Subgroups — C₂×#13128524 #16770831

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	#13128524	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719363	C₂	1	8	yes	maximal, complemented
3	C₂×#11719296	C₂	1	8	yes	maximal, complemented
4	C₂×#11719188	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719322	C₂	1	4	yes	maximal, complemented
6	C₂×#11719311	C₂	1	4	yes	maximal, complemented
7	C₂²×#88191	C₂	1	2	yes	maximal, complemented
8	C₂×#11719503	C₂	1	2	yes	maximal, complemented
9	C₂²×C₂²⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
14	C₂²×#6129	C₂²	1	4	yes	complemented
15	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
16	C₁₃×#534	C₂²	1	16	yes	complemented
17	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
22	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
24	C₂×#88193	C₂²	1	8	yes	complemented
25	C₂×#88192	C₂²	1	4	yes	complemented
26	C₂×#88191	C₂²	1	8	yes	—
27	C₂×#88191	C₂²	1	4	yes	complemented
28	C₂×#88191	C₂²	1	4	yes	complemented
29	C₂×#88191	C₂²	1	32	yes	complemented
30	#11719503	C₂²	1	32	yes	complemented
31	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
32	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
33	C₂²×#6103	C₂²	1	2	yes	complemented
34	C₂²×#6103	C₂²	1	4	yes	complemented
35	C₂×#88180	C₂²	1	4	yes	complemented
36	C₂×#88178	C₂²	1	4	yes	complemented
37	#11719363	C₂²	1	128	yes	complemented
38	#11719322	C₂²	1	64	yes	complemented
39	#11719311	C₂²	1	64	yes	complemented
40	#11719296	C₂²	1	128	yes	complemented
41	C₂×#88152	C₂²	1	8	yes	complemented
42	C₂×#88151	C₂²	1	4	yes	complemented
43	C₂×#88146	C₂²	1	4	yes	complemented
44	C₂×#88140	C₂²	1	8	yes	complemented
45	C₂×#88139	C₂²	1	8	yes	complemented
46	C₂×#88137	C₂²	1	8	yes	complemented
47	C₂×#88135	C₂²	1	8	yes	complemented
48	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
49	C₂×C₂²⋊C₄×D₁₃	C₂²	1	16	yes	complemented
50	#11719188	C₂²	1	16	yes	complemented
51	C₂×#88132	C₂²	1	8	yes	complemented
52	C₂⁵×C₁₃	C₂³	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁴×D₁₃	—	2	8	no	—
55	C₂⁴×D₁₃	—	4	8	no	—
56	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
57	C₂⁴×D₁₃	C₂³	1	4	yes	—
58	C₂⁴×D₁₃	C₂³	1	8	yes	—
59	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	16	no	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₂²⋊D₁₃	—	4	16	no	—
68	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
69	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
70	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
71	C₂³×Dic₁₃	C₂³	1	4	yes	—
72	C₂³×Dic₁₃	C₂³	1	2	yes	—
73	C₂³×Dic₁₃	C₂³	1	8	yes	complemented
74	C₂×#6129	—	4	16	no	—
75	C₂×#6129	C₂³	1	32	yes	complemented
76	C₂²×C₄×D₁₃	—	4	8	no	—
77	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
78	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
79	C₂²×C₄×D₁₃	C₂³	1	16	yes	complemented
80	C₂²×Dic₂₆	C₂³	1	4	yes	complemented
