Subgroups — C₂²×C₁₃×#546 #15749036

Order 3328.

14462 conjugacy classes of subgroups.

The subgroup lattice has 546 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	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#546	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₃×#120	C₂	1	2	yes	maximal, complemented
10	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂⁶×C₁₃	C₂²	1	2	yes	—
14	C₂²×C₁₃×#41	—	2	16	no	—
15	C₂²×C₁₃×#41	C₂²	1	24	yes	complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₁₃	—	2	16	no	—
18	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₁₃	C₂²	1	24	yes	complemented
23	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
24	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
25	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
27	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#546	C₂²	1	256	yes	direct product factor
30	C₂×C₁₃×#124	C₂²	1	24	yes	complemented
31	C₂×C₁₃×#123	C₂²	1	48	yes	complemented
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
33	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
34	C₂×C₁₃×#121	C₂²	1	48	yes	complemented
35	C₂×C₁₃×#120	C₂²	1	48	yes	complemented
36	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
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	48	yes	complemented
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
47	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
49	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
50	C₂⁵×C₁₃	—	2	16	no	—
51	C₂⁵×C₁₃	—	2	16	no	—
52	C₂⁵×C₁₃	—	4	8	no	—
53	C₂⁵×C₁₃	C₂³	1	2	yes	—
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁵×C₁₃	C₂³	1	24	yes	—
56	C₂⁵×C₁₃	C₂³	1	2	yes	—
57	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×#41	—	2	192	no	—
59	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
60	C₂²×Q₈×C₁₃	—	2	8	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
62	C₂²×D₄×C₁₃	—	2	16	no	—
63	C₂²×D₄×C₁₃	—	2	16	no	—
64	C₂²×D₄×C₁₃	—	2	8	no	—
65	C₂²×D₄×C₁₃	—	2	192	no	—
66	C₂²×D₄×C₁₃	—	2	8	no	—
67	C₂²×D₄×C₁₃	—	4	8	no	—
68	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
69	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
74	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
75	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
76	C₂³×C₄×C₁₃	—	2	16	no	—
77	C₂³×C₄×C₁₃	—	2	8	no	—
78	C₂³×C₄×C₁₃	—	2	8	no	—
79	C₂³×C₄×C₁₃	—	4	8	no	—
80	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
89	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
90	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
91	C₁₃×#124	C₂³	1	64	yes	complemented
92	C₁₃×#123	C₂³	1	128	yes	complemented
93	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
94	C₁₃×#121	C₂³	1	64	yes	complemented
95	C₁₃×#121	C₂³	1	128	yes	complemented
96	C₁₃×#120	C₂³	1	128	yes	complemented
97	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
98	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	128	yes	complemented
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
110	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
111	C₂²×#546	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	8	no	—
114	C₂⁴×C₁₃	—	2	8	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	96	no	—
118	C₂⁴×C₁₃	—	2	8	no	—
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₂⁴×C₁₃	—	2	8	no	—
121	C₂⁴×C₁₃	—	2	96	no	—
122	C₂⁴×C₁₃	—	2	4	no	—
123	C₂⁴×C₁₃	—	2	8	no	—
124	C₂⁴×C₁₃	—	4	48	no	—
125	C₂⁴×C₁₃	—	4	128	no	—
126	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
127	C₂⁴×C₁₃	#41	1	8	yes	complemented
128	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
130	C₂⁴×C₁₃	C₂⁴	1	32	yes	—
131	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
132	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
133	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×#41	—	2	256	no	—
135	C₂×Q₈×C₁₃	—	2	48	no	—
136	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
