	—
344	C₂²×Q₈	—	13	2	no	—
345	C₂²×D₄	—	2	16	no	—
346	C₂²×D₄	—	2	64	no	—
347	C₂²×D₄	—	2	128	no	—
348	C₂²×D₄	—	2	8	no	—
349	C₂²×D₄	—	13	8	no	—
350	C₂²×D₄	—	13	4	no	—
351	C₂²×D₄	—	13	8	no	—
352	C₂²×D₄	—	13	32	no	—
353	C₂²×D₄	—	13	16	no	—
354	C₂²×D₄	—	13	64	no	—
355	C₂²×D₄	—	13	32	no	—
356	C₂²×D₄	—	13	2	no	—
357	C₂²×D₄	—	26	32	no	—
358	C₂²×D₄	—	26	32	no	—
359	C₂²×D₄	—	52	32	no	—
360	C₂²×D₄	C₂²⋊D₁₃	1	16	yes	complemented
361	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
362	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
363	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
364	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
365	C₂²×D₄	C₂²×D₁₃	1	16	yes	complemented
366	C₂²×D₄	C₂²×D₁₃	1	8	yes	complemented
367	C₂²×D₄	C₂²×D₁₃	1	64	yes	complemented
368	C₂³×C₄	—	2	8	no	—
369	C₂³×C₄	—	13	4	no	—
370	C₂³×C₄	—	13	8	no	—
371	C₂³×C₄	—	13	4	no	—
372	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
373	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
376	#127	—	13	32	no	—
377	#124	—	13	32	no	—
378	#123	—	13	64	no	—
379	#123	—	13	32	no	—
380	C₂²⋊Q₈	—	13	32	no	—
381	#121	—	13	128	no	—
382	#121	—	13	64	no	—
383	#121	—	13	32	no	—
384	#120	—	13	32	no	—
385	#120	—	13	64	no	—
386	#120	—	13	128	no	—
387	#120	—	13	64	no	—
388	C₄×D₄	—	13	64	no	—
389	C₄×D₄	—	13	64	no	—
390	#117	—	13	16	no	—
391	C₂×C₄⋊C₄	—	13	4	no	—
392	C₂×C₄⋊C₄	—	13	8	no	—
393	C₂×C₂²⋊C₄	—	13	4	no	—
394	C₂×C₂²⋊C₄	—	13	8	no	—
395	C₂×C₂²⋊C₄	—	13	8	no	—
396	C₂×C₂²⋊C₄	—	13	32	no	—
397	C₂×C₂²⋊C₄	—	13	16	no	—
398	C₂×C₂²⋊C₄	—	13	64	no	—
399	C₂×C₂²⋊C₄	—	13	8	no	—
400	C₂×C₄²	—	13	4	no	—
401	C₂×C₁₃	—	2	16	no	—
402	C₂×C₁₃	—	2	4	no	—
403	C₂×C₁₃	—	2	8	no	—
404	C₂×C₁₃	—	4	8	no	—
405	C₂×C₁₃	#3484	1	4	yes	complemented
406	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
407	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
408	D₁₃	—	4	8	no	—
409	C₂⁴	—	2	8	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	32	no	—
412	C₂⁴	—	2	32	no	—
413	C₂⁴	—	2	8	no	—
414	C₂⁴	—	2	64	no	—
415	C₂⁴	—	4	8	no	—
416	C₂⁴	—	4	16	no	—
417	C₂⁴	—	4	8	no	—
418	C₂⁴	—	4	64	no	—
419	C₂⁴	—	4	128	no	—
420	C₂⁴	—	13	4	no	—
421	C₂⁴	—	13	16	no	—
422	C₂⁴	—	26	16	no	—
423	C₂⁴	—	52	16	no	—
424	C₂⁴	C₂×C₂²⋊D₁₃	1	16	yes	complemented
425	C₂⁴	C₂³×D₁₃	1	4	yes	—
426	C₂⁴	C₂³×D₁₃	1	4	yes	—
427	C₂⁴	C₂³×D₁₃	1	32	yes	—
428	C₂⁴	C₂³×D₁₃	1	2	yes	—
429	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
430	C₂⁴	C₂³×D₁₃	1	4	yes	—
431	C₂⁴	C₂³×D₁₃	1	8	yes	—
432	C₂⁴	C₂³×D₁₃	1	8	yes	—
433	#41	—	26	128	no	—
434	#41	—	26	64	no	—
435	C₂×Q₈	—	13	8	no	—
436	C₂×Q₈	—	26	8	no	—
437	C₂×D₄	—	2	32	no	—
438	C₂×D₄	—	2	64	no	—
439	C₂×D₄	—	2	256	no	—
440	C₂×D₄	—	2	16	no	—
441	C₂×D₄	—	2	32	no	—
442	C₂×D₄	—	13	32	no	—
443	C₂×D₄	—	13	16	no	—
444	C₂×D₄	—	13	32	no	—
445	C₂×D₄	—	13	64	no	—
446	C₂×D₄	—	13	8	no	—
447	C₂×D₄	—	26	32	no	—
