Subgroups — C₂×#13128525 #16770832

Order 3328.

9502 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128525	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719200	C₂	1	8	yes	maximal, complemented
3	C₂×#11719195	C₂	1	8	yes	maximal, complemented
4	C₂×#11719188	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719199	C₂	1	4	yes	maximal, complemented
6	C₂×#11719198	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11719496	C₂	1	4	yes	maximal, complemented
8	C₂²×#88207	C₂	1	2	yes	maximal, complemented
9	C₂×#11719191	C₂	1	2	yes	maximal, complemented
10	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
13	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
14	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
15	C₂²×#6127	C₂²	1	4	yes	complemented
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
21	C₂×#88207	C₂²	1	8	yes	—
22	C₂×#88207	C₂²	1	4	yes	complemented
23	C₂×#88207	C₂²	1	4	yes	complemented
24	C₂×#88207	C₂²	1	32	yes	complemented
25	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
26	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
27	#11719496	C₂²	1	64	yes	complemented
28	C₂×#88184	C₂²	1	4	yes	complemented
29	C₂×#88184	C₂²	1	4	yes	complemented
30	C₂×#88183	C₂²	1	8	yes	complemented
31	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
32	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
33	C₂×#88180	C₂²	1	4	yes	complemented
34	C₂×#88178	C₂²	1	4	yes	complemented
35	C₂×#88178	C₂²	1	4	yes	complemented
36	#11719200	C₂²	1	128	yes	complemented
37	#11719199	C₂²	1	64	yes	complemented
38	#11719198	C₂²	1	16	yes	complemented
39	C₂×#88140	C₂²	1	4	yes	complemented
40	C₂×#88139	C₂²	1	8	yes	complemented
41	#11719195	C₂²	1	128	yes	complemented
42	C₂×#88138	C₂²	1	8	yes	complemented
43	C₂×#88137	C₂²	1	8	yes	complemented
44	C₂×#88136	C₂²	1	4	yes	complemented
45	#11719191	C₂²	1	32	yes	complemented
46	C₂×#88135	C₂²	1	8	yes	complemented
47	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
48	#11719188	C₂²	1	16	yes	complemented
49	C₂×#88133	C₂²	1	8	yes	complemented
50	C₂×#88132	C₂²	1	8	yes	complemented
51	C₂×#88131	C₂²	1	4	yes	complemented
52	C₂⁵×C₁₃	—	2	8	no	—
53	C₂⁵×C₁₃	—	4	8	no	—
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁵×C₁₃	C₂³	1	4	yes	—
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂⁵×C₁₃	C₂³	1	8	yes	—
58	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
59	C₂⁴×D₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	—	4	8	no	—
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
66	C₂²×C₂²⋊D₁₃	—	2	16	no	—
67	C₂²×C₂²⋊D₁₃	—	4	16	no	—
68	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
69	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
70	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
71	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
72	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
73	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
74	C₂³×Dic₁₃	C₂³	1	2	yes	—
75	C₂³×Dic₁₃	C₂³	1	4	yes	—
76	C₂×#6127	—	4	16	no	—
77	C₂×#6127	C₂³	1	32	yes	complemented
