Subgroups — C₂²×C₁₃×#547 #15749038

Order 3328.

12230 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#547	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#123	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×#41	—	2	32	no	—
11	C₂²×C₁₃×#41	C₂²	1	48	yes	complemented
12	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#547	C₂²	1	256	yes	direct product factor
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	96	yes	complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	48	yes	complemented
23	C₂×C₁₃×#121	C₂²	1	48	yes	complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	48	yes	complemented
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	4	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂⁵×C₁₃	C₂³	1	2	yes	—
38	C₂×C₁₃×#41	—	2	384	no	—
39	C₂×C₁₃×#41	C₂³	1	128	yes	complemented
40	C₂²×Q₈×C₁₃	—	2	16	no	—
41	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
42	C₂²×D₄×C₁₃	—	2	32	no	—
43	C₂²×D₄×C₁₃	—	2	8	no	—
44	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
45	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	48	yes	—
47	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
48	C₂³×C₄×C₁₃	—	2	32	no	—
49	C₂³×C₄×C₁₃	—	2	16	no	—
50	C₂³×C₄×C₁₃	—	2	16	no	—
51	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	48	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
61	C₁₃×#123	C₂³	1	256	yes	complemented
62	C₁₃×C₂²⋊Q₈	C₂³	1	128	yes	complemented
63	C₁₃×#121	C₂³	1	128	yes	complemented
64	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
65	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	128	yes	complemented
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
76	C₂²×#547	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	8	no	—
78	C₂⁴×C₁₃	—	2	8	no	—
79	C₂⁴×C₁₃	—	2	8	no	—
80	C₂⁴×C₁₃	—	2	8	no	—
81	C₂⁴×C₁₃	—	2	8	no	—
82	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
83	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
84	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₁₃×#41	—	2	512	no	—
87	C₂×Q₈×C₁₃	—	2	96	no	—
88	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
89	C₂×D₄×C₁₃	—	2	192	no	—
90	C₂×D₄×C₁₃	—	2	48	no	—
91	C₂×D₄×C₁₃	C₂×D₄	1	96	yes	complemented
92	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
93	C₂×D₄×C₁₃	C₂⁴	1	64	yes	—
94	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
95	C₂²×C₄×C₁₃	—	2	8	no	—
96	C₂²×C₄×C₁₃	—	2	16	no	—
97	C₂²×C₄×C₁₃	—	2	192	no	—
98	C₂²×C₄×C₁₃	—	2	8	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	96	no	—
101	C₂²×C₄×C₁₃	—	2	96	no	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
104	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	64	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
113	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
114	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
115	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
116	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
117	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
118	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
119	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
120	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
121	C₄²×C₁₃	C₂⁴	1	16	yes	—
122	C₂³×#41	C₂×C₁₃	1	2	yes	complemented
123	C₂×#547	C₂×C₁₃	1	48	yes	direct product factor
124	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂²×#123	C₂×C₁₃	1	4	yes	complemented
126	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
127	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
128	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
130	C₂³×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
131	C₂³×C₁₃	—	2	64	no	—
132	C₂³×C₁₃	—	2	24	no	—
133	C₂³×C₁₃	—	2	24	no	—
134	C₂³×C₁₃	—	2	24	no	—
135	C₂³×C₁₃	—	2	24	no	—
136	C₂³×C₁₃	—	2	24	no	—
137	C₂³×C₁₃	—	4	32	no	—
138	C₂³×C₁₃	C₂²×D₄	1	48	yes	—
139	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
140	C₂³×C₁₃	C₂×#41	1	4	yes	—
141	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
142	C₂³×C₁₃	C₂⁵	1	8	yes	—
143	C₂³×C₁₃	C₂⁵	1	8	yes	—
144	C₂³×C₁₃	C₂⁵	1	3	yes	—
145	Q₈×C₁₃	—	2	64	no	—
146	D₄×C₁₃	—	2	128	no	—
147	D₄×C₁₃	—	2	32	no	—
148	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
149	C₂×C₄×C₁₃	—	2	24	no	—
150	C₂×C₄×C₁₃	—	2	48	no	—
151	C₂×C₄×C₁₃	—	2	128	no	—
152	C₂×C₄×C₁₃	—	2	24	no	—
153	C₂×C₄×C₁₃	—	2	12	no	—
154	C₂×C₄×C₁₃	—	2	64	no	—
155	C₂×C₄×C₁₃	—	2	64	no	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
157	C₂×C₄×C₁₃	C₂×#41	1	24	yes	complemented
158	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
159	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
160	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
161	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
162	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
163	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
164	C₂²×#41	—	2	32	no	—
165	C₂²×#41	C₂²×C₁₃	1	48	yes	complemented
