Subgroups — C₂×C₁₃×#3507 #15749116

Order 3328.

7130 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#559	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#557	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#556	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#552	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#559	C₂²	1	32	yes	complemented
18	C₁₃×#557	C₂²	1	32	yes	complemented
19	C₁₃×#556	C₂²	1	32	yes	complemented
20	C₁₃×#556	C₂²	1	64	yes	complemented
21	C₁₃×#554	C₂²	1	32	yes	complemented
22	C₁₃×#552	C₂²	1	64	yes	complemented
23	C₁₃×#539	C₂²	1	64	yes	complemented
24	C₁₃×#536	C₂²	1	32	yes	complemented
25	C₁₃×#533	C₂²	1	16	yes	complemented
26	C₁₃×#532	C₂²	1	16	yes	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#529	C₂²	1	64	yes	complemented
33	C₂×C₁₃×#126	C₂²	1	8	yes	—
34	C₂×C₁₃×#126	C₂²	1	8	yes	—
35	C₂×C₁₃×#125	C₂²	1	4	yes	—
36	C₂×C₁₃×#125	C₂²	1	2	yes	—
37	C₂×C₁₃×#125	C₂²	1	8	yes	—
38	C₂×C₁₃×#124	C₂²	1	4	yes	—
39	C₂×C₁₃×#124	C₂²	1	2	yes	—
40	C₂×C₁₃×#124	C₂²	1	4	yes	—
41	C₂×C₁₃×#123	C₂²	1	8	yes	—
42	C₂×C₁₃×#123	C₂²	1	8	yes	—
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
48	C₂×C₁₃×#121	C₂²	1	2	yes	—
49	C₂×C₁₃×#121	C₂²	1	2	yes	—
50	C₁₃×#520	C₂²	1	32	yes	complemented
51	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
52	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
54	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
55	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
56	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
57	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
58	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
60	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
61	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
62	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
63	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
64	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
65	C₂×C₁₃×#117	C₂²	1	2	yes	—
66	C₂×C₁₃×#117	C₂²	1	4	yes	—
67	C₂×C₁₃×#117	C₂²	1	8	yes	—
68	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
71	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
72	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#41	—	2	16	no	—
74	C₂×C₁₃×#41	C₂³	1	16	yes	—
75	C₂²×Q₈×C₁₃	—	2	8	no	—
76	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
80	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	—
97	C₁₃×#127	C₂³	1	8	yes	—
98	C₁₃×#126	C₂³	1	64	yes	—
99	C₁₃×#126	C₂³	1	64	yes	—
100	C₁₃×#125	C₂³	1	32	yes	—
101	C₁₃×#125	C₂³	1	16	yes	—
102	C₁₃×#125	C₂³	1	64	yes	—
103	C₁₃×#124	C₂³	1	32	yes	—
104	C₁₃×#124	C₂³	1	16	yes	—
105	C₁₃×#124	C₂³	1	32	yes	—
106	C₁₃×#123	C₂³	1	64	yes	—
107	C₁₃×#123	C₂³	1	64	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
112	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	—
113	C₁₃×#121	C₂³	1	16	yes	—
114	C₁₃×#121	C₂³	1	16	yes	—
115	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
117	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
123	C₄×D₄×C₁₃	C₂³	1	64	yes	—
124	C₄×D₄×C₁₃	C₂³	1	32	yes	—
125	C₄×D₄×C₁₃	C₂³	1	32	yes	—
126	C₄×D₄×C₁₃	C₂³	1	16	yes	—
127	C₄×D₄×C₁₃	C₂³	1	16	yes	—
128	C₁₃×#117	C₂³	1	16	yes	—
129	C₁₃×#117	C₂³	1	32	yes	—
130	C₁₃×#117	C₂³	1	64	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
165	C₂×#3507	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×#41	—	2	64	no	—
169	C₂×Q₈×C₁₃	—	2	8	no	—
170	C₂×Q₈×C₁₃	—	2	8	no	—
171	C₂×Q₈×C₁₃	—	2	32	no	—
172	C₂×Q₈×C₁₃	—	2	8	no	—
173	C₂×Q₈×C₁₃	—	2	8	no	—
174	C₂×Q₈×C₁₃	—	4	4	no	—
175	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
179	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
180	C₂×D₄×C₁₃	—	2	16	no	—
181	C₂×D₄×C₁₃	—	2	8	no	—
182	C₂×D₄×C₁₃	—	2	8	no	—
183	C₂×D₄×C₁₃	—	4	4	no	—
184	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
186	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
188	C₂²×C₄×C₁₃	—	2	8	no	—
189	C₂²×C₄×C₁₃	—	2	16	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	4	4	no	—
192	C₂²×C₄×C₁₃	—	4	16	no	—
193	C₂²×C₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	#41	1	8	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
