Subgroups — C₂²×#11719250 #16769497

Order 3328.

14590 conjugacy classes of subgroups.

The subgroup lattice has 504 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
2	C₂×#11719250	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88147	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#88135	C₂	1	2	yes	maximal, complemented
8	C₂²×#88146	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88126	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×#6103	C₂	1	2	yes	maximal, complemented
11	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
16	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
17	C₂⁴×Dic₁₃	C₂²	1	2	yes	complemented
18	C₂²×D₄×D₁₃	C₄	1	32	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	24	yes	—
20	C₂³×D₅₂	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
23	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
29	C₂×D₄×Dic₁₃	C₂²	1	24	yes	complemented
30	C₂×C₄×C₂²⋊D₁₃	C₂²	1	48	yes	complemented
31	C₂²×#6103	C₂²	1	1	yes	characteristic
32	C₂²×#6103	C₂²	1	2	yes	—
33	C₂²×#6103	C₂²	1	1	yes	characteristic
34	C₂²×#6103	C₂²	1	48	yes	complemented
35	C₂²×#6103	C₂²	1	2	yes	complemented
36	C₂²×#6103	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
39	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	complemented
42	#11719250	C₂²	1	256	yes	direct product factor
43	C₂×#88147	C₂²	1	24	yes	complemented
44	C₂×#88146	C₂²	1	24	yes	complemented
45	C₂×#88135	C₂²	1	48	yes	complemented
46	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	complemented
47	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
48	C₂×#88126	C₂²	1	24	yes	complemented
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁴×D₁₃	—	4	8	no	—
51	C₂⁴×D₁₃	—	4	8	no	—
52	C₂⁴×D₁₃	C₂×C₄	1	32	yes	complemented
53	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
54	C₂⁴×D₁₃	C₂³	1	2	yes	—
55	C₂⁴×D₁₃	C₂³	1	24	yes	—
56	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
57	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
58	C₂³×C₄×C₁₃	—	4	8	no	—
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
64	C₂²×C₂²⋊D₁₃	C₂×C₄	1	32	yes	complemented
65	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
66	C₂³×Dic₁₃	—	4	8	no	—
67	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
68	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
69	C₂³×Dic₁₃	C₂³	1	2	yes	—
70	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
71	C₂³×Dic₁₃	C₂³	1	24	yes	complemented
72	C₂×D₄×D₁₃	C₂×C₄	1	384	yes	complemented
73	C₂×D₄×D₁₃	C₂³	1	64	yes	—
74	C₂²×D₅₂	C₂×C₄	1	16	yes	complemented
75	C₂²×D₅₂	C₂³	1	12	yes	—
76	C₂²×C₄×D₁₃	—	4	8	no	—
77	C₂²×C₄×D₁₃	—	4	8	no	—
78	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	complemented
79	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
80	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
81	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
82	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
