Subgroups — C₂×C₁₃×#3481 #15749053

Order 3328.

8722 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3481	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#553	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#546	C₂	1	4	yes	maximal, complemented
7	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×D₄×C₁₃	C₂	1	4	yes	maximal, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
15	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	complemented
17	C₁₃×#559	C₂²	1	16	yes	complemented
18	C₁₃×#554	C₂²	1	32	yes	complemented
19	C₁₃×#553	C₂²	1	64	yes	complemented
20	C₁₃×#551	C₂²	1	64	yes	complemented
21	C₁₃×#546	C₂²	1	64	yes	complemented
22	D₄²×C₁₃	C₂²	1	16	yes	complemented
23	C₁₃×#532	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₁₃×#529	C₂²	1	64	yes	complemented
27	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
31	C₁₃×#525	C₂²	1	64	yes	complemented
32	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#121	C₂²	1	4	yes	—
38	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#120	C₂²	1	4	yes	—
41	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
42	C₄×C₁₃×#41	C₂²	1	32	yes	complemented
43	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
44	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
49	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
50	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
51	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
52	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
53	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
54	C₂×C₄×D₄×C₁₃	C₂²	1	64	yes	complemented
55	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
57	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
59	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
60	C₂²×C₄²×C₁₃	C₂²	1	4	yes	complemented
61	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₁₃	C₂³	1	4	yes	—
63	C₂×C₁₃×#41	—	2	16	no	—
64	C₂×C₁₃×#41	—	4	8	no	—
65	C₂×C₁₃×#41	C₂³	1	16	yes	—
66	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	—	2	32	no	—
70	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	32	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	—	4	16	no	—
78	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	32	yes	complemented
87	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
88	C₁₃×#127	C₂³	1	8	yes	—
89	C₁₃×#126	C₂³	1	64	yes	complemented
90	C₁₃×#125	C₂³	1	32	yes	complemented
91	C₁₃×#124	C₂³	1	32	yes	complemented
92	C₁₃×#124	C₂³	1	16	yes	complemented
93	C₁₃×#123	C₂³	1	32	yes	complemented
94	C₁₃×#123	C₂³	1	32	yes	complemented
95	C₁₃×#123	C₂³	1	64	yes	complemented
96	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
97	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
98	C₁₃×#121	C₂³	1	32	yes	—
99	C₁₃×#121	C₂³	1	64	yes	complemented
100	C₁₃×#121	C₂³	1	32	yes	complemented
101	C₁₃×#120	C₂³	1	32	yes	—
102	C₁₃×#120	C₂³	1	32	yes	complemented
103	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
104	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
105	C₄×D₄×C₁₃	C₂³	1	16	yes	—
106	C₄×D₄×C₁₃	C₂³	1	32	yes	—
107	C₄×D₄×C₁₃	C₂³	1	16	yes	—
108	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
109	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
110	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
111	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
112	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
113	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
114	C₁₃×#117	C₂³	1	32	yes	complemented
115	C₁₃×#117	C₂³	1	16	yes	complemented
116	C₁₃×#117	C₂³	1	32	yes	complemented
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	64	yes	complemented
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	32	yes	complemented
141	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
142	C₂×#3481	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	32	no	—
144	C₂⁴×C₁₃	—	4	8	no	—
145	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