81	C₁₃×#123	C₂³	1	32	yes	complemented
82	C₁₃×#121	C₂³	1	32	yes	complemented
83	C₁₃×#120	C₂³	1	32	yes	complemented
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
88	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
90	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
92	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
94	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	complemented
95	#88193	C₂³	1	64	yes	complemented
96	#88192	C₂³	1	32	yes	complemented
97	#88191	C₂³	1	64	yes	—
98	#88191	C₂³	1	32	yes	complemented
99	#88191	C₂³	1	32	yes	complemented
100	D₄×Dic₁₃	C₂³	1	64	yes	complemented
101	D₄×Dic₁₃	C₂³	1	64	yes	complemented
102	C₂×#6103	C₂³	1	8	yes	—
103	C₂×#6103	C₂³	1	8	yes	—
104	C₂×#6103	C₂³	1	8	yes	—
105	C₂×#6103	C₂³	1	16	yes	complemented
106	C₂×#6103	C₂³	1	32	yes	complemented
107	#88180	C₂³	1	32	yes	complemented
108	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
109	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	complemented
110	#88178	C₂³	1	32	yes	complemented
111	C₂×#6101	C₂³	1	8	yes	complemented
112	C₂×C₄×Dic₁₃	C₂³	1	8	yes	complemented
113	#88152	C₂³	1	64	yes	complemented
114	#88151	C₂³	1	32	yes	complemented
115	#88146	C₂³	1	32	yes	complemented
116	#88140	C₂³	1	64	yes	complemented
117	#88139	C₂³	1	64	yes	complemented
118	#88137	C₂³	1	64	yes	complemented
119	#88135	C₂³	1	64	yes	complemented
120	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
121	#88132	C₂³	1	64	yes	complemented
122	C₂×#3490	—	13	1	no	maximal, Sylow
123	C₂⁴×C₁₃	—	2	8	no	—
124	C₂⁴×C₁₃	—	4	4	no	—
125	C₂⁴×C₁₃	—	4	8	no	—
126	C₂⁴×C₁₃	#41	1	8	yes	complemented
127	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
131	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
132	C₂³×D₁₃	—	2	4	no	—
133	C₂³×D₁₃	—	2	8	no	—
134	C₂³×D₁₃	—	2	16	no	—
135	C₂³×D₁₃	—	2	4	no	—
136	C₂³×D₁₃	—	2	32	no	—
137	C₂³×D₁₃	—	2	16	no	—
138	C₂³×D₁₃	—	4	32	no	—
139	C₂³×D₁₃	—	4	8	no	—
140	C₂³×D₁₃	—	4	4	no	—
141	C₂³×D₁₃	—	4	64	no	—
142	C₂³×D₁₃	C₂⁴	1	2	yes	—
143	C₂³×D₁₃	C₂⁴	1	4	yes	—
144	C₂³×D₁₃	C₂⁴	1	16	yes	—
145	C₂³×D₁₃	C₂⁴	1	2	yes	—
146	C₂³×D₁₃	C₂⁴	1	4	yes	—
147	C₂×D₄×C₁₃	—	2	16	no	—
148	C₂×D₄×C₁₃	—	2	16	no	—
149	C₂×D₄×C₁₃	—	2	64	no	—
150	C₂×D₄×C₁₃	—	4	8	no	—
151	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	16	yes	complemented
154	C₂²×C₄×C₁₃	—	2	8	no	—
155	C₂²×C₄×C₁₃	—	4	4	no	—
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
160	C₂×C₂²⋊D₁₃	—	2	32	no	—
161	C₂×C₂²⋊D₁₃	—	4	16	no	—
162	C₂×C₂²⋊D₁₃	—	4	64	no	—
163	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
164	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
165	C₂²×Dic₁₃	—	4	4	no	—
166	C₂²×Dic₁₃	—	4	16	no	—
167	C₂²×Dic₁₃	—	4	8	no	—
168	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
169	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
170	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