78	C₂²×D₅₂	C₂³	1	4	yes	complemented
79	C₂²×C₄×D₁₃	C₂³	1	8	yes	complemented
80	C₂²×Dic₂₆	C₂³	1	4	yes	complemented
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	64	yes	complemented
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
88	#88207	C₂³	1	64	yes	—
89	#88207	C₂³	1	32	yes	complemented
90	#88207	C₂³	1	32	yes	complemented
91	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
93	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
94	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
96	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
97	#88184	C₂³	1	32	yes	complemented
98	#88184	C₂³	1	32	yes	complemented
99	#88183	C₂³	1	64	yes	complemented
100	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
101	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
102	C₂×#6103	C₂³	1	8	yes	complemented
103	C₂×#6103	C₂³	1	8	yes	complemented
104	#88180	C₂³	1	32	yes	complemented
105	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
106	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
107	#88178	C₂³	1	32	yes	complemented
108	#88178	C₂³	1	32	yes	complemented
109	C₂×#6101	C₂³	1	8	yes	complemented
110	C₂×#6101	C₂³	1	8	yes	complemented
111	C₂×C₄×Dic₁₃	C₂³	1	8	yes	complemented
112	#88140	C₂³	1	32	yes	complemented
113	#88139	C₂³	1	64	yes	complemented
114	#88138	C₂³	1	64	yes	complemented
115	#88137	C₂³	1	64	yes	complemented
116	#88136	C₂³	1	32	yes	complemented
117	#88135	C₂³	1	64	yes	complemented
118	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
119	#88133	C₂³	1	64	yes	complemented
120	#88132	C₂³	1	64	yes	complemented
121	#88131	C₂³	1	32	yes	complemented
122	C₂×#3490	—	13	1	no	maximal, Sylow
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	—	2	8	no	—
125	C₂⁴×C₁₃	—	2	16	no	—
126	C₂⁴×C₁₃	—	2	4	no	—
127	C₂⁴×C₁₃	—	2	32	no	—
128	C₂⁴×C₁₃	—	2	16	no	—
129	C₂⁴×C₁₃	—	4	4	no	—
130	C₂⁴×C₁₃	—	4	8	no	—
131	C₂⁴×C₁₃	—	4	32	no	—
132	C₂⁴×C₁₃	—	4	4	no	—
133	C₂⁴×C₁₃	—	4	64	no	—
134	C₂⁴×C₁₃	#41	1	8	yes	complemented
135	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
137	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
138	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
140	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
142	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
143	C₂³×D₁₃	—	2	8	no	—
144	C₂³×D₁₃	—	4	8	no	—
145	C₂³×D₁₃	C₂⁴	1	4	yes	—
146	C₂³×D₁₃	C₂⁴	1	8	yes	—
147	C₂²×C₄×C₁₃	—	2	16	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	—	4	8	no	—
150	C₂²×C₄×C₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₃	—	4	32	no	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
158	C₂×C₂²⋊D₁₃	—	2	16	no	—
159	C₂×C₂²⋊D₁₃	—	2	16	no	—
160	C₂×C₂²⋊D₁₃	—	2	64	no	—
161	C₂×C₂²⋊D₁₃	—	2	32	no	—
162	C₂×C₂²⋊D₁₃	—	4	16	no	—
163	C₂×C₂²⋊D₁₃	—	4	64	no	—
164	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
165	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
166	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
167	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
168	C₂²×Dic₁₃	—	2	8	no	—
169	C₂²×Dic₁₃	—	4	8	no	—