149	C₁₃×#41	—	2	64	no	—
150	C₁₃×#41	—	4	32	no	—
151	C₂×Q₈×C₁₃	—	2	8	no	—
152	C₂×Q₈×C₁₃	—	4	4	no	—
153	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
154	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
155	C₂×D₄×C₁₃	—	2	32	no	—
156	C₂×D₄×C₁₃	—	2	16	no	—
157	C₂×D₄×C₁₃	—	2	128	no	—
158	C₂×D₄×C₁₃	—	2	16	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	4	4	no	—
161	C₂×D₄×C₁₃	#41	1	16	yes	complemented
162	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
168	C₂²×C₄×C₁₃	—	2	16	no	—
169	C₂²×C₄×C₁₃	—	2	16	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	2	16	no	—
172	C₂²×C₄×C₁₃	—	2	16	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	4	64	no	—
175	C₂²×C₄×C₁₃	—	4	8	no	—
176	C₂²×C₄×C₁₃	—	4	16	no	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
200	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
201	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
202	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
203	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
204	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
205	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
206	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
207	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
208	C₄²×C₁₃	C₂⁴	1	8	yes	—
209	C₄²×C₁₃	C₂⁴	1	4	yes	—
210	C₄²×C₁₃	C₂⁴	1	16	yes	—
211	C₄²×C₁₃	C₂⁴	1	16	yes	—
212	C₄²×C₁₃	C₂⁴	1	4	yes	—
213	C₄²×C₁₃	C₂⁴	1	16	yes	—
214	#3481	C₂×C₁₃	1	32	yes	direct product factor
215	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#554	C₂×C₁₃	1	2	yes	complemented
217	C₂×#553	C₂×C₁₃	1	4	yes	complemented
218	C₂×#551	C₂×C₁₃	1	4	yes	complemented
219	C₂×#546	C₂×C₁₃	1	4	yes	complemented
220	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×#529	C₂×C₁₃	1	4	yes	complemented
223	C₂×#525	C₂×C₁₃	1	4	yes	complemented
224	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
225	C₂²×C₄×D₄	C₂×C₁₃	1	4	yes	complemented
226	C₂³×C₁₃	—	2	8	no	—
227	C₂³×C₁₃	—	2	8	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	64	no	—
230	C₂³×C₁₃	—	2	16	no	—
231	C₂³×C₁₃	—	2	8	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	4	16	no	—
234	C₂³×C₁₃	—	4	64	no	—
235	C₂³×C₁₃	C₂×#41	1	16	yes	—
236	C₂³×C₁₃	C₂⁵	1	8	yes	—
237	C₂³×C₁₃	C₂⁵	1	2	yes	—
238	C₂³×C₁₃	C₂⁵	1	8	yes	—
239	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	16	no	—
241	Q₈×C₁₃	—	4	8	no	—
242	D₄×C₁₃	—	2	64	no	—
243	D₄×C₁₃	—	2	32	no	—
244	D₄×C₁₃	—	2	32	no	—
245	D₄×C₁₃	—	4	16	no	—
246	D₄×C₁₃	—	4	8	no	—
247	D₄×C₁₃	C₂×#41	1	32	yes	complemented
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	8	no	—
250	C₂×C₄×C₁₃	—	2	8	no	—
251	C₂×C₄×C₁₃	—	2	32	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	32	no	—
256	C₂×C₄×C₁₃	—	2	16	no	—
257	C₂×C₄×C₁₃	—	2	32	no	—
258	C₂×C₄×C₁₃	—	2	32	no	—
259	C₂×C₄×C₁₃	—	2	8	no	—
260	C₂×C₄×C₁₃	—	4	16	no	—
261	C₂×C₄×C₁₃	—	4	32	no	—
262	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
263	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
264	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
269	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
270	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
271	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
272	C₂²×#41	C₂²×C₁₃	1	2	yes	—
273	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
274	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
275	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	complemented
276	#559	C₂²×C₁₃	1	16	yes	complemented
277	#554	C₂²×C₁₃	1	32	yes	complemented
278	#553	C₂²×C₁₃	1	64	yes	complemented
279	#551	C₂²×C₁₃	1	64	yes	complemented
280	#546	C₂²×C₁₃	1	64	yes	complemented
281	D₄²	C₂²×C₁₃	1	16	yes	complemented
282	#532	C₂²×C₁₃	1	16	yes	complemented
283	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
284	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
285	#529	C₂²×C₁₃	1	64	yes	complemented
286	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
