Subgroups — C₂×C₁₃×#3543 #15749083

Order 3328.

8814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3543	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#550	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#546	C₂	1	4	yes	maximal, complemented
6	C₂×D₄²×C₁₃	C₂	1	4	yes	maximal, complemented
7	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#540	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#535	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#534	C₂	1	4	yes	maximal, complemented
11	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
15	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
17	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
18	C₁₃×#560	C₂²	1	64	yes	complemented
19	C₁₃×#559	C₂²	1	16	yes	complemented
20	C₁₃×#550	C₂²	1	32	yes	complemented
21	C₁₃×#546	C₂²	1	64	yes	complemented
22	D₄²×C₁₃	C₂²	1	64	yes	complemented
23	D₄²×C₁₃	C₂²	1	16	yes	complemented
24	C₁₃×#540	C₂²	1	64	yes	complemented
25	C₁₃×#535	C₂²	1	64	yes	complemented
26	C₁₃×#534	C₂²	1	64	yes	complemented
27	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#127	C₂²	1	16	yes	complemented
33	C₁₃×#529	C₂²	1	32	yes	complemented
34	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
38	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
39	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#121	C₂²	1	2	yes	—
44	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
45	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
47	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
49	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
50	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
51	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
52	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
53	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
54	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
56	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
58	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
59	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
60	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
61	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₁₃	C₂³	1	4	yes	—
63	C₂⁵×C₁₃	C₂³	1	4	yes	—
64	C₂×C₁₃×#41	—	4	16	no	—
65	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
66	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃	—	4	16	no	—
68	C₂²×D₄×C₁₃	—	4	16	no	—
69	C₂²×D₄×C₁₃	—	4	8	no	—
70	C₂²×D₄×C₁₃	—	4	16	no	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
83	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
84	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
85	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
91	C₁₃×#127	C₂³	1	8	yes	—
92	C₁₃×#127	C₂³	1	32	yes	complemented
93	C₁₃×#127	C₂³	1	8	yes	complemented
94	C₁₃×#127	C₂³	1	16	yes	complemented
95	C₁₃×#127	C₂³	1	32	yes	complemented
96	C₁₃×#126	C₂³	1	32	yes	complemented
97	C₁₃×#125	C₂³	1	16	yes	complemented
98	C₁₃×#124	C₂³	1	16	yes	complemented
99	C₁₃×#124	C₂³	1	32	yes	complemented
100	C₁₃×#123	C₂³	1	32	yes	complemented
101	C₁₃×#123	C₂³	1	32	yes	complemented
102	C₁₃×#123	C₂³	1	32	yes	complemented
103	C₁₃×#123	C₂³	1	64	yes	complemented
104	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
105	C₁₃×#121	C₂³	1	16	yes	—
106	C₁₃×#121	C₂³	1	64	yes	complemented
107	C₁₃×#121	C₂³	1	64	yes	complemented
108	C₁₃×#121	C₂³	1	64	yes	complemented
109	C₁₃×#121	C₂³	1	32	yes	complemented
110	C₁₃×#121	C₂³	1	32	yes	complemented
111	C₁₃×#121	C₂³	1	64	yes	complemented
112	C₁₃×#120	C₂³	1	32	yes	complemented
113	C₁₃×#120	C₂³	1	64	yes	complemented