166	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
167	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
168	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
169	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
170	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	—
171	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
172	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
173	#547	C₂²×C₁₃	1	256	yes	direct product factor
174	C₂×C₄⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
175	C₂×#123	C₂²×C₁₃	1	96	yes	complemented
176	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
177	C₂×#121	C₂²×C₁₃	1	48	yes	complemented
178	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
179	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
180	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₁₃	1	48	yes	complemented
186	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
189	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₁₃	—	2	8	no	—
191	C₂²×C₁₃	—	2	8	no	—
192	C₂²×C₁₃	—	2	96	no	—
193	C₂²×C₁₃	—	2	8	no	—
194	C₂²×C₁₃	—	2	8	no	—
195	C₂²×C₁₃	—	2	8	no	—
196	C₂²×C₁₃	—	4	48	no	—
197	C₂²×C₁₃	#547	1	16	yes	direct product factor
198	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
199	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
200	C₂²×C₁₃	C₂²×#41	1	6	yes	—
201	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
202	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
203	C₄×C₁₃	—	2	8	no	—
204	C₄×C₁₃	—	2	16	no	—
205	C₄×C₁₃	—	2	8	no	—
206	C₄×C₁₃	—	2	4	no	—
207	C₄×C₁₃	C₂³×D₄	1	8	yes	—
208	C₄×C₁₃	C₂²×#41	1	8	yes	complemented
209	C₂⁵	C₂³×C₁₃	1	2	yes	—
210	C₂⁵	C₂³×C₁₃	1	2	yes	—
211	C₂×#41	—	2	384	no	—
212	C₂×#41	C₂³×C₁₃	1	128	yes	complemented
213	C₂²×Q₈	—	2	16	no	—
214	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
215	C₂²×D₄	—	2	32	no	—
216	C₂²×D₄	—	2	8	no	—
217	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
218	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
219	C₂²×D₄	C₂³×C₁₃	1	48	yes	—
220	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
221	C₂³×C₄	—	2	32	no	—
222	C₂³×C₄	—	2	16	no	—
223	C₂³×C₄	—	2	16	no	—
224	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
226	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
227	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
228	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
229	C₂³×C₄	C₂³×C₁₃	1	48	yes	—
230	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
231	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₄⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
234	#123	C₂³×C₁₃	1	256	yes	complemented
235	C₂²⋊Q₈	C₂³×C₁₃	1	128	yes	complemented
236	#121	C₂³×C₁₃	1	128	yes	complemented
237	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
238	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₃	1	128	yes	complemented
245	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
246	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
248	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
249	C₂×C₁₃	—	2	16	no	—
250	C₂×C₁₃	—	4	8	no	—
251	C₂×C₁₃	C₂×#547	1	12	yes	direct product factor
252	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
253	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
254	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
255	C₂⁴	—	2	8	no	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
261	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
262	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
263	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
264	#41	—	2	512	no	—
265	C₂×Q₈	—	2	96	no	—
266	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
267	C₂×D₄	—	2	192	no	—
268	C₂×D₄	—	2	48	no	—
269	C₂×D₄	C₂×D₄×C₁₃	1	96	yes	complemented
270	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
271	C₂×D₄	C₂⁴×C₁₃	1	64	yes	—
272	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	2	192	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	96	no	—
279	C₂²×C₄	—	2	96	no	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
281	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
282	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
283	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
284	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
285	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
286	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
287	C₂²×C₄	C₂⁴×C₁₃	1	64	yes	—
288	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
289	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
290	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
291	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
292	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
293	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
294	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
295	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