287	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
288	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
289	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
290	#525	C₂²×C₁₃	1	64	yes	complemented
291	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
292	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
293	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
294	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
295	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
296	C₂×#121	C₂²×C₁₃	1	4	yes	—
297	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
298	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
299	C₂×#120	C₂²×C₁₃	1	4	yes	—
300	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
301	C₄×#41	C₂²×C₁₃	1	32	yes	complemented
302	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
303	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
304	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
306	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
307	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
308	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
309	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
310	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
311	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
312	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
313	C₂×C₄×D₄	C₂²×C₁₃	1	64	yes	complemented
314	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
315	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
316	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
317	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
318	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
319	C₂²×C₄²	C₂²×C₁₃	1	4	yes	complemented
320	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	C₂²×C₁₃	—	2	8	no	—
322	C₂²×C₁₃	—	2	8	no	—
323	C₂²×C₁₃	—	2	32	no	—
324	C₂²×C₁₃	—	2	4	no	—
325	C₂²×C₁₃	—	2	16	no	—
326	C₂²×C₁₃	—	2	8	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	4	64	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	16	no	—
331	C₂²×C₁₃	C₂²×#41	1	16	yes	—
332	C₂²×C₁₃	C₂²×#41	1	4	yes	—
333	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
334	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
335	C₄×C₁₃	—	2	4	no	—
336	C₄×C₁₃	—	2	8	no	—
337	C₄×C₁₃	—	2	8	no	—
338	C₄×C₁₃	—	2	8	no	—
339	C₄×C₁₃	—	2	8	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	C₂²×#41	1	8	yes	—
342	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
343	C₂⁵	C₂³×C₁₃	1	4	yes	—
344	C₂×#41	—	2	16	no	—
345	C₂×#41	—	4	8	no	—
346	C₂×#41	C₂³×C₁₃	1	16	yes	—
347	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
348	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
349	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
350	C₂²×D₄	—	2	32	no	—
351	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
352	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
353	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
354	C₂²×D₄	C₂³×C₁₃	1	32	yes	—
355	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
356	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
357	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	—	4	16	no	—
359	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
360	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
361	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
362	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
366	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
367	C₂³×C₄	C₂³×C₁₃	1	32	yes	complemented
368	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
369	#127	C₂³×C₁₃	1	8	yes	—
370	#126	C₂³×C₁₃	1	64	yes	complemented
371	#125	C₂³×C₁₃	1	32	yes	complemented
372	#124	C₂³×C₁₃	1	32	yes	complemented
373	#124	C₂³×C₁₃	1	16	yes	complemented
374	#123	C₂³×C₁₃	1	32	yes	complemented
375	#123	C₂³×C₁₃	1	32	yes	complemented
376	#123	C₂³×C₁₃	1	64	yes	complemented
377	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