114	C₁₃×#120	C₂³	1	32	yes	complemented
115	C₁₃×#120	C₂³	1	64	yes	complemented
116	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
117	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
118	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
119	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
120	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
121	C₁₃×#117	C₂³	1	32	yes	complemented
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
143	C₂×#3543	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂⁴×C₁₃	—	2	16	no	—
145	C₂⁴×C₁₃	—	4	16	no	—
146	C₂⁴×C₁₃	—	4	16	no	—
147	C₂⁴×C₁₃	—	4	8	no	—
148	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
149	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
150	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
151	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
154	C₁₃×#41	—	4	64	no	—
155	C₂×Q₈×C₁₃	—	2	8	no	—
156	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
157	C₂×D₄×C₁₃	—	2	16	no	—
158	C₂×D₄×C₁₃	—	2	8	no	—
159	C₂×D₄×C₁₃	—	2	16	no	—
160	C₂×D₄×C₁₃	—	2	16	no	—
161	C₂×D₄×C₁₃	—	4	64	no	—
162	C₂×D₄×C₁₃	—	4	64	no	—
163	C₂×D₄×C₁₃	—	4	16	no	—
164	C₂×D₄×C₁₃	—	4	16	no	—
165	C₂×D₄×C₁₃	—	4	4	no	—
166	C₂×D₄×C₁₃	—	4	8	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	4	16	no	—
169	C₂×D₄×C₁₃	—	4	32	no	—
170	C₂×D₄×C₁₃	—	4	16	no	—
171	C₂×D₄×C₁₃	—	4	64	no	—
172	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
173	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
174	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
175	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
176	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
177	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
178	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
179	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	8	no	—
185	C₂²×C₄×C₁₃	—	2	16	no	—
186	C₂²×C₄×C₁₃	—	4	8	no	—
187	C₂²×C₄×C₁₃	—	4	16	no	—
188	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
206	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
207	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
208	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
209	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
210	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
211	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
212	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
213	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
214	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
215	C₄²×C₁₃	C₂⁴	1	8	yes	—
216	C₄²×C₁₃	C₂⁴	1	4	yes	—
217	C₄²×C₁₃	C₂⁴	1	4	yes	—
218	C₄²×C₁₃	C₂⁴	1	16	yes	—
219	#3543	C₂×C₁₃	1	32	yes	direct product factor
220	C₂×#560	C₂×C₁₃	1	4	yes	complemented
221	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×#550	C₂×C₁₃	1	2	yes	complemented
223	C₂×#546	C₂×C₁₃	1	4	yes	complemented
224	C₂×D₄²	C₂×C₁₃	1	4	yes	complemented
225	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂×#540	C₂×C₁₃	1	4	yes	complemented
227	C₂×#535	C₂×C₁₃	1	4	yes	complemented
228	C₂×#534	C₂×C₁₃	1	4	yes	complemented
229	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂×#529	C₂×C₁₃	1	2	yes	complemented
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	8	no	—
233	C₂³×C₁₃	—	2	16	no	—
234	C₂³×C₁₃	—	2	8	no	—
235	C₂³×C₁₃	—	2	8	no	—
236	C₂³×C₁₃	—	2	8	no	—
237	C₂³×C₁₃	—	2	16	no	—
238	C₂³×C₁₃	—	2	8	no	—
239	C₂³×C₁₃	—	2	32	no	—
240	C₂³×C₁₃	—	4	32	no	—
241	C₂³×C₁₃	—	4	32	no	—
242	C₂³×C₁₃	—	4	16	no	—
243	C₂³×C₁₃	—	8	32	no	—
244	C₂³×C₁₃	—	8	32	no	—
245	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
