Subgroups — C₁₃×#60804 #15747143

Order 3328.

2164 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3216	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3215	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3210	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3152	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3037	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3007	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
15	C₁₃×#533	—	2	1	no	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#533	—	2	1	no	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#533	C₂²	1	2	yes	—
20	C₁₃×#533	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	2	yes	complemented
22	C₁₃×#533	C₂²	1	2	yes	complemented
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	—	2	1	no	—
25	C₁₃×#532	—	2	1	no	—
26	C₁₃×#532	—	2	1	no	—
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₁₃×#532	C₂²	1	2	yes	—
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#125	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₁₃×#121	—	2	1	no	—
40	C₂×C₁₃×#121	—	2	1	no	—
41	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
42	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₁₃	—	2	1	no	—
44	C₂×C₄×D₄×C₁₃	—	2	1	no	—
45	C₂×C₁₃×#117	—	2	1	no	—
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#497	C₂²	1	8	yes	complemented
48	C₁₃×#494	C₂²	1	4	yes	complemented
49	C₁₃×#492	C₂²	1	4	yes	complemented
50	C₁₃×#489	C₂²	1	8	yes	complemented
51	C₁₃×#487	C₂²	1	4	yes	complemented
52	C₁₃×#486	C₂²	1	4	yes	complemented
53	C₁₃×#464	C₂²	1	16	yes	complemented
54	C₁₃×#462	C₂²	1	8	yes	complemented
55	C₁₃×#460	C₂²	1	8	yes	complemented
56	C₁₃×#452	C₂²	1	16	yes	complemented
57	C₁₃×#451	C₂²	1	8	yes	—
58	C₁₃×#450	C₂²	1	8	yes	—
59	C₁₃×#432	C₂²	1	2	yes	—
60	C₁₃×#432	C₂²	1	2	yes	complemented
61	C₁₃×#431	C₂²	1	2	yes	—
62	C₁₃×#431	C₂²	1	2	yes	complemented
63	C₁₃×#423	C₂²	1	2	yes	complemented
64	C₁₃×#417	C₂²	1	8	yes	complemented
65	C₁₃×#407	C₂²	1	2	yes	—
66	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	4	8	no	—
70	C₂×C₁₃×#41	C₂³	1	4	yes	—
71	C₂×C₁₃×#41	C₂³	1	4	yes	—
72	C₂²×Q₈×C₁₃	—	2	1	no	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	—	2	2	no	—
80	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#137	—	4	16	no	—
84	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
86	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	—	2	1	no	—
90	C₁₃×C₄⋊Q₈	—	2	1	no	—
91	C₁₃×C₄⋊Q₈	—	2	1	no	—
92	C₁₃×C₄⋊Q₈	—	2	1	no	—
93	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₁₃×#127	—	2	1	no	—
100	C₁₃×#127	—	2	1	no	—
101	C₁₃×#127	C₂³	1	2	yes	—
102	C₁₃×#127	C₂³	1	2	yes	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	—	2	2	no	—
105	C₁₃×#125	—	2	2	no	—
106	C₁₃×#125	—	2	2	no	—
107	C₁₃×#124	—	2	2	no	—
108	C₁₃×#124	—	2	2	no	—
109	C₁₃×#124	C₂³	1	4	yes	—
110	C₁₃×#124	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
118	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₁₃×#121	—	2	2	no	—
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	2	no	—
124	C₁₃×#121	—	2	2	no	—
125	C₁₃×#121	—	2	2	no	—
126	C₁₃×#121	—	2	2	no	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	2	no	—
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	—	2	2	no	—
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	2	no	—
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	2	no	—
145	C₁₃×#117	—	2	2	no	—
146	C₁₃×#117	—	2	2	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₂×C₄²×C₁₃	—	2	2	no	—
159	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	16	yes	—
174	C₁₃×#102	C₂³	1	16	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₁₃	C₂³	1	4	yes	—
179	#60804	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	2	no	—