378	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
379	#121	C₂³×C₁₃	1	32	yes	—
380	#121	C₂³×C₁₃	1	64	yes	complemented
381	#121	C₂³×C₁₃	1	32	yes	complemented
382	#120	C₂³×C₁₃	1	32	yes	—
383	#120	C₂³×C₁₃	1	32	yes	complemented
384	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
385	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
386	C₄×D₄	C₂³×C₁₃	1	16	yes	—
387	C₄×D₄	C₂³×C₁₃	1	32	yes	—
388	C₄×D₄	C₂³×C₁₃	1	16	yes	—
389	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
390	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
391	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
392	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
393	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
394	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
395	#117	C₂³×C₁₃	1	32	yes	complemented
396	#117	C₂³×C₁₃	1	16	yes	complemented
397	#117	C₂³×C₁₃	1	32	yes	complemented
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
406	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	64	yes	complemented
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
417	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	32	yes	complemented
422	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
423	C₂×C₁₃	—	2	16	no	—
424	C₂×C₁₃	—	4	2	no	—
425	C₂×C₁₃	—	4	8	no	—
426	C₂×C₁₃	#3481	1	4	yes	direct product factor
427	C₂×C₁₃	C₂³×#41	1	2	yes	—
428	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂⁴	—	2	32	no	—
430	C₂⁴	—	4	8	no	—
431	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
432	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
433	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
434	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
435	#41	—	2	64	no	—
436	#41	—	4	32	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
440	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
441	C₂×D₄	—	2	32	no	—
442	C₂×D₄	—	2	16	no	—
443	C₂×D₄	—	2	128	no	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	C₁₃×#41	1	16	yes	complemented
448	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
449	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
450	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
451	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
452	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
453	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
454	C₂²×C₄	—	2	16	no	—
455	C₂²×C₄	—	2	16	no	—
456	C₂²×C₄	—	2	8	no	—
457	C₂²×C₄	—	2	16	no	—
458	C₂²×C₄	—	2	16	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	4	64	no	—
461	C₂²×C₄	—	4	8	no	—
462	C₂²×C₄	—	4	16	no	—
463	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
480	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
481	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
482	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
483	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
484	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
485	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
486	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
487	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
488	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
489	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
490	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
491	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
492	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
493	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
494	C₄²	C₂⁴×C₁₃	1	8	yes	—
495	C₄²	C₂⁴×C₁₃	1	4	yes	—
496	C₄²	C₂⁴×C₁₃	1	16	yes	—
497	C₄²	C₂⁴×C₁₃	1	16	yes	—
498	C₄²	C₂⁴×C₁₃	1	4	yes	—
499	C₄²	C₂⁴×C₁₃	1	16	yes	—
500	C₁₃	C₂×#3481	1	1	yes	characteristic, direct product factor, Sylow
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	64	no	—
505	C₂³	—	2	16	no	—
506	C₂³	—	2	8	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	16	no	—
509	C₂³	—	4	64	no	—
510	C₂³	C₂×C₁₃×#41	1	16	yes	—
