Subgroups — C₂²×C₁₃×#538 #15749010

Order 3328.

9566 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×#126	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#120	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
10	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, 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	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
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	complemented
20	C₁₃×#538	C₂²	1	256	yes	direct product factor
21	C₂×C₁₃×#126	C₂²	1	48	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	48	yes	complemented
23	C₂×C₁₃×#123	C₂²	1	48	yes	complemented
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	48	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	48	yes	complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	48	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×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	complemented
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₃	—	2	8	no	—
43	C₂⁵×C₁₃	—	4	4	no	—
44	C₂⁵×C₁₃	—	4	4	no	—
45	C₂⁵×C₁₃	C₂³	1	2	yes	—
46	C₂⁵×C₁₃	C₂³	1	2	yes	—
47	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
48	C₂⁵×C₁₃	C₂³	1	12	yes	—
49	C₂²×Q₈×C₁₃	—	4	4	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
51	C₂²×D₄×C₁₃	—	2	16	no	—
52	C₂²×D₄×C₁₃	—	4	8	no	—
53	C₂²×D₄×C₁₃	—	4	8	no	—
54	C₂²×D₄×C₁₃	—	4	4	no	—
55	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	12	yes	complemented
59	C₂³×C₄×C₁₃	—	4	4	no	—
60	C₂³×C₄×C₁₃	—	4	4	no	—
61	C₂³×C₄×C₁₃	—	4	8	no	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
71	C₁₃×#126	C₂³	1	128	yes	complemented
72	C₁₃×#124	C₂³	1	128	yes	complemented
73	C₁₃×#123	C₂³	1	128	yes	complemented
74	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
75	C₁₃×#121	C₂³	1	128	yes	complemented
76	C₁₃×#121	C₂³	1	64	yes	complemented
77	C₁₃×#120	C₂³	1	128	yes	complemented
78	C₄×D₄×C₁₃	C₂³	1	128	yes	complemented
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
91	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
92	C₂²×#538	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	8	no	—
96	C₂⁴×C₁₃	—	2	48	no	—
97	C₂⁴×C₁₃	—	2	8	no	—
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	8	no	—
100	C₂⁴×C₁₃	—	2	8	no	—
101	C₂⁴×C₁₃	—	2	8	no	—
102	C₂⁴×C₁₃	—	4	24	no	—
103	C₂⁴×C₁₃	—	4	24	no	—
104	C₂⁴×C₁₃	—	4	64	no	—
105	C₂⁴×C₁₃	#41	1	8	yes	—
106	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
107	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
110	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂×Q₈×C₁₃	—	4	24	no	—
112	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
113	C₂×D₄×C₁₃	—	2	96	no	—
114	C₂×D₄×C₁₃	—	4	48	no	—
115	C₂×D₄×C₁₃	—	4	48	no	—
116	C₂×D₄×C₁₃	—	4	24	no	—
117	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
118	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
119	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
120	C₂×D₄×C₁₃	C₂⁴	1	16	yes	complemented
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	8	no	—
127	C₂²×C₄×C₁₃	—	4	24	no	—
128	C₂²×C₄×C₁₃	—	4	24	no	—
129	C₂²×C₄×C₁₃	—	4	48	no	—
130	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	12	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	12	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
139	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
140	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
141	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
142	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
143	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
144	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
145	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
146	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
147	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
148	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
149	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
150	C₄²×C₁₃	C₂⁴	1	32	yes	complemented
151	C₂×#538	C₂×C₁₃	1	48	yes	direct product factor
152	C₂²×#126	C₂×C₁₃	1	2	yes	complemented
153	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
154	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
155	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
157	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂²×#120	C₂×C₁₃	1	2	yes	complemented
159	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
160	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	32	no	—
162	C₂³×C₁₃	—	2	12	no	—
163	C₂³×C₁₃	—	2	12	no	—
164	C₂³×C₁₃	—	2	24	no	—
165	C₂³×C₁₃	—	2	32	no	—