181	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₁₃×#41	—	2	16	no	—
183	C₁₃×#41	—	4	8	no	—
184	C₁₃×#41	—	4	8	no	—
185	C₁₃×#41	—	4	8	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	8	no	—
191	C₂×Q₈×C₁₃	—	4	4	no	—
192	C₂×Q₈×C₁₃	—	4	4	no	—
193	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
194	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	2	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	4	no	—
204	C₂×D₄×C₁₃	—	4	8	no	—
205	C₂×D₄×C₁₃	—	4	4	no	—
206	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	4	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	4	2	no	—
215	C₂²×C₄×C₁₃	—	4	8	no	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₁₃×Q₁₆	—	4	16	no	—
235	C₁₃×SD₁₆	—	4	16	no	—
236	C₁₃×M₁₆	—	2	8	no	—
237	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
280	#3216	C₂×C₁₃	1	4	yes	complemented
281	#3215	C₂×C₁₃	1	4	yes	complemented
282	#3210	C₂×C₁₃	1	4	yes	complemented
283	#3209	C₂×C₁₃	1	2	yes	complemented
284	#3208	C₂×C₁₃	1	2	yes	complemented
285	#3152	C₂×C₁₃	1	2	yes	complemented
286	#3141	C₂×C₁₃	1	2	yes	complemented
287	#3037	C₂×C₁₃	1	4	yes	complemented
288	#3007	C₂×C₁₃	1	4	yes	complemented
289	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	4	no	—
293	C₂³×C₁₃	—	4	1	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	4	4	no	—
296	C₂³×C₁₃	—	4	4	no	—
297	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₁₃	—	2	8	no	—
301	Q₈×C₁₃	—	2	8	no	—
302	Q₈×C₁₃	—	4	4	no	—
303	Q₈×C₁₃	—	4	4	no	—
304	Q₈×C₁₃	—	4	4	no	—
305	Q₈×C₁₃	—	4	4	no	—
306	D₄×C₁₃	—	2	8	no	—
307	D₄×C₁₃	—	4	4	no	—
308	D₄×C₁₃	—	4	4	no	—
309	D₄×C₁₃	—	4	8	no	—
310	D₄×C₁₃	—	4	8	no	—
311	D₄×C₁₃	—	4	4	no	—
312	D₄×C₁₃	—	4	4	no	—
313	D₄×C₁₃	—	4	4	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	2	4	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	8	no	—
334	C₂×C₄×C₁₃	—	4	4	no	—
335	C₂×C₄×C₁₃	—	4	4	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	8	no	—
338	C₂×C₄×C₁₃	#137	1	4	yes	complemented
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
351	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₈×C₁₃	—	2	8	no	—
353	C₂²×#41	C₂²×C₁₃	1	2	yes	—
354	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
355	#533	—	2	1	no	—
356	#533	—	2	1	no	—
357	#533	—	2	1	no	—
358	#533	—	2	1	no	—
359	#533	C₂²×C₁₃	1	2	yes	—
360	#533	C₂²×C₁₃	1	2	yes	—
361	#533	C₂²×C₁₃	1	2	yes	complemented
362	#533	C₂²×C₁₃	1	2	yes	complemented
363	#532	—	2	1	no	—
364	#532	—	2	1	no	—
365	#532	—	2	1	no	—
366	#532	—	2	1	no	—
367	#532	C₂²×C₁₃	1	2	yes	—
368	#532	C₂²×C₁₃	1	2	yes	—
369	#532	C₂²×C₁₃	1	2	yes	—
370	#532	C₂²×C₁₃	1	2	yes	—
371	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
374	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#125	—	2	1	no	—
376	C₂×#124	C₂²×C₁₃	1	2	yes	—
377	C₂×C₂²⋊Q₈	—	2	1	no	—
378	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
379	C₂×#121	—	2	1	no	—
380	C₂×#121	—	2	1	no	—
381	C₂×C₄×Q₈	—	2	1	no	—
382	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
383	C₂×C₄×D₄	—	2	1	no	—
384	C₂×C₄×D₄	—	2	1	no	—
385	C₂×#117	—	2	1	no	—
386	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
387	#497	C₂²×C₁₃	1	8	yes	complemented
388	#494	C₂²×C₁₃	1	4	yes	complemented
389	#492	C₂²×C₁₃	1	4	yes	complemented
390	#489	C₂²×C₁₃	1	8	yes	complemented
391	#487	C₂²×C₁₃	1	4	yes	complemented
392	#486	C₂²×C₁₃	1	4	yes	complemented
393	#464	C₂²×C₁₃	1	16	yes	complemented
394	#462	C₂²×C₁₃	1	8	yes	complemented
395	#460	C₂²×C₁₃	1	8	yes	complemented
396	#452	C₂²×C₁₃	1	16	yes	complemented
397	#451	C₂²×C₁₃	1	8	yes	—
398	#450	C₂²×C₁₃	1	8	yes	—
399	#432	C₂²×C₁₃	1	2	yes	—
400	#432	C₂²×C₁₃	1	2	yes	complemented
401	#431	C₂²×C₁₃	1	2	yes	—
