Subgroups — C₂×#13128467 #16770799

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	C₂³×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128467	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719534	C₂	1	8	yes	maximal, complemented
4	C₂×D₄×C₂²⋊D₁₃	C₂	1	8	yes	maximal, complemented
5	C₂×#11719535	C₂	1	2	yes	maximal, complemented
6	C₂×#11719509	C₂	1	4	yes	maximal, complemented
7	C₂×#11719533	C₂	1	2	yes	maximal, complemented
8	C₂²×#88191	C₂	1	4	yes	maximal, complemented
9	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	2	yes	complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	16	no	—
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
14	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
15	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
18	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
19	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
20	C₂³×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
21	C₂²×D₄×D₁₃	—	2	16	no	—
22	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
23	C₂²×D₄×D₁₃	C₂²	1	16	yes	complemented
24	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#88207	C₂²	1	8	yes	complemented
27	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
28	#11719535	C₂²	1	32	yes	complemented
29	#11719534	C₂²	1	128	yes	complemented
30	#11719533	C₂²	1	32	yes	complemented
31	C₂×#88201	C₂²	1	4	yes	complemented
32	C₂×#88200	C₂²	1	4	yes	complemented
33	#11719509	C₂²	1	64	yes	complemented
34	C₂×#88194	C₂²	1	4	yes	complemented
35	C₂×#88193	C₂²	1	16	yes	complemented
36	D₄×C₂²⋊D₁₃	C₂²	1	128	yes	complemented
37	C₂×#88192	C₂²	1	4	yes	complemented
38	C₂×#88191	C₂²	1	4	yes	complemented
39	C₂×#88191	C₂²	1	16	yes	complemented
40	C₂×#88191	C₂²	1	8	yes	complemented
41	C₂×#88191	C₂²	1	64	yes	complemented
42	#11719503	C₂²	1	16	yes	complemented
43	C₂×#88189	C₂²	1	4	yes	complemented
44	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
45	C₂×#88184	C₂²	1	8	yes	complemented
46	C₂×#88183	C₂²	1	8	yes	complemented
47	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
48	C₂²×#6103	C₂²	1	8	yes	complemented
49	C₂×#88180	C₂²	1	2	yes	complemented
50	C₂⁵×C₁₃	C₂³	1	2	yes	—
51	C₂⁵×C₁₃	C₂³	1	4	yes	complemented
52	C₂⁴×D₁₃	—	2	16	no	—
53	C₂⁴×D₁₃	—	4	16	no	—
54	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
55	C₂⁴×D₁₃	C₂³	1	8	yes	—
56	C₂⁴×D₁₃	C₂³	1	2	yes	—
57	C₂⁴×D₁₃	C₂³	1	16	yes	complemented
58	C₁₃×H(5,𝔽₂)	—	2	128	no	—
59	C₂×C₁₃×#41	—	2	32	no	—
60	C₂×C₁₃×#41	—	2	16	no	—
61	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
62	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
63	C₂²×Q₈×C₁₃	C₂³	1	2	yes	complemented
64	C₂²×D₄×C₁₃	—	2	32	no	—
65	C₂²×D₄×C₁₃	—	2	32	no	—