448	C₂×D₄	—	26	16	no	—
449	C₂×D₄	—	26	32	no	—
450	C₂×D₄	—	26	128	no	—
451	C₂×D₄	—	26	128	no	—
452	C₂×D₄	—	26	8	no	—
453	C₂×D₄	—	52	32	no	—
454	C₂×D₄	—	52	128	no	—
455	C₂×D₄	C₂×C₂²⋊D₁₃	1	32	yes	complemented
456	C₂×D₄	C₂×C₂²⋊D₁₃	1	64	yes	complemented
457	C₂×D₄	C₂³×D₁₃	1	32	yes	—
458	C₂×D₄	C₂³×D₁₃	1	16	yes	—
459	C₂×D₄	C₂³×D₁₃	1	16	yes	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	16	no	—
462	C₂²×C₄	—	2	32	no	—
463	C₂²×C₄	—	13	16	no	—
464	C₂²×C₄	—	13	8	no	—
465	C₂²×C₄	—	13	4	no	—
466	C₂²×C₄	—	13	32	no	—
467	C₂²×C₄	—	13	16	no	—
468	C₂²×C₄	—	26	16	no	—
469	C₂²×C₄	—	26	16	no	—
470	C₂²×C₄	—	52	16	no	—
471	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	complemented
472	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
473	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
474	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
475	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
476	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
477	C₄⋊C₄	—	13	16	no	—
478	C₄⋊C₄	—	13	32	no	—
479	C₂²⋊C₄	—	13	16	no	—
480	C₂²⋊C₄	—	13	32	no	—
481	C₂²⋊C₄	—	13	32	no	—
482	C₂²⋊C₄	—	13	64	no	—
483	C₂²⋊C₄	—	13	32	no	—
484	C₄²	—	13	16	no	—
485	C₁₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
486	C₂³	—	2	32	no	—
487	C₂³	—	2	16	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	16	no	—
491	C₂³	—	2	8	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	16	no	—
494	C₂³	—	2	64	no	—
495	C₂³	—	2	64	no	—
496	C₂³	—	2	16	no	—
497	C₂³	—	2	8	no	—
498	C₂³	—	4	32	no	—
499	C₂³	—	4	16	no	—
500	C₂³	—	4	32	no	—
501	C₂³	—	4	16	no	—
502	C₂³	—	4	128	no	—
503	C₂³	—	4	256	no	—
504	C₂³	—	4	32	no	—
505	C₂³	—	13	8	no	—
506	C₂³	—	26	16	no	—
507	C₂³	—	26	8	no	—
508	C₂³	—	26	32	no	—
509	C₂³	—	52	32	no	—
510	C₂³	—	104	32	no	—
511	C₂³	#88251	1	8	yes	complemented
512	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
513	C₂³	C₂²×C₂²⋊D₁₃	1	16	yes	—
514	C₂³	C₂²×C₂²⋊D₁₃	1	32	yes	complemented
515	C₂³	C₂⁴×D₁₃	1	8	yes	—
516	C₂³	C₂⁴×D₁₃	1	4	yes	—
517	C₂³	C₂⁴×D₁₃	1	2	yes	—
518	C₂³	C₂⁴×D₁₃	1	8	yes	—
519	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
520	Q₈	—	26	16	no	—
521	D₄	—	2	64	no	—
522	D₄	—	2	32	no	—
523	D₄	—	26	64	no	—
524	D₄	—	26	32	no	—
525	D₄	—	26	64	no	—
526	D₄	—	26	16	no	—
527	D₄	—	52	64	no	—
528	D₄	C₂²×C₂²⋊D₁₃	1	64	yes	complemented
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	32	no	—
532	C₂×C₄	—	13	16	no	—
533	C₂×C₄	—	13	8	no	—
534	C₂×C₄	—	26	16	no	—
535	C₂×C₄	—	26	8	no	—
536	C₂×C₄	—	26	32	no	—
537	C₂×C₄	—	26	32	no	—
538	C₂×C₄	—	52	32	no	—
539	C₂×C₄	C₂²×C₂²⋊D₁₃	1	8	yes	—
540	C₂×C₄	C₂²×C₂²⋊D₁₃	1	16	yes	complemented
541	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
542	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
543	C₂²	—	2	32	no	—