216	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
217	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
222	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
223	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
224	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
225	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
227	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
228	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
229	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
230	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
231	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
232	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
233	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
234	C₄²×C₁₃	C₂⁴	1	16	yes	—
235	C₄²×C₁₃	C₂⁴	1	4	yes	—
236	C₄²×C₁₃	C₂⁴	1	4	yes	—
237	C₄²×C₁₃	C₂⁴	1	16	yes	—
238	C₄²×C₁₃	C₂⁴	1	4	yes	—
239	C₄²×C₁₃	C₂⁴	1	4	yes	—
240	C₄²×C₁₃	C₂⁴	1	32	yes	—
241	C₄²×C₁₃	C₂⁴	1	16	yes	—
242	#3507	C₂×C₁₃	1	32	yes	direct product factor
243	C₂×#559	C₂×C₁₃	1	2	yes	complemented
244	C₂×#557	C₂×C₁₃	1	2	yes	complemented
245	C₂×#556	C₂×C₁₃	1	2	yes	complemented
246	C₂×#556	C₂×C₁₃	1	4	yes	complemented
247	C₂×#554	C₂×C₁₃	1	2	yes	complemented
248	C₂×#552	C₂×C₁₃	1	4	yes	complemented
249	C₂×#539	C₂×C₁₃	1	4	yes	complemented
250	C₂×#536	C₂×C₁₃	1	2	yes	complemented
251	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
253	C₂×#529	C₂×C₁₃	1	4	yes	complemented
254	C₂×#520	C₂×C₁₃	1	2	yes	complemented
255	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	8	no	—
259	C₂³×C₁₃	—	2	8	no	—
260	C₂³×C₁₃	—	2	8	no	—
261	C₂³×C₁₃	C₂×#41	1	4	yes	—
262	C₂³×C₁₃	C₂⁵	1	8	yes	—
263	C₂³×C₁₃	C₂⁵	1	2	yes	—
264	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
265	Q₈×C₁₃	—	2	16	no	—
266	Q₈×C₁₃	—	2	16	no	—
267	Q₈×C₁₃	—	2	16	no	—
268	Q₈×C₁₃	—	2	16	no	—
269	Q₈×C₁₃	—	4	8	no	—
270	D₄×C₁₃	—	2	32	no	—
271	D₄×C₁₃	—	2	16	no	—
272	D₄×C₁₃	—	2	16	no	—
273	D₄×C₁₃	—	4	8	no	—
274	C₂×C₄×C₁₃	—	2	8	no	—
275	C₂×C₄×C₁₃	—	2	16	no	—
276	C₂×C₄×C₁₃	—	2	8	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	8	no	—
279	C₂×C₄×C₁₃	—	2	8	no	—
280	C₂×C₄×C₁₃	—	2	8	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	32	no	—
284	C₂×C₄×C₁₃	—	2	8	no	—
285	C₂×C₄×C₁₃	—	4	8	no	—
286	C₂×C₄×C₁₃	—	4	32	no	—
287	C₂×C₄×C₁₃	—	4	4	no	—
288	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
290	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
291	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
293	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
294	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
295	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
296	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
297	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
298	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
299	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
300	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
301	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
302	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
303	C₂²×#41	C₂²×C₁₃	1	2	yes	—
304	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	#559	C₂²×C₁₃	1	32	yes	complemented
306	#557	C₂²×C₁₃	1	32	yes	complemented
307	#556	C₂²×C₁₃	1	32	yes	complemented
308	#556	C₂²×C₁₃	1	64	yes	complemented
309	#554	C₂²×C₁₃	1	32	yes	complemented
310	#552	C₂²×C₁₃	1	64	yes	complemented
311	#539	C₂²×C₁₃	1	64	yes	complemented
312	#536	C₂²×C₁₃	1	32	yes	complemented
313	#533	C₂²×C₁₃	1	16	yes	complemented
314	#532	C₂²×C₁₃	1	16	yes	—
315	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
319	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
320	#529	C₂²×C₁₃	1	64	yes	complemented
321	C₂×#126	C₂²×C₁₃	1	8	yes	—
322	C₂×#126	C₂²×C₁₃	1	8	yes	—
323	C₂×#125	C₂²×C₁₃	1	4	yes	—
324	C₂×#125	C₂²×C₁₃	1	2	yes	—
325	C₂×#125	C₂²×C₁₃	1	8	yes	—
326	C₂×#124	C₂²×C₁₃	1	4	yes	—
327	C₂×#124	C₂²×C₁₃	1	2	yes	—
328	C₂×#124	C₂²×C₁₃	1	4	yes	—
329	C₂×#123	C₂²×C₁₃	1	8	yes	—
330	C₂×#123	C₂²×C₁₃	1	8	yes	—