246	C₂³×C₁₃	C₂⁵	1	8	yes	—
247	C₂³×C₁₃	C₂⁵	1	8	yes	—
248	C₂³×C₁₃	C₂⁵	1	8	yes	—
249	C₂³×C₁₃	C₂⁵	1	2	yes	—
250	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	16	no	—
252	D₄×C₁₃	—	2	32	no	—
253	D₄×C₁₃	—	2	16	no	—
254	D₄×C₁₃	—	2	32	no	—
255	D₄×C₁₃	—	2	32	no	—
256	D₄×C₁₃	—	4	32	no	—
257	D₄×C₁₃	—	4	32	no	—
258	D₄×C₁₃	—	4	8	no	—
259	D₄×C₁₃	—	4	16	no	—
260	D₄×C₁₃	—	4	8	no	—
261	D₄×C₁₃	—	4	32	no	—
262	D₄×C₁₃	—	4	32	no	—
263	C₂×C₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	8	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	8	no	—
269	C₂×C₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	2	16	no	—
271	C₂×C₄×C₁₃	—	2	32	no	—
272	C₂×C₄×C₁₃	—	4	16	no	—
273	C₂×C₄×C₁₃	—	4	32	no	—
274	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	—
275	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
278	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
279	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
280	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
282	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
283	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
284	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
285	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
286	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
287	#560	C₂²×C₁₃	1	64	yes	complemented
288	#559	C₂²×C₁₃	1	16	yes	complemented
289	#550	C₂²×C₁₃	1	32	yes	complemented
290	#546	C₂²×C₁₃	1	64	yes	complemented
291	D₄²	C₂²×C₁₃	1	64	yes	complemented
292	D₄²	C₂²×C₁₃	1	16	yes	complemented
293	#540	C₂²×C₁₃	1	64	yes	complemented
294	#535	C₂²×C₁₃	1	64	yes	complemented
295	#534	C₂²×C₁₃	1	64	yes	complemented
296	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
298	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
300	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
301	C₂×#127	C₂²×C₁₃	1	16	yes	complemented
302	#529	C₂²×C₁₃	1	32	yes	complemented
303	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
304	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
305	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
306	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
307	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
308	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
309	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
310	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
311	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
312	C₂×#121	C₂²×C₁₃	1	2	yes	—
313	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
314	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
315	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
316	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
317	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
318	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
319	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
320	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
321	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
322	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
323	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
324	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
325	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
326	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
327	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
328	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
329	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
330	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	2	8	no	—