66	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	8	yes	complemented
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
72	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
73	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
77	C₂²×C₂²⋊D₁₃	—	2	16	no	—
78	C₂²×C₂²⋊D₁₃	—	4	32	no	—
79	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
80	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
81	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
82	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
83	C₂²×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
84	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₂³×Dic₁₃	C₂³	1	8	yes	complemented
86	C₂×D₄×D₁₃	—	2	64	no	—
87	C₂×D₄×D₁₃	—	2	128	no	—
88	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
89	C₂²×D₅₂	—	2	8	no	—
90	C₂²×D₅₂	C₂³	1	4	yes	—
91	C₂²×D₅₂	C₂³	1	8	yes	complemented
92	C₂²×C₄×D₁₃	—	2	8	no	—
93	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
94	C₂²×C₄×D₁₃	C₂³	1	8	yes	complemented
95	#88207	C₂³	1	64	yes	complemented
96	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
98	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	complemented
99	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	complemented
100	#88201	C₂³	1	32	yes	complemented
101	#88200	C₂³	1	32	yes	complemented
102	#88194	C₂³	1	32	yes	complemented
103	#88193	C₂³	1	128	yes	complemented
104	#88192	C₂³	1	32	yes	complemented
105	#88191	C₂³	1	32	yes	complemented
106	#88191	C₂³	1	128	yes	complemented
107	#88191	C₂³	1	64	yes	complemented
108	#88189	C₂³	1	32	yes	complemented
109	D₄×Dic₁₃	C₂³	1	64	yes	complemented
110	#88184	C₂³	1	64	yes	complemented
111	#88183	C₂³	1	64	yes	complemented
112	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
113	C₂×#6103	C₂³	1	8	yes	—
114	C₂×#6103	C₂³	1	64	yes	complemented
115	C₂×#6103	C₂³	1	16	yes	complemented
116	#88180	C₂³	1	16	yes	complemented
117	C₂×C₄⋊Dic₁₃	C₂³	1	4	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	16	no	—
122	C₂⁴×C₁₃	—	4	8	no	—
123	C₂⁴×C₁₃	—	4	16	no	—
124	C₂⁴×C₁₃	C₂×D₄	1	16	yes	complemented
125	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	16	yes	complemented
130	C₂³×D₁₃	—	2	4	no	—
131	C₂³×D₁₃	—	2	8	no	—
132	C₂³×D₁₃	—	2	8	no	—
133	C₂³×D₁₃	—	2	32	no	—
134	C₂³×D₁₃	—	2	64	no	—
135	C₂³×D₁₃	—	2	32	no	—
136	C₂³×D₁₃	—	4	64	no	—
137	C₂³×D₁₃	—	4	16	no	—
138	C₂³×D₁₃	—	4	8	no	—
139	C₂³×D₁₃	—	4	128	no	—
140	C₂³×D₁₃	C₂⁴	1	4	yes	—
141	C₂³×D₁₃	C₂⁴	1	4	yes	—
142	C₂³×D₁₃	C₂⁴	1	32	yes	—
143	C₂³×D₁₃	C₂⁴	1	2	yes	—
144	C₂³×D₁₃	C₂⁴	1	8	yes	—
145	C₁₃×#41	—	2	128	no	—
146	C₁₃×#41	—	2	64	no	—
147	C₂×Q₈×C₁₃	—	2	8	no	—
148	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	complemented
149	C₂×D₄×C₁₃	—	2	16	no	—
150	C₂×D₄×C₁₃	—	2	32	no	—
