Subgroups — C₂²×C₁₃×#553 #15749044

Order 3328.

8798 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#553	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×#126	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
20	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#553	C₂²	1	256	yes	direct product factor
22	C₂×C₁₃×#126	C₂²	1	48	yes	complemented
23	C₂×C₁₃×#125	C₂²	1	24	yes	complemented
24	C₂×C₁₃×#123	C₂²	1	48	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	48	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
27	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	48	yes	complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
30	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
31	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	24	yes	complemented
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
48	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	16	no	—
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	4	8	no	—
55	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
59	C₂³×C₄×C₁₃	—	2	8	no	—
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	—	4	8	no	—
62	C₂³×C₄×C₁₃	—	4	8	no	—
63	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#126	C₂³	1	128	yes	complemented
76	C₁₃×#125	C₂³	1	64	yes	complemented
77	C₁₃×#123	C₂³	1	128	yes	complemented
78	C₁₃×#121	C₂³	1	128	yes	complemented
79	C₁₃×#121	C₂³	1	64	yes	complemented
80	C₁₃×#121	C₂³	1	64	yes	complemented
81	C₄×D₄×C₁₃	C₂³	1	128	yes	complemented
82	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
83	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
84	C₁₃×#117	C₂³	1	64	yes	complemented
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	64	yes	complemented
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
101	C₂²×#553	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	4	no	—
103	C₂⁴×C₁₃	—	2	4	no	—
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	4	no	—
106	C₂⁴×C₁₃	—	2	8	no	—
107	C₂⁴×C₁₃	—	2	8	no	—
108	C₂⁴×C₁₃	—	2	8	no	—
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	#41	1	8	yes	—
111	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
112	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₂×D₄×C₁₃	—	2	96	no	—
116	C₂×D₄×C₁₃	—	2	48	no	—
117	C₂×D₄×C₁₃	—	2	48	no	—
118	C₂×D₄×C₁₃	—	4	48	no	—
119	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
120	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
121	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
122	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	48	no	—
131	C₂²×C₄×C₁₃	—	2	48	no	—
132	C₂²×C₄×C₁₃	—	4	48	no	—
133	C₂²×C₄×C₁₃	—	4	48	no	—
134	C₂²×C₄×C₁₃	#41	1	8	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
147	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
148	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
149	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
150	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
151	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
152	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
153	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
154	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
155	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
156	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
157	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
158	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
159	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
160	C₄²×C₁₃	C₂⁴	1	32	yes	—
161	C₄²×C₁₃	C₂⁴	1	16	yes	—
162	C₂×#553	C₂×C₁₃	1	48	yes	direct product factor
163	C₂²×#126	C₂×C₁₃	1	2	yes	complemented
164	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
166	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
167	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
170	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	32	no	—