333	C₂²×C₁₃	—	2	8	no	—
334	C₂²×C₁₃	—	2	16	no	—
335	C₂²×C₁₃	—	2	8	no	—
336	C₂²×C₁₃	—	2	8	no	—
337	C₂²×C₁₃	—	2	8	no	—
338	C₂²×C₁₃	—	2	16	no	—
339	C₂²×C₁₃	—	2	8	no	—
340	C₂²×C₁₃	—	4	16	no	—
341	C₂²×C₁₃	—	4	16	no	—
342	C₂²×C₁₃	—	4	16	no	—
343	C₂²×C₁₃	—	8	32	no	—
344	C₂²×C₁₃	—	8	32	no	—
345	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
346	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
347	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
348	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
349	C₄×C₁₃	—	2	8	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	4	no	—
353	C₄×C₁₃	—	2	8	no	—
354	C₄×C₁₃	—	2	8	no	—
355	C₄×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
356	C₂⁵	C₂³×C₁₃	1	4	yes	—
357	C₂⁵	C₂³×C₁₃	1	4	yes	—
358	C₂×#41	—	4	16	no	—
359	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
360	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
361	C₂²×D₄	—	4	16	no	—
362	C₂²×D₄	—	4	16	no	—
363	C₂²×D₄	—	4	8	no	—
364	C₂²×D₄	—	4	16	no	—
365	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
366	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
367	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
368	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
369	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
370	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
371	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
372	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
373	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
374	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
375	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
377	C₂²×D₄	C₂³×C₁₃	1	32	yes	complemented
378	C₂²×D₄	C₂³×C₁₃	1	32	yes	complemented
379	C₂²×D₄	C₂³×C₁₃	1	32	yes	complemented
380	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
381	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
385	#127	C₂³×C₁₃	1	8	yes	—
386	#127	C₂³×C₁₃	1	32	yes	complemented
387	#127	C₂³×C₁₃	1	8	yes	complemented
388	#127	C₂³×C₁₃	1	16	yes	complemented
389	#127	C₂³×C₁₃	1	32	yes	complemented
390	#126	C₂³×C₁₃	1	32	yes	complemented
391	#125	C₂³×C₁₃	1	16	yes	complemented
392	#124	C₂³×C₁₃	1	16	yes	complemented
393	#124	C₂³×C₁₃	1	32	yes	complemented
394	#123	C₂³×C₁₃	1	32	yes	complemented
395	#123	C₂³×C₁₃	1	32	yes	complemented
396	#123	C₂³×C₁₃	1	32	yes	complemented
397	#123	C₂³×C₁₃	1	64	yes	complemented
398	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
399	#121	C₂³×C₁₃	1	16	yes	—
400	#121	C₂³×C₁₃	1	64	yes	complemented
401	#121	C₂³×C₁₃	1	64	yes	complemented
402	#121	C₂³×C₁₃	1	64	yes	complemented
403	#121	C₂³×C₁₃	1	32	yes	complemented
404	#121	C₂³×C₁₃	1	32	yes	complemented
405	#121	C₂³×C₁₃	1	64	yes	complemented
406	#120	C₂³×C₁₃	1	32	yes	complemented
407	#120	C₂³×C₁₃	1	64	yes	complemented
408	#120	C₂³×C₁₃	1	32	yes	complemented
409	#120	C₂³×C₁₃	1	64	yes	complemented
410	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
411	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
412	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
413	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
414	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
415	#117	C₂³×C₁₃	1	32	yes	complemented
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
432	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
434	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
437	C₂×C₁₃	—	2	4	no	—
438	C₂×C₁₃	—	4	8	no	—
439	C₂×C₁₃	—	4	8	no	—
440	C₂×C₁₃	—	4	8	no	—
441	C₂×C₁₃	#3543	1	4	yes	direct product factor
442	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