171	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
172	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
173	#6129	—	4	64	no	—
174	C₂×C₄×D₁₃	—	2	16	no	—
175	C₂×C₄×D₁₃	—	4	32	no	—
176	C₂×C₄×D₁₃	—	4	8	no	—
177	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
178	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
179	C₂×Dic₂₆	—	4	8	no	—
180	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
181	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
182	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
184	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
185	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
186	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
187	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
188	#6103	C₂⁴	1	32	yes	—
189	#6103	C₂⁴	1	32	yes	—
190	#6103	C₂⁴	1	32	yes	—
191	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
192	C₄⋊Dic₁₃	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	D₁₃	1	1	yes	characteristic, complemented
201	C₂×#525	—	13	4	no	—
202	C₂²×#120	—	13	2	no	—
203	C₂×#518	—	13	2	no	—
204	C₂³×C₂²⋊C₄	—	13	1	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	8	no	—
207	C₂³×C₁₃	—	2	8	no	—
208	C₂³×C₁₃	—	2	16	no	—
209	C₂³×C₁₃	—	2	16	no	—
210	C₂³×C₁₃	—	4	16	no	—
211	C₂³×C₁₃	—	4	8	no	—
212	C₂³×C₁₃	—	4	16	no	—
213	C₂³×C₁₃	—	8	16	no	—
214	C₂³×C₁₃	C₂×#41	1	8	yes	—
215	C₂³×C₁₃	C₂×#41	1	4	yes	—
216	C₂³×C₁₃	C₂×#41	1	16	yes	complemented
217	C₂³×C₁₃	C₂⁵	1	8	yes	—
218	C₂³×C₁₃	C₂⁵	1	4	yes	—
219	C₂³×C₁₃	C₂⁵	1	2	yes	—
220	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
221	C₂²×D₁₃	—	2	32	no	—
222	C₂²×D₁₃	—	2	8	no	—
223	C₂²×D₁₃	—	2	4	no	—
224	C₂²×D₁₃	—	2	4	no	—
225	C₂²×D₁₃	—	2	16	no	—
226	C₂²×D₁₃	—	2	32	no	—
227	C₂²×D₁₃	—	2	8	no	—
228	C₂²×D₁₃	—	2	4	no	—
229	C₂²×D₁₃	—	2	8	no	—
230	C₂²×D₁₃	—	2	32	no	—
231	C₂²×D₁₃	—	4	16	no	—
232	C₂²×D₁₃	—	4	8	no	—
233	C₂²×D₁₃	—	4	64	no	—
234	C₂²×D₁₃	—	4	128	no	—
235	C₂²×D₁₃	—	4	16	no	—
236	C₂²×D₁₃	H(5,𝔽₂)	1	8	yes	—
237	C₂²×D₁₃	C₂⁵	1	4	yes	—
238	C₂²×D₁₃	C₂⁵	1	4	yes	—
239	D₄×C₁₃	—	2	32	no	—
240	D₄×C₁₃	—	2	32	no	—
241	D₄×C₁₃	—	4	16	no	—
242	C₂×C₄×C₁₃	—	2	16	no	—
243	C₂×C₄×C₁₃	—	2	8	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	4	8	no	—
246	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
248	C₂²⋊D₁₃	—	2	64	no	—
249	C₂²⋊D₁₃	—	4	32	no	—
250	C₂×Dic₁₃	—	2	16	no	—
251	C₂×Dic₁₃	—	2	8	no	—
252	C₂×Dic₁₃	—	4	8	no	—
253	C₂×Dic₁₃	—	4	32	no	—
254	C₂×Dic₁₃	—	4	16	no	—
255	C₂×Dic₁₃	C₂⁵	1	8	yes	—
256	C₂×Dic₁₃	C₂⁵	1	16	yes	—
257	C₄×D₁₃	—	2	32	no	—
258	C₄×D₁₃	—	4	16	no	—
259	Dic₂₆	—	4	16	no	—
260	C₂⁶	—	13	1	no	—
261	C₂²×#41	—	13	4	no	—
262	C₂³×D₄	—	13	4	no	—
263	C₂³×D₄	C₂×D₁₃	1	2	yes	—
264	C₂⁴×C₄	—	13	2	no	—
265	#551	—	13	128	no	—
266	#546	—	13	128	no	—
267	#543	—	13	16	no	—
268	#538	—	13	64	no	—
269	#534	C₂×D₁₃	1	16	yes	complemented
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	C₂×D₁₃	1	4	yes	complemented