296	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
297	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
298	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
299	C₄²	C₂⁴×C₁₃	1	16	yes	—
300	C₁₃	C₂²×#547	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	—	2	64	no	—
302	C₂³	—	2	24	no	—
303	C₂³	—	2	24	no	—
304	C₂³	—	2	24	no	—
305	C₂³	—	2	24	no	—
306	C₂³	—	2	24	no	—
307	C₂³	—	4	32	no	—
308	C₂³	C₂²×D₄×C₁₃	1	48	yes	—
309	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
310	C₂³	C₂×C₁₃×#41	1	4	yes	—
311	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
312	C₂³	C₂⁵×C₁₃	1	8	yes	—
313	C₂³	C₂⁵×C₁₃	1	8	yes	—
314	C₂³	C₂⁵×C₁₃	1	3	yes	—
315	Q₈	—	2	64	no	—
316	D₄	—	2	128	no	—
317	D₄	—	2	32	no	—
318	D₄	C₂²×D₄×C₁₃	1	64	yes	complemented
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	48	no	—
321	C₂×C₄	—	2	128	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	12	no	—
324	C₂×C₄	—	2	64	no	—
325	C₂×C₄	—	2	64	no	—
326	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
327	C₂×C₄	C₂×C₁₃×#41	1	24	yes	complemented
328	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
329	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
330	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
331	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
332	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
333	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
334	C₂²	—	2	8	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	96	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	4	48	no	—
341	C₂²	C₁₃×#547	1	16	yes	direct product factor
342	C₂²	C₂³×D₄×C₁₃	1	16	yes	—
343	C₂²	C₂³×D₄×C₁₃	1	6	yes	—
344	C₂²	C₂²×C₁₃×#41	1	6	yes	—
345	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	6	yes	—
346	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	2	16	no	—
349	C₄	—	2	8	no	—
350	C₄	—	2	4	no	—
351	C₄	C₂³×D₄×C₁₃	1	8	yes	—
352	C₄	C₂²×C₁₃×#41	1	8	yes	complemented
353	C₂	—	2	16	no	—
354	C₂	—	4	8	no	—
355	C₂	C₂×C₁₃×#547	1	12	yes	direct product factor
356	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
357	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
358	C₂	C₂²×C₁₃×2₋¹⁺⁴	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. C₂³×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#547	C₂	direct (N × H)
3. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
4. C₂²×C₁₃×#123	C₂	semidirect
5. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₁₃×#121	C₂	semidirect
7. C₂²×C₄×D₄×C₁₃	C₂	semidirect
8. C₂²×C₄×D₄×C₁₃	C₂	semidirect
9. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
19. C₁₃×#547	C₂²	direct (N × H)
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#123	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×#121	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
39. C₂×C₁₃×#41	C₂³	semidirect
44. C₂²×D₄×C₁₃	D₄	semidirect
60. C₁₃×C₄⋊Q₈	C₂³	semidirect
61. C₁₃×#123	C₂³	semidirect
62. C₁₃×C₂²⋊Q₈	C₂³	semidirect
63. C₁₃×#121	C₂³	semidirect
64. C₄×D₄×C₁₃	C₂³	semidirect
65. C₄×D₄×C₁₃	C₂³	semidirect
71. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
76. C₂²×#547	C₁₃	direct (N × H)
91. C₂×D₄×C₁₃	C₂×D₄	semidirect
103. C₂²×C₄×C₁₃	#41	semidirect
122. C₂³×#41	C₂×C₁₃	semidirect
123. C₂×#547	C₂×C₁₃	direct (N × H)
124. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
125. C₂²×#123	C₂×C₁₃	semidirect
126. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
127. C₂²×#121	C₂×C₁₃	semidirect
128. C₂²×C₄×D₄	C₂×C₁₃	semidirect
129. C₂²×C₄×D₄	C₂×C₁₃	semidirect
130. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
148. D₄×C₁₃	C₂²×D₄	semidirect
157. C₂×C₄×C₁₃	C₂×#41	semidirect
165. C₂²×#41	C₂²×C₁₃	semidirect
173. #547	C₂²×C₁₃	direct (N × H)
174. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
175. C₂×#123	C₂²×C₁₃	semidirect
176. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
177. C₂×#121	C₂²×C₁₃	semidirect
178. C₂×C₄×D₄	C₂²×C₁₃	semidirect
179. C₂×C₄×D₄	C₂²×C₁₃	semidirect
185. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
197. C₂²×C₁₃	#547	direct (N × H)
208. C₄×C₁₃	C₂²×#41	semidirect
212. C₂×#41	C₂³×C₁₃	semidirect
217. C₂²×D₄	D₄×C₁₃	semidirect
233. C₄⋊Q₈	C₂³×C₁₃	semidirect
234. #123	C₂³×C₁₃	semidirect
235. C₂²⋊Q₈	C₂³×C₁₃	semidirect
236. #121	C₂³×C₁₃	semidirect
237. C₄×D₄	C₂³×C₁₃	semidirect
238. C₄×D₄	C₂³×C₁₃	semidirect
244. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
251. C₂×C₁₃	C₂×#547	direct (N × H)
269. C₂×D₄	C₂×D₄×C₁₃	semidirect
281. C₂²×C₄	C₁₃×#41	semidirect
300. C₁₃	C₂²×#547	direct (N × H)
318. D₄	C₂²×D₄×C₁₃	semidirect
327. C₂×C₄	C₂×C₁₃×#41	semidirect
341. C₂²	C₁₃×#547	direct (N × H)
352. C₄	C₂²×C₁₃×#41	semidirect
355. C₂	C₂×C₁₃×#547	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×C₁₃×#41	2
C₂×C₁₃×#547	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
C₂²×#547	13

Subgroups — C22×C13×#547 #15749038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#547 #15749038