444	C₂⁴	—	2	16	no	—
445	C₂⁴	—	4	16	no	—
446	C₂⁴	—	4	16	no	—
447	C₂⁴	—	4	8	no	—
448	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
449	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
450	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
451	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
453	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
454	#41	—	4	64	no	—
455	C₂×Q₈	—	2	8	no	—
456	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
457	C₂×D₄	—	2	16	no	—
458	C₂×D₄	—	2	8	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	4	64	no	—
462	C₂×D₄	—	4	64	no	—
463	C₂×D₄	—	4	16	no	—
464	C₂×D₄	—	4	16	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	4	16	no	—
469	C₂×D₄	—	4	32	no	—
470	C₂×D₄	—	4	16	no	—
471	C₂×D₄	—	4	64	no	—
472	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
473	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
474	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
475	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
476	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
477	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
478	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
479	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
480	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
481	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
482	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	2	16	no	—
486	C₂²×C₄	—	4	8	no	—
487	C₂²×C₄	—	4	16	no	—
488	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
500	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
505	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
506	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
507	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
508	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
509	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
510	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
511	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
512	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
513	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
514	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
515	C₄²	C₂⁴×C₁₃	1	8	yes	—
516	C₄²	C₂⁴×C₁₃	1	4	yes	—
517	C₄²	C₂⁴×C₁₃	1	4	yes	—
518	C₄²	C₂⁴×C₁₃	1	16	yes	—
519	C₁₃	C₂×#3543	1	1	yes	characteristic, direct product factor, Sylow
520	C₂³	—	2	4	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	16	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	16	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	32	no	—
529	C₂³	—	4	32	no	—
530	C₂³	—	4	32	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	8	32	no	—
533	C₂³	—	8	32	no	—
534	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
535	C₂³	C₂⁵×C₁₃	1	8	yes	—
536	C₂³	C₂⁵×C₁₃	1	8	yes	—
537	C₂³	C₂⁵×C₁₃	1	8	yes	—
538	C₂³	C₂⁵×C₁₃	1	2	yes	—
539	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
540	Q₈	—	2	16	no	—
541	D₄	—	2	32	no	—
542	D₄	—	2	16	no	—
543	D₄	—	2	32	no	—
544	D₄	—	2	32	no	—
545	D₄	—	4	32	no	—
546	D₄	—	4	32	no	—
547	D₄	—	4	8	no	—
548	D₄	—	4	16	no	—
549	D₄	—	4	8	no	—
550	D₄	—	4	32	no	—
551	D₄	—	4	32	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	2	32	no	—
561	C₂×C₄	—	4	16	no	—
562	C₂×C₄	—	4	32	no	—
563	C₂×C₄	C₁₃×H(5,𝔽₂)	1	8	yes	—
564	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
565	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
566	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
567	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
568	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