137	C₂×D₄×C₁₃	—	2	96	no	—
138	C₂×D₄×C₁₃	—	2	96	no	—
139	C₂×D₄×C₁₃	—	2	48	no	—
140	C₂×D₄×C₁₃	—	2	256	no	—
141	C₂×D₄×C₁₃	—	2	48	no	—
142	C₂×D₄×C₁₃	—	4	48	no	—
143	C₂×D₄×C₁₃	C₂×D₄	1	96	yes	complemented
144	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
149	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	—	2	96	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	8	no	—
157	C₂²×C₄×C₁₃	—	2	48	no	—
158	C₂²×C₄×C₁₃	—	2	48	no	—
159	C₂²×C₄×C₁₃	—	4	48	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
170	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
171	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
172	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
173	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
174	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
175	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
176	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
177	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
178	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
179	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
180	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
181	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
182	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
183	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂⁴×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#546	C₂×C₁₃	1	48	yes	direct product factor
186	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
188	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
191	C₂²×#120	C₂×C₁₃	1	2	yes	complemented
192	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
195	C₂³×C₁₃	—	2	32	no	—
196	C₂³×C₁₃	—	2	64	no	—
197	C₂³×C₁₃	—	2	12	no	—
198	C₂³×C₁₃	—	2	24	no	—
199	C₂³×C₁₃	—	2	24	no	—
200	C₂³×C₁₃	—	2	12	no	—
201	C₂³×C₁₃	—	2	12	no	—
202	C₂³×C₁₃	—	2	64	no	—
203	C₂³×C₁₃	—	2	24	no	—
204	C₂³×C₁₃	—	2	12	no	—
205	C₂³×C₁₃	—	2	24	no	—
206	C₂³×C₁₃	—	2	64	no	—
207	C₂³×C₁₃	—	2	12	no	—
208	C₂³×C₁₃	—	2	24	no	—
209	C₂³×C₁₃	—	4	32	no	—
210	C₂³×C₁₃	—	4	384	no	—
211	C₂³×C₁₃	—	4	16	no	—
212	C₂³×C₁₃	—	4	32	no	—
213	C₂³×C₁₃	C₂²×D₄	1	48	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
215	C₂³×C₁₃	C₂×#41	1	4	yes	—
216	C₂³×C₁₃	C₂×#41	1	24	yes	complemented
217	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
218	C₂³×C₁₃	C₂⁵	1	8	yes	—
219	C₂³×C₁₃	C₂⁵	1	4	yes	—
220	C₂³×C₁₃	C₂⁵	1	8	yes	—
221	C₂³×C₁₃	C₂⁵	1	4	yes	—
222	C₂³×C₁₃	C₂⁵	1	3	yes	—
223	Q₈×C₁₃	—	2	32	no	—
224	D₄×C₁₃	—	2	64	no	—
225	D₄×C₁₃	—	2	64	no	—
226	D₄×C₁₃	—	2	32	no	—
227	D₄×C₁₃	—	2	32	no	—
228	D₄×C₁₃	—	4	32	no	—
229	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
230	C₂×C₄×C₁₃	—	2	12	no	—
231	C₂×C₄×C₁₃	—	2	12	no	—
232	C₂×C₄×C₁₃	—	2	24	no	—
233	C₂×C₄×C₁₃	—	2	64	no	—
234	C₂×C₄×C₁₃	—	2	12	no	—
235	C₂×C₄×C₁₃	—	2	12	no	—
236	C₂×C₄×C₁₃	—	2	24	no	—
237	C₂×C₄×C₁₃	—	2	32	no	—
238	C₂×C₄×C₁₃	—	2	32	no	—
239	C₂×C₄×C₁₃	—	4	32	no	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
244	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
248	C₂⁶	C₂²×C₁₃	1	2	yes	—
249	C₂²×#41	—	2	16	no	—
250	C₂²×#41	C₂²×C₁₃	1	24	yes	complemented
251	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
252	C₂³×D₄	—	2	16	no	—
253	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
254	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂³×D₄	C₂²×C₁₃	1	24	yes	complemented
258	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
259	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
260	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
262	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
263	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
264	#546	C₂²×C₁₃	1	256	yes	direct product factor
265	C₂×#124	C₂²×C₁₃	1	24	yes	complemented
266	C₂×#123	C₂²×C₁₃	1	48	yes	complemented
267	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
