Subgroups — C₂²×D₄×C₂²⋊D₁₃ #16769827

Order 3328.

20038 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂⁴×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂⁴×D₄	D₁₃
hypocenter	C₁₃	C₂²×D₄²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₂²⋊D₁₃	C₂	semidirect
2. C₂³×D₄×D₁₃	C₂	semidirect
3. C₂×D₄×C₂²⋊D₁₃	C₂	direct (N × H)
4. C₂²×#88194	C₂	semidirect
5. C₂²×#88184	C₂	semidirect
6. C₂²×#88193	C₂	semidirect
7. C₂²×#88192	C₂	semidirect
8. C₂²×#88207	C₂	semidirect
9. C₂²×#88191	C₂	semidirect
10. C₂²×D₄×Dic₁₃	C₂	semidirect
11. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
12. C₂⁴×D₄×C₁₃	C₂	semidirect
13. C₂⁶×C₁₃	C₂²	semidirect
14. C₂⁵×D₁₃	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂³×D₄×C₁₃	C₂²	semidirect
20. C₂⁴×C₄×C₁₃	C₂²	semidirect
23. C₂³×C₂²⋊D₁₃	C₂²	semidirect
24. C₂³×C₂²⋊D₁₃	C₂²	semidirect
25. C₂³×C₂²⋊D₁₃	C₂²	semidirect
26. C₂³×C₂²⋊D₁₃	C₂²	semidirect
27. C₂³×C₂²⋊D₁₃	C₂²	semidirect
28. C₂³×C₂²⋊D₁₃	C₂²	semidirect
29. C₂⁴×Dic₁₃	C₂²	semidirect
31. C₂²×D₄×D₁₃	C₂²	semidirect
32. C₂³×D₅₂	C₂²	semidirect
33. C₂³×C₄×D₁₃	C₂²	semidirect
34. C₂×#88207	C₂²	semidirect
35. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
36. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
37. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
38. C₂×#88194	C₂²	semidirect
39. C₂×#88193	C₂²	semidirect
40. D₄×C₂²⋊D₁₃	C₂²	direct (N × H)
41. C₂×#88192	C₂²	semidirect
42. C₂×#88191	C₂²	semidirect
43. C₂×D₄×Dic₁₃	C₂²	semidirect
44. C₂×#88184	C₂²	semidirect
45. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
46. C₂²×#6103	C₂²	semidirect
47. C₂²×#6103	C₂²	semidirect
48. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
49. C₂²×#6101	C₂²	semidirect
50. C₂²×C₄×Dic₁₃	C₂²	semidirect
57. C₂⁵×C₁₃	C₂³	semidirect
63. C₂⁴×D₁₃	C₂³	semidirect
67. C₂²×D₄×C₁₃	D₄	semidirect
69. C₂²×D₄×C₁₃	C₂³	semidirect
70. C₂²×D₄×C₁₃	C₂³	semidirect
71. C₂²×D₄×C₁₃	C₂³	semidirect
75. C₂³×C₄×C₁₃	C₂³	semidirect
82. C₂²×C₂²⋊D₁₃	D₄	direct (N × H)
84. C₂²×C₂²⋊D₁₃	C₂³	semidirect
85. C₂²×C₂²⋊D₁₃	C₂³	semidirect
86. C₂²×C₂²⋊D₁₃	C₂³	semidirect
87. C₂²×C₂²⋊D₁₃	C₂³	semidirect
88. C₂²×C₂²⋊D₁₃	C₂³	semidirect
89. C₂²×C₂²⋊D₁₃	C₂³	semidirect
95. C₂³×Dic₁₃	C₂³	semidirect
97. C₂×D₄×D₁₃	C₂³	semidirect
99. C₂²×D₅₂	C₂³	semidirect
101. C₂²×C₄×D₁₃	C₂³	semidirect
102. #88207	C₂³	semidirect
103. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
104. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
105. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
106. #88194	C₂³	semidirect
107. #88193	C₂³	semidirect
108. #88192	C₂³	semidirect
109. #88191	C₂³	semidirect
110. D₄×Dic₁₃	C₂³	semidirect
111. #88184	C₂³	semidirect
112. C₄×C₂²⋊D₁₃	C₂³	semidirect
113. C₂×#6103	C₂³	semidirect
114. C₂×#6103	C₂³	semidirect
115. C₂×C₄⋊Dic₁₃	C₂³	semidirect