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	8	no	—
281	C₂×#121	C₂×D₁₃	1	4	yes	complemented
282	C₂×#120	—	13	8	no	—
283	C₂×#120	—	13	4	no	—
284	C₂×#120	—	13	4	no	—
285	C₂×#120	—	13	32	no	—
286	C₂×#120	C₂×D₁₃	1	4	yes	complemented
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	1	no	—
294	C₂²×C₂²⋊C₄	—	13	2	no	—
295	C₂²×C₂²⋊C₄	—	13	4	no	—
296	C₂²×C₂²⋊C₄	—	13	2	no	—
297	C₂²×C₂²⋊C₄	—	13	4	no	—
298	C₂²×C₂²⋊C₄	—	13	8	no	—
299	C₂²×C₂²⋊C₄	—	13	16	no	—
300	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
301	C₂²×C₁₃	—	2	4	no	—
302	C₂²×C₁₃	—	2	8	no	—
303	C₂²×C₁₃	—	2	8	no	—
304	C₂²×C₁₃	—	2	16	no	—
305	C₂²×C₁₃	—	2	8	no	—
306	C₂²×C₁₃	—	2	16	no	—
307	C₂²×C₁₃	—	4	16	no	—
308	C₂²×C₁₃	—	4	16	no	—
309	C₂²×C₁₃	—	8	16	no	—
310	C₂²×C₁₃	C₂²×#41	1	8	yes	—
311	C₂²×C₁₃	C₂²×#41	1	4	yes	—
312	C₂²×C₁₃	C₂²×#41	1	2	yes	—
313	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
314	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
315	C₂×D₁₃	—	2	32	no	—
316	C₂×D₁₃	—	2	4	no	—
317	C₂×D₁₃	—	2	4	no	—
318	C₂×D₁₃	—	2	16	no	—
319	C₂×D₁₃	—	2	4	no	—
320	C₂×D₁₃	—	2	8	no	—
321	C₂×D₁₃	—	4	64	no	—
322	C₂×D₁₃	—	4	16	no	—
323	C₂×D₁₃	—	4	8	no	—
324	C₂×D₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
325	C₄×C₁₃	—	2	8	no	—
326	C₄×C₁₃	—	2	8	no	—
327	Dic₁₃	—	2	16	no	—
328	Dic₁₃	—	2	8	no	—
329	C₂⁵	—	13	1	no	—
330	C₂⁵	—	13	4	no	—
331	C₂⁵	—	13	8	no	—
332	C₂⁵	—	13	1	no	—
333	C₂⁵	—	26	8	no	—
334	C₂⁵	—	52	8	no	—
335	C₂⁵	C₂²×D₁₃	1	2	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	—	2	16	no	—
341	C₂²×D₄	—	13	8	no	—
342	C₂²×D₄	—	13	8	no	—
343	C₂²×D₄	—	13	32	no	—
344	C₂²×D₄	—	52	16	no	—
345	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
346	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
347	C₂²×D₄	C₂²×D₁₃	1	16	yes	—
348	C₂²×D₄	C₂²×D₁₃	1	4	yes	complemented
349	C₂³×C₄	—	13	2	no	—
350	C₂³×C₄	—	13	4	no	—
351	C₂³×C₄	—	13	8	no	—
352	C₂³×C₄	—	13	4	no	—
353	C₂³×C₄	—	13	4	no	—
354	C₂³×C₄	—	13	16	no	—
355	C₂³×C₄	—	52	8	no	—
356	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
357	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
358	#126	—	13	64	no	—
359	#124	—	13	64	no	—
360	#123	—	13	64	no	—
361	#123	—	13	64	no	—
362	#123	C₂²×D₁₃	1	32	yes	complemented
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	64	no	—
368	#121	C₂²×D₁₃	1	32	yes	complemented
369	#120	—	13	32	no	—
370	#120	—	13	32	no	—
371	#120	—	13	64	no	—
372	#120	C₂²×D₁₃	1	32	yes	complemented
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	8	no	—
381	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
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	4	no	—
386	C₂×C₂²⋊C₄	—	13	8	no	—
387	C₂×C₂²⋊C₄	—	13	16	no	—
388	C₂×C₂²⋊C₄	—	13	32	no	—
389	C₂×C₂²⋊C₄	—	13	8	no	—
390	C₂×C₂²⋊C₄	—	13	16	no	—
391	C₂×C₂²⋊C₄	—	13	8	no	—
392	C₂×C₂²⋊C₄	—	13	8	no	—
393	C₂×C₂²⋊C₄	—	13	32	no	—
394	C₂×C₂²⋊C₄	—	13	64	no	—