268	C₂×#121	C₂²×C₁₃	1	24	yes	complemented
269	C₂×#121	C₂²×C₁₃	1	48	yes	complemented
270	C₂×#120	C₂²×C₁₃	1	48	yes	complemented
271	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
272	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
276	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	48	yes	complemented
279	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
280	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
281	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
282	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
283	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
284	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
285	C₂²×C₁₃	—	2	4	no	—
286	C₂²×C₁₃	—	2	8	no	—
287	C₂²×C₁₃	—	2	8	no	—
288	C₂²×C₁₃	—	2	4	no	—
289	C₂²×C₁₃	—	2	48	no	—
290	C₂²×C₁₃	—	2	96	no	—
291	C₂²×C₁₃	—	2	4	no	—
292	C₂²×C₁₃	—	2	8	no	—
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	2	8	no	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	2	8	no	—
297	C₂²×C₁₃	—	4	128	no	—
298	C₂²×C₁₃	—	4	24	no	—
299	C₂²×C₁₃	—	4	48	no	—
300	C₂²×C₁₃	#546	1	16	yes	direct product factor
301	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
302	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
303	C₂²×C₁₃	C₂²×#41	1	6	yes	—
304	C₂²×C₁₃	C₂²×#41	1	8	yes	complemented
305	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
306	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	8	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	2	8	no	—
313	C₄×C₁₃	C₂³×D₄	1	8	yes	—
314	C₂⁵	—	2	16	no	—
315	C₂⁵	—	2	16	no	—
316	C₂⁵	—	4	8	no	—
317	C₂⁵	C₂³×C₁₃	1	2	yes	—
318	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
319	C₂⁵	C₂³×C₁₃	1	24	yes	—
320	C₂⁵	C₂³×C₁₃	1	2	yes	—
321	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×#41	—	2	192	no	—
323	C₂×#41	C₂³×C₁₃	1	64	yes	complemented
324	C₂²×Q₈	—	2	8	no	—
325	C₂²×Q₈	C₂³×C₁₃	1	12	yes	complemented
326	C₂²×D₄	—	2	16	no	—
327	C₂²×D₄	—	2	16	no	—
328	C₂²×D₄	—	2	8	no	—
329	C₂²×D₄	—	2	192	no	—
330	C₂²×D₄	—	2	8	no	—
331	C₂²×D₄	—	4	8	no	—
332	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
333	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	64	yes	complemented
338	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
339	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
340	C₂³×C₄	—	2	16	no	—
341	C₂³×C₄	—	2	8	no	—
342	C₂³×C₄	—	2	8	no	—
343	C₂³×C₄	—	4	8	no	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
351	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
353	C₂³×C₄	C₂³×C₁₃	1	12	yes	complemented
354	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
355	#124	C₂³×C₁₃	1	64	yes	complemented
356	#123	C₂³×C₁₃	1	128	yes	complemented
357	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
358	#121	C₂³×C₁₃	1	64	yes	complemented
359	#121	C₂³×C₁₃	1	128	yes	complemented
360	#120	C₂³×C₁₃	1	128	yes	complemented
361	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
362	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	128	yes	complemented
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	complemented
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
374	C₂×C₄²	C₂³×C₁₃	1	12	yes	complemented
375	C₂×C₁₃	—	2	8	no	—
376	C₂×C₁₃	—	2	16	no	—
377	C₂×C₁₃	—	4	4	no	—
378	C₂×C₁₃	—	4	8	no	—
379	C₂×C₁₃	C₂×#546	1	12	yes	direct product factor
380	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
381	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
382	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	8	no	—
385	C₂⁴	—	2	8	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	96	no	—
389	C₂⁴	—	2	8	no	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	8	no	—
392	C₂⁴	—	2	96	no	—
393	C₂⁴	—	2	4	no	—
394	C₂⁴	—	2	8	no	—
395	C₂⁴	—	4	48	no	—
396	C₂⁴	—	4	128	no	—
397	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
398	C₂⁴	C₁₃×#41	1	8	yes	complemented