175	C₂³×C₁₃	—	2	12	no	—
176	C₂³×C₁₃	—	2	12	no	—
177	C₂³×C₁₃	—	2	12	no	—
178	C₂³×C₁₃	—	2	12	no	—
179	C₂³×C₁₃	—	2	24	no	—
180	C₂³×C₁₃	—	2	24	no	—
181	C₂³×C₁₃	—	2	24	no	—
182	C₂³×C₁₃	—	2	12	no	—
183	C₂³×C₁₃	—	4	16	no	—
184	C₂³×C₁₃	—	4	32	no	—
185	C₂³×C₁₃	C₂×#41	1	24	yes	—
186	C₂³×C₁₃	C₂×#41	1	4	yes	—
187	C₂³×C₁₃	C₂×#41	1	4	yes	—
188	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
189	C₂³×C₁₃	C₂⁵	1	4	yes	—
190	C₂³×C₁₃	C₂⁵	1	8	yes	—
191	C₂³×C₁₃	C₂⁵	1	4	yes	—
192	C₂³×C₁₃	C₂⁵	1	3	yes	—
193	D₄×C₁₃	—	2	64	no	—
194	D₄×C₁₃	—	2	32	no	—
195	D₄×C₁₃	—	2	32	no	—
196	D₄×C₁₃	—	4	32	no	—
197	C₂×C₄×C₁₃	—	2	12	no	—
198	C₂×C₄×C₁₃	—	2	12	no	—
199	C₂×C₄×C₁₃	—	2	24	no	—
200	C₂×C₄×C₁₃	—	2	12	no	—
201	C₂×C₄×C₁₃	—	2	12	no	—
202	C₂×C₄×C₁₃	—	2	24	no	—
203	C₂×C₄×C₁₃	—	2	24	no	—
204	C₂×C₄×C₁₃	—	2	32	no	—
205	C₂×C₄×C₁₃	—	2	32	no	—
206	C₂×C₄×C₁₃	—	4	32	no	—
207	C₂×C₄×C₁₃	—	4	32	no	—
208	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
209	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
210	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
211	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
212	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
213	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
214	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
216	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
217	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
218	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
220	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
221	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
224	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
225	#553	C₂²×C₁₃	1	256	yes	direct product factor
226	C₂×#126	C₂²×C₁₃	1	48	yes	complemented
227	C₂×#125	C₂²×C₁₃	1	24	yes	complemented
228	C₂×#123	C₂²×C₁₃	1	48	yes	complemented
229	C₂×#121	C₂²×C₁₃	1	48	yes	complemented
230	C₂×#121	C₂²×C₁₃	1	24	yes	complemented
231	C₂×#121	C₂²×C₁₃	1	24	yes	complemented
232	C₂×C₄×D₄	C₂²×C₁₃	1	48	yes	complemented
233	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
234	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
235	C₂×#117	C₂²×C₁₃	1	24	yes	complemented
236	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₄⋊C₄	C₂²×C₁₃	1	24	yes	complemented
244	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₁₃	—	2	4	no	—
253	C₂²×C₁₃	—	2	4	no	—
254	C₂²×C₁₃	—	2	48	no	—
255	C₂²×C₁₃	—	2	4	no	—
256	C₂²×C₁₃	—	2	4	no	—
257	C₂²×C₁₃	—	2	8	no	—
258	C₂²×C₁₃	—	2	8	no	—
259	C₂²×C₁₃	—	2	8	no	—
260	C₂²×C₁₃	—	2	4	no	—
261	C₂²×C₁₃	—	4	24	no	—
262	C₂²×C₁₃	—	4	48	no	—
263	C₂²×C₁₃	#553	1	16	yes	direct product factor
264	C₂²×C₁₃	C₂²×#41	1	8	yes	—
265	C₂²×C₁₃	C₂²×#41	1	6	yes	—
266	C₂²×C₁₃	C₂²×#41	1	6	yes	—
267	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
268	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	4	no	—
271	C₄×C₁₃	—	2	8	no	—
272	C₄×C₁₃	—	2	4	no	—
273	C₄×C₁₃	—	2	4	no	—
274	C₄×C₁₃	—	2	8	no	—
275	C₄×C₁₃	—	2	8	no	—
276	C₄×C₁₃	C₂²×#41	1	8	yes	—
277	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
278	C₂⁵	C₂³×C₁₃	1	2	yes	—
279	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	16	no	—
281	C₂²×D₄	—	2	8	no	—
282	C₂²×D₄	—	2	8	no	—
283	C₂²×D₄	—	4	8	no	—
284	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
285	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
286	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
287	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
288	C₂³×C₄	—	2	8	no	—
289	C₂³×C₄	—	2	8	no	—
290	C₂³×C₄	—	4	8	no	—
291	C₂³×C₄	—	4	8	no	—
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
301	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
302	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
303	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
304	#126	C₂³×C₁₃	1	128	yes	complemented
305	#125	C₂³×C₁₃	1	64	yes	complemented