511	C₂³	C₂⁵×C₁₃	1	8	yes	—
512	C₂³	C₂⁵×C₁₃	1	2	yes	—
513	C₂³	C₂⁵×C₁₃	1	8	yes	—
514	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
515	Q₈	—	2	16	no	—
516	Q₈	—	4	8	no	—
517	D₄	—	2	64	no	—
518	D₄	—	2	32	no	—
519	D₄	—	2	32	no	—
520	D₄	—	4	16	no	—
521	D₄	—	4	8	no	—
522	D₄	C₂×C₁₃×#41	1	32	yes	complemented
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	32	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	32	no	—
531	C₂×C₄	—	2	16	no	—
532	C₂×C₄	—	2	32	no	—
533	C₂×C₄	—	2	32	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	4	16	no	—
536	C₂×C₄	—	4	32	no	—
537	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
538	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
539	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
540	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
541	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
542	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
543	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
544	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
545	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
546	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	32	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	16	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	64	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	16	no	—
557	C₂²	C₂²×C₁₃×#41	1	16	yes	—
558	C₂²	C₂²×C₁₃×#41	1	4	yes	—
559	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
560	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
561	C₄	—	2	4	no	—
562	C₄	—	2	8	no	—
563	C₄	—	2	8	no	—
564	C₄	—	2	8	no	—
565	C₄	—	2	8	no	—
566	C₄	—	2	2	no	—
567	C₄	C₂²×C₁₃×#41	1	8	yes	—
568	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
569	C₂	—	2	16	no	—
570	C₂	—	4	8	no	—
571	C₂	—	4	2	no	—
572	C₂	C₁₃×#3481	1	4	yes	direct product factor
573	C₂	C₂³×C₁₃×#41	1	2	yes	—
574	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3481	C₂	direct (N × H)
2. C₂×C₁₃×#559	C₂	semidirect
3. C₂×C₁₃×#554	C₂	semidirect
4. C₂×C₁₃×#553	C₂	semidirect
5. C₂×C₁₃×#551	C₂	semidirect
6. C₂×C₁₃×#546	C₂	semidirect
7. C₂×D₄²×C₁₃	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂×C₄×C₁₃×#41	C₂	semidirect
12. C₂²×C₄×D₄×C₁₃	C₂	semidirect
14. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂⁴×C₄×C₁₃	C₂²	semidirect
17. C₁₃×#559	C₂²	semidirect
18. C₁₃×#554	C₂²	semidirect
19. C₁₃×#553	C₂²	semidirect
20. C₁₃×#551	C₂²	semidirect
21. C₁₃×#546	C₂²	semidirect
22. D₄²×C₁₃	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#529	C₂²	semidirect
27. C₂×C₁₃×#126	C₂²	semidirect
28. C₂×C₁₃×#125	C₂²	semidirect
29. C₂×C₁₃×#124	C₂²	semidirect
30. C₂×C₁₃×#124	C₂²	semidirect
31. C₁₃×#525	C₂²	semidirect
32. C₂×C₁₃×#123	C₂²	semidirect
33. C₂×C₁₃×#123	C₂²	semidirect
34. C₂×C₁₃×#123	C₂²	semidirect
35. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
39. C₂×C₁₃×#121	C₂²	semidirect
41. C₂×C₁₃×#120	C₂²	semidirect
42. C₄×C₁₃×#41	C₂²	semidirect
43. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
44. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₂×C₄×D₄×C₁₃	C₂²	semidirect
51. C₂×C₄×D₄×C₁₃	C₂²	semidirect
52. C₂×C₄×D₄×C₁₃	C₂²	semidirect
53. C₂×C₄×D₄×C₁₃	C₂²	semidirect
54. C₂×C₄×D₄×C₁₃	C₂²	semidirect
55. C₂×C₁₃×#117	C₂²	semidirect
56. C₂×C₁₃×#117	C₂²	semidirect
57. C₂×C₁₃×#117	C₂²	semidirect
58. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
60. C₂²×C₄²×C₁₃	C₂²	semidirect
61. C₂²×C₄²×C₁₃	C₂²	semidirect
66. C₂×C₁₃×#41	C₂³	semidirect
86. C₂³×C₄×C₁₃	C₂³	semidirect
87. C₁₃×C₄⋊Q₈	C₂³	semidirect
89. C₁₃×#126	C₂³	semidirect
90. C₁₃×#125	C₂³	semidirect
91. C₁₃×#124	C₂³	semidirect
92. C₁₃×#124	C₂³	semidirect
93. C₁₃×#123	C₂³	semidirect
94. C₁₃×#123	C₂³	semidirect
95. C₁₃×#123	C₂³	semidirect
96. C₁₃×C₂²⋊Q₈	C₂³	semidirect
97. C₁₃×C₂²⋊Q₈	C₂³	semidirect
99. C₁₃×#121	C₂³	semidirect
100. C₁₃×#121	C₂³	semidirect
102. C₁₃×#120	C₂³	semidirect
103. C₄×Q₈×C₁₃	C₂³	semidirect
104. C₄×Q₈×C₁₃	C₂³	semidirect