151	C₂×D₄×C₁₃	—	2	128	no	—
152	C₂×D₄×C₁₃	—	2	128	no	—
153	C₂×D₄×C₁₃	—	2	8	no	—
154	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	complemented
155	C₂×D₄×C₁₃	C₂×D₄	1	64	yes	complemented
156	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
159	C₂×D₄×C₁₃	C₂⁴	1	8	yes	complemented
160	C₂²×C₄×C₁₃	—	2	16	no	—
161	C₂²×C₄×C₁₃	—	2	16	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
167	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
168	C₂×C₂²⋊D₁₃	—	2	32	no	—
169	C₂×C₂²⋊D₁₃	—	2	64	no	—
170	C₂×C₂²⋊D₁₃	—	2	32	no	—
171	C₂×C₂²⋊D₁₃	—	4	32	no	—
172	C₂×C₂²⋊D₁₃	—	4	128	no	—
173	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
174	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
175	C₂×C₂²⋊D₁₃	C₂⁴	1	64	yes	complemented
176	C₂²×Dic₁₃	—	2	4	no	—
177	C₂²×Dic₁₃	—	4	16	no	—
178	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
179	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
180	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
181	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
182	D₄×D₁₃	—	2	256	no	—
183	C₂×D₅₂	—	2	16	no	—
184	C₂×D₅₂	—	2	32	no	—
185	C₂×D₅₂	C₂⁴	1	16	yes	—
186	C₂×C₄×D₁₃	—	2	16	no	—
187	C₂×C₄×D₁₃	—	2	32	no	—
188	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
189	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
190	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
191	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
192	#6103	C₂⁴	1	32	yes	—
193	#6103	C₂⁴	1	64	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)	D₁₃	1	1	yes	characteristic, complemented
198	C₂⁴×D₄	—	13	1	no	—
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	16	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	8	no	—
210	C₂³×C₁₃	—	2	16	no	—
211	C₂³×C₁₃	—	2	32	no	—
212	C₂³×C₁₃	—	4	32	no	—
213	C₂³×C₁₃	—	4	16	no	—
214	C₂³×C₁₃	—	4	32	no	—
215	C₂³×C₁₃	—	8	32	no	—
216	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
217	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	32	yes	complemented
219	C₂³×C₁₃	C₂⁵	1	8	yes	—
220	C₂³×C₁₃	C₂⁵	1	2	yes	—
221	C₂³×C₁₃	C₂⁵	1	8	yes	—
222	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
223	C₂²×D₁₃	—	2	32	no	—
224	C₂²×D₁₃	—	2	8	no	—
225	C₂²×D₁₃	—	2	4	no	—
226	C₂²×D₁₃	—	2	4	no	—
227	C₂²×D₁₃	—	2	16	no	—
228	C₂²×D₁₃	—	2	16	no	—
229	C₂²×D₁₃	—	2	8	no	—
230	C₂²×D₁₃	—	2	64	no	—
231	C₂²×D₁₃	—	2	16	no	—
232	C₂²×D₁₃	—	2	64	no	—
233	C₂²×D₁₃	—	4	32	no	—
234	C₂²×D₁₃	—	4	16	no	—
235	C₂²×D₁₃	—	4	128	no	—
236	C₂²×D₁₃	—	4	256	no	—
237	C₂²×D₁₃	—	4	32	no	—
238	C₂²×D₁₃	H(5,𝔽₂)	1	8	yes	complemented
239	C₂²×D₁₃	C₂⁵	1	8	yes	—
240	C₂²×D₁₃	C₂⁵	1	4	yes	—
241	Q₈×C₁₃	—	2	16	no	—
242	D₄×C₁₃	—	2	32	no	—
243	D₄×C₁₃	—	2	64	no	—
244	D₄×C₁₃	—	2	16	no	—