85	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
86	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
87	D₄×Dic₁₃	C₂³	1	64	yes	complemented
88	C₄×C₂²⋊D₁₃	C₂³	1	128	yes	complemented
89	C₂×#6103	C₂³	1	12	yes	—
90	C₂×#6103	C₂³	1	12	yes	—
91	C₂×#6103	C₂³	1	24	yes	—
92	C₂×#6103	C₂³	1	128	yes	complemented
93	C₂×#6103	C₂³	1	24	yes	complemented
94	C₂×#6103	C₂³	1	24	yes	complemented
95	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
96	C₂×#6101	C₂³	1	12	yes	complemented
97	C₂×#6101	C₂³	1	12	yes	complemented
98	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
99	C₂×C₄×Dic₁₃	C₂³	1	24	yes	complemented
100	#88147	C₂³	1	64	yes	complemented
101	#88146	C₂³	1	64	yes	complemented
102	#88135	C₂³	1	128	yes	complemented
103	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	complemented
104	C₄×D₅₂	C₂³	1	64	yes	complemented
105	#88126	C₂³	1	64	yes	complemented
106	C₂²×#518	—	13	1	no	maximal, Sylow
107	C₂⁴×C₁₃	—	2	8	no	—
108	C₂⁴×C₁₃	—	2	8	no	—
109	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
110	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
111	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂³×D₁₃	—	2	8	no	—
113	C₂³×D₁₃	—	2	8	no	—
114	C₂³×D₁₃	—	2	4	no	—
115	C₂³×D₁₃	—	2	4	no	—
116	C₂³×D₁₃	—	4	128	no	—
117	C₂³×D₁₃	—	4	48	no	—
118	C₂³×D₁₃	—	4	48	no	—
119	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
120	C₂³×D₁₃	C₂²×C₄	1	16	yes	—
121	C₂³×D₁₃	C₂²×C₄	1	192	yes	complemented
122	C₂³×D₁₃	C₂⁴	1	6	yes	—
123	C₂³×D₁₃	C₂⁴	1	12	yes	—
124	C₂³×D₁₃	C₂⁴	1	32	yes	—
125	C₂×D₄×C₁₃	C₂²×C₄	1	96	yes	complemented
126	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	4	48	no	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
137	C₂×C₂²⋊D₁₃	C₂²×C₄	1	192	yes	complemented
138	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
139	C₂²×Dic₁₃	—	2	4	no	—
140	C₂²×Dic₁₃	—	2	8	no	—
141	C₂²×Dic₁₃	—	2	4	no	—
142	C₂²×Dic₁₃	—	4	48	no	—
143	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
144	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
145	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
146	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
147	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
148	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
149	D₄×D₁₃	C₂²×C₄	1	512	yes	complemented
150	C₂×D₅₂	C₂²×C₄	1	96	yes	complemented
151	C₂×D₅₂	C₂⁴	1	16	yes	—
152	C₂×C₄×D₁₃	—	4	48	no	—
153	C₂×C₄×D₁₃	—	4	48	no	—
154	C₂×C₄×D₁₃	C₂²×C₄	1	96	yes	complemented
155	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
156	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
157	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
158	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
159	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
160	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
161	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
162	#6103	C₂⁴	1	16	yes	—
163	#6103	C₂⁴	1	16	yes	—
164	#6103	C₂⁴	1	32	yes	—