331	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
332	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
333	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
334	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
335	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
336	C₂×#121	C₂²×C₁₃	1	2	yes	—
337	C₂×#121	C₂²×C₁₃	1	2	yes	—
338	#520	C₂²×C₁₃	1	32	yes	complemented
339	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
340	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
341	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
342	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
343	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
344	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
345	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
346	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
347	C₂×C₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
348	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
349	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
350	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
351	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
352	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
353	C₂×#117	C₂²×C₁₃	1	2	yes	—
354	C₂×#117	C₂²×C₁₃	1	4	yes	—
355	C₂×#117	C₂²×C₁₃	1	8	yes	—
356	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
358	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
359	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
360	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×C₁₃	—	2	2	no	—
362	C₂²×C₁₃	—	2	2	no	—
363	C₂²×C₁₃	—	2	8	no	—
364	C₂²×C₁₃	—	2	8	no	—
365	C₂²×C₁₃	—	2	8	no	—
366	C₂²×C₁₃	—	2	8	no	—
367	C₂²×C₁₃	—	4	16	no	—
368	C₂²×C₁₃	C₂²×#41	1	4	yes	—
369	C₂²×C₁₃	C₂²×#41	1	2	yes	—
370	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
371	C₂²×C₁₃	#585	1	2	yes	—
372	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
373	C₄×C₁₃	—	2	8	no	—
374	C₄×C₁₃	—	2	8	no	—
375	C₄×C₁₃	—	2	2	no	—
376	C₄×C₁₃	—	2	8	no	—
377	C₄×C₁₃	—	2	8	no	—
378	C₄×C₁₃	—	2	8	no	—
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	2	2	no	—
381	C₄×C₁₃	C₂²×#41	1	4	yes	—
382	C₄×C₁₃	C₂²×#41	1	4	yes	—
383	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
384	C₂×#41	—	2	16	no	—
385	C₂×#41	C₂³×C₁₃	1	16	yes	—
386	C₂²×Q₈	—	2	8	no	—
387	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
388	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
389	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
390	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
391	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
392	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
393	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
394	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
395	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
396	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
397	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
398	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
401	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
403	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
405	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
406	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
407	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	—
408	#127	C₂³×C₁₃	1	8	yes	—
409	#126	C₂³×C₁₃	1	64	yes	—
410	#126	C₂³×C₁₃	1	64	yes	—
411	#125	C₂³×C₁₃	1	32	yes	—
412	#125	C₂³×C₁₃	1	16	yes	—
413	#125	C₂³×C₁₃	1	64	yes	—
414	#124	C₂³×C₁₃	1	32	yes	—
415	#124	C₂³×C₁₃	1	16	yes	—
416	#124	C₂³×C₁₃	1	32	yes	—
417	#123	C₂³×C₁₃	1	64	yes	—
418	#123	C₂³×C₁₃	1	64	yes	—
419	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
420	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
421	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
422	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
423	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	—
424	#121	C₂³×C₁₃	1	16	yes	—
425	#121	C₂³×C₁₃	1	16	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
427	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