245	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	32	no	—
248	C₂×C₄×C₁₃	—	2	32	no	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	complemented
251	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
252	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
253	C₂²⋊D₁₃	—	2	64	no	—
254	C₂²⋊D₁₃	—	2	64	no	—
255	C₂²⋊D₁₃	—	4	64	no	—
256	C₂×Dic₁₃	—	2	8	no	—
257	C₂×Dic₁₃	—	2	4	no	—
258	C₂×Dic₁₃	—	2	16	no	—
259	C₂×Dic₁₃	—	4	32	no	—
260	C₂×Dic₁₃	C₂⁵	1	16	yes	—
261	C₂×Dic₁₃	C₂⁵	1	4	yes	—
262	D₅₂	—	2	32	no	—
263	C₄×D₁₃	—	2	32	no	—
264	C₂⁶	—	13	2	no	—
265	C₂×H(5,𝔽₂)	—	2	16	no	—
266	C₂×H(5,𝔽₂)	C₂×D₁₃	1	16	yes	complemented
267	C₂²×#41	C₂×D₁₃	1	2	yes	complemented
268	C₂²×#41	C₂×D₁₃	1	4	yes	complemented
269	C₂³×D₄	—	13	2	no	—
270	C₂³×D₄	—	13	8	no	—
271	C₂³×D₄	—	13	8	no	—
272	C₂³×D₄	—	13	16	no	—
273	C₂³×D₄	—	13	1	no	—
274	C₂³×D₄	—	26	16	no	—
275	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
276	C₂³×D₄	C₂×D₁₃	1	4	yes	complemented
277	C₂³×D₄	C₂×D₁₃	1	4	yes	complemented
278	C₂⁴×C₄	—	13	1	no	—
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	4	no	—
287	C₂×#123	—	13	8	no	—
288	C₂×C₂²⋊Q₈	—	13	4	no	—
289	C₂×#121	—	13	4	no	—
290	C₂×#121	—	13	16	no	—
291	C₂×#121	—	13	8	no	—
292	C₂×#120	—	13	8	no	—
293	C₂×#120	—	13	4	no	—
294	C₂×#120	—	13	8	no	—
295	C₂×#120	—	13	16	no	—
296	C₂×#120	—	13	64	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	16	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	8	no	—
306	C₂²×C₁₃	—	2	32	no	—
307	C₂²×C₁₃	—	2	8	no	—
308	C₂²×C₁₃	—	2	16	no	—
309	C₂²×C₁₃	—	4	32	no	—
310	C₂²×C₁₃	—	4	16	no	—
311	C₂²×C₁₃	—	8	32	no	—
312	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
313	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
314	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
315	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
316	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
317	C₂×D₁₃	—	2	32	no	—
318	C₂×D₁₃	—	2	4	no	—
319	C₂×D₁₃	—	2	4	no	—
320	C₂×D₁₃	—	2	16	no	—
321	C₂×D₁₃	—	2	8	no	—
322	C₂×D₁₃	—	2	16	no	—
323	C₂×D₁₃	—	4	128	no	—
324	C₂×D₁₃	—	4	32	no	—
325	C₂×D₁₃	—	4	16	no	—
326	C₂×D₁₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
327	C₄×C₁₃	—	2	8	no	—
328	C₄×C₁₃	C₂³×D₄	1	8	yes	—
329	Dic₁₃	—	2	4	no	—
330	Dic₁₃	—	2	16	no	—
331	C₂⁵	—	13	1	no	—
332	C₂⁵	—	13	8	no	—
333	C₂⁵	—	13	2	no	—
334	C₂⁵	—	13	16	no	—
335	C₂⁵	—	26	16	no	—
336	C₂⁵	—	52	16	no	—
337	C₂⁵	C₂²×D₁₃	1	2	yes	—
338	C₂⁵	C₂²×D₁₃	1	4	yes	complemented
339	H(5,𝔽₂)	—	2	128	no	—
340	C₂×#41	—	2	32	no	—
341	C₂×#41	—	2	16	no	—
342	C₂×#41	C₂²×D₁₃	1	16	yes	complemented
343	C₂×#41	C₂²×D₁₃	1	32	yes	complemented
344	C₂²×Q₈	C₂²×D₁₃	1	2	yes	complemented
345	C₂²×D₄	—	2	32	no	—
346	C₂²×D₄	—	2	32	no	—
347	C₂²×D₄	—	13	8	no	—