399	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
400	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
401	C₂⁴	C₂⁴×C₁₃	1	32	yes	—
402	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
403	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
404	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
405	#41	—	2	256	no	—
406	C₂×Q₈	—	2	48	no	—
407	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	complemented
408	C₂×D₄	—	2	96	no	—
409	C₂×D₄	—	2	96	no	—
410	C₂×D₄	—	2	48	no	—
411	C₂×D₄	—	2	256	no	—
412	C₂×D₄	—	2	48	no	—
413	C₂×D₄	—	4	48	no	—
414	C₂×D₄	C₂×D₄×C₁₃	1	96	yes	complemented
415	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
416	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
417	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
418	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
419	C₂×D₄	C₂⁴×C₁₃	1	32	yes	complemented
420	C₂×D₄	C₂⁴×C₁₃	1	32	yes	complemented
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	96	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	2	48	no	—
429	C₂²×C₄	—	2	48	no	—
430	C₂²×C₄	—	4	48	no	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	complemented
441	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	complemented
442	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	complemented
443	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	complemented
444	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	complemented
445	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
446	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
447	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
448	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
449	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
450	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
451	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	complemented
452	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
453	C₄²	C₂⁴×C₁₃	1	16	yes	complemented
454	C₁₃	C₂²×#546	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	32	no	—
456	C₂³	—	2	64	no	—
457	C₂³	—	2	12	no	—
458	C₂³	—	2	24	no	—
459	C₂³	—	2	24	no	—
460	C₂³	—	2	12	no	—
461	C₂³	—	2	12	no	—
462	C₂³	—	2	64	no	—
463	C₂³	—	2	24	no	—
464	C₂³	—	2	12	no	—
465	C₂³	—	2	24	no	—
466	C₂³	—	2	64	no	—
467	C₂³	—	2	12	no	—
468	C₂³	—	2	24	no	—
469	C₂³	—	4	32	no	—
470	C₂³	—	4	384	no	—
471	C₂³	—	4	32	no	—
472	C₂³	—	4	16	no	—
473	C₂³	C₂²×D₄×C₁₃	1	48	yes	—
474	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
475	C₂³	C₂×C₁₃×#41	1	4	yes	—
476	C₂³	C₂×C₁₃×#41	1	24	yes	complemented
477	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
478	C₂³	C₂⁵×C₁₃	1	8	yes	—
479	C₂³	C₂⁵×C₁₃	1	4	yes	—
480	C₂³	C₂⁵×C₁₃	1	8	yes	—
481	C₂³	C₂⁵×C₁₃	1	4	yes	—
482	C₂³	C₂⁵×C₁₃	1	3	yes	—
483	Q₈	—	2	32	no	—
484	D₄	—	2	64	no	—
485	D₄	—	2	64	no	—
486	D₄	—	2	32	no	—
487	D₄	—	2	32	no	—
488	D₄	—	4	32	no	—
489	D₄	C₂²×D₄×C₁₃	1	64	yes	complemented
490	C₂×C₄	—	2	12	no	—
491	C₂×C₄	—	2	12	no	—
492	C₂×C₄	—	2	24	no	—
493	C₂×C₄	—	2	64	no	—
494	C₂×C₄	—	2	12	no	—
495	C₂×C₄	—	2	12	no	—
496	C₂×C₄	—	2	24	no	—
497	C₂×C₄	—	2	32	no	—
498	C₂×C₄	—	2	32	no	—
499	C₂×C₄	—	4	32	no	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
501	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
502	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
503	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
504	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
505	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
506	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
507	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	2	8	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	48	no	—
513	C₂²	—	2	96	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	8	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	8	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	8	no	—