395	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
397	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	complemented
398	C₂×C₄²	—	13	8	no	—
399	C₂×C₁₃	—	2	4	no	—
400	C₂×C₁₃	—	2	8	no	—
401	C₂×C₁₃	—	4	8	no	—
402	C₂×C₁₃	#3490	1	4	yes	complemented
403	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
404	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
405	D₁₃	—	2	8	no	—
406	D₁₃	—	4	4	no	—
407	C₂⁴	—	2	8	no	—
408	C₂⁴	—	4	4	no	—
409	C₂⁴	—	4	8	no	—
410	C₂⁴	—	13	2	no	—
411	C₂⁴	—	13	4	no	—
412	C₂⁴	—	13	2	no	—
413	C₂⁴	—	13	16	no	—
414	C₂⁴	—	13	4	no	—
415	C₂⁴	—	26	8	no	—
416	C₂⁴	—	26	16	no	—
417	C₂⁴	—	26	4	no	—
418	C₂⁴	—	26	16	no	—
419	C₂⁴	—	26	4	no	—
420	C₂⁴	—	26	32	no	—
421	C₂⁴	—	52	4	no	—
422	C₂⁴	—	52	8	no	—
423	C₂⁴	—	52	32	no	—
424	C₂⁴	—	52	64	no	—
425	C₂⁴	#6129	1	8	yes	complemented
426	C₂⁴	C₂³×D₁₃	1	4	yes	—
427	C₂⁴	C₂³×D₁₃	1	2	yes	—
428	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
429	C₂⁴	C₂³×D₁₃	1	8	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	—	2	16	no	—
435	C₂×D₄	—	2	16	no	—
436	C₂×D₄	—	2	64	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	13	32	no	—
439	C₂×D₄	—	13	32	no	—
440	C₂×D₄	—	26	32	no	—
441	C₂×D₄	—	52	16	no	—
442	C₂×D₄	—	52	64	no	—
443	C₂×D₄	C₂³×D₁₃	1	16	yes	—
444	C₂×D₄	C₂³×D₁₃	1	16	yes	—
445	C₂×D₄	C₂³×D₁₃	1	16	yes	complemented
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	13	4	no	—
449	C₂²×C₄	—	13	8	no	—
450	C₂²×C₄	—	13	8	no	—
451	C₂²×C₄	—	13	16	no	—
452	C₂²×C₄	—	13	32	no	—
453	C₂²×C₄	—	13	16	no	—
454	C₂²×C₄	—	13	16	no	—
455	C₂²×C₄	—	26	16	no	—
456	C₂²×C₄	—	52	8	no	—
457	C₂²×C₄	—	52	32	no	—
458	C₂²×C₄	—	52	4	no	—
459	C₂²×C₄	—	52	8	no	—
460	C₂²×C₄	—	52	16	no	—
461	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
462	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
463	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
464	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
465	C₄⋊C₄	—	13	32	no	—
466	C₄⋊C₄	—	13	16	no	—
467	C₄⋊C₄	—	13	32	no	—
468	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
469	C₂²⋊C₄	—	13	16	no	—
470	C₂²⋊C₄	—	13	16	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	—	13	32	no	—
476	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
477	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	complemented
478	C₄²	—	13	32	no	—
479	C₁₃	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
480	C₂³	—	2	4	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	16	no	—
484	C₂³	—	2	16	no	—
485	C₂³	—	4	16	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	16	no	—
488	C₂³	—	8	16	no	—
489	C₂³	—	13	8	no	—
490	C₂³	—	13	4	no	—
491	C₂³	—	13	4	no	—
492	C₂³	—	26	16	no	—
493	C₂³	—	26	32	no	—
494	C₂³	—	26	32	no	—
495	C₂³	—	26	8	no	—
496	C₂³	—	26	4	no	—
497	C₂³	—	26	4	no	—
498	C₂³	—	26	32	no	—
499	C₂³	—	26	8	no	—
500	C₂³	—	26	4	no	—
501	C₂³	—	26	8	no	—
502	C₂³	—	52	8	no	—
503	C₂³	—	52	16	no	—