306	#123	C₂³×C₁₃	1	128	yes	complemented
307	#121	C₂³×C₁₃	1	128	yes	complemented
308	#121	C₂³×C₁₃	1	64	yes	complemented
309	#121	C₂³×C₁₃	1	64	yes	complemented
310	C₄×D₄	C₂³×C₁₃	1	128	yes	complemented
311	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
312	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
313	#117	C₂³×C₁₃	1	64	yes	complemented
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	64	yes	complemented
322	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
328	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
329	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
330	C₂×C₁₃	—	2	8	no	—
331	C₂×C₁₃	—	4	4	no	—
332	C₂×C₁₃	—	4	8	no	—
333	C₂×C₁₃	C₂×#553	1	12	yes	direct product factor
334	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
335	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
336	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	8	no	—
342	C₂⁴	—	2	8	no	—
343	C₂⁴	—	2	8	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	C₁₃×#41	1	8	yes	—
346	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
347	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
348	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
349	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
350	C₂×D₄	—	2	96	no	—
351	C₂×D₄	—	2	48	no	—
352	C₂×D₄	—	2	48	no	—
353	C₂×D₄	—	4	48	no	—
354	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
355	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
356	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
357	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	48	no	—
366	C₂²×C₄	—	2	48	no	—
367	C₂²×C₄	—	4	48	no	—
368	C₂²×C₄	—	4	48	no	—
369	C₂²×C₄	C₁₃×#41	1	8	yes	—
370	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
371	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
372	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
381	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
382	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
383	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
384	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
385	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
386	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
387	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
388	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
389	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
390	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
391	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
392	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
393	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
394	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
395	C₄²	C₂⁴×C₁₃	1	32	yes	—
396	C₄²	C₂⁴×C₁₃	1	16	yes	—
397	C₁₃	C₂²×#553	1	1	yes	characteristic, direct product factor, Sylow
398	C₂³	—	2	32	no	—
399	C₂³	—	2	12	no	—
400	C₂³	—	2	12	no	—
401	C₂³	—	2	12	no	—
402	C₂³	—	2	12	no	—
403	C₂³	—	2	24	no	—
404	C₂³	—	2	24	no	—
405	C₂³	—	2	24	no	—
406	C₂³	—	2	12	no	—
407	C₂³	—	4	16	no	—
408	C₂³	—	4	32	no	—
409	C₂³	C₂×C₁₃×#41	1	24	yes	—
410	C₂³	C₂×C₁₃×#41	1	4	yes	—
411	C₂³	C₂×C₁₃×#41	1	4	yes	—
412	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
413	C₂³	C₂⁵×C₁₃	1	4	yes	—
414	C₂³	C₂⁵×C₁₃	1	8	yes	—
415	C₂³	C₂⁵×C₁₃	1	4	yes	—
416	C₂³	C₂⁵×C₁₃	1	3	yes	—
417	D₄	—	2	64	no	—
418	D₄	—	2	32	no	—
419	D₄	—	2	32	no	—
420	D₄	—	4	32	no	—
421	C₂×C₄	—	2	12	no	—
422	C₂×C₄	—	2	12	no	—
423	C₂×C₄	—	2	24	no	—
424	C₂×C₄	—	2	12	no	—
425	C₂×C₄	—	2	12	no	—
426	C₂×C₄	—	2	24	no	—
427	C₂×C₄	—	2	24	no	—
428	C₂×C₄	—	2	32	no	—
429	C₂×C₄	—	2	32	no	—
430	C₂×C₄	—	4	32	no	—
431	C₂×C₄	—	4	32	no	—
432	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
433	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
434	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
435	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