520	C₂²	—	4	128	no	—
521	C₂²	—	4	24	no	—
522	C₂²	—	4	48	no	—
523	C₂²	C₁₃×#546	1	16	yes	direct product factor
524	C₂²	C₂³×D₄×C₁₃	1	16	yes	—
525	C₂²	C₂³×D₄×C₁₃	1	6	yes	—
526	C₂²	C₂²×C₁₃×#41	1	6	yes	—
527	C₂²	C₂²×C₁₃×#41	1	8	yes	complemented
528	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
529	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	8	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	4	no	—
535	C₄	—	2	8	no	—
536	C₄	C₂³×D₄×C₁₃	1	8	yes	—
537	C₂	—	2	8	no	—
538	C₂	—	2	16	no	—
539	C₂	—	4	8	no	—
540	C₂	—	4	4	no	—
541	C₂	C₂×C₁₃×#546	1	12	yes	direct product factor
542	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
543	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
544	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. C₂³×C₁₃×#41	C₂	semidirect
2. C₂⁴×D₄×C₁₃	C₂	semidirect
3. C₂×C₁₃×#546	C₂	direct (N × H)
4. C₂²×C₁₃×#124	C₂	semidirect
5. C₂²×C₁₃×#123	C₂	semidirect
6. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
7. C₂²×C₁₃×#121	C₂	semidirect
8. C₂²×C₁₃×#121	C₂	semidirect
9. C₂²×C₁₃×#120	C₂	semidirect
10. C₂²×C₄×D₄×C₁₃	C₂	semidirect
11. C₂²×C₄×D₄×C₁₃	C₂	semidirect
12. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂³×Q₈×C₁₃	C₂²	semidirect
22. C₂³×D₄×C₁₃	C₂²	semidirect
23. C₂³×D₄×C₁₃	C₂²	semidirect
24. C₂³×D₄×C₁₃	C₂²	semidirect
26. C₂⁴×C₄×C₁₃	C₂²	semidirect
27. C₂⁴×C₄×C₁₃	C₂²	semidirect
28. C₂⁴×C₄×C₁₃	C₂²	semidirect
29. C₁₃×#546	C₂²	direct (N × H)
30. C₂×C₁₃×#124	C₂²	semidirect
31. C₂×C₁₃×#123	C₂²	semidirect
32. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
34. C₂×C₁₃×#121	C₂²	semidirect
35. C₂×C₁₃×#120	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
39. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
40. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
45. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
46. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
47. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
48. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
49. C₂²×C₄²×C₁₃	C₂²	semidirect
59. C₂×C₁₃×#41	C₂³	semidirect
61. C₂²×Q₈×C₁₃	C₂³	semidirect
68. C₂²×D₄×C₁₃	D₄	semidirect
73. C₂²×D₄×C₁₃	C₂³	semidirect
74. C₂²×D₄×C₁₃	C₂³	semidirect
75. C₂²×D₄×C₁₃	C₂³	semidirect
88. C₂³×C₄×C₁₃	C₂³	semidirect
89. C₂³×C₄×C₁₃	C₂³	semidirect
90. C₂³×C₄×C₁₃	C₂³	semidirect
91. C₁₃×#124	C₂³	semidirect
92. C₁₃×#123	C₂³	semidirect
93. C₁₃×C₂²⋊Q₈	C₂³	semidirect
94. C₁₃×#121	C₂³	semidirect
95. C₁₃×#121	C₂³	semidirect
96. C₁₃×#120	C₂³	semidirect
97. C₄×D₄×C₁₃	C₂³	semidirect
98. C₄×D₄×C₁₃	C₂³	semidirect
99. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
100. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
101. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
104. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
105. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
106. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
107. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
108. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
109. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
110. C₂×C₄²×C₁₃	C₂³	semidirect
111. C₂²×#546	C₁₃	direct (N × H)
127. C₂⁴×C₁₃	#41	semidirect
136. C₂×Q₈×C₁₃	C₂⁴	semidirect
143. C₂×D₄×C₁₃	C₂×D₄	semidirect
148. C₂×D₄×C₁₃	C₂⁴	semidirect
149. C₂×D₄×C₁₃	C₂⁴	semidirect
169. C₂²×C₄×C₁₃	C₂⁴	semidirect
170. C₂²×C₄×C₁₃	C₂⁴	semidirect
171. C₂²×C₄×C₁₃	C₂⁴	semidirect
172. C₁₃×C₄⋊C₄	C₂⁴	semidirect
173. C₁₃×C₄⋊C₄	C₂⁴	semidirect
174. C₁₃×C₄⋊C₄	C₂⁴	semidirect
177. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
178. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
179. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
180. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
181. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
182. C₄²×C₁₃	C₂⁴	semidirect
183. C₂³×#41	C₂×C₁₃	semidirect
184. C₂⁴×D₄	C₂×C₁₃	semidirect