428	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
429	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
430	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
431	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
432	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
433	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
434	C₄×D₄	C₂³×C₁₃	1	64	yes	—
435	C₄×D₄	C₂³×C₁₃	1	32	yes	—
436	C₄×D₄	C₂³×C₁₃	1	32	yes	—
437	C₄×D₄	C₂³×C₁₃	1	16	yes	—
438	C₄×D₄	C₂³×C₁₃	1	16	yes	—
439	#117	C₂³×C₁₃	1	16	yes	—
440	#117	C₂³×C₁₃	1	32	yes	—
441	#117	C₂³×C₁₃	1	64	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
467	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
468	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
475	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
476	C₂×C₁₃	—	2	4	no	—
477	C₂×C₁₃	—	4	8	no	—
478	C₂×C₁₃	#3507	1	4	yes	direct product factor
479	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
480	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
481	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
482	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
483	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
484	#41	—	2	64	no	—
485	C₂×Q₈	—	2	8	no	—
486	C₂×Q₈	—	2	8	no	—
487	C₂×Q₈	—	2	32	no	—
488	C₂×Q₈	—	2	8	no	—
489	C₂×Q₈	—	2	8	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
492	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
493	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
494	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
495	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
496	C₂×D₄	—	2	16	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	4	4	no	—
500	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
501	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
502	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
503	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
504	C₂²×C₄	—	2	8	no	—
505	C₂²×C₄	—	2	16	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	—	4	16	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	C₁₃×#41	1	8	yes	—
511	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
516	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
530	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
531	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
532	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
533	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
534	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
535	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
536	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
537	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
538	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
539	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
540	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
541	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
542	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
543	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
544	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
545	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
546	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
547	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
548	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
549	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
550	C₄²	C₂⁴×C₁₃	1	16	yes	—
551	C₄²	C₂⁴×C₁₃	1	4	yes	—
552	C₄²	C₂⁴×C₁₃	1	4	yes	—
553	C₄²	C₂⁴×C₁₃	1	16	yes	—
554	C₄²	C₂⁴×C₁₃	1	4	yes	—
555	C₄²	C₂⁴×C₁₃	1	4	yes	—
556	C₄²	C₂⁴×C₁₃	1	32	yes	—
557	C₄²	C₂⁴×C₁₃	1	16	yes	—
558	C₁₃	C₂×#3507	1	1	yes	characteristic, direct product factor, Sylow
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	8	no	—
562	C₂³	—	2	8	no	—
563	C₂³	—	2	8	no	—
564	C₂³	C₂×C₁₃×#41	1	4	yes	—
565	C₂³	C₂⁵×C₁₃	1	8	yes	—
566	C₂³	C₂⁵×C₁₃	1	2	yes	—
567	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
568	Q₈	—	2	16	no	—
569	Q₈	—	2	16	no	—
570	Q₈	—	2	16	no	—
571	Q₈	—	2	16	no	—
572	Q₈	—	4	8	no	—
573	D₄	—	2	32	no	—
574	D₄	—	2	16	no	—