108. C₄×D₄×C₁₃	C₂³	semidirect
109. C₄×D₄×C₁₃	C₂³	semidirect
110. C₄×D₄×C₁₃	C₂³	semidirect
111. C₄×D₄×C₁₃	C₂³	semidirect
112. C₄×D₄×C₁₃	C₂³	semidirect
113. C₄×D₄×C₁₃	C₂³	semidirect
114. C₁₃×#117	C₂³	semidirect
115. C₁₃×#117	C₂³	semidirect
116. C₁₃×#117	C₂³	semidirect
124. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
133. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
140. C₂×C₄²×C₁₃	C₂³	semidirect
141. C₂×C₄²×C₁₃	C₂³	semidirect
142. C₂×#3481	C₁₃	direct (N × H)
161. C₂×D₄×C₁₃	#41	semidirect
214. #3481	C₂×C₁₃	direct (N × H)
215. C₂×#559	C₂×C₁₃	semidirect
216. C₂×#554	C₂×C₁₃	semidirect
217. C₂×#553	C₂×C₁₃	semidirect
218. C₂×#551	C₂×C₁₃	semidirect
219. C₂×#546	C₂×C₁₃	semidirect
220. C₂×D₄²	C₂×C₁₃	semidirect
221. C₂×#532	C₂×C₁₃	semidirect
222. C₂×#529	C₂×C₁₃	semidirect
223. C₂×#525	C₂×C₁₃	semidirect
224. C₂×C₄×#41	C₂×C₁₃	semidirect
225. C₂²×C₄×D₄	C₂×C₁₃	semidirect
247. D₄×C₁₃	C₂×#41	semidirect
273. C₂²×#41	C₂²×C₁₃	semidirect
275. C₂⁴×C₄	C₂²×C₁₃	semidirect
276. #559	C₂²×C₁₃	semidirect
277. #554	C₂²×C₁₃	semidirect
278. #553	C₂²×C₁₃	semidirect
279. #551	C₂²×C₁₃	semidirect
280. #546	C₂²×C₁₃	semidirect
281. D₄²	C₂²×C₁₃	semidirect
282. #532	C₂²×C₁₃	semidirect
283. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
285. #529	C₂²×C₁₃	semidirect
286. C₂×#126	C₂²×C₁₃	semidirect
287. C₂×#125	C₂²×C₁₃	semidirect
288. C₂×#124	C₂²×C₁₃	semidirect
289. C₂×#124	C₂²×C₁₃	semidirect
290. #525	C₂²×C₁₃	semidirect
291. C₂×#123	C₂²×C₁₃	semidirect
292. C₂×#123	C₂²×C₁₃	semidirect
293. C₂×#123	C₂²×C₁₃	semidirect
294. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
295. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
297. C₂×#121	C₂²×C₁₃	semidirect
298. C₂×#121	C₂²×C₁₃	semidirect
300. C₂×#120	C₂²×C₁₃	semidirect
301. C₄×#41	C₂²×C₁₃	semidirect
302. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
303. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
307. C₂×C₄×D₄	C₂²×C₁₃	semidirect
308. C₂×C₄×D₄	C₂²×C₁₃	semidirect
309. C₂×C₄×D₄	C₂²×C₁₃	semidirect
310. C₂×C₄×D₄	C₂²×C₁₃	semidirect
311. C₂×C₄×D₄	C₂²×C₁₃	semidirect
312. C₂×C₄×D₄	C₂²×C₁₃	semidirect
313. C₂×C₄×D₄	C₂²×C₁₃	semidirect
314. C₂×#117	C₂²×C₁₃	semidirect
315. C₂×#117	C₂²×C₁₃	semidirect
316. C₂×#117	C₂²×C₁₃	semidirect
317. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
318. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
319. C₂²×C₄²	C₂²×C₁₃	semidirect
320. C₂²×C₄²	C₂²×C₁₃	semidirect
347. C₂×#41	C₂³×C₁₃	semidirect
367. C₂³×C₄	C₂³×C₁₃	semidirect
368. C₄⋊Q₈	C₂³×C₁₃	semidirect
370. #126	C₂³×C₁₃	semidirect
371. #125	C₂³×C₁₃	semidirect
372. #124	C₂³×C₁₃	semidirect
373. #124	C₂³×C₁₃	semidirect
374. #123	C₂³×C₁₃	semidirect
375. #123	C₂³×C₁₃	semidirect
376. #123	C₂³×C₁₃	semidirect
377. C₂²⋊Q₈	C₂³×C₁₃	semidirect
378. C₂²⋊Q₈	C₂³×C₁₃	semidirect
380. #121	C₂³×C₁₃	semidirect
381. #121	C₂³×C₁₃	semidirect
383. #120	C₂³×C₁₃	semidirect
384. C₄×Q₈	C₂³×C₁₃	semidirect
385. C₄×Q₈	C₂³×C₁₃	semidirect
389. C₄×D₄	C₂³×C₁₃	semidirect
390. C₄×D₄	C₂³×C₁₃	semidirect
391. C₄×D₄	C₂³×C₁₃	semidirect
392. C₄×D₄	C₂³×C₁₃	semidirect
393. C₄×D₄	C₂³×C₁₃	semidirect
394. C₄×D₄	C₂³×C₁₃	semidirect
395. #117	C₂³×C₁₃	semidirect
396. #117	C₂³×C₁₃	semidirect
397. #117	C₂³×C₁₃	semidirect
405. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
414. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
421. C₂×C₄²	C₂³×C₁₃	semidirect
422. C₂×C₄²	C₂³×C₁₃	semidirect
426. C₂×C₁₃	#3481	direct (N × H)
447. C₂×D₄	C₁₃×#41	semidirect
500. C₁₃	C₂×#3481	direct (N × H)
522. D₄	C₂×C₁₃×#41	semidirect
572. C₂	C₁₃×#3481	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×#3481	2
C₂×C₁₃×#559	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#551	2
C₂×C₁₃×#546	2
C₂×D₄²×C₁₃	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×C₄×C₁₃×#41	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3481	13

Subgroups — C2×C13×#3481 #15749053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3481 #15749053