166	C₂³×C₁₃	—	2	24	no	—
167	C₂³×C₁₃	—	2	24	no	—
168	C₂³×C₁₃	—	2	24	no	—
169	C₂³×C₁₃	—	2	24	no	—
170	C₂³×C₁₃	—	2	24	no	—
171	C₂³×C₁₃	—	4	16	no	—
172	C₂³×C₁₃	—	4	16	no	—
173	C₂³×C₁₃	—	4	192	no	—
174	C₂³×C₁₃	—	4	32	no	—
175	C₂³×C₁₃	—	4	32	no	—
176	C₂³×C₁₃	C₂×#41	1	24	yes	—
177	C₂³×C₁₃	C₂×#41	1	4	yes	—
178	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
179	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
180	C₂³×C₁₃	C₂⁵	1	8	yes	—
181	C₂³×C₁₃	C₂⁵	1	8	yes	—
182	C₂³×C₁₃	C₂⁵	1	4	yes	—
183	C₂³×C₁₃	C₂⁵	1	3	yes	—
184	Q₈×C₁₃	—	4	16	no	—
185	D₄×C₁₃	—	2	64	no	—
186	D₄×C₁₃	—	4	32	no	—
187	D₄×C₁₃	—	4	32	no	—
188	D₄×C₁₃	—	4	16	no	—
189	C₂×C₄×C₁₃	—	2	24	no	—
190	C₂×C₄×C₁₃	—	2	24	no	—
191	C₂×C₄×C₁₃	—	2	12	no	—
192	C₂×C₄×C₁₃	—	2	24	no	—
193	C₂×C₄×C₁₃	—	2	12	no	—
194	C₂×C₄×C₁₃	—	2	24	no	—
195	C₂×C₄×C₁₃	—	4	16	no	—
196	C₂×C₄×C₁₃	—	4	16	no	—
197	C₂×C₄×C₁₃	—	4	32	no	—
198	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
200	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
201	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
202	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
204	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
205	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
206	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
207	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
208	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
209	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
210	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
213	#538	C₂²×C₁₃	1	256	yes	direct product factor
214	C₂×#126	C₂²×C₁₃	1	48	yes	complemented
215	C₂×#124	C₂²×C₁₃	1	48	yes	complemented
216	C₂×#123	C₂²×C₁₃	1	48	yes	complemented
217	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
218	C₂×#121	C₂²×C₁₃	1	48	yes	complemented
219	C₂×#121	C₂²×C₁₃	1	24	yes	complemented
220	C₂×#120	C₂²×C₁₃	1	48	yes	complemented
221	C₂×C₄×D₄	C₂²×C₁₃	1	48	yes	complemented
222	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
223	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
226	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	24	yes	complemented
232	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
233	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
234	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	2	48	no	—
238	C₂²×C₁₃	—	2	8	no	—
239	C₂²×C₁₃	—	2	8	no	—
240	C₂²×C₁₃	—	2	8	no	—
241	C₂²×C₁₃	—	2	8	no	—
242	C₂²×C₁₃	—	2	8	no	—
243	C₂²×C₁₃	—	2	8	no	—
244	C₂²×C₁₃	—	4	64	no	—
245	C₂²×C₁₃	—	4	48	no	—
246	C₂²×C₁₃	—	4	48	no	—
247	C₂²×C₁₃	#538	1	16	yes	direct product factor
248	C₂²×C₁₃	C₂²×#41	1	8	yes	—
249	C₂²×C₁₃	C₂²×#41	1	6	yes	—
250	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
251	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
252	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
253	C₄×C₁₃	—	2	8	no	—
254	C₄×C₁₃	—	2	8	no	—
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	2	8	no	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	8	no	—
259	C₂⁵	—	2	8	no	—
260	C₂⁵	—	4	4	no	—
261	C₂⁵	—	4	4	no	—
262	C₂⁵	C₂³×C₁₃	1	2	yes	—
263	C₂⁵	C₂³×C₁₃	1	2	yes	—
264	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
265	C₂⁵	C₂³×C₁₃	1	12	yes	—
266	C₂²×Q₈	—	4	4	no	—
267	C₂²×Q₈	C₂³×C₁₃	1	12	yes	complemented
268	C₂²×D₄	—	2	16	no	—
269	C₂²×D₄	—	4	8	no	—
270	C₂²×D₄	—	4	8	no	—
271	C₂²×D₄	—	4	4	no	—
272	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
274	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
275	C₂²×D₄	C₂³×C₁₃	1	12	yes	complemented
276	C₂³×C₄	—	4	4	no	—
277	C₂³×C₄	—	4	4	no	—
278	C₂³×C₄	—	4	8	no	—
279	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
282	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
286	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
287	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
288	#126	C₂³×C₁₃	1	128	yes	complemented
289	#124	C₂³×C₁₃	1	128	yes	complemented
290	#123	C₂³×C₁₃	1	128	yes	complemented
291	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
292	#121	C₂³×C₁₃	1	128	yes	complemented
293	#121	C₂³×C₁₃	1	64	yes	complemented
294	#120	C₂³×C₁₃	1	128	yes	complemented
295	C₄×D₄	C₂³×C₁₃	1	128	yes	complemented
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
300	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃	1	64	yes	complemented
306	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
307	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
308	C₂×C₄²	C₂³×C₁₃	1	24	yes	complemented
309	C₂×C₁₃	—	2	8	no	—
310	C₂×C₁₃	—	4	8	no	—
311	C₂×C₁₃	—	4	8	no	—
312	C₂×C₁₃	C₂×#538	1	12	yes	direct product factor