165	#6103	C₂⁴	1	32	yes	complemented
166	#6103	C₂⁴	1	32	yes	complemented
167	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
168	#6101	C₂⁴	1	16	yes	complemented
169	#6101	C₂⁴	1	16	yes	complemented
170	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
171	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
172	C₂⁴×D₄	—	13	1	no	—
173	C₂×#518	—	13	48	no	—
174	C₂²×C₄×D₄	—	13	1	no	—
175	C₂²×C₄×D₄	—	13	1	no	—
176	C₂²×C₄×D₄	—	13	2	no	—
177	C₂²×C₄×D₄	—	13	1	no	—
178	C₂²×C₄×D₄	—	13	2	no	—
179	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
180	C₂²×#117	—	13	1	no	—
181	C₂²×#117	—	13	1	no	—
182	C₂³×C₂²⋊C₄	—	13	2	no	—
183	C₂³×C₂²⋊C₄	—	13	2	no	—
184	C₂³×C₁₃	—	2	64	no	—
185	C₂³×C₁₃	—	2	24	no	—
186	C₂³×C₁₃	—	2	24	no	—
187	C₂³×C₁₃	C₂³×C₄	1	48	yes	—
188	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
189	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
190	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
191	C₂³×C₁₃	C₂⁵	1	8	yes	—
192	C₂³×C₁₃	C₂⁵	1	3	yes	—
193	C₂²×D₁₃	—	2	32	no	—
194	C₂²×D₁₃	—	2	64	no	—
195	C₂²×D₁₃	—	2	24	no	—
196	C₂²×D₁₃	—	2	24	no	—
197	C₂²×D₁₃	—	2	12	no	—
198	C₂²×D₁₃	—	2	12	no	—
199	C₂²×D₁₃	—	4	384	no	—
200	C₂²×D₁₃	—	4	32	no	—
201	C₂²×D₁₃	—	4	32	no	—
202	C₂²×D₁₃	C₂³×C₄	1	24	yes	—
203	C₂²×D₁₃	C₂³×C₄	1	48	yes	—
204	C₂²×D₁₃	C₂³×C₄	1	128	yes	complemented
205	C₂²×D₁₃	C₂⁵	1	4	yes	—
206	C₂²×D₁₃	C₂⁵	1	8	yes	—
207	D₄×C₁₃	C₂³×C₄	1	64	yes	complemented
208	C₂×C₄×C₁₃	—	2	12	no	—
209	C₂×C₄×C₁₃	—	2	24	no	—
210	C₂×C₄×C₁₃	—	2	12	no	—
211	C₂×C₄×C₁₃	—	4	32	no	—
212	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
213	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
214	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
216	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
217	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
218	C₂×Dic₁₃	—	2	12	no	—
219	C₂×Dic₁₃	—	2	24	no	—
220	C₂×Dic₁₃	—	2	12	no	—
221	C₂×Dic₁₃	—	4	32	no	—
222	C₂×Dic₁₃	C₂³×C₄	1	24	yes	—
223	C₂×Dic₁₃	C₂⁵	1	4	yes	—
224	C₂×Dic₁₃	C₂⁵	1	4	yes	—
225	C₂×Dic₁₃	C₂⁵	1	8	yes	—
226	C₂×Dic₁₃	C₂⁵	1	4	yes	—
227	D₅₂	C₂³×C₄	1	64	yes	complemented
228	C₄×D₁₃	—	4	32	no	—
229	C₄×D₁₃	—	4	32	no	—
230	C₄×D₁₃	C₂³×C₄	1	64	yes	complemented
231	C₂⁶	—	13	2	no	—
232	C₂³×D₄	—	13	2	no	—
233	C₂³×D₄	—	13	32	no	—
234	C₂³×D₄	—	13	24	no	—
235	C₂³×D₄	—	13	1	no	—
236	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
237	C₂⁴×C₄	—	13	1	no	—
238	C₂⁴×C₄	—	13	2	no	—
239	C₂⁴×C₄	—	13	2	no	—
240	C₂⁴×C₄	—	13	2	no	—
241	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
242	#518	—	13	256	no	—
243	C₂×C₄×D₄	—	13	24	no	—
244	C₂×C₄×D₄	—	13	48	no	—
245	C₂×C₄×D₄	—	13	24	no	—
246	C₂×C₄×D₄	—	13	48	no	—
247	C₂×C₄×D₄	—	13	24	no	—
248	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	complemented
249	C₂×#117	—	13	24	no	—
250	C₂×#117	—	13	24	no	—
251	C₂²×C₄⋊C₄	—	13	1	no	—
252	C₂²×C₄⋊C₄	—	13	1	no	—
253	C₂²×C₄⋊C₄	—	13	1	no	—
254	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
