Subgroups — C₂²×C₁₃×#551 #15749042

Order 3328.

9526 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#551	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×#126	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₃×#117	C₂	1	2	yes	maximal, complemented
10	C₂³×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#551	C₂²	1	256	yes	direct product factor
19	C₂×C₁₃×#126	C₂²	1	48	yes	complemented
20	C₂×C₁₃×#124	C₂²	1	24	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	24	yes	complemented
22	C₂×C₁₃×#123	C₂²	1	48	yes	complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	48	yes	complemented
24	C₂×C₁₃×#120	C₂²	1	24	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	48	yes	complemented
26	C₂×C₁₃×#117	C₂²	1	48	yes	complemented
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	48	yes	complemented
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₃	—	2	16	no	—
43	C₂⁵×C₁₃	—	4	4	no	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
46	C₂⁵×C₁₃	C₂³	1	12	yes	—
47	C₂⁵×C₁₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃	—	4	4	no	—
49	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
50	C₂²×D₄×C₁₃	—	2	16	no	—
51	C₂²×D₄×C₁₃	—	4	4	no	—
52	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
54	C₂³×C₄×C₁₃	—	2	16	no	—
55	C₂³×C₄×C₁₃	—	4	8	no	—
56	C₂³×C₄×C₁₃	—	4	4	no	—
57	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
66	C₁₃×#126	C₂³	1	128	yes	complemented
67	C₁₃×#124	C₂³	1	64	yes	complemented
68	C₁₃×#123	C₂³	1	64	yes	complemented
69	C₁₃×#123	C₂³	1	128	yes	complemented
70	C₁₃×C₂²⋊Q₈	C₂³	1	128	yes	complemented
71	C₁₃×#120	C₂³	1	64	yes	—
72	C₄×D₄×C₁₃	C₂³	1	128	yes	complemented
73	C₁₃×#117	C₂³	1	128	yes	complemented
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	128	yes	complemented
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
87	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
88	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
89	C₂²×#551	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	8	no	—
91	C₂⁴×C₁₃	—	2	8	no	—
92	C₂⁴×C₁₃	—	2	8	no	—
93	C₂⁴×C₁₃	—	2	96	no	—
94	C₂⁴×C₁₃	—	2	8	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	4	no	—
97	C₂⁴×C₁₃	—	4	24	no	—
98	C₂⁴×C₁₃	—	4	64	no	—
99	C₂⁴×C₁₃	#41	1	16	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
102	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
103	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
104	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂×Q₈×C₁₃	—	4	24	no	—
106	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
107	C₂×D₄×C₁₃	—	2	96	no	—
108	C₂×D₄×C₁₃	—	4	24	no	—
109	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
110	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
111	C₂²×C₄×C₁₃	—	2	96	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	8	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	4	48	no	—
119	C₂²×C₄×C₁₃	—	4	24	no	—
120	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
129	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
130	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
131	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
132	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
133	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
134	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
135	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
136	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
137	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
138	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
139	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
140	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
141	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
142	C₄²×C₁₃	C₂⁴	1	32	yes	complemented
143	C₂×#551	C₂×C₁₃	1	48	yes	direct product factor
144	C₂²×#126	C₂×C₁₃	1	2	yes	complemented
145	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
148	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
149	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic
150	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
151	C₂²×#117	C₂×C₁₃	1	2	yes	complemented
152	C₂³×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
153	C₂³×C₁₃	—	2	64	no	—
154	C₂³×C₁₃	—	2	24	no	—
155	C₂³×C₁₃	—	2	24	no	—
156	C₂³×C₁₃	—	2	24	no	—
157	C₂³×C₁₃	—	2	64	no	—
158	C₂³×C₁₃	—	2	24	no	—
159	C₂³×C₁₃	—	2	12	no	—