170	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
171	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
172	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
173	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
174	#6127	—	4	64	no	—
175	C₂×D₅₂	—	4	8	no	—
176	C₂×D₅₂	C₂⁴	1	16	yes	complemented
177	C₂×C₄×D₁₃	—	4	16	no	—
178	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
179	C₂×Dic₂₆	—	4	8	no	—
180	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
181	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
182	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
184	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
185	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
186	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
187	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
188	#6103	C₂⁴	1	32	yes	complemented
189	#6103	C₂⁴	1	32	yes	complemented
190	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
191	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
192	#6101	C₂⁴	1	32	yes	complemented
193	#6101	C₂⁴	1	32	yes	complemented
194	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
195	#3490	—	13	32	no	—
196	C₂×#551	—	13	8	no	—
197	C₂×#546	—	13	8	no	—
198	C₂×#543	—	13	1	no	—
199	C₂×#538	—	13	4	no	—
200	C₂×#534	—	13	1	no	—
201	C₂×#525	—	13	4	no	—
202	C₂²×#120	—	13	2	no	—
203	C₂×#518	—	13	2	no	—
204	C₂³×C₂²⋊C₄	D₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	32	no	—
206	C₂³×C₁₃	—	2	8	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	16	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	32	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	2	32	no	—
216	C₂³×C₁₃	—	2	8	no	—
217	C₂³×C₁₃	—	4	16	no	—
218	C₂³×C₁₃	—	4	8	no	—
219	C₂³×C₁₃	—	4	16	no	—
220	C₂³×C₁₃	—	4	8	no	—
221	C₂³×C₁₃	—	4	64	no	—
222	C₂³×C₁₃	—	4	128	no	—
223	C₂³×C₁₃	—	4	16	no	—
224	C₂³×C₁₃	C₂×#41	1	8	yes	—
225	C₂³×C₁₃	C₂×#41	1	4	yes	—
226	C₂³×C₁₃	C₂×#41	1	16	yes	complemented
227	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
228	C₂³×C₁₃	C₂⁵	1	4	yes	—
229	C₂³×C₁₃	C₂⁵	1	2	yes	—
230	C₂³×C₁₃	C₂⁵	1	4	yes	—
231	C₂³×C₁₃	C₂⁵	1	4	yes	—
232	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
233	C₂²×D₁₃	—	2	8	no	—
234	C₂²×D₁₃	—	2	16	no	—
235	C₂²×D₁₃	—	2	16	no	—
236	C₂²×D₁₃	—	4	16	no	—
237	C₂²×D₁₃	—	8	16	no	—
238	C₂²×D₁₃	C₂⁵	1	8	yes	—
239	C₂×C₄×C₁₃	—	2	8	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	32	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	4	16	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
247	C₂²⋊D₁₃	—	2	32	no	—
248	C₂²⋊D₁₃	—	2	32	no	—
249	C₂²⋊D₁₃	—	2	64	no	—
250	C₂²⋊D₁₃	—	4	32	no	—
251	C₂×Dic₁₃	—	2	16	no	—
252	C₂×Dic₁₃	—	2	8	no	—
253	C₂×Dic₁₃	—	2	16	no	—
254	C₂×Dic₁₃	—	4	16	no	—
255	C₂×Dic₁₃	C₂⁵	1	8	yes	—
256	C₂×Dic₁₃	C₂⁵	1	16	yes	—
257	D₅₂	—	4	16	no	—
258	C₄×D₁₃	—	4	32	no	—
259	Dic₂₆	—	4	16	no	—
260	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
261	C₂²×#41	—	13	4	no	—
262	C₂³×D₄	—	13	2	no	—
263	C₂³×D₄	—	13	4	no	—
264	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
265	#551	—	13	128	no	—
266	#546	—	13	128	no	—