569	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
570	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	16	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	16	no	—
582	C₂²	—	4	16	no	—
583	C₂²	—	8	32	no	—
584	C₂²	—	8	32	no	—
585	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
586	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
587	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
588	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
589	C₄	—	2	8	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	C₂×C₁₃×H(5,𝔽₂)	1	8	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	4	8	no	—
599	C₂	—	4	8	no	—
600	C₂	C₁₃×#3543	1	4	yes	direct product factor
601	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3543	C₂	direct (N × H)
2. C₂×C₁₃×#560	C₂	semidirect
3. C₂×C₁₃×#559	C₂	semidirect
4. C₂×C₁₃×#550	C₂	semidirect
5. C₂×C₁₃×#546	C₂	semidirect
6. C₂×D₄²×C₁₃	C₂	semidirect
7. C₂×D₄²×C₁₃	C₂	semidirect
8. C₂×C₁₃×#540	C₂	semidirect
9. C₂×C₁₃×#535	C₂	semidirect
10. C₂×C₁₃×#534	C₂	semidirect
11. C₂²×C₁₃×#127	C₂	semidirect
12. C₂×C₁₃×#529	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₁₃×#560	C₂²	semidirect
19. C₁₃×#559	C₂²	semidirect
20. C₁₃×#550	C₂²	semidirect
21. C₁₃×#546	C₂²	semidirect
22. D₄²×C₁₃	C₂²	semidirect
23. D₄²×C₁₃	C₂²	semidirect
24. C₁₃×#540	C₂²	semidirect
25. C₁₃×#535	C₂²	semidirect
26. C₁₃×#534	C₂²	semidirect
28. C₂×C₁₃×#127	C₂²	semidirect
29. C₂×C₁₃×#127	C₂²	semidirect
30. C₂×C₁₃×#127	C₂²	semidirect
31. C₂×C₁₃×#127	C₂²	semidirect
32. C₂×C₁₃×#127	C₂²	semidirect
33. C₁₃×#529	C₂²	semidirect
34. C₂×C₁₃×#126	C₂²	semidirect
35. C₂×C₁₃×#125	C₂²	semidirect
36. C₂×C₁₃×#124	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
38. C₂×C₁₃×#123	C₂²	semidirect
39. C₂×C₁₃×#123	C₂²	semidirect
40. C₂×C₁₃×#123	C₂²	semidirect
41. C₂×C₁₃×#123	C₂²	semidirect
42. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₁₃×#121	C₂²	semidirect
45. C₂×C₁₃×#121	C₂²	semidirect
46. C₂×C₁₃×#121	C₂²	semidirect
47. C₂×C₁₃×#121	C₂²	semidirect
48. C₂×C₁₃×#121	C₂²	semidirect
49. C₂×C₁₃×#121	C₂²	semidirect
50. C₂×C₁₃×#120	C₂²	semidirect
51. C₂×C₁₃×#120	C₂²	semidirect
52. C₂×C₁₃×#120	C₂²	semidirect
53. C₂×C₁₃×#120	C₂²	semidirect
54. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
55. C₂×C₄×D₄×C₁₃	C₂²	semidirect
56. C₂×C₄×D₄×C₁₃	C₂²	semidirect
57. C₂×C₄×D₄×C₁₃	C₂²	semidirect
58. C₂×C₄×D₄×C₁₃	C₂²	semidirect
59. C₂×C₁₃×#117	C₂²	semidirect
60. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
61. C₂²×C₄²×C₁₃	C₂²	semidirect
65. C₂×C₁₃×#41	C₂³	semidirect
82. C₂²×D₄×C₁₃	C₂³	semidirect
83. C₂²×D₄×C₁₃	C₂³	semidirect
84. C₂²×D₄×C₁₃	C₂³	semidirect
85. C₂²×D₄×C₁₃	C₂³	semidirect
92. C₁₃×#127	C₂³	semidirect
93. C₁₃×#127	C₂³	semidirect
94. C₁₃×#127	C₂³	semidirect
95. C₁₃×#127	C₂³	semidirect
96. C₁₃×#126	C₂³	semidirect
97. C₁₃×#125	C₂³	semidirect
98. C₁₃×#124	C₂³	semidirect
99. C₁₃×#124	C₂³	semidirect
100. C₁₃×#123	C₂³	semidirect
101. C₁₃×#123	C₂³	semidirect
102. C₁₃×#123	C₂³	semidirect
103. C₁₃×#123	C₂³	semidirect
104. C₁₃×C₂²⋊Q₈	C₂³	semidirect
106. C₁₃×#121	C₂³	semidirect
107. C₁₃×#121	C₂³	semidirect
108. C₁₃×#121	C₂³	semidirect
109. C₁₃×#121	C₂³	semidirect
110. C₁₃×#121	C₂³	semidirect
111. C₁₃×#121	C₂³	semidirect
112. C₁₃×#120	C₂³	semidirect
113. C₁₃×#120	C₂³	semidirect
114. C₁₃×#120	C₂³	semidirect
115. C₁₃×#120	C₂³	semidirect
116. C₄×Q₈×C₁₃	C₂³	semidirect
117. C₄×D₄×C₁₃	C₂³	semidirect
118. C₄×D₄×C₁₃	C₂³	semidirect
119. C₄×D₄×C₁₃	C₂³	semidirect
120. C₄×D₄×C₁₃	C₂³	semidirect
121. C₁₃×#117	C₂³	semidirect
137. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