348	C₂²×D₄	—	13	8	no	—
349	C₂²×D₄	—	13	16	no	—
350	C₂²×D₄	—	13	16	no	—
351	C₂²×D₄	—	13	64	no	—
352	C₂²×D₄	—	13	64	no	—
353	C₂²×D₄	—	13	4	no	—
354	C₂²×D₄	—	13	8	no	—
355	C₂²×D₄	—	26	16	no	—
356	C₂²×D₄	—	26	64	no	—
357	C₂²×D₄	—	26	128	no	—
358	C₂²×D₄	—	26	8	no	—
359	C₂²×D₄	—	52	32	no	—
360	C₂²×D₄	C₂²⋊D₁₃	1	16	yes	complemented
361	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
362	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
363	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
364	C₂²×D₄	C₂²×D₁₃	1	8	yes	complemented
365	C₂²×D₄	C₂²×D₁₃	1	2	yes	complemented
366	C₂²×D₄	C₂²×D₁₃	1	32	yes	complemented
367	C₂²×D₄	C₂²×D₁₃	1	32	yes	complemented
368	C₂³×C₄	—	13	1	no	—
369	C₂³×C₄	—	13	8	no	—
370	C₂³×C₄	—	13	4	no	—
371	C₂³×C₄	—	13	8	no	—
372	C₂³×C₄	—	26	8	no	—
373	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂²×D₁₃	1	4	yes	complemented
375	C₂³×C₄	C₂²×D₁₃	1	4	yes	complemented
376	#127	—	13	32	no	—
377	#124	—	13	32	no	—
378	#123	—	13	32	no	—
379	#123	—	13	64	no	—
380	C₂²⋊Q₈	—	13	32	no	—
381	#121	—	13	32	no	—
382	#121	—	13	128	no	—
383	#121	—	13	64	no	—
384	#120	—	13	64	no	—
385	#120	—	13	32	no	—
386	#120	—	13	64	no	—
387	#120	—	13	128	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	32	no	—
396	C₂×C₂²⋊C₄	—	13	8	no	—
397	C₂×C₂²⋊C₄	—	13	8	no	—
398	C₂×C₂²⋊C₄	—	13	16	no	—
399	C₂×C₂²⋊C₄	—	13	64	no	—
400	C₂×C₄²	—	13	4	no	—
401	C₂×C₁₃	—	2	4	no	—
402	C₂×C₁₃	—	2	16	no	—
403	C₂×C₁₃	—	4	8	no	—
404	C₂×C₁₃	#3484	1	4	yes	complemented
405	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
406	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
407	D₁₃	—	2	8	no	—
408	D₁₃	—	4	8	no	—
409	C₂⁴	—	2	16	no	—
410	C₂⁴	—	4	8	no	—
411	C₂⁴	—	4	16	no	—
412	C₂⁴	—	13	2	no	—
413	C₂⁴	—	13	4	no	—
414	C₂⁴	—	13	4	no	—
415	C₂⁴	—	13	32	no	—
416	C₂⁴	—	13	8	no	—
417	C₂⁴	—	26	8	no	—
418	C₂⁴	—	26	32	no	—
419	C₂⁴	—	26	4	no	—
420	C₂⁴	—	26	32	no	—
421	C₂⁴	—	26	8	no	—
422	C₂⁴	—	26	64	no	—
423	C₂⁴	—	52	16	no	—
424	C₂⁴	—	52	8	no	—
425	C₂⁴	—	52	64	no	—
426	C₂⁴	—	52	128	no	—
427	C₂⁴	C₂×C₂²⋊D₁₃	1	16	yes	complemented
428	C₂⁴	C₂³×D₁₃	1	4	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	16	yes	complemented
433	#41	—	2	128	no	—
434	#41	—	2	64	no	—
435	C₂×Q₈	—	2	8	no	—
436	C₂×Q₈	C₂³×D₁₃	1	8	yes	complemented
437	C₂×D₄	—	2	16	no	—
438	C₂×D₄	—	2	32	no	—
439	C₂×D₄	—	2	128	no	—
440	C₂×D₄	—	2	128	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	13	32	no	—
443	C₂×D₄	—	13	32	no	—
444	C₂×D₄	—	13	64	no	—
445	C₂×D₄	—	13	16	no	—
446	C₂×D₄	—	26	32	no	—
447	C₂×D₄	—	26	32	no	—
448	C₂×D₄	—	26	64	no	—
449	C₂×D₄	—	26	256	no	—
450	C₂×D₄	—	26	16	no	—
451	C₂×D₄	—	26	32	no	—
452	C₂×D₄	—	52	32	no	—
453	C₂×D₄	—	52	128	no	—
454	C₂×D₄	C₂×C₂²⋊D₁₃	1	32	yes	complemented