160	C₂³×C₁₃	—	2	12	no	—
161	C₂³×C₁₃	—	4	16	no	—
162	C₂³×C₁₃	—	4	192	no	—
163	C₂³×C₁₃	—	4	16	no	—
164	C₂³×C₁₃	—	4	16	no	—
165	C₂³×C₁₃	C₂×#41	1	48	yes	—
166	C₂³×C₁₃	C₂×#41	1	8	yes	—
167	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
168	C₂³×C₁₃	C₂⁵	1	4	yes	—
169	C₂³×C₁₃	C₂⁵	1	4	yes	—
170	C₂³×C₁₃	C₂⁵	1	8	yes	—
171	C₂³×C₁₃	C₂⁵	1	3	yes	—
172	Q₈×C₁₃	—	4	16	no	—
173	D₄×C₁₃	—	2	64	no	—
174	D₄×C₁₃	—	4	16	no	—
175	C₂×C₄×C₁₃	—	2	64	no	—
176	C₂×C₄×C₁₃	—	2	24	no	—
177	C₂×C₄×C₁₃	—	2	24	no	—
178	C₂×C₄×C₁₃	—	2	24	no	—
179	C₂×C₄×C₁₃	—	2	24	no	—
180	C₂×C₄×C₁₃	—	2	24	no	—
181	C₂×C₄×C₁₃	—	2	12	no	—
182	C₂×C₄×C₁₃	—	4	32	no	—
183	C₂×C₄×C₁₃	—	4	16	no	—
184	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
185	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
186	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
187	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
188	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
189	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
190	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
191	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
193	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
194	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
195	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
196	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
197	#551	C₂²×C₁₃	1	256	yes	direct product factor
198	C₂×#126	C₂²×C₁₃	1	48	yes	complemented
199	C₂×#124	C₂²×C₁₃	1	24	yes	complemented
200	C₂×#123	C₂²×C₁₃	1	24	yes	complemented
201	C₂×#123	C₂²×C₁₃	1	48	yes	complemented
202	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
203	C₂×#120	C₂²×C₁₃	1	24	yes	—
204	C₂×C₄×D₄	C₂²×C₁₃	1	48	yes	complemented
205	C₂×#117	C₂²×C₁₃	1	48	yes	complemented
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
207	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
208	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
209	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
210	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	48	yes	complemented
217	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
218	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
221	C₂²×C₁₃	—	2	8	no	—
222	C₂²×C₁₃	—	2	8	no	—
223	C₂²×C₁₃	—	2	96	no	—
224	C₂²×C₁₃	—	2	8	no	—
225	C₂²×C₁₃	—	2	8	no	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	4	64	no	—
229	C₂²×C₁₃	—	4	24	no	—
230	C₂²×C₁₃	—	4	24	no	—
231	C₂²×C₁₃	#551	1	16	yes	direct product factor
232	C₂²×C₁₃	C₂²×#41	1	16	yes	—
233	C₂²×C₁₃	C₂²×#41	1	12	yes	—
234	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
235	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
236	C₄×C₁₃	—	2	8	no	—
237	C₄×C₁₃	—	2	8	no	—
238	C₄×C₁₃	—	2	8	no	—
239	C₄×C₁₃	—	2	8	no	—
240	C₄×C₁₃	—	2	8	no	—
241	C₄×C₁₃	—	2	4	no	—
242	C₂⁵	—	2	16	no	—
243	C₂⁵	—	4	4	no	—
244	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
245	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
246	C₂⁵	C₂³×C₁₃	1	12	yes	—
247	C₂⁵	C₂³×C₁₃	1	2	yes	—
248	C₂²×Q₈	—	4	4	no	—
249	C₂²×Q₈	C₂³×C₁₃	1	12	yes	complemented
250	C₂²×D₄	—	2	16	no	—
251	C₂²×D₄	—	4	4	no	—
252	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
253	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
254	C₂³×C₄	—	2	16	no	—
255	C₂³×C₄	—	4	8	no	—
256	C₂³×C₄	—	4	4	no	—
257	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
262	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
264	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
265	C₂³×C₄	C₂³×C₁₃	1	12	yes	complemented
266	#126	C₂³×C₁₃	1	128	yes	complemented
267	#124	C₂³×C₁₃	1	64	yes	complemented
268	#123	C₂³×C₁₃	1	64	yes	complemented
269	#123	C₂³×C₁₃	1	128	yes	complemented
270	C₂²⋊Q₈	C₂³×C₁₃	1	128	yes	complemented
271	#120	C₂³×C₁₃	1	64	yes	—
272	C₄×D₄	C₂³×C₁₃	1	128	yes	complemented
273	#117	C₂³×C₁₃	1	128	yes	complemented
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
278	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₁₃	1	128	yes	complemented
285	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
286	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	complemented
287	C₂×C₄²	C₂³×C₁₃	1	12	yes	complemented
288	C₂×C₄²	C₂³×C₁₃	1	24	yes	complemented
289	C₂×C₁₃	—	2	16	no	—
290	C₂×C₁₃	—	4	4	no	—
291	C₂×C₁₃	—	4	4	no	—
292	C₂×C₁₃	C₂×#551	1	12	yes	direct product factor
293	C₂×C₁₃	C₂³×#41	1	2	yes	—