142. C₂×C₄²×C₁₃	C₂³	semidirect
143. C₂×#3543	C₁₃	direct (N × H)
219. #3543	C₂×C₁₃	direct (N × H)
220. C₂×#560	C₂×C₁₃	semidirect
221. C₂×#559	C₂×C₁₃	semidirect
222. C₂×#550	C₂×C₁₃	semidirect
223. C₂×#546	C₂×C₁₃	semidirect
224. C₂×D₄²	C₂×C₁₃	semidirect
225. C₂×D₄²	C₂×C₁₃	semidirect
226. C₂×#540	C₂×C₁₃	semidirect
227. C₂×#535	C₂×C₁₃	semidirect
228. C₂×#534	C₂×C₁₃	semidirect
229. C₂²×#127	C₂×C₁₃	semidirect
230. C₂×#529	C₂×C₁₃	semidirect
282. C₂²×#41	C₂²×C₁₃	semidirect
283. C₂³×D₄	C₂²×C₁₃	semidirect
284. C₂³×D₄	C₂²×C₁₃	semidirect
285. C₂³×D₄	C₂²×C₁₃	semidirect
286. C₂³×D₄	C₂²×C₁₃	semidirect
287. #560	C₂²×C₁₃	semidirect
288. #559	C₂²×C₁₃	semidirect
289. #550	C₂²×C₁₃	semidirect
290. #546	C₂²×C₁₃	semidirect
291. D₄²	C₂²×C₁₃	semidirect
292. D₄²	C₂²×C₁₃	semidirect
293. #540	C₂²×C₁₃	semidirect
294. #535	C₂²×C₁₃	semidirect
295. #534	C₂²×C₁₃	semidirect
297. C₂×#127	C₂²×C₁₃	semidirect
298. C₂×#127	C₂²×C₁₃	semidirect
299. C₂×#127	C₂²×C₁₃	semidirect
300. C₂×#127	C₂²×C₁₃	semidirect
301. C₂×#127	C₂²×C₁₃	semidirect
302. #529	C₂²×C₁₃	semidirect
303. C₂×#126	C₂²×C₁₃	semidirect
304. C₂×#125	C₂²×C₁₃	semidirect
305. C₂×#124	C₂²×C₁₃	semidirect
306. C₂×#124	C₂²×C₁₃	semidirect
307. C₂×#123	C₂²×C₁₃	semidirect
308. C₂×#123	C₂²×C₁₃	semidirect
309. C₂×#123	C₂²×C₁₃	semidirect
310. C₂×#123	C₂²×C₁₃	semidirect
311. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
313. C₂×#121	C₂²×C₁₃	semidirect
314. C₂×#121	C₂²×C₁₃	semidirect
315. C₂×#121	C₂²×C₁₃	semidirect
316. C₂×#121	C₂²×C₁₃	semidirect
317. C₂×#121	C₂²×C₁₃	semidirect
318. C₂×#121	C₂²×C₁₃	semidirect
319. C₂×#120	C₂²×C₁₃	semidirect
320. C₂×#120	C₂²×C₁₃	semidirect
321. C₂×#120	C₂²×C₁₃	semidirect
322. C₂×#120	C₂²×C₁₃	semidirect
323. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
324. C₂×C₄×D₄	C₂²×C₁₃	semidirect
325. C₂×C₄×D₄	C₂²×C₁₃	semidirect
326. C₂×C₄×D₄	C₂²×C₁₃	semidirect
327. C₂×C₄×D₄	C₂²×C₁₃	semidirect
328. C₂×#117	C₂²×C₁₃	semidirect
329. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
330. C₂²×C₄²	C₂²×C₁₃	semidirect
359. C₂×#41	C₂³×C₁₃	semidirect
376. C₂²×D₄	C₂³×C₁₃	semidirect
377. C₂²×D₄	C₂³×C₁₃	semidirect
378. C₂²×D₄	C₂³×C₁₃	semidirect
379. C₂²×D₄	C₂³×C₁₃	semidirect
386. #127	C₂³×C₁₃	semidirect
387. #127	C₂³×C₁₃	semidirect
388. #127	C₂³×C₁₃	semidirect
389. #127	C₂³×C₁₃	semidirect
390. #126	C₂³×C₁₃	semidirect
391. #125	C₂³×C₁₃	semidirect
392. #124	C₂³×C₁₃	semidirect
393. #124	C₂³×C₁₃	semidirect
394. #123	C₂³×C₁₃	semidirect
395. #123	C₂³×C₁₃	semidirect
396. #123	C₂³×C₁₃	semidirect
397. #123	C₂³×C₁₃	semidirect
398. C₂²⋊Q₈	C₂³×C₁₃	semidirect
400. #121	C₂³×C₁₃	semidirect
401. #121	C₂³×C₁₃	semidirect
402. #121	C₂³×C₁₃	semidirect
403. #121	C₂³×C₁₃	semidirect
404. #121	C₂³×C₁₃	semidirect
405. #121	C₂³×C₁₃	semidirect
406. #120	C₂³×C₁₃	semidirect
407. #120	C₂³×C₁₃	semidirect
408. #120	C₂³×C₁₃	semidirect
409. #120	C₂³×C₁₃	semidirect
410. C₄×Q₈	C₂³×C₁₃	semidirect
411. C₄×D₄	C₂³×C₁₃	semidirect
412. C₄×D₄	C₂³×C₁₃	semidirect
413. C₄×D₄	C₂³×C₁₃	semidirect
414. C₄×D₄	C₂³×C₁₃	semidirect
415. #117	C₂³×C₁₃	semidirect
431. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
436. C₂×C₄²	C₂³×C₁₃	semidirect
441. C₂×C₁₃	#3543	direct (N × H)
519. C₁₃	C₂×#3543	direct (N × H)
600. C₂	C₁₃×#3543	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3543	2
C₂×C₁₃×#560	2
C₂×C₁₃×#559	2
C₂×C₁₃×#550	2
C₂×C₁₃×#546	2
C₂×D₄²×C₁₃	2
C₂×C₁₃×#540	2
C₂×C₁₃×#535	2
C₂×C₁₃×#534	2
C₂²×C₁₃×#127	2
C₂×C₁₃×#529	2
C₂×#3543	13

Subgroups — C2×C13×#3543 #15749083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3543 #15749083