267	#543	—	13	16	no	—
268	#538	—	13	64	no	—
269	#534	—	13	16	no	—
270	C₂×#126	—	13	8	no	—
271	C₂×#124	—	13	8	no	—
272	#525	—	13	64	no	—
273	C₂×#123	—	13	8	no	—
274	C₂×#123	—	13	8	no	—
275	C₂×#123	—	13	4	no	—
276	C₂×C₂²⋊Q₈	—	13	4	no	—
277	C₂×C₂²⋊Q₈	—	13	4	no	—
278	C₂×C₂²⋊Q₈	—	13	8	no	—
279	C₂×#121	—	13	4	no	—
280	C₂×#121	—	13	4	no	—
281	C₂×#121	—	13	8	no	—
282	C₂×#120	—	13	4	no	—
283	C₂×#120	—	13	8	no	—
284	C₂×#120	—	13	4	no	—
285	C₂×#120	—	13	32	no	—
286	C₂×#120	—	13	4	no	—
287	#518	—	13	32	no	—
288	C₂×C₄×D₄	—	13	8	no	—
289	C₂×C₄×D₄	—	13	8	no	—
290	C₂×C₄×D₄	—	13	8	no	—
291	C₂×#117	—	13	4	no	—
292	C₂×#117	—	13	4	no	—
293	C₂²×C₂²⋊C₄	—	13	2	no	—
294	C₂²×C₂²⋊C₄	—	13	4	no	—
295	C₂²×C₂²⋊C₄	—	13	4	no	—
296	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
298	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
299	C₂²×C₂²⋊C₄	C₂×D₁₃	1	8	yes	complemented
300	C₂²×C₂²⋊C₄	C₂×D₁₃	1	16	yes	complemented
301	C₂²×C₁₃	—	2	32	no	—
302	C₂²×C₁₃	—	2	4	no	—
303	C₂²×C₁₃	—	2	8	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	16	no	—
307	C₂²×C₁₃	—	2	8	no	—
308	C₂²×C₁₃	—	2	16	no	—
309	C₂²×C₁₃	—	2	4	no	—
310	C₂²×C₁₃	—	2	8	no	—
311	C₂²×C₁₃	—	4	16	no	—
312	C₂²×C₁₃	—	4	64	no	—
313	C₂²×C₁₃	—	4	16	no	—
314	C₂²×C₁₃	—	4	8	no	—
315	C₂²×C₁₃	C₂²×#41	1	8	yes	—
316	C₂²×C₁₃	C₂²×#41	1	4	yes	—
317	C₂²×C₁₃	C₂²×#41	1	2	yes	—
318	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
319	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
320	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
321	C₂×D₁₃	—	2	8	no	—
322	C₂×D₁₃	—	2	16	no	—
323	C₂×D₁₃	—	4	16	no	—
324	C₂×D₁₃	—	8	16	no	—
325	C₄×C₁₃	—	2	8	no	—
326	C₄×C₁₃	—	2	8	no	—
327	Dic₁₃	—	2	8	no	—
328	Dic₁₃	—	2	16	no	—
329	C₂⁵	—	2	8	no	—
330	C₂⁵	—	4	8	no	—
331	C₂⁵	—	13	2	no	—
332	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
333	C₂⁵	C₂²×D₁₃	1	4	yes	—
334	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
335	C₂⁵	C₂²×D₁₃	1	8	yes	—
336	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
337	C₂×#41	—	13	32	no	—
338	C₂×#41	—	52	16	no	—
339	C₂²×Q₈	—	13	4	no	—
340	C₂²×D₄	—	13	4	no	—
341	C₂²×D₄	—	13	4	no	—
342	C₂²×D₄	—	13	8	no	—
343	C₂²×D₄	—	13	16	no	—
344	C₂²×D₄	—	13	8	no	—
345	C₂²×D₄	—	13	32	no	—
346	C₂²×D₄	—	13	4	no	—
347	C₂²×D₄	—	26	16	no	—
348	C₂²×D₄	—	52	16	no	—
349	C₂³×C₄	—	4	8	no	—
350	C₂³×C₄	—	13	2	no	—
351	C₂³×C₄	—	13	4	no	—
352	C₂³×C₄	—	13	8	no	—
353	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
354	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
355	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
356	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
357	C₂³×C₄	C₂²×D₁₃	1	16	yes	complemented
358	#126	—	13	64	no	—
359	#124	—	13	64	no	—
360	#123	—	13	64	no	—
361	#123	—	13	32	no	—
362	#123	—	13	64	no	—
363	C₂²⋊Q₈	—	13	32	no	—
364	C₂²⋊Q₈	—	13	32	no	—
365	C₂²⋊Q₈	—	13	64	no	—
366	#121	—	13	32	no	—
367	#121	—	13	32	no	—
368	#121	—	13	64	no	—
369	#120	—	13	32	no	—
370	#120	—	13	32	no	—
371	#120	—	13	64	no	—
372	#120	—	13	32	no	—
373	C₄×D₄	—	13	64	no	—
374	C₄×D₄	—	13	64	no	—
375	C₄×D₄	—	13	64	no	—