455	C₂×D₄	C₂×C₂²⋊D₁₃	1	64	yes	complemented
456	C₂×D₄	C₂³×D₁₃	1	16	yes	—
457	C₂×D₄	C₂³×D₁₃	1	16	yes	—
458	C₂×D₄	C₂³×D₁₃	1	32	yes	complemented
459	C₂×D₄	C₂³×D₁₃	1	8	yes	complemented
460	C₂²×C₄	—	2	16	no	—
461	C₂²×C₄	—	2	16	no	—
462	C₂²×C₄	—	13	4	no	—
463	C₂²×C₄	—	13	8	no	—
464	C₂²×C₄	—	13	2	no	—
465	C₂²×C₄	—	13	32	no	—
466	C₂²×C₄	—	13	16	no	—
467	C₂²×C₄	—	26	4	no	—
468	C₂²×C₄	—	26	16	no	—
469	C₂²×C₄	—	26	32	no	—
470	C₂²×C₄	—	52	16	no	—
471	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	complemented
472	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
473	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
474	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
475	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
476	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
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	32	no	—
483	C₂²⋊C₄	—	13	64	no	—
484	C₄²	—	13	16	no	—
485	C₁₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
486	C₂³	—	2	16	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	16	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	32	no	—
491	C₂³	—	4	32	no	—
492	C₂³	—	4	16	no	—
493	C₂³	—	4	32	no	—
494	C₂³	—	8	32	no	—
495	C₂³	—	13	8	no	—
496	C₂³	—	13	4	no	—
497	C₂³	—	13	8	no	—
498	C₂³	—	26	16	no	—
499	C₂³	—	26	64	no	—
500	C₂³	—	26	32	no	—
501	C₂³	—	26	4	no	—
502	C₂³	—	26	8	no	—
503	C₂³	—	26	4	no	—
504	C₂³	—	26	16	no	—
505	C₂³	—	26	64	no	—
506	C₂³	—	26	16	no	—
507	C₂³	—	26	8	no	—
508	C₂³	—	52	32	no	—
509	C₂³	—	52	16	no	—
510	C₂³	—	52	128	no	—
511	C₂³	—	52	32	no	—
512	C₂³	—	52	256	no	—
513	C₂³	C₂²×C₂²⋊D₁₃	1	16	yes	—
514	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
515	C₂³	C₂²×C₂²⋊D₁₃	1	32	yes	complemented
516	C₂³	C₂⁴×D₁₃	1	8	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	—	2	16	no	—
521	D₄	—	2	32	no	—
522	D₄	—	2	64	no	—
523	D₄	—	2	16	no	—
524	D₄	—	26	64	no	—
525	D₄	—	26	64	no	—
526	D₄	—	26	32	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	32	no	—
531	C₂×C₄	—	2	32	no	—
532	C₂×C₄	—	13	16	no	—
533	C₂×C₄	—	13	4	no	—
534	C₂×C₄	—	26	16	no	—
535	C₂×C₄	—	26	8	no	—
536	C₂×C₄	—	26	4	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	8	yes	—
542	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	32	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	16	no	—
549	C₂²	—	4	32	no	—
550	C₂²	—	4	16	no	—
551	C₂²	—	8	32	no	—
552	C₂²	—	13	8	no	—
553	C₂²	—	26	32	no	—
554	C₂²	—	26	16	no	—
555	C₂²	—	26	4	no	—
556	C₂²	—	26	4	no	—
557	C₂²	—	26	8	no	—
558	C₂²	—	26	16	no	—
559	C₂²	—	52	128	no	—
560	C₂²	—	52	32	no	—
561	C₂²	—	52	16	no	—
562	C₂²	D₁₃×H(5,𝔽₂)	1	4	yes	—
563	C₂²	C₂³×C₂²⋊D₁₃	1	16	yes	—
564	C₂²	C₂³×C₂²⋊D₁₃	1	4	yes	—
565	C₂²	C₂³×C₂²⋊D₁₃	1	2	yes	—