544	C₂²	—	2	16	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	2	32	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	16	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	16	no	—
553	C₂²	—	4	32	no	—
554	C₂²	—	4	128	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	26	8	no	—
558	C₂²	—	26	16	no	—
559	C₂²	—	52	16	no	—
560	C₂²	—	104	32	no	—
561	C₂²	C₂×#88251	1	4	yes	—
562	C₂²	C₂×#88251	1	8	yes	complemented
563	C₂²	C₂³×C₂²⋊D₁₃	1	4	yes	—
564	C₂²	C₂³×C₂²⋊D₁₃	1	16	yes	—
565	C₂²	C₂³×C₂²⋊D₁₃	1	2	yes	—
566	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
567	C₄	—	2	4	no	—
568	C₄	—	26	8	no	—
569	C₄	—	26	16	no	—
570	C₄	C₂³×C₂²⋊D₁₃	1	8	yes	—
571	C₂	—	2	8	no	—
572	C₂	—	2	4	no	—
573	C₂	—	2	16	no	—
574	C₂	—	4	8	no	—
575	C₂	—	52	8	no	—
576	C₂	#13128471	1	4	yes	direct product factor
577	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
578	C₂	C₂²×#88251	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂⁴×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂⁴×D₄	D₁₃
hypocenter	C₁₃	C₂×#3484
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#88251	C₂	semidirect
2. #13128471	C₂	direct (N × H)
3. C₂×#11719511	C₂	semidirect
4. C₂×D₄×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#11719510	C₂	semidirect
6. C₂×#11719509	C₂	semidirect
7. C₂×#11719496	C₂	semidirect
8. C₂²×#88207	C₂	semidirect
9. C₂×#11719503	C₂	semidirect
10. C₂⁴×D₄×C₁₃	C₂	semidirect
11. C₂⁶×C₁₃	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂⁴×C₄×C₁₃	C₂²	semidirect
19. C₂³×C₂²⋊D₁₃	C₂²	semidirect
20. C₂³×C₂²⋊D₁₃	C₂²	semidirect
22. C₂×#88251	C₂²	semidirect
23. C₂²×#6129	C₂²	semidirect
24. C₂²×D₄×D₁₃	C₂²	semidirect
25. C₂²×#6127	C₂²	semidirect
26. C₂×#88207	C₂²	semidirect
27. C₂×#88207	C₂²	semidirect
28. C₂×#88207	C₂²	semidirect
29. C₂×#88207	C₂²	semidirect
30. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
31. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
32. #11719511	C₂²	semidirect
33. #11719510	C₂²	semidirect
34. #11719509	C₂²	semidirect
35. C₂×#88194	C₂²	semidirect
36. C₂×#88193	C₂²	semidirect
37. D₄×C₂²⋊D₁₃	C₂²	semidirect
38. C₂×#88192	C₂²	semidirect
39. C₂×#88191	C₂²	semidirect
40. #11719503	C₂²	semidirect
41. C₂×#88190	C₂²	semidirect
42. C₂×#88189	C₂²	semidirect
43. C₂×D₄×Dic₁₃	C₂²	semidirect
44. #11719496	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88183	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
48. C₂×#88180	C₂²	semidirect
49. C₂×#88178	C₂²	semidirect
56. C₂⁵×C₁₃	C₂³	semidirect
57. C₂⁴×D₁₃	C₂³	semidirect
62. C₂²×D₄×C₁₃	D₄	semidirect
67. C₂²×D₄×C₁₃	C₂³	semidirect
68. C₂²×D₄×C₁₃	C₂³	semidirect
69. C₂²×D₄×C₁₃	C₂³	semidirect
74. C₂³×C₄×C₁₃	C₂³	semidirect
79. C₂²×C₂²⋊D₁₃	C₂³	semidirect
80. C₂²×C₂²⋊D₁₃	C₂³	semidirect
81. C₂²×C₂²⋊D₁₃	C₂³	semidirect
82. C₂²×C₂²⋊D₁₃	C₂³	semidirect
83. C₂³×Dic₁₃	C₂³	semidirect
84. C₂³×Dic₁₃	C₂³	semidirect
87. C₂×#6129	C₂³	semidirect