575	D₄	—	2	16	no	—
576	D₄	—	4	8	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	16	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	8	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	32	no	—
587	C₂×C₄	—	2	8	no	—
588	C₂×C₄	—	4	8	no	—
589	C₂×C₄	—	4	32	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
592	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
593	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
594	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
595	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
596	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
597	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
598	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
599	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
600	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
601	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
602	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
603	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
604	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
605	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	8	no	—
612	C₂²	—	4	16	no	—
613	C₂²	C₂²×C₁₃×#41	1	4	yes	—
614	C₂²	C₂²×C₁₃×#41	1	2	yes	—
615	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
616	C₂²	C₁₃×#585	1	2	yes	—
617	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
618	C₄	—	2	8	no	—
619	C₄	—	2	8	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	8	no	—
622	C₄	—	2	8	no	—
623	C₄	—	2	8	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	C₂²×C₁₃×#41	1	4	yes	—
627	C₄	C₂²×C₁₃×#41	1	4	yes	—
628	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
629	C₂	—	2	4	no	—
630	C₂	—	4	8	no	—
631	C₂	C₁₃×#3507	1	4	yes	direct product factor
632	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
633	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
634	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂×C₁₃×#532	C₂
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×#3507	C₂	direct (N × H)
2. C₂×C₁₃×#559	C₂	semidirect
3. C₂×C₁₃×#557	C₂	semidirect
4. C₂×C₁₃×#556	C₂	semidirect
5. C₂×C₁₃×#556	C₂	semidirect
6. C₂×C₁₃×#554	C₂	semidirect
7. C₂×C₁₃×#552	C₂	semidirect
8. C₂×C₁₃×#539	C₂	semidirect
9. C₂×C₁₃×#536	C₂	semidirect
10. C₂×C₁₃×#533	C₂	semidirect
12. C₂×C₁₃×#529	C₂	semidirect
13. C₂×C₁₃×#520	C₂	semidirect
14. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
17. C₁₃×#559	C₂²	semidirect
18. C₁₃×#557	C₂²	semidirect
19. C₁₃×#556	C₂²	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
22. C₁₃×#552	C₂²	semidirect
23. C₁₃×#539	C₂²	semidirect
24. C₁₃×#536	C₂²	semidirect
25. C₁₃×#533	C₂²	semidirect
32. C₁₃×#529	C₂²	semidirect
50. C₁₃×#520	C₂²	semidirect
59. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
165. C₂×#3507	C₁₃	direct (N × H)
242. #3507	C₂×C₁₃	direct (N × H)
243. C₂×#559	C₂×C₁₃	semidirect
244. C₂×#557	C₂×C₁₃	semidirect
245. C₂×#556	C₂×C₁₃	semidirect
246. C₂×#556	C₂×C₁₃	semidirect
247. C₂×#554	C₂×C₁₃	semidirect
248. C₂×#552	C₂×C₁₃	semidirect
249. C₂×#539	C₂×C₁₃	semidirect
250. C₂×#536	C₂×C₁₃	semidirect
251. C₂×#533	C₂×C₁₃	semidirect
253. C₂×#529	C₂×C₁₃	semidirect
254. C₂×#520	C₂×C₁₃	semidirect
255. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
305. #559	C₂²×C₁₃	semidirect
306. #557	C₂²×C₁₃	semidirect
307. #556	C₂²×C₁₃	semidirect
308. #556	C₂²×C₁₃	semidirect
309. #554	C₂²×C₁₃	semidirect
310. #552	C₂²×C₁₃	semidirect
311. #539	C₂²×C₁₃	semidirect
312. #536	C₂²×C₁₃	semidirect
313. #533	C₂²×C₁₃	semidirect
320. #529	C₂²×C₁₃	semidirect
338. #520	C₂²×C₁₃	semidirect
347. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
478. C₂×C₁₃	#3507	direct (N × H)
558. C₁₃	C₂×#3507	direct (N × H)
631. C₂	C₁₃×#3507	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×#3507	2
C₂×C₁₃×#559	2
C₂×C₁₃×#557	2
C₂×C₁₃×#556	2
C₂×C₁₃×#554	2
C₂×C₁₃×#552	2
C₂×C₁₃×#539	2
C₂×C₁₃×#536	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#520	2
C₂²×C₄×Q₈×C₁₃	2
C₂×#3507	13

Subgroups — C2×C13×#3507 #15749116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3507 #15749116