294	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	8	no	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	2	96	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	4	24	no	—
303	C₂⁴	—	4	64	no	—
304	C₂⁴	C₁₃×#41	1	16	yes	—
305	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
306	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
307	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
308	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
309	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
310	C₂×Q₈	—	4	24	no	—
311	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	complemented
312	C₂×D₄	—	2	96	no	—
313	C₂×D₄	—	4	24	no	—
314	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
315	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
316	C₂²×C₄	—	2	96	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	4	48	no	—
324	C₂²×C₄	—	4	24	no	—
325	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
326	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
329	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	complemented
334	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
335	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
336	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
337	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
338	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
339	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
340	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
341	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
342	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
343	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
344	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
345	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	complemented
346	C₄²	C₂⁴×C₁₃	1	16	yes	complemented
347	C₄²	C₂⁴×C₁₃	1	32	yes	complemented
348	C₁₃	C₂²×#551	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	64	no	—
350	C₂³	—	2	24	no	—
351	C₂³	—	2	24	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	2	64	no	—
354	C₂³	—	2	24	no	—
355	C₂³	—	2	12	no	—
356	C₂³	—	2	12	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	4	192	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	4	16	no	—
361	C₂³	C₂×C₁₃×#41	1	48	yes	—
362	C₂³	C₂×C₁₃×#41	1	8	yes	—
363	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
364	C₂³	C₂⁵×C₁₃	1	4	yes	—
365	C₂³	C₂⁵×C₁₃	1	4	yes	—
366	C₂³	C₂⁵×C₁₃	1	8	yes	—
367	C₂³	C₂⁵×C₁₃	1	3	yes	—
368	Q₈	—	4	16	no	—
369	D₄	—	2	64	no	—
370	D₄	—	4	16	no	—
371	C₂×C₄	—	2	64	no	—
372	C₂×C₄	—	2	24	no	—
373	C₂×C₄	—	2	24	no	—
374	C₂×C₄	—	2	24	no	—
375	C₂×C₄	—	2	24	no	—
376	C₂×C₄	—	2	24	no	—
377	C₂×C₄	—	2	12	no	—
378	C₂×C₄	—	4	32	no	—
379	C₂×C₄	—	4	16	no	—
380	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
381	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
382	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
383	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
384	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
385	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
386	C₂²	—	2	8	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	96	no	—
389	C₂²	—	2	8	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	64	no	—
394	C₂²	—	4	24	no	—
395	C₂²	—	4	24	no	—
396	C₂²	C₁₃×#551	1	16	yes	direct product factor
397	C₂²	C₂²×C₁₃×#41	1	16	yes	—
398	C₂²	C₂²×C₁₃×#41	1	12	yes	—
399	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
400	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	8	no	—
403	C₄	—	2	8	no	—
404	C₄	—	2	8	no	—
405	C₄	—	2	8	no	—
406	C₄	—	2	4	no	—
407	C₂	—	2	16	no	—
408	C₂	—	4	4	no	—
409	C₂	—	4	4	no	—
410	C₂	C₂×C₁₃×#551	1	12	yes	direct product factor
411	C₂	C₂³×C₁₃×#41	1	2	yes	—
412	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂²×C₁₃×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#551	C₂	direct (N × H)
2. C₂²×C₁₃×#126	C₂	semidirect
3. C₂²×C₁₃×#124	C₂	semidirect
4. C₂²×C₁₃×#123	C₂	semidirect
5. C₂²×C₁₃×#123	C₂	semidirect
6. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
8. C₂²×C₄×D₄×C₁₃	C₂	semidirect
9. C₂²×C₁₃×#117	C₂	semidirect
10. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
17. C₂⁴×C₄×C₁₃	C₂²	semidirect
18. C₁₃×#551	C₂²	direct (N × H)
19. C₂×C₁₃×#126	C₂²	semidirect
20. C₂×C₁₃×#124	C₂²	semidirect
21. C₂×C₁₃×#123	C₂²	semidirect
22. C₂×C₁₃×#123	C₂²	semidirect
23. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₂×C₁₃×#117	C₂²	semidirect
27. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
28. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
29. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
37. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
38. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
39. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
40. C₂²×C₄²×C₁₃	C₂²	semidirect
41. C₂²×C₄²×C₁₃	C₂²	semidirect
49. C₂²×Q₈×C₁₃	C₂³	semidirect
65. C₂³×C₄×C₁₃	C₂³	semidirect
66. C₁₃×#126	C₂³	semidirect
67. C₁₃×#124	C₂³	semidirect
68. C₁₃×#123	C₂³	semidirect
69. C₁₃×#123	C₂³	semidirect
70. C₁₃×C₂²⋊Q₈	C₂³	semidirect
72. C₄×D₄×C₁₃	C₂³	semidirect
73. C₁₃×#117	C₂³	semidirect
74. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
75. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
76. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
77. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
84. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
85. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
86. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
87. C₂×C₄²×C₁₃	C₂³	semidirect
88. C₂×C₄²×C₁₃	C₂³	semidirect
89. C₂²×#551	C₁₃	direct (N × H)
106. C₂×Q₈×C₁₃	C₂⁴	semidirect
128. C₂²×C₄×C₁₃	C₂⁴	semidirect
129. C₁₃×C₄⋊C₄	C₂⁴	semidirect
130. C₁₃×C₄⋊C₄	C₂⁴	semidirect
131. C₁₃×C₄⋊C₄	C₂⁴	semidirect
132. C₁₃×C₄⋊C₄	C₂⁴	semidirect
139. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
140. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
141. C₄²×C₁₃	C₂⁴	semidirect
142. C₄²×C₁₃	C₂⁴	semidirect
143. C₂×#551	C₂×C₁₃	direct (N × H)
144. C₂²×#126	C₂×C₁₃	semidirect
145. C₂²×#124	C₂×C₁₃	semidirect
146. C₂²×#123	C₂×C₁₃	semidirect
147. C₂²×#123	C₂×C₁₃	semidirect
148. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
150. C₂²×C₄×D₄	C₂×C₁₃	semidirect
151. C₂²×#117	C₂×C₁₃	semidirect
152. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
191. C₂³×Q₈	C₂²×C₁₃	semidirect
196. C₂⁴×C₄	C₂²×C₁₃	semidirect
197. #551	C₂²×C₁₃	direct (N × H)
198. C₂×#126	C₂²×C₁₃	semidirect
199. C₂×#124	C₂²×C₁₃	semidirect
200. C₂×#123	C₂²×C₁₃	semidirect
201. C₂×#123	C₂²×C₁₃	semidirect
202. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
204. C₂×C₄×D₄	C₂²×C₁₃	semidirect
205. C₂×#117	C₂²×C₁₃	semidirect
206. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
207. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
208. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
209. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
216. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
217. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
218. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
219. C₂²×C₄²	C₂²×C₁₃	semidirect
220. C₂²×C₄²	C₂²×C₁₃	semidirect
231. C₂²×C₁₃	#551	direct (N × H)
249. C₂²×Q₈	C₂³×C₁₃	semidirect
265. C₂³×C₄	C₂³×C₁₃	semidirect
266. #126	C₂³×C₁₃	semidirect
267. #124	C₂³×C₁₃	semidirect
268. #123	C₂³×C₁₃	semidirect
269. #123	C₂³×C₁₃	semidirect
270. C₂²⋊Q₈	C₂³×C₁₃	semidirect
272. C₄×D₄	C₂³×C₁₃	semidirect
273. #117	C₂³×C₁₃	semidirect
274. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
275. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
276. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
277. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
284. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
285. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
286. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
287. C₂×C₄²	C₂³×C₁₃	semidirect
288. C₂×C₄²	C₂³×C₁₃	semidirect
292. C₂×C₁₃	C₂×#551	direct (N × H)
311. C₂×Q₈	C₂⁴×C₁₃	semidirect
333. C₂²×C₄	C₂⁴×C₁₃	semidirect
334. C₄⋊C₄	C₂⁴×C₁₃	semidirect
335. C₄⋊C₄	C₂⁴×C₁₃	semidirect
336. C₄⋊C₄	C₂⁴×C₁₃	semidirect
337. C₄⋊C₄	C₂⁴×C₁₃	semidirect
344. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
345. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
346. C₄²	C₂⁴×C₁₃	semidirect
347. C₄²	C₂⁴×C₁₃	semidirect
348. C₁₃	C₂²×#551	direct (N × H)
396. C₂²	C₁₃×#551	direct (N × H)
410. C₂	C₂×C₁₃×#551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#551	2
C₂²×C₁₃×#126	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#120	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₁₃×#117	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂²×#551	13

Subgroups — C22×C13×#551 #15749042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#551 #15749042