376	#117	—	13	32	no	—
377	#117	—	13	32	no	—
378	C₂×C₄⋊C₄	—	13	8	no	—
379	C₂×C₄⋊C₄	—	13	4	no	—
380	C₂×C₄⋊C₄	—	13	4	no	—
381	C₂×C₄⋊C₄	—	13	8	no	—
382	C₂×C₂²⋊C₄	—	13	4	no	—
383	C₂×C₂²⋊C₄	—	13	8	no	—
384	C₂×C₂²⋊C₄	—	13	4	no	—
385	C₂×C₂²⋊C₄	—	13	16	no	—
386	C₂×C₂²⋊C₄	—	13	8	no	—
387	C₂×C₂²⋊C₄	—	13	32	no	—
388	C₂×C₂²⋊C₄	—	13	8	no	—
389	C₂×C₂²⋊C₄	—	13	8	no	—
390	C₂×C₂²⋊C₄	—	13	32	no	—
391	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	complemented
397	C₂×C₂²⋊C₄	C₂²×D₁₃	1	64	yes	complemented
398	C₂×C₄²	—	13	8	no	—
399	C₂×C₁₃	—	2	8	no	—
400	C₂×C₁₃	—	2	4	no	—
401	C₂×C₁₃	—	2	8	no	—
402	C₂×C₁₃	—	4	4	no	—
403	C₂×C₁₃	#3490	1	4	yes	complemented
404	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
405	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
406	D₁₃	—	4	8	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	8	no	—
409	C₂⁴	—	2	16	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	32	no	—
412	C₂⁴	—	2	16	no	—
413	C₂⁴	—	4	4	no	—
414	C₂⁴	—	4	8	no	—
415	C₂⁴	—	4	32	no	—
416	C₂⁴	—	4	4	no	—
417	C₂⁴	—	4	64	no	—
418	C₂⁴	—	13	4	no	—
419	C₂⁴	—	13	8	no	—
420	C₂⁴	—	26	8	no	—
421	C₂⁴	—	52	8	no	—
422	C₂⁴	#6127	1	8	yes	complemented
423	C₂⁴	C₂³×D₁₃	1	4	yes	—
424	C₂⁴	C₂³×D₁₃	1	2	yes	—
425	C₂⁴	C₂³×D₁₃	1	16	yes	—
426	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
427	C₂⁴	C₂³×D₁₃	1	2	yes	—
428	C₂⁴	C₂³×D₁₃	1	2	yes	—
429	C₂⁴	C₂³×D₁₃	1	4	yes	—
430	C₂⁴	C₂³×D₁₃	1	4	yes	—
431	#41	—	52	64	no	—
432	C₂×Q₈	—	13	16	no	—
433	C₂×Q₈	—	52	8	no	—
434	C₂×D₄	—	13	16	no	—
435	C₂×D₄	—	13	16	no	—
436	C₂×D₄	—	13	32	no	—
437	C₂×D₄	—	13	32	no	—
438	C₂×D₄	—	13	16	no	—
439	C₂×D₄	—	26	16	no	—
440	C₂×D₄	—	26	16	no	—
441	C₂×D₄	—	26	64	no	—
442	C₂×D₄	—	26	32	no	—
443	C₂×D₄	—	52	8	no	—
444	C₂×D₄	—	52	16	no	—
445	C₂×D₄	—	52	64	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	32	no	—
451	C₂²×C₄	—	13	8	no	—
452	C₂²×C₄	—	13	4	no	—
453	C₂²×C₄	—	13	8	no	—
454	C₂²×C₄	—	13	16	no	—
455	C₂²×C₄	—	13	32	no	—
456	C₂²×C₄	—	26	8	no	—
457	C₂²×C₄	—	52	16	no	—
458	C₂²×C₄	—	52	8	no	—
459	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
460	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
461	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
462	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
463	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
464	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
465	C₄⋊C₄	—	13	32	no	—
466	C₄⋊C₄	—	13	16	no	—
467	C₄⋊C₄	—	13	16	no	—
468	C₄⋊C₄	—	13	32	no	—
469	C₂²⋊C₄	—	13	16	no	—
470	C₂²⋊C₄	—	13	32	no	—
471	C₂²⋊C₄	—	13	16	no	—
472	C₂²⋊C₄	—	13	32	no	—
473	C₂²⋊C₄	—	13	32	no	—
474	C₂²⋊C₄	—	13	32	no	—
475	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
476	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
477	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
478	C₄²	—	13	32	no	—
479	C₁₃	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
480	C₂³	—	2	32	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	16	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	32	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	32	no	—