402	#431	C₂²×C₁₃	1	2	yes	complemented
403	#423	C₂²×C₁₃	1	2	yes	complemented
404	#417	C₂²×C₁₃	1	8	yes	complemented
405	#407	C₂²×C₁₃	1	2	yes	—
406	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
407	C₂²×C₁₃	—	2	1	no	—
408	C₂²×C₁₃	—	2	1	no	—
409	C₂²×C₁₃	—	2	1	no	—
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	2	1	no	—
412	C₂²×C₁₃	—	2	1	no	—
413	C₂²×C₁₃	—	2	1	no	—
414	C₂²×C₁₃	—	4	4	no	—
415	C₂²×C₁₃	—	4	4	no	—
416	C₂²×C₁₃	—	4	4	no	—
417	C₂²×C₁₃	—	4	4	no	—
418	C₂²×C₁₃	—	8	8	no	—
419	C₂²×C₁₃	#535	1	2	yes	—
420	C₂²×C₁₃	C₂×#137	1	2	yes	—
421	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₁₃	—	2	1	no	—
423	C₄×C₁₃	—	2	1	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	2	1	no	—
427	C₄×C₁₃	—	2	1	no	—
428	C₄×C₁₃	—	2	1	no	—
429	C₄×C₁₃	—	4	4	no	—
430	C₄×C₁₃	—	4	4	no	—
431	C₄×C₁₃	—	4	4	no	—
432	C₄×C₁₃	#535	1	2	yes	—
433	C₄×C₁₃	C₂×#137	1	2	yes	—
434	C₄×C₁₃	C₂×#137	1	2	yes	—
435	C₄×C₁₃	#575	1	2	yes	—
436	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₂×#41	—	2	2	no	—
438	C₂×#41	—	2	2	no	—
439	C₂×#41	—	4	8	no	—
440	C₂×#41	C₂³×C₁₃	1	4	yes	—
441	C₂×#41	C₂³×C₁₃	1	4	yes	—
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
444	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	—	2	1	no	—
448	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
449	C₂³×C₄	—	2	2	no	—
450	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
451	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
453	#137	—	4	16	no	—
454	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
455	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
456	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
457	C₄⋊Q₈	—	2	1	no	—
458	C₄⋊Q₈	—	2	1	no	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
464	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
469	#127	—	2	1	no	—
470	#127	—	2	1	no	—
471	#127	C₂³×C₁₃	1	2	yes	—
472	#127	C₂³×C₁₃	1	2	yes	—
473	#125	—	2	2	no	—
474	#125	—	2	2	no	—
475	#125	—	2	2	no	—
476	#125	—	2	2	no	—
477	#124	—	2	2	no	—
478	#124	—	2	2	no	—
479	#124	C₂³×C₁₃	1	4	yes	—
480	#124	C₂³×C₁₃	1	4	yes	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
488	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
504	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	#117	—	2	2	no	—
514	#117	—	2	2	no	—
515	#117	—	2	2	no	—
516	#117	—	2	2	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	2	no	—
523	C₂×C₄⋊C₄	—	2	2	no	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₂²⋊C₄	—	2	2	no	—
526	C₂×C₂²⋊C₄	—	2	2	no	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₄²	—	2	2	no	—
529	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
530	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
542	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
543	#103	C₂³×C₁₃	1	16	yes	—
544	#102	C₂³×C₁₃	1	16	yes	—
545	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
546	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
547	#97	C₂³×C₁₃	1	4	yes	—
548	C₄×C₈	C₂³×C₁₃	1	4	yes	—
549	C₂×C₁₃	—	2	2	no	—
550	C₂×C₁₃	—	2	2	no	—
551	C₂×C₁₃	—	4	1	no	—
552	C₂×C₁₃	—	8	4	no	—
553	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
554	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
555	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
556	C₂⁴	—	2	2	no	—
557	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
558	#41	—	2	16	no	—
559	#41	—	4	8	no	—
560	#41	—	4	8	no	—
561	#41	—	4	8	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	8	no	—
567	C₂×Q₈	—	4	4	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
570	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	8	no	—
581	C₂×D₄	—	4	4	no	—
582	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	8	no	—