504	C₂³	—	52	64	no	—
505	C₂³	—	52	16	no	—
506	C₂³	—	52	128	no	—
507	C₂³	C₂×#6129	1	8	yes	—
508	C₂³	C₂×#6129	1	4	yes	—
509	C₂³	C₂×#6129	1	16	yes	complemented
510	C₂³	C₂⁴×D₁₃	1	8	yes	—
511	C₂³	C₂⁴×D₁₃	1	4	yes	—
512	C₂³	C₂⁴×D₁₃	1	2	yes	—
513	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
514	Q₈	—	52	16	no	—
515	D₄	—	2	32	no	—
516	D₄	—	2	32	no	—
517	D₄	—	4	16	no	—
518	D₄	—	26	64	no	—
519	D₄	—	52	32	no	—
520	C₂×C₄	—	2	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	13	8	no	—
525	C₂×C₄	—	13	16	no	—
526	C₂×C₄	—	26	32	no	—
527	C₂×C₄	—	26	8	no	—
528	C₂×C₄	—	26	16	no	—
529	C₂×C₄	—	52	16	no	—
530	C₂×C₄	—	52	8	no	—
531	C₂×C₄	—	52	16	no	—
532	C₂×C₄	—	52	32	no	—
533	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
534	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
535	C₂²	—	2	16	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	2	16	no	—
541	C₂²	—	4	16	no	—
542	C₂²	—	4	16	no	—
543	C₂²	—	8	16	no	—
544	C₂²	—	13	8	no	—
545	C₂²	—	26	32	no	—
546	C₂²	—	26	16	no	—
547	C₂²	—	26	4	no	—
548	C₂²	—	26	4	no	—
549	C₂²	—	26	4	no	—
550	C₂²	—	26	8	no	—
551	C₂²	—	52	64	no	—
552	C₂²	—	52	16	no	—
553	C₂²	—	52	8	no	—
554	C₂²	C₂²×#6129	1	8	yes	—
555	C₂²	C₂²×#6129	1	4	yes	—
556	C₂²	C₂²×#6129	1	2	yes	—
557	C₂²	D₁₃×H(5,𝔽₂)	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	8	no	—
564	C₂	—	2	4	no	—
565	C₂	—	4	8	no	—
566	C₂	—	26	8	no	—
567	C₂	—	52	4	no	—
568	C₂	#13128524	1	4	yes	direct product factor
569	C₂	C₂³×#6129	1	1	yes	characteristic
570	C₂	C₂×D₁₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#534	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#534	D₁₃
hypocenter	C₁₃	C₂×#3490
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#534

Complements

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

N	H ≅ G/N	type
1. #13128524	C₂	direct (N × H)
2. C₂×#11719363	C₂	semidirect
3. C₂×#11719296	C₂	semidirect
4. C₂×#11719188	C₂	semidirect
5. C₂×#11719322	C₂	semidirect
6. C₂×#11719311	C₂	semidirect
7. C₂²×#88191	C₂	semidirect
8. C₂×#11719503	C₂	semidirect
9. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
10. C₂×C₁₃×#534	C₂	semidirect
13. C₂³×C₂²⋊D₁₃	C₂²	semidirect
14. C₂²×#6129	C₂²	semidirect
15. C₂³×C₄×D₁₃	C₂²	semidirect
16. C₁₃×#534	C₂²	semidirect
17. C₂×C₁₃×#123	C₂²	semidirect
18. C₂×C₁₃×#121	C₂²	semidirect
19. C₂×C₁₃×#120	C₂²	semidirect
23. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
24. C₂×#88193	C₂²	semidirect
25. C₂×#88192	C₂²	semidirect
27. C₂×#88191	C₂²	semidirect
28. C₂×#88191	C₂²	semidirect
29. C₂×#88191	C₂²	semidirect
30. #11719503	C₂²	semidirect
31. C₂×D₄×Dic₁₃	C₂²	semidirect
32. C₂×D₄×Dic₁₃	C₂²	semidirect
33. C₂²×#6103	C₂²	semidirect
34. C₂²×#6103	C₂²	semidirect
35. C₂×#88180	C₂²	semidirect
36. C₂×#88178	C₂²	semidirect
37. #11719363	C₂²	semidirect
38. #11719322	C₂²	semidirect
39. #11719311	C₂²	semidirect
40. #11719296	C₂²	semidirect
41. C₂×#88152	C₂²	semidirect