491	C₂³	—	2	8	no	—
492	C₂³	—	4	16	no	—
493	C₂³	—	4	8	no	—
494	C₂³	—	4	16	no	—
495	C₂³	—	4	8	no	—
496	C₂³	—	4	64	no	—
497	C₂³	—	4	128	no	—
498	C₂³	—	4	16	no	—
499	C₂³	—	13	8	no	—
500	C₂³	—	26	8	no	—
501	C₂³	—	26	16	no	—
502	C₂³	—	26	16	no	—
503	C₂³	—	52	16	no	—
504	C₂³	—	104	16	no	—
505	C₂³	C₂×#6127	1	8	yes	—
506	C₂³	C₂×#6127	1	4	yes	—
507	C₂³	C₂×#6127	1	16	yes	complemented
508	C₂³	#88251	1	8	yes	—
509	C₂³	C₂⁴×D₁₃	1	4	yes	—
510	C₂³	C₂⁴×D₁₃	1	2	yes	—
511	C₂³	C₂⁴×D₁₃	1	4	yes	—
512	C₂³	C₂⁴×D₁₃	1	4	yes	—
513	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
514	Q₈	—	52	16	no	—
515	D₄	—	26	32	no	—
516	D₄	—	26	32	no	—
517	D₄	—	26	64	no	—
518	D₄	—	52	16	no	—
519	D₄	—	52	32	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	32	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	16	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	—	13	8	no	—
527	C₂×C₄	—	13	16	no	—
528	C₂×C₄	—	26	16	no	—
529	C₂×C₄	—	26	8	no	—
530	C₂×C₄	—	26	16	no	—
531	C₂×C₄	—	52	32	no	—
532	C₂×C₄	—	52	16	no	—
533	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
534	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
535	C₂²	—	2	32	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	2	16	no	—
538	C₂²	—	2	16	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	8	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	4	16	no	—
546	C₂²	—	4	64	no	—
547	C₂²	—	4	16	no	—
548	C₂²	—	4	8	no	—
549	C₂²	—	26	8	no	—
550	C₂²	—	26	16	no	—
551	C₂²	—	52	16	no	—
552	C₂²	—	104	16	no	—
553	C₂²	C₂²×#6127	1	8	yes	—
554	C₂²	C₂²×#6127	1	4	yes	—
555	C₂²	C₂²×#6127	1	2	yes	—
556	C₂²	C₂×#88251	1	8	yes	—
557	C₂²	C₂×#88251	1	4	yes	—
558	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
559	C₄	—	2	8	no	—
560	C₄	—	2	8	no	—
561	C₄	—	26	8	no	—
562	C₄	—	26	16	no	—
563	C₂	—	2	4	no	—
564	C₂	—	2	8	no	—
565	C₂	—	2	8	no	—
566	C₂	—	4	4	no	—
567	C₂	—	52	8	no	—
568	C₂	#13128525	1	4	yes	direct product factor
569	C₂	C₂³×#6127	1	1	yes	characteristic
570	C₂	C₂²×#88251	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₁₃×C₂²⋊C₄	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂³×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	C₂×#3490
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #13128525	C₂	direct (N × H)
2. C₂×#11719200	C₂	semidirect
3. C₂×#11719195	C₂	semidirect
4. C₂×#11719188	C₂	semidirect
5. C₂×#11719199	C₂	semidirect
6. C₂×#11719198	C₂	semidirect
7. C₂×#11719496	C₂	semidirect
8. C₂²×#88207	C₂	semidirect
9. C₂×#11719191	C₂	semidirect
10. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
12. C₂⁴×C₄×C₁₃	C₂²	semidirect
14. C₂³×C₂²⋊D₁₃	C₂²	semidirect
15. C₂²×#6127	C₂²	semidirect
18. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
19. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
20. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
22. C₂×#88207	C₂²	semidirect
23. C₂×#88207	C₂²	semidirect
24. C₂×#88207	C₂²	semidirect
26. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
27. #11719496	C₂²	semidirect
28. C₂×#88184	C₂²	semidirect
29. C₂×#88184	C₂²	semidirect
30. C₂×#88183	C₂²	semidirect
31. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
32. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
33. C₂×#88180	C₂²	semidirect
34. C₂×#88178	C₂²	semidirect
35. C₂×#88178	C₂²	semidirect
36. #11719200	C₂²	semidirect
37. #11719199	C₂²	semidirect
38. #11719198	C₂²	semidirect
39. C₂×#88140	C₂²	semidirect
40. C₂×#88139	C₂²	semidirect
41. #11719195	C₂²	semidirect
42. C₂×#88138	C₂²	semidirect
43. C₂×#88137	C₂²	semidirect
44. C₂×#88136	C₂²	semidirect
45. #11719191	C₂²	semidirect
46. C₂×#88135	C₂²	semidirect
47. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
48. #11719188	C₂²	semidirect
49. C₂×#88133	C₂²	semidirect
50. C₂×#88132	C₂²	semidirect
51. C₂×#88131	C₂²	semidirect
65. C₂³×C₄×C₁₃	C₂³	semidirect
73. C₂²×C₂²⋊D₁₃	C₂³	semidirect
77. C₂×#6127	C₂³	semidirect
78. C₂²×D₅₂	C₂³	semidirect
79. C₂²×C₄×D₁₃	C₂³	semidirect
80. C₂²×Dic₂₆	C₂³	semidirect
86. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
87. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
89. #88207	C₂³	semidirect
90. #88207	C₂³	semidirect
96. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
97. #88184	C₂³	semidirect
98. #88184	C₂³	semidirect
99. #88183	C₂³	semidirect
100. C₄×C₂²⋊D₁₃	C₂³	semidirect
101. C₄×C₂²⋊D₁₃	C₂³	semidirect
102. C₂×#6103	C₂³	semidirect
103. C₂×#6103	C₂³	semidirect
104. #88180	C₂³	semidirect
105. C₂×C₄⋊Dic₁₃	C₂³	semidirect
106. C₂×C₄⋊Dic₁₃	C₂³	semidirect
107. #88178	C₂³	semidirect
108. #88178	C₂³	semidirect
109. C₂×#6101	C₂³	semidirect
110. C₂×#6101	C₂³	semidirect
111. C₂×C₄×Dic₁₃	C₂³	semidirect
112. #88140	C₂³	semidirect
113. #88139	C₂³	semidirect
114. #88138	C₂³	semidirect
115. #88137	C₂³	semidirect
116. #88136	C₂³	semidirect
117. #88135	C₂³	semidirect
118. C₂²⋊C₄×D₁₃	C₂³	semidirect
119. #88133	C₂³	semidirect
120. #88132	C₂³	semidirect
121. #88131	C₂³	semidirect
134. C₂⁴×C₁₃	#41	semidirect
176. C₂×D₅₂	C₂⁴	semidirect
178. C₂×C₄×D₁₃	C₂⁴	semidirect
180. C₂×Dic₂₆	C₂⁴	semidirect
188. #6103	C₂⁴	semidirect
189. #6103	C₂⁴	semidirect
190. C₄⋊Dic₁₃	C₂⁴	semidirect
191. C₄⋊Dic₁₃	C₂⁴	semidirect
192. #6101	C₂⁴	semidirect
193. #6101	C₂⁴	semidirect
194. C₄×Dic₁₃	C₂⁴	semidirect
204. C₂³×C₂²⋊C₄	D₁₃	semidirect
226. C₂³×C₁₃	C₂×#41	semidirect
264. C₂⁴×C₄	C₂×D₁₃	semidirect
298. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
299. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
300. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
357. C₂³×C₄	C₂²×D₁₃	semidirect
396. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
397. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
403. C₂×C₁₃	#3490	semidirect
422. C₂⁴	#6127	semidirect
479. C₁₃	C₂×#3490	semidirect
507. C₂³	C₂×#6127	semidirect
568. C₂	#13128525	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128525	2
C₂×#11719200	2
C₂×#11719195	2
C₂×#11719188	2
C₂×#11719199	2
C₂×#11719198	2
C₂×#11719496	2
C₂²×#88207	2
C₂×#11719191	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂×#3490	13

Subgroups — C2×#13128525 #16770832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128525 #16770832