255	C₂²×C₂²⋊C₄	—	13	2	no	—
256	C₂²×C₂²⋊C₄	—	13	1	no	—
257	C₂²×C₂²⋊C₄	—	13	2	no	—
258	C₂²×C₂²⋊C₄	—	13	1	no	—
259	C₂²×C₂²⋊C₄	—	13	2	no	—
260	C₂²×C₂²⋊C₄	—	13	2	no	—
261	C₂²×C₂²⋊C₄	—	13	48	no	—
262	C₂²×C₂²⋊C₄	—	13	48	no	—
263	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
264	C₂²×C₄²	—	13	2	no	—
265	C₂²×C₄²	—	13	1	no	—
266	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
267	C₂²×C₁₃	—	2	8	no	—
268	C₂²×C₁₃	—	2	8	no	—
269	C₂²×C₁₃	—	2	96	no	—
270	C₂²×C₁₃	#518	1	16	yes	complemented
271	C₂²×C₁₃	C₂⁴×C₄	1	16	yes	—
272	C₂²×C₁₃	C₂⁴×C₄	1	6	yes	—
273	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
274	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
275	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
276	C₂×D₁₃	—	2	8	no	—
277	C₂×D₁₃	—	2	8	no	—
278	C₂×D₁₃	—	2	4	no	—
279	C₂×D₁₃	—	2	4	no	—
280	C₂×D₁₃	—	2	48	no	—
281	C₂×D₁₃	—	2	96	no	—
282	C₂×D₁₃	—	4	128	no	—
283	C₂×D₁₃	C₂⁴×C₄	1	8	yes	—
284	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
285	C₄×C₁₃	—	2	4	no	—
286	C₄×C₁₃	—	2	8	no	—
287	C₄×C₁₃	—	2	4	no	—
288	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
289	Dic₁₃	—	2	4	no	—
290	Dic₁₃	—	2	8	no	—
291	Dic₁₃	—	2	4	no	—
292	Dic₁₃	C₂⁴×C₄	1	8	yes	—
293	C₂⁵	—	13	1	no	—
294	C₂⁵	—	13	2	no	—
295	C₂⁵	—	13	32	no	—
296	C₂⁵	—	13	24	no	—
297	C₂⁵	—	52	8	no	—
298	C₂⁵	—	52	8	no	—
299	C₂⁵	C₂²×D₁₃	1	2	yes	—
300	C₂²×D₄	—	13	32	no	—
301	C₂²×D₄	—	13	24	no	—
302	C₂²×D₄	—	13	384	no	—
303	C₂²×D₄	—	13	64	no	—
304	C₂²×D₄	—	13	16	no	—
305	C₂²×D₄	—	13	12	no	—
306	C₂²×D₄	C₄×D₁₃	1	16	yes	complemented
307	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
308	C₂³×C₄	—	4	8	no	—
309	C₂³×C₄	—	13	1	no	—
310	C₂³×C₄	—	13	16	no	—
311	C₂³×C₄	—	13	12	no	—
312	C₂³×C₄	—	13	1	no	—
313	C₂³×C₄	—	13	2	no	—
314	C₂³×C₄	—	13	1	no	—
315	C₂³×C₄	—	13	24	no	—
316	C₂³×C₄	—	13	24	no	—
317	C₂³×C₄	—	13	24	no	—
318	C₂³×C₄	—	52	8	no	—
319	C₂³×C₄	—	52	8	no	—
320	C₂³×C₄	—	52	8	no	—
321	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
322	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
323	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
324	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂²×D₁₃	1	24	yes	complemented
326	C₄×D₄	—	13	64	no	—
327	C₄×D₄	—	13	128	no	—
328	C₄×D₄	—	13	64	no	—
329	C₄×D₄	—	13	128	no	—
330	C₄×D₄	—	13	64	no	—
331	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
332	#117	—	13	64	no	—
333	#117	—	13	64	no	—
334	C₂×C₄⋊C₄	—	13	12	no	—
335	C₂×C₄⋊C₄	—	13	12	no	—
336	C₂×C₄⋊C₄	—	13	12	no	—
337	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
338	C₂×C₂²⋊C₄	—	13	24	no	—
339	C₂×C₂²⋊C₄	—	13	24	no	—
340	C₂×C₂²⋊C₄	—	13	12	no	—
341	C₂×C₂²⋊C₄	—	13	12	no	—
342	C₂×C₂²⋊C₄	—	13	24	no	—
343	C₂×C₂²⋊C₄	—	13	24	no	—
344	C₂×C₂²⋊C₄	—	13	128	no	—
345	C₂×C₂²⋊C₄	—	13	128	no	—
346	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	complemented
347	C₂×C₄²	—	13	24	no	—
348	C₂×C₄²	—	13	12	no	—
349	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