42. C₂×#88151	C₂²	semidirect
43. C₂×#88146	C₂²	semidirect
44. C₂×#88140	C₂²	semidirect
45. C₂×#88139	C₂²	semidirect
46. C₂×#88137	C₂²	semidirect
47. C₂×#88135	C₂²	semidirect
48. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
49. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
50. #11719188	C₂²	semidirect
51. C₂×#88132	C₂²	semidirect
64. C₂²×D₄×C₁₃	C₂³	semidirect
70. C₂²×C₂²⋊D₁₃	C₂³	semidirect
73. C₂³×Dic₁₃	C₂³	semidirect
75. C₂×#6129	C₂³	semidirect
79. C₂²×C₄×D₁₃	C₂³	semidirect
80. C₂²×Dic₂₆	C₂³	semidirect
81. C₁₃×#123	C₂³	semidirect
82. C₁₃×#121	C₂³	semidirect
83. C₁₃×#120	C₂³	semidirect
84. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
87. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
93. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
94. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
95. #88193	C₂³	semidirect
96. #88192	C₂³	semidirect
98. #88191	C₂³	semidirect
99. #88191	C₂³	semidirect
100. D₄×Dic₁₃	C₂³	semidirect
101. D₄×Dic₁₃	C₂³	semidirect
105. C₂×#6103	C₂³	semidirect
106. C₂×#6103	C₂³	semidirect
107. #88180	C₂³	semidirect
108. C₂×C₄⋊Dic₁₃	C₂³	semidirect
109. C₂×C₄⋊Dic₁₃	C₂³	semidirect
110. #88178	C₂³	semidirect
111. C₂×#6101	C₂³	semidirect
112. C₂×C₄×Dic₁₃	C₂³	semidirect
113. #88152	C₂³	semidirect
114. #88151	C₂³	semidirect
115. #88146	C₂³	semidirect
116. #88140	C₂³	semidirect
117. #88139	C₂³	semidirect
118. #88137	C₂³	semidirect
119. #88135	C₂³	semidirect
120. C₂²⋊C₄×D₁₃	C₂³	semidirect
121. #88132	C₂³	semidirect
126. C₂⁴×C₁₃	#41	semidirect
153. C₂×D₄×C₁₃	C₂⁴	semidirect
172. C₂²×Dic₁₃	C₂⁴	semidirect
180. C₂×Dic₂₆	C₂⁴	semidirect
181. C₁₃×C₄⋊C₄	C₂⁴	semidirect
183. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
187. C₂²⋊Dic₁₃	C₂⁴	semidirect
191. C₄⋊Dic₁₃	C₂⁴	semidirect
192. C₄⋊Dic₁₃	C₂⁴	semidirect
193. #6101	C₂⁴	semidirect
194. C₄×Dic₁₃	C₂⁴	semidirect
200. C₂×#534	D₁₃	semidirect
216. C₂³×C₁₃	C₂×#41	semidirect
269. #534	C₂×D₁₃	semidirect
275. C₂×#123	C₂×D₁₃	semidirect
281. C₂×#121	C₂×D₁₃	semidirect
286. C₂×#120	C₂×D₁₃	semidirect
348. C₂²×D₄	C₂²×D₁₃	semidirect
362. #123	C₂²×D₁₃	semidirect
368. #121	C₂²×D₁₃	semidirect
372. #120	C₂²×D₁₃	semidirect
381. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
397. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
402. C₂×C₁₃	#3490	semidirect
425. C₂⁴	#6129	semidirect
445. C₂×D₄	C₂³×D₁₃	semidirect
468. C₄⋊C₄	C₂³×D₁₃	semidirect
477. C₂²⋊C₄	C₂³×D₁₃	semidirect
479. C₁₃	C₂×#3490	semidirect
509. C₂³	C₂×#6129	semidirect
568. C₂	#13128524	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128524	2
C₂×#11719363	2
C₂×#11719296	2
C₂×#11719188	2
C₂×#11719322	2
C₂×#11719311	2
C₂²×#88191	2
C₂×#11719503	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂×C₁₃×#534	2
C₂×#3490	13

Subgroups — C2×#13128524 #16770831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128524 #16770831