185. C₂×#546	C₂×C₁₃	direct (N × H)
186. C₂²×#124	C₂×C₁₃	semidirect
187. C₂²×#123	C₂×C₁₃	semidirect
188. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
189. C₂²×#121	C₂×C₁₃	semidirect
190. C₂²×#121	C₂×C₁₃	semidirect
191. C₂²×#120	C₂×C₁₃	semidirect
192. C₂²×C₄×D₄	C₂×C₁₃	semidirect
193. C₂²×C₄×D₄	C₂×C₁₃	semidirect
194. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
216. C₂³×C₁₃	C₂×#41	semidirect
229. D₄×C₁₃	C₂²×D₄	semidirect
250. C₂²×#41	C₂²×C₁₃	semidirect
251. C₂³×Q₈	C₂²×C₁₃	semidirect
257. C₂³×D₄	C₂²×C₁₃	semidirect
258. C₂³×D₄	C₂²×C₁₃	semidirect
259. C₂³×D₄	C₂²×C₁₃	semidirect
261. C₂⁴×C₄	C₂²×C₁₃	semidirect
262. C₂⁴×C₄	C₂²×C₁₃	semidirect
263. C₂⁴×C₄	C₂²×C₁₃	semidirect
264. #546	C₂²×C₁₃	direct (N × H)
265. C₂×#124	C₂²×C₁₃	semidirect
266. C₂×#123	C₂²×C₁₃	semidirect
267. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
268. C₂×#121	C₂²×C₁₃	semidirect
269. C₂×#121	C₂²×C₁₃	semidirect
270. C₂×#120	C₂²×C₁₃	semidirect
271. C₂×C₄×D₄	C₂²×C₁₃	semidirect
272. C₂×C₄×D₄	C₂²×C₁₃	semidirect
273. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
274. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
275. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
278. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
279. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
280. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
281. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
282. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
283. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
284. C₂²×C₄²	C₂²×C₁₃	semidirect
300. C₂²×C₁₃	#546	direct (N × H)
304. C₂²×C₁₃	C₂²×#41	semidirect
323. C₂×#41	C₂³×C₁₃	semidirect
325. C₂²×Q₈	C₂³×C₁₃	semidirect
332. C₂²×D₄	D₄×C₁₃	semidirect
337. C₂²×D₄	C₂³×C₁₃	semidirect
338. C₂²×D₄	C₂³×C₁₃	semidirect
339. C₂²×D₄	C₂³×C₁₃	semidirect
352. C₂³×C₄	C₂³×C₁₃	semidirect
353. C₂³×C₄	C₂³×C₁₃	semidirect
354. C₂³×C₄	C₂³×C₁₃	semidirect
355. #124	C₂³×C₁₃	semidirect
356. #123	C₂³×C₁₃	semidirect
357. C₂²⋊Q₈	C₂³×C₁₃	semidirect
358. #121	C₂³×C₁₃	semidirect
359. #121	C₂³×C₁₃	semidirect
360. #120	C₂³×C₁₃	semidirect
361. C₄×D₄	C₂³×C₁₃	semidirect
362. C₄×D₄	C₂³×C₁₃	semidirect
363. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
364. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
365. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
368. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
369. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
370. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
371. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
372. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
373. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
374. C₂×C₄²	C₂³×C₁₃	semidirect
379. C₂×C₁₃	C₂×#546	direct (N × H)
398. C₂⁴	C₁₃×#41	semidirect
407. C₂×Q₈	C₂⁴×C₁₃	semidirect
414. C₂×D₄	C₂×D₄×C₁₃	semidirect
419. C₂×D₄	C₂⁴×C₁₃	semidirect
420. C₂×D₄	C₂⁴×C₁₃	semidirect
440. C₂²×C₄	C₂⁴×C₁₃	semidirect
441. C₂²×C₄	C₂⁴×C₁₃	semidirect
442. C₂²×C₄	C₂⁴×C₁₃	semidirect
443. C₄⋊C₄	C₂⁴×C₁₃	semidirect
444. C₄⋊C₄	C₂⁴×C₁₃	semidirect
445. C₄⋊C₄	C₂⁴×C₁₃	semidirect
448. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
449. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
450. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
451. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
452. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
453. C₄²	C₂⁴×C₁₃	semidirect
454. C₁₃	C₂²×#546	direct (N × H)
476. C₂³	C₂×C₁₃×#41	semidirect
489. D₄	C₂²×D₄×C₁₃	semidirect
523. C₂²	C₁₃×#546	direct (N × H)
527. C₂²	C₂²×C₁₃×#41	semidirect
541. C₂	C₂×C₁₃×#546	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
C₂⁴×D₄×C₁₃	2
C₂×C₁₃×#546	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×#546	13

Subgroups — C22×C13×#546 #15749036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#546 #15749036