350	C₂×C₁₃	—	2	16	no	—
351	C₂×C₁₃	C₂×#518	1	12	yes	complemented
352	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
353	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
355	D₁₃	—	2	8	no	—
356	D₁₃	—	2	16	no	—
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	2	8	no	—
359	C₂⁴	—	13	8	no	—
360	C₂⁴	—	13	16	no	—
361	C₂⁴	—	13	6	no	—
362	C₂⁴	—	13	12	no	—
363	C₂⁴	—	13	192	no	—
364	C₂⁴	—	13	32	no	—
365	C₂⁴	—	26	8	no	—
366	C₂⁴	—	26	4	no	—
367	C₂⁴	—	26	8	no	—
368	C₂⁴	—	26	4	no	—
369	C₂⁴	—	52	128	no	—
370	C₂⁴	—	52	48	no	—
371	C₂⁴	—	52	48	no	—
372	C₂⁴	C₂×C₄×D₁₃	1	16	yes	—
373	C₂⁴	C₂³×D₁₃	1	12	yes	—
374	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
375	C₂×D₄	—	13	192	no	—
376	C₂×D₄	—	13	32	no	—
377	C₂×D₄	—	13	512	no	—
378	C₂×D₄	—	13	96	no	—
379	C₂×D₄	—	13	16	no	—
380	C₂×D₄	C₂×C₄×D₁₃	1	96	yes	complemented
381	C₂×D₄	C₂³×D₁₃	1	16	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	4	48	no	—
386	C₂²×C₄	—	13	8	no	—
387	C₂²×C₄	—	13	6	no	—
388	C₂²×C₄	—	13	96	no	—
389	C₂²×C₄	—	13	16	no	—
390	C₂²×C₄	—	13	6	no	—
391	C₂²×C₄	—	13	12	no	—
392	C₂²×C₄	—	13	6	no	—
393	C₂²×C₄	—	13	32	no	—
394	C₂²×C₄	—	13	32	no	—
395	C₂²×C₄	—	13	32	no	—
396	C₂²×C₄	—	26	4	no	—
397	C₂²×C₄	—	26	8	no	—
398	C₂²×C₄	—	26	4	no	—
399	C₂²×C₄	—	52	48	no	—
400	C₂²×C₄	—	52	48	no	—
401	C₂²×C₄	—	52	48	no	—
402	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
403	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
404	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
405	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
406	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
407	C₂²×C₄	C₂³×D₁₃	1	32	yes	complemented
408	C₄⋊C₄	—	13	16	no	—
409	C₄⋊C₄	—	13	16	no	—
410	C₄⋊C₄	—	13	16	no	—
411	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
412	C₂²⋊C₄	—	13	32	no	—
413	C₂²⋊C₄	—	13	32	no	—
414	C₂²⋊C₄	—	13	16	no	—
415	C₂²⋊C₄	—	13	16	no	—
416	C₂²⋊C₄	—	13	32	no	—
417	C₂²⋊C₄	—	13	32	no	—
418	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	complemented
419	C₄²	—	13	32	no	—
420	C₄²	—	13	16	no	—
421	C₄²	C₂³×D₁₃	1	16	yes	complemented
422	C₁₃	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
423	C₂³	—	2	64	no	—
424	C₂³	—	2	24	no	—
425	C₂³	—	2	24	no	—
426	C₂³	—	13	24	no	—
427	C₂³	—	13	48	no	—
428	C₂³	—	13	4	no	—
429	C₂³	—	13	8	no	—
430	C₂³	—	13	128	no	—
431	C₂³	—	26	32	no	—
432	C₂³	—	26	64	no	—
433	C₂³	—	26	24	no	—
434	C₂³	—	26	12	no	—
435	C₂³	—	26	24	no	—
436	C₂³	—	26	12	no	—
437	C₂³	—	52	384	no	—
438	C₂³	—	52	32	no	—
439	C₂³	—	52	32	no	—
440	C₂³	C₂²×C₄×D₁₃	1	48	yes	—
441	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
442	C₂³	#88251	1	4	yes	—
443	C₂³	#88256	1	4	yes	—
444	C₂³	C₂⁴×D₁₃	1	8	yes	—
445	C₂³	C₂⁴×D₁₃	1	3	yes	—
446	D₄	—	13	128	no	—
447	D₄	—	13	64	no	—
448	D₄	C₂²×C₄×D₁₃	1	64	yes	complemented
449	C₂×C₄	—	2	12	no	—
450	C₂×C₄	—	2	24	no	—
451	C₂×C₄	—	2	12	no	—
452	C₂×C₄	—	4	32	no	—
453	C₂×C₄	—	13	24	no	—
454	C₂×C₄	—	13	4	no	—
455	C₂×C₄	—	13	64	no	—