313	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
314	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	8	no	—
319	C₂⁴	—	2	48	no	—
320	C₂⁴	—	2	8	no	—
321	C₂⁴	—	2	8	no	—
322	C₂⁴	—	2	8	no	—
323	C₂⁴	—	2	8	no	—
324	C₂⁴	—	2	8	no	—
325	C₂⁴	—	4	24	no	—
326	C₂⁴	—	4	24	no	—
327	C₂⁴	—	4	64	no	—
328	C₂⁴	C₁₃×#41	1	8	yes	—
329	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
330	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
331	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
332	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
333	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
334	C₂×Q₈	—	4	24	no	—
335	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	complemented
336	C₂×D₄	—	2	96	no	—
337	C₂×D₄	—	4	48	no	—
338	C₂×D₄	—	4	48	no	—
339	C₂×D₄	—	4	24	no	—
340	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
341	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
342	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
343	C₂×D₄	C₂⁴×C₁₃	1	16	yes	complemented
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	4	24	no	—
351	C₂²×C₄	—	4	24	no	—
352	C₂²×C₄	—	4	48	no	—
353	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
354	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
357	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
360	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	complemented
362	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
363	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
364	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	complemented
365	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	complemented
366	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
367	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
368	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
369	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
370	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
371	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
372	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
373	C₄²	C₂⁴×C₁₃	1	32	yes	complemented
374	C₁₃	C₂²×#538	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	32	no	—
376	C₂³	—	2	12	no	—
377	C₂³	—	2	12	no	—
378	C₂³	—	2	24	no	—
379	C₂³	—	2	32	no	—
380	C₂³	—	2	24	no	—
381	C₂³	—	2	24	no	—
382	C₂³	—	2	24	no	—
383	C₂³	—	2	24	no	—
384	C₂³	—	2	24	no	—
385	C₂³	—	4	16	no	—
386	C₂³	—	4	16	no	—
387	C₂³	—	4	192	no	—
388	C₂³	—	4	32	no	—
389	C₂³	—	4	32	no	—
390	C₂³	C₂×C₁₃×#41	1	24	yes	—
391	C₂³	C₂×C₁₃×#41	1	4	yes	—
392	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
393	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
394	C₂³	C₂⁵×C₁₃	1	8	yes	—
395	C₂³	C₂⁵×C₁₃	1	8	yes	—
396	C₂³	C₂⁵×C₁₃	1	4	yes	—
397	C₂³	C₂⁵×C₁₃	1	3	yes	—
398	Q₈	—	4	16	no	—
399	D₄	—	2	64	no	—
400	D₄	—	4	32	no	—
401	D₄	—	4	32	no	—
402	D₄	—	4	16	no	—
403	C₂×C₄	—	2	24	no	—
404	C₂×C₄	—	2	24	no	—
405	C₂×C₄	—	2	12	no	—
406	C₂×C₄	—	2	24	no	—
407	C₂×C₄	—	2	12	no	—
408	C₂×C₄	—	2	24	no	—
409	C₂×C₄	—	4	16	no	—
410	C₂×C₄	—	4	16	no	—
411	C₂×C₄	—	4	32	no	—
412	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
413	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
414	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
415	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
416	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
417	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	48	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	4	64	no	—
428	C₂²	—	4	48	no	—
429	C₂²	—	4	48	no	—
430	C₂²	C₁₃×#538	1	16	yes	direct product factor
431	C₂²	C₂²×C₁₃×#41	1	8	yes	—
432	C₂²	C₂²×C₁₃×#41	1	6	yes	—
433	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
434	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
435	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
436	C₄	—	2	8	no	—
437	C₄	—	2	8	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	8	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	8	no	—
442	C₂	—	2	8	no	—
443	C₂	—	4	8	no	—
444	C₂	—	4	8	no	—
445	C₂	C₂×C₁₃×#538	1	12	yes	direct product factor
446	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
447	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
448	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×#538	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×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₁₃×#121	C₂	semidirect
7. C₂²×C₁₃×#121	C₂	semidirect
8. C₂²×C₁₃×#120	C₂	semidirect
9. C₂²×C₄×D₄×C₁₃	C₂	semidirect
10. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂⁴×C₄×C₁₃	C₂²	semidirect
20. C₁₃×#538	C₂²	direct (N × H)