89. C₂×D₄×D₁₃	C₂³	semidirect
91. C₂×#6127	C₂³	semidirect
92. C₂²×D₅₂	C₂³	semidirect
93. C₂²×C₄×D₁₃	C₂³	semidirect
94. C₂²×Dic₂₆	C₂³	semidirect
95. #88207	C₂³	semidirect
96. #88207	C₂³	semidirect
97. #88207	C₂³	semidirect
100. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
101. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
102. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
103. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
104. #88194	C₂³	semidirect
105. #88193	C₂³	semidirect
106. #88192	C₂³	semidirect
107. #88191	C₂³	semidirect
108. #88190	C₂³	semidirect
109. #88189	C₂³	semidirect
110. D₄×Dic₁₃	C₂³	semidirect
111. #88184	C₂³	semidirect
112. #88183	C₂³	semidirect
113. C₄×C₂²⋊D₁₃	C₂³	semidirect
114. C₂×#6103	C₂³	semidirect
115. #88180	C₂³	semidirect
116. C₂×C₄⋊Dic₁₃	C₂³	semidirect
117. #88178	C₂³	semidirect
118. C₂×#6101	C₂³	semidirect
119. C₂×C₄×Dic₁₃	C₂³	semidirect
132. C₂⁴×C₁₃	C₂×D₄	semidirect
144. C₂³×D₁₃	C₂⁴	semidirect
150. C₂×D₄×C₁₃	C₂×D₄	semidirect
151. C₂×D₄×C₁₃	C₂×D₄	semidirect
158. C₂²×C₄×C₁₃	C₂×D₄	semidirect
172. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
173. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
178. C₂²×Dic₁₃	C₂⁴	semidirect
179. C₂²×Dic₁₃	C₂⁴	semidirect
184. C₂×D₅₂	C₂⁴	semidirect
186. C₂×C₄×D₁₃	C₂⁴	semidirect
188. C₂×Dic₂₆	C₂⁴	semidirect
191. C₂²⋊Dic₁₃	C₂⁴	semidirect
192. C₂²⋊Dic₁₃	C₂⁴	semidirect
193. #6103	C₂⁴	semidirect
194. C₄⋊Dic₁₃	C₂⁴	semidirect
195. #6101	C₂⁴	semidirect
196. C₄×Dic₁₃	C₂⁴	semidirect
198. C₂⁴×D₄	D₁₃	semidirect
228. C₂³×C₁₃	C₂²×D₄	semidirect
229. C₂³×C₁₃	H(5,𝔽₂)	semidirect
243. D₄×C₁₃	C₂²×D₄	semidirect
248. C₂×C₄×C₁₃	C₂²×D₄	semidirect
264. C₂⁶	C₂×D₁₃	semidirect
274. C₂³×D₄	C₂×D₁₃	semidirect
275. C₂³×D₄	C₂×D₁₃	semidirect
276. C₂³×D₄	C₂×D₁₃	semidirect
277. C₂³×D₄	C₂×D₁₃	semidirect
278. C₂⁴×C₄	C₂×D₁₃	semidirect
321. C₂²×C₁₃	C₂×H(5,𝔽₂)	semidirect
338. C₂⁵	C₂²×D₁₃	semidirect
360. C₂²×D₄	C₂²⋊D₁₃	semidirect
365. C₂²×D₄	C₂²×D₁₃	semidirect
366. C₂²×D₄	C₂²×D₁₃	semidirect
367. C₂²×D₄	C₂²×D₁₃	semidirect
375. C₂³×C₄	C₂²×D₁₃	semidirect
405. C₂×C₁₃	#3484	semidirect
424. C₂⁴	C₂×C₂²⋊D₁₃	semidirect
455. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
456. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
471. C₂²×C₄	C₂×C₂²⋊D₁₃	semidirect
485. C₁₃	C₂×#3484	semidirect
511. C₂³	#88251	semidirect
514. C₂³	C₂²×C₂²⋊D₁₃	semidirect
528. D₄	C₂²×C₂²⋊D₁₃	semidirect
540. C₂×C₄	C₂²×C₂²⋊D₁₃	semidirect
562. C₂²	C₂×#88251	semidirect
576. C₂	#13128471	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×#88251	2
#13128471	2
C₂×#11719511	2
C₂×D₄×C₂²⋊D₁₃	2
C₂×#11719510	2
C₂×#11719509	2
C₂×#11719496	2
C₂²×#88207	2
C₂×#11719503	2
C₂⁴×D₄×C₁₃	2
C₂×#3484	13

Subgroups — C2×#13128471 #16770802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128471 #16770802