436	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
437	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
438	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
439	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
440	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	48	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	8	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	4	24	no	—
451	C₂²	—	4	48	no	—
452	C₂²	C₁₃×#553	1	16	yes	direct product factor
453	C₂²	C₂²×C₁₃×#41	1	8	yes	—
454	C₂²	C₂²×C₁₃×#41	1	6	yes	—
455	C₂²	C₂²×C₁₃×#41	1	6	yes	—
456	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
457	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
458	C₄	—	2	4	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	8	no	—
461	C₄	—	2	4	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	8	no	—
464	C₄	—	2	8	no	—
465	C₄	C₂²×C₁₃×#41	1	8	yes	—
466	C₂	—	2	8	no	—
467	C₂	—	4	4	no	—
468	C₂	—	4	8	no	—
469	C₂	C₂×C₁₃×#553	1	12	yes	direct product factor
470	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
471	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
472	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
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×#553	C₂	direct (N × H)
2. C₂²×C₁₃×#126	C₂	semidirect
3. C₂²×C₁₃×#125	C₂	semidirect
4. C₂²×C₁₃×#123	C₂	semidirect
5. C₂²×C₁₃×#121	C₂	semidirect
6. C₂²×C₁₃×#121	C₂	semidirect
7. C₂²×C₁₃×#121	C₂	semidirect
8. C₂²×C₄×D₄×C₁₃	C₂	semidirect
9. C₂²×C₄×D₄×C₁₃	C₂	semidirect
10. C₂²×C₄×D₄×C₁₃	C₂	semidirect
11. C₂²×C₁₃×#117	C₂	semidirect
12. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
21. C₁₃×#553	C₂²	direct (N × H)
22. C₂×C₁₃×#126	C₂²	semidirect
23. C₂×C₁₃×#125	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₁₃×#117	C₂²	semidirect
39. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
75. C₁₃×#126	C₂³	semidirect
76. C₁₃×#125	C₂³	semidirect
77. C₁₃×#123	C₂³	semidirect
78. C₁₃×#121	C₂³	semidirect
79. C₁₃×#121	C₂³	semidirect
80. C₁₃×#121	C₂³	semidirect
81. C₄×D₄×C₁₃	C₂³	semidirect
82. C₄×D₄×C₁₃	C₂³	semidirect
83. C₄×D₄×C₁₃	C₂³	semidirect
84. C₁₃×#117	C₂³	semidirect
92. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
101. C₂²×#553	C₁₃	direct (N × H)
162. C₂×#553	C₂×C₁₃	direct (N × H)
163. C₂²×#126	C₂×C₁₃	semidirect
164. C₂²×#125	C₂×C₁₃	semidirect
165. C₂²×#123	C₂×C₁₃	semidirect
166. C₂²×#121	C₂×C₁₃	semidirect
167. C₂²×#121	C₂×C₁₃	semidirect
168. C₂²×#121	C₂×C₁₃	semidirect
169. C₂²×C₄×D₄	C₂×C₁₃	semidirect
170. C₂²×C₄×D₄	C₂×C₁₃	semidirect
171. C₂²×C₄×D₄	C₂×C₁₃	semidirect
172. C₂²×#117	C₂×C₁₃	semidirect
173. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
225. #553	C₂²×C₁₃	direct (N × H)
226. C₂×#126	C₂²×C₁₃	semidirect
227. C₂×#125	C₂²×C₁₃	semidirect
228. C₂×#123	C₂²×C₁₃	semidirect
229. C₂×#121	C₂²×C₁₃	semidirect
230. C₂×#121	C₂²×C₁₃	semidirect
231. C₂×#121	C₂²×C₁₃	semidirect
232. C₂×C₄×D₄	C₂²×C₁₃	semidirect
233. C₂×C₄×D₄	C₂²×C₁₃	semidirect
234. C₂×C₄×D₄	C₂²×C₁₃	semidirect
235. C₂×#117	C₂²×C₁₃	semidirect
243. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
263. C₂²×C₁₃	#553	direct (N × H)
304. #126	C₂³×C₁₃	semidirect
305. #125	C₂³×C₁₃	semidirect
306. #123	C₂³×C₁₃	semidirect
307. #121	C₂³×C₁₃	semidirect
308. #121	C₂³×C₁₃	semidirect
309. #121	C₂³×C₁₃	semidirect
310. C₄×D₄	C₂³×C₁₃	semidirect
311. C₄×D₄	C₂³×C₁₃	semidirect
312. C₄×D₄	C₂³×C₁₃	semidirect
313. #117	C₂³×C₁₃	semidirect
321. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
333. C₂×C₁₃	C₂×#553	direct (N × H)
397. C₁₃	C₂²×#553	direct (N × H)
452. C₂²	C₁₃×#553	direct (N × H)
469. C₂	C₂×C₁₃×#553	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×#553	2
C₂²×C₁₃×#126	2
C₂²×C₁₃×#125	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₁₃×#117	2
C₂³×C₁₃×C₄⋊C₄	2
C₂²×#553	13

Subgroups — C22×C13×#553 #15749044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#553 #15749044