21. C₂×C₁₃×#126	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₁₃×#123	C₂²	semidirect
24. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
27. C₂×C₁₃×#120	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
31. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
32. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
38. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
39. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
40. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
41. C₂²×C₄²×C₁₃	C₂²	semidirect
50. C₂²×Q₈×C₁₃	C₂³	semidirect
58. C₂²×D₄×C₁₃	C₂³	semidirect
70. C₂³×C₄×C₁₃	C₂³	semidirect
71. C₁₃×#126	C₂³	semidirect
72. C₁₃×#124	C₂³	semidirect
73. C₁₃×#123	C₂³	semidirect
74. C₁₃×C₂²⋊Q₈	C₂³	semidirect
75. C₁₃×#121	C₂³	semidirect
76. C₁₃×#121	C₂³	semidirect
77. C₁₃×#120	C₂³	semidirect
78. C₄×D₄×C₁₃	C₂³	semidirect
79. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
80. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
81. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
82. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
88. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
89. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
90. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
91. C₂×C₄²×C₁₃	C₂³	semidirect
92. C₂²×#538	C₁₃	direct (N × H)
112. C₂×Q₈×C₁₃	C₂⁴	semidirect
120. C₂×D₄×C₁₃	C₂⁴	semidirect
138. C₂²×C₄×C₁₃	C₂⁴	semidirect
139. C₁₃×C₄⋊C₄	C₂⁴	semidirect
140. C₁₃×C₄⋊C₄	C₂⁴	semidirect
141. C₁₃×C₄⋊C₄	C₂⁴	semidirect
142. C₁₃×C₄⋊C₄	C₂⁴	semidirect
148. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
149. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
150. C₄²×C₁₃	C₂⁴	semidirect
151. C₂×#538	C₂×C₁₃	direct (N × H)
152. C₂²×#126	C₂×C₁₃	semidirect
153. C₂²×#124	C₂×C₁₃	semidirect
154. C₂²×#123	C₂×C₁₃	semidirect
155. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
156. C₂²×#121	C₂×C₁₃	semidirect
157. C₂²×#121	C₂×C₁₃	semidirect
158. C₂²×#120	C₂×C₁₃	semidirect
159. C₂²×C₄×D₄	C₂×C₁₃	semidirect
160. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
205. C₂³×Q₈	C₂²×C₁₃	semidirect
209. C₂³×D₄	C₂²×C₁₃	semidirect
212. C₂⁴×C₄	C₂²×C₁₃	semidirect
213. #538	C₂²×C₁₃	direct (N × H)
214. C₂×#126	C₂²×C₁₃	semidirect
215. C₂×#124	C₂²×C₁₃	semidirect
216. C₂×#123	C₂²×C₁₃	semidirect
217. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
218. C₂×#121	C₂²×C₁₃	semidirect
219. C₂×#121	C₂²×C₁₃	semidirect
220. C₂×#120	C₂²×C₁₃	semidirect
221. C₂×C₄×D₄	C₂²×C₁₃	semidirect
222. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
223. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
224. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
225. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
231. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
232. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
233. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
234. C₂²×C₄²	C₂²×C₁₃	semidirect
247. C₂²×C₁₃	#538	direct (N × H)
267. C₂²×Q₈	C₂³×C₁₃	semidirect
275. C₂²×D₄	C₂³×C₁₃	semidirect
287. C₂³×C₄	C₂³×C₁₃	semidirect
288. #126	C₂³×C₁₃	semidirect
289. #124	C₂³×C₁₃	semidirect
290. #123	C₂³×C₁₃	semidirect
291. C₂²⋊Q₈	C₂³×C₁₃	semidirect
292. #121	C₂³×C₁₃	semidirect
293. #121	C₂³×C₁₃	semidirect
294. #120	C₂³×C₁₃	semidirect
295. C₄×D₄	C₂³×C₁₃	semidirect
296. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
297. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
298. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
299. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
305. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
306. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
307. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
308. C₂×C₄²	C₂³×C₁₃	semidirect
312. C₂×C₁₃	C₂×#538	direct (N × H)
335. C₂×Q₈	C₂⁴×C₁₃	semidirect
343. C₂×D₄	C₂⁴×C₁₃	semidirect
361. C₂²×C₄	C₂⁴×C₁₃	semidirect
362. C₄⋊C₄	C₂⁴×C₁₃	semidirect
363. C₄⋊C₄	C₂⁴×C₁₃	semidirect
364. C₄⋊C₄	C₂⁴×C₁₃	semidirect
365. C₄⋊C₄	C₂⁴×C₁₃	semidirect
371. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
372. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
373. C₄²	C₂⁴×C₁₃	semidirect
374. C₁₃	C₂²×#538	direct (N × H)
430. C₂²	C₁₃×#538	direct (N × H)
445. C₂	C₂×C₁₃×#538	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×#538	2
C₂²×C₁₃×#126	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₁₃×#120	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂²×#538	13

Subgroups — C22×C13×#538 #15749010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#538 #15749010