592	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
610	Q₁₆	—	4	16	no	—
611	SD₁₆	—	4	16	no	—
612	M₁₆	—	2	8	no	—
613	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₁₃	#60804	1	1	yes	characteristic, direct product factor, Sylow
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	4	no	—
662	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
663	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
664	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
665	Q₈	—	2	8	no	—
666	Q₈	—	2	8	no	—
667	Q₈	—	4	4	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	4	4	no	—
670	Q₈	—	4	4	no	—
671	D₄	—	2	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	C₁₃×#137	1	4	yes	complemented
704	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
715	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
716	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
717	C₈	—	2	8	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	8	8	no	—
730	C₂²	C₁₃×#535	1	2	yes	—
731	C₂²	C₂×C₁₃×#137	1	2	yes	—
732	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	C₁₃×#535	1	2	yes	—
744	C₄	C₂×C₁₃×#137	1	2	yes	—
745	C₄	C₂×C₁₃×#137	1	2	yes	—
746	C₄	C₁₃×#575	1	2	yes	—
747	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
748	C₂	—	2	2	no	—
749	C₂	—	2	2	no	—
750	C₂	—	4	1	no	—
751	C₂	—	8	4	no	—
752	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
753	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
754	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3216	C₂	semidirect
4. C₁₃×#3215	C₂	semidirect
5. C₁₃×#3210	C₂	semidirect
6. C₁₃×#3209	C₂	semidirect
7. C₁₃×#3208	C₂	semidirect
8. C₁₃×#3152	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3037	C₂	semidirect
11. C₁₃×#3007	C₂	semidirect
12. C₁₃×#2920	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
21. C₁₃×#533	C₂²	semidirect
22. C₁₃×#533	C₂²	semidirect
32. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
48. C₁₃×#494	C₂²	semidirect
49. C₁₃×#492	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#464	C₂²	semidirect
54. C₁₃×#462	C₂²	semidirect
55. C₁₃×#460	C₂²	semidirect
56. C₁₃×#452	C₂²	semidirect
60. C₁₃×#432	C₂²	semidirect
62. C₁₃×#431	C₂²	semidirect
63. C₁₃×#423	C₂²	semidirect
64. C₁₃×#417	C₂²	semidirect
66. C₄×C₁₃×M₁₆	C₂²	semidirect
179. #60804	C₁₃	direct (N × H)
278. C₂×#533	C₂×C₁₃	semidirect
280. #3216	C₂×C₁₃	semidirect
281. #3215	C₂×C₁₃	semidirect
282. #3210	C₂×C₁₃	semidirect
283. #3209	C₂×C₁₃	semidirect
284. #3208	C₂×C₁₃	semidirect
285. #3152	C₂×C₁₃	semidirect
286. #3141	C₂×C₁₃	semidirect
287. #3037	C₂×C₁₃	semidirect
288. #3007	C₂×C₁₃	semidirect
289. #2920	C₂×C₁₃	semidirect
338. C₂×C₄×C₁₃	#137	semidirect
354. C₂×#137	C₂²×C₁₃	semidirect
361. #533	C₂²×C₁₃	semidirect
362. #533	C₂²×C₁₃	semidirect
372. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
373. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
382. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
387. #497	C₂²×C₁₃	semidirect
388. #494	C₂²×C₁₃	semidirect
389. #492	C₂²×C₁₃	semidirect
390. #489	C₂²×C₁₃	semidirect
391. #487	C₂²×C₁₃	semidirect
392. #486	C₂²×C₁₃	semidirect
393. #464	C₂²×C₁₃	semidirect
394. #462	C₂²×C₁₃	semidirect
395. #460	C₂²×C₁₃	semidirect
396. #452	C₂²×C₁₃	semidirect
400. #432	C₂²×C₁₃	semidirect
402. #431	C₂²×C₁₃	semidirect
403. #423	C₂²×C₁₃	semidirect
404. #417	C₂²×C₁₃	semidirect
406. C₄×M₁₆	C₂²×C₁₃	semidirect
654. C₁₃	#60804	direct (N × H)
703. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₁₃×#3216	2
C₁₃×#3215	2
C₁₃×#3210	2
C₁₃×#3209	2
C₁₃×#3208	2
C₁₃×#3152	2
C₁₃×#3141	2
C₁₃×#3037	2
C₁₃×#3007	2
C₁₃×#2920	2
#60804	13

Subgroups — C13×#60804 #15747143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60804 #15747143