116. C₂×#6101	C₂³	semidirect
117. C₂×C₄×Dic₁₃	C₂³	semidirect
130. C₂⁴×C₁₃	C₂×D₄	semidirect
131. C₂⁴×C₁₃	C₂×D₄	semidirect
136. C₂⁴×C₁₃	C₂⁴	semidirect
146. C₂³×D₁₃	C₂×D₄	semidirect
149. C₂³×D₁₃	C₂⁴	semidirect
153. C₂×D₄×C₁₃	C₂×D₄	semidirect
155. C₂×D₄×C₁₃	C₂⁴	semidirect
156. C₂×D₄×C₁₃	C₂⁴	semidirect
159. C₂²×C₄×C₁₃	C₂×D₄	semidirect
162. C₂²×C₄×C₁₃	C₂⁴	semidirect
169. C₂×C₂²⋊D₁₃	C₂×D₄	direct (N × H)
171. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
172. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
173. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
174. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
175. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
180. C₂²×Dic₁₃	C₂×D₄	semidirect
185. C₂²×Dic₁₃	C₂⁴	semidirect
188. C₂×D₅₂	C₂⁴	semidirect
190. C₂×C₄×D₁₃	C₂⁴	semidirect
191. C₂²⋊Dic₁₃	C₂⁴	semidirect
192. C₂²⋊Dic₁₃	C₂⁴	semidirect
193. C₂²⋊Dic₁₃	C₂⁴	semidirect
194. #6103	C₂⁴	semidirect
195. #6103	C₂⁴	semidirect
196. C₄⋊Dic₁₃	C₂⁴	semidirect
197. #6101	C₂⁴	semidirect
198. C₄×Dic₁₃	C₂⁴	semidirect
201. C₂⁴×D₄	D₁₃	semidirect
227. C₂³×C₁₃	C₂²×D₄	semidirect
228. C₂³×C₁₃	C₂²×D₄	semidirect
245. C₂²×D₁₃	C₂²×D₄	semidirect
250. D₄×C₁₃	C₂²×D₄	semidirect
253. C₂×C₄×C₁₃	C₂²×D₄	semidirect
261. C₂²⋊D₁₃	C₂²×D₄	direct (N × H)
266. C₂×Dic₁₃	C₂²×D₄	semidirect
274. C₂⁶	C₂×D₁₃	semidirect
288. C₂³×D₄	C₂×D₁₃	semidirect
289. C₂³×D₄	C₂×D₁₃	semidirect
290. C₂³×D₄	C₂×D₁₃	semidirect
293. C₂⁴×C₄	C₂×D₁₃	semidirect
322. C₂²×C₁₃	D₄²	semidirect
325. C₂²×C₁₃	C₂³×D₄	semidirect
326. C₂²×C₁₃	C₂³×D₄	semidirect
337. C₂×D₁₃	C₂³×D₄	semidirect
339. C₄×C₁₃	C₂³×D₄	semidirect
343. Dic₁₃	C₂³×D₄	semidirect
356. C₂⁵	C₂²×D₁₃	semidirect
378. C₂²×D₄	C₂²⋊D₁₃	direct (N × H)
380. C₂²×D₄	C₂²×D₁₃	semidirect
381. C₂²×D₄	C₂²×D₁₃	semidirect
382. C₂²×D₄	C₂²×D₁₃	semidirect
394. C₂³×C₄	C₂²×D₁₃	semidirect
414. C₂×C₁₃	C₂×D₄²	semidirect
444. C₂⁴	D₄×D₁₃	semidirect
445. C₂⁴	C₂×C₂²⋊D₁₃	semidirect
450. C₂⁴	C₂³×D₁₃	semidirect
470. C₂×D₄	C₂×C₂²⋊D₁₃	direct (N × H)
472. C₂×D₄	C₂³×D₁₃	semidirect
473. C₂×D₄	C₂³×D₁₃	semidirect
488. C₂²×C₄	C₂×C₂²⋊D₁₃	semidirect
491. C₂²×C₄	C₂³×D₁₃	semidirect
500. C₁₃	C₂²×D₄²	semidirect
530. C₂³	C₂×D₄×D₁₃	semidirect
533. C₂³	C₂²×C₂²⋊D₁₃	semidirect
547. D₄	C₂²×C₂²⋊D₁₃	direct (N × H)
560. C₂×C₄	C₂²×C₂²⋊D₁₃	semidirect
583. C₂²	D₄×C₂²⋊D₁₃	direct (N × H)
585. C₂²	C₂²×D₄×D₁₃	semidirect
588. C₂²	C₂³×C₂²⋊D₁₃	semidirect
595. C₄	C₂³×C₂²⋊D₁₃	semidirect
601. C₂	C₂×D₄×C₂²⋊D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₂²⋊D₁₃	2
C₂³×D₄×D₁₃	2
C₂×D₄×C₂²⋊D₁₃	2
C₂²×#88194	2
C₂²×#88184	2
C₂²×#88193	2
C₂²×#88192	2
C₂²×#88207	2
C₂²×#88191	2
C₂²×D₄×Dic₁₃	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂⁴×D₄×C₁₃	2
C₂²×D₄²	13

Subgroups — C22×D4×C22⋊D13 #16769827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄×C₂²⋊D₁₃ #16769827