566	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
567	C₄	—	2	8	no	—
568	C₄	—	26	4	no	—
569	C₄	—	26	16	no	—
570	C₄	C₂³×C₂²⋊D₁₃	1	8	yes	—
571	C₂	—	2	4	no	—
572	C₂	—	2	16	no	—
573	C₂	—	4	8	no	—
574	C₂	—	26	8	no	—
575	C₂	—	52	8	no	—
576	C₂	#13128467	1	4	yes	direct product factor
577	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
578	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	C₂²×C₁₃×H(5,𝔽₂)	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×H(5,𝔽₂)	D₁₃
hypocenter	C₁₃	C₂×#3484
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₁₃	C₂	semidirect
2. #13128467	C₂	direct (N × H)
3. C₂×#11719534	C₂	semidirect
4. C₂×D₄×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#11719535	C₂	semidirect
6. C₂×#11719509	C₂	semidirect
7. C₂×#11719533	C₂	semidirect
8. C₂²×#88191	C₂	semidirect
9. C₂×#11719503	C₂	semidirect
10. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
11. C₂⁵×D₁₃	C₂²	semidirect
13. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂²×C₁₃×#41	C₂²	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂³×C₂²⋊D₁₃	C₂²	semidirect
20. C₂³×C₂²⋊D₁₃	C₂²	semidirect
22. C₂²×D₄×D₁₃	C₂²	semidirect
23. C₂²×D₄×D₁₃	C₂²	semidirect
24. C₂³×D₅₂	C₂²	semidirect
25. C₂³×C₄×D₁₃	C₂²	semidirect
26. C₂×#88207	C₂²	semidirect
27. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
28. #11719535	C₂²	semidirect
29. #11719534	C₂²	semidirect
30. #11719533	C₂²	semidirect
31. C₂×#88201	C₂²	semidirect
32. C₂×#88200	C₂²	semidirect
33. #11719509	C₂²	semidirect
34. C₂×#88194	C₂²	semidirect
35. C₂×#88193	C₂²	semidirect
36. D₄×C₂²⋊D₁₃	C₂²	semidirect
37. C₂×#88192	C₂²	semidirect
38. C₂×#88191	C₂²	semidirect
39. C₂×#88191	C₂²	semidirect
40. C₂×#88191	C₂²	semidirect
41. C₂×#88191	C₂²	semidirect
42. #11719503	C₂²	semidirect
43. C₂×#88189	C₂²	semidirect
44. C₂×D₄×Dic₁₃	C₂²	semidirect
45. C₂×#88184	C₂²	semidirect
46. C₂×#88183	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
48. C₂²×#6103	C₂²	semidirect
49. C₂×#88180	C₂²	semidirect
51. C₂⁵×C₁₃	C₂³	semidirect
57. C₂⁴×D₁₃	C₂³	semidirect
61. C₂×C₁₃×#41	C₂³	semidirect
62. C₂×C₁₃×#41	C₂³	semidirect
63. C₂²×Q₈×C₁₃	C₂³	semidirect
66. C₂²×D₄×C₁₃	D₄	semidirect
70. C₂²×D₄×C₁₃	C₂³	semidirect
71. C₂²×D₄×C₁₃	C₂³	semidirect
72. C₂²×D₄×C₁₃	C₂³	semidirect
73. C₂²×D₄×C₁₃	C₂³	semidirect
75. C₂³×C₄×C₁₃	C₂³	semidirect
76. C₂³×C₄×C₁₃	C₂³	semidirect
81. C₂²×C₂²⋊D₁₃	C₂³	semidirect
82. C₂²×C₂²⋊D₁₃	C₂³	semidirect
83. C₂²×C₂²⋊D₁₃	C₂³	semidirect
85. C₂³×Dic₁₃	C₂³	semidirect
88. C₂×D₄×D₁₃	C₂³	semidirect
91. C₂²×D₅₂	C₂³	semidirect
94. C₂²×C₄×D₁₃	C₂³	semidirect
95. #88207	C₂³	semidirect
97. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
98. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
99. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
100. #88201	C₂³	semidirect
101. #88200	C₂³	semidirect
102. #88194	C₂³	semidirect
103. #88193	C₂³	semidirect
104. #88192	C₂³	semidirect
105. #88191	C₂³	semidirect
106. #88191	C₂³	semidirect
107. #88191	C₂³	semidirect
108. #88189	C₂³	semidirect
109. D₄×Dic₁₃	C₂³	semidirect
110. #88184	C₂³	semidirect
111. #88183	C₂³	semidirect
112. C₄×C₂²⋊D₁₃	C₂³	semidirect
114. C₂×#6103	C₂³	semidirect
115. C₂×#6103	C₂³	semidirect
116. #88180	C₂³	semidirect
117. C₂×C₄⋊Dic₁₃	C₂³	semidirect
118. C₂×#6101	C₂³	semidirect
119. C₂×C₄×Dic₁₃	C₂³	semidirect
124. C₂⁴×C₁₃	C₂×D₄	semidirect
129. C₂⁴×C₁₃	C₂⁴	semidirect
148. C₂×Q₈×C₁₃	C₂⁴	semidirect
154. C₂×D₄×C₁₃	C₂×D₄	semidirect
155. C₂×D₄×C₁₃	C₂×D₄	semidirect
158. C₂×D₄×C₁₃	C₂⁴	semidirect
159. C₂×D₄×C₁₃	C₂⁴	semidirect
162. C₂²×C₄×C₁₃	C₂×D₄	semidirect
166. C₂²×C₄×C₁₃	C₂⁴	semidirect
167. C₂²×C₄×C₁₃	C₂⁴	semidirect
175. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
181. C₂²×Dic₁₃	C₂⁴	semidirect
190. C₂²⋊Dic₁₃	C₂⁴	semidirect
191. C₂²⋊Dic₁₃	C₂⁴	semidirect
193. #6103	C₂⁴	semidirect
194. C₄⋊Dic₁₃	C₂⁴	semidirect
195. #6101	C₂⁴	semidirect
196. C₄×Dic₁₃	C₂⁴	semidirect
197. C₂²×H(5,𝔽₂)	D₁₃	semidirect
218. C₂³×C₁₃	C₂²×D₄	semidirect
238. C₂²×D₁₃	H(5,𝔽₂)	semidirect
245. D₄×C₁₃	C₂²×D₄	semidirect
250. C₂×C₄×C₁₃	C₂²×D₄	semidirect
266. C₂×H(5,𝔽₂)	C₂×D₁₃	semidirect
267. C₂²×#41	C₂×D₁₃	semidirect
268. C₂²×#41	C₂×D₁₃	semidirect
276. C₂³×D₄	C₂×D₁₃	semidirect
277. C₂³×D₄	C₂×D₁₃	semidirect
326. C₂×D₁₃	C₂×H(5,𝔽₂)	semidirect
338. C₂⁵	C₂²×D₁₃	semidirect
342. C₂×#41	C₂²×D₁₃	semidirect
343. C₂×#41	C₂²×D₁₃	semidirect
344. C₂²×Q₈	C₂²×D₁₃	semidirect
360. C₂²×D₄	C₂²⋊D₁₃	semidirect
364. C₂²×D₄	C₂²×D₁₃	semidirect
365. C₂²×D₄	C₂²×D₁₃	semidirect
366. C₂²×D₄	C₂²×D₁₃	semidirect
367. C₂²×D₄	C₂²×D₁₃	semidirect
374. C₂³×C₄	C₂²×D₁₃	semidirect
375. C₂³×C₄	C₂²×D₁₃	semidirect
404. C₂×C₁₃	#3484	semidirect
427. C₂⁴	C₂×C₂²⋊D₁₃	semidirect
432. C₂⁴	C₂³×D₁₃	semidirect
436. C₂×Q₈	C₂³×D₁₃	semidirect
454. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
455. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
458. C₂×D₄	C₂³×D₁₃	semidirect
459. C₂×D₄	C₂³×D₁₃	semidirect
471. C₂²×C₄	C₂×C₂²⋊D₁₃	semidirect
475. C₂²×C₄	C₂³×D₁₃	semidirect
476. C₂²×C₄	C₂³×D₁₃	semidirect
485. C₁₃	C₂×#3484	semidirect
515. C₂³	C₂²×C₂²⋊D₁₃	semidirect
528. D₄	C₂²×C₂²⋊D₁₃	semidirect
540. C₂×C₄	C₂²×C₂²⋊D₁₃	semidirect
576. C₂	#13128467	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
#13128467	2
C₂×#11719534	2
C₂×D₄×C₂²⋊D₁₃	2
C₂×#11719535	2
C₂×#11719509	2
C₂×#11719533	2
C₂²×#88191	2
C₂×#11719503	2
C₂²×C₁₃×H(5,𝔽₂)	2
C₂×#3484	13

Subgroups — C2×#13128467 #16770799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128467 #16770799