456	C₂×C₄	—	13	4	no	—
457	C₂×C₄	—	13	8	no	—
458	C₂×C₄	—	13	4	no	—
459	C₂×C₄	—	26	12	no	—
460	C₂×C₄	—	26	24	no	—
461	C₂×C₄	—	26	12	no	—
462	C₂×C₄	—	52	32	no	—
463	C₂×C₄	—	52	32	no	—
464	C₂×C₄	—	52	32	no	—
465	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
466	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
467	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
468	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
469	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
470	C₂²	—	2	96	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	13	8	no	—
474	C₂²	—	13	16	no	—
475	C₂²	—	26	96	no	—
476	C₂²	—	26	48	no	—
477	C₂²	—	26	8	no	—
478	C₂²	—	26	4	no	—
479	C₂²	—	26	8	no	—
480	C₂²	—	26	4	no	—
481	C₂²	—	52	128	no	—
482	C₂²	#11719250	1	16	yes	direct product factor
483	C₂²	C₂³×C₄×D₁₃	1	16	yes	—
484	C₂²	C₂³×C₄×D₁₃	1	6	yes	—
485	C₂²	C₂×#88251	1	6	yes	—
486	C₂²	C₂×#88256	1	6	yes	—
487	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	8	no	—
490	C₄	—	2	4	no	—
491	C₄	—	13	8	no	—
492	C₄	—	26	4	no	—
493	C₄	—	26	8	no	—
494	C₄	—	26	4	no	—
495	C₄	C₂³×C₄×D₁₃	1	8	yes	—
496	C₂	—	2	16	no	—
497	C₂	—	26	8	no	—
498	C₂	—	26	16	no	—
499	C₂	C₂×#11719250	1	12	yes	direct product factor
500	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
501	C₂	C₂²×#88251	1	1	yes	characteristic
502	C₂	C₂²×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₄×D₁₃	C₂
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×#518
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#11719250	C₂	direct (N × H)
3. C₂²×C₄×D₅₂	C₂	semidirect
4. C₂²×D₄×Dic₁₃	C₂	semidirect
5. C₂²×#88147	C₂	semidirect
6. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
7. C₂²×#88135	C₂	semidirect
8. C₂²×#88146	C₂	semidirect
9. C₂²×#88126	C₂	semidirect
10. C₂³×#6103	C₂	semidirect
11. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
12. C₂²×C₄×D₄×C₁₃	C₂	semidirect
15. C₂⁴×C₄×C₁₃	C₂²	semidirect
17. C₂⁴×Dic₁₃	C₂²	semidirect
18. C₂²×D₄×D₁₃	C₄	semidirect
22. C₂³×C₄×D₁₃	C₂²	semidirect
23. C₂³×C₄×D₁₃	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
25. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₄²×C₁₃	C₂²	semidirect
28. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
29. C₂×D₄×Dic₁₃	C₂²	semidirect
30. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
34. C₂²×#6103	C₂²	semidirect
35. C₂²×#6103	C₂²	semidirect
36. C₂²×#6103	C₂²	semidirect
37. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
38. C₂²×#6101	C₂²	semidirect
39. C₂²×#6101	C₂²	semidirect
40. C₂²×C₄×Dic₁₃	C₂²	semidirect
41. C₂²×C₄×Dic₁₃	C₂²	semidirect
42. #11719250	C₂²	direct (N × H)
43. C₂×#88147	C₂²	semidirect
44. C₂×#88146	C₂²	semidirect
45. C₂×#88135	C₂²	semidirect
46. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
47. C₂×C₄×D₅₂	C₂²	semidirect
48. C₂×#88126	C₂²	semidirect
52. C₂⁴×D₁₃	C₂×C₄	semidirect
56. C₂²×D₄×C₁₃	C₂×C₄	semidirect
63. C₂³×C₄×C₁₃	C₂³	semidirect
64. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
71. C₂³×Dic₁₃	C₂³	semidirect
72. C₂×D₄×D₁₃	C₂×C₄	semidirect
74. C₂²×D₅₂	C₂×C₄	semidirect
78. C₂²×C₄×D₁₃	C₂×C₄	semidirect
80. C₂²×C₄×D₁₃	C₂³	semidirect
81. C₂²×C₄×D₁₃	C₂³	semidirect
82. C₄×D₄×C₁₃	C₂³	semidirect
83. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
84. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
85. C₂×C₄²×C₁₃	C₂³	semidirect
86. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
87. D₄×Dic₁₃	C₂³	semidirect
88. C₄×C₂²⋊D₁₃	C₂³	semidirect
92. C₂×#6103	C₂³	semidirect
93. C₂×#6103	C₂³	semidirect
94. C₂×#6103	C₂³	semidirect
95. C₂×C₄⋊Dic₁₃	C₂³	semidirect
96. C₂×#6101	C₂³	semidirect
97. C₂×#6101	C₂³	semidirect
98. C₂×C₄×Dic₁₃	C₂³	semidirect
99. C₂×C₄×Dic₁₃	C₂³	semidirect
100. #88147	C₂³	semidirect
101. #88146	C₂³	semidirect
102. #88135	C₂³	semidirect
103. C₂²⋊C₄×D₁₃	C₂³	semidirect
104. C₄×D₅₂	C₂³	semidirect
105. #88126	C₂³	semidirect
121. C₂³×D₁₃	C₂²×C₄	semidirect
125. C₂×D₄×C₁₃	C₂²×C₄	semidirect
136. C₂²×C₄×C₁₃	C₂⁴	semidirect
137. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
148. C₂²×Dic₁₃	C₂⁴	semidirect
149. D₄×D₁₃	C₂²×C₄	semidirect
150. C₂×D₅₂	C₂²×C₄	semidirect
154. C₂×C₄×D₁₃	C₂²×C₄	semidirect
156. C₂×C₄×D₁₃	C₂⁴	semidirect
157. C₂×C₄×D₁₃	C₂⁴	semidirect
158. C₁₃×C₄⋊C₄	C₂⁴	semidirect
159. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
160. C₄²×C₁₃	C₂⁴	semidirect
161. C₂²⋊Dic₁₃	C₂⁴	semidirect
165. #6103	C₂⁴	semidirect
166. #6103	C₂⁴	semidirect
167. C₄⋊Dic₁₃	C₂⁴	semidirect
168. #6101	C₂⁴	semidirect
169. #6101	C₂⁴	semidirect
170. C₄×Dic₁₃	C₂⁴	semidirect
171. C₄×Dic₁₃	C₂⁴	semidirect
179. C₂²×C₄×D₄	D₁₃	semidirect
204. C₂²×D₁₃	C₂³×C₄	semidirect
207. D₄×C₁₃	C₂³×C₄	semidirect
217. C₂²⋊D₁₃	C₂³×C₄	semidirect
227. D₅₂	C₂³×C₄	semidirect
230. C₄×D₁₃	C₂³×C₄	semidirect
241. C₂⁴×C₄	C₂×D₁₃	semidirect
248. C₂×C₄×D₄	C₂×D₁₃	semidirect
254. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
263. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
266. C₂²×C₄²	C₂×D₁₃	semidirect
270. C₂²×C₁₃	#518	semidirect
306. C₂²×D₄	C₄×D₁₃	semidirect
325. C₂³×C₄	C₂²×D₁₃	semidirect
331. C₄×D₄	C₂²×D₁₃	semidirect
337. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
346. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
349. C₂×C₄²	C₂²×D₁₃	semidirect
351. C₂×C₁₃	C₂×#518	semidirect
380. C₂×D₄	C₂×C₄×D₁₃	semidirect
407. C₂²×C₄	C₂³×D₁₃	semidirect
411. C₄⋊C₄	C₂³×D₁₃	semidirect
418. C₂²⋊C₄	C₂³×D₁₃	semidirect
421. C₄²	C₂³×D₁₃	semidirect
422. C₁₃	C₂²×#518	semidirect
448. D₄	C₂²×C₄×D₁₃	semidirect
482. C₂²	#11719250	direct (N × H)
499. C₂	C₂×#11719250	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
C₂×#11719250	2
C₂²×C₄×D₅₂	2
C₂²×D₄×Dic₁₃	2
C₂²×#88147	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88135	2
C₂²×#88146	2
C₂²×#88126	2
C₂³×#6103	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂²×#518	13

Subgroups — C22×#11719250 #16769497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719250 #16769497