Subgroups — C₁₃×#21773 #15708112

Order 3328.

1622 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1896	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1871	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1826	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1789	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
11	C₁₃×#525	—	2	1	no	—
12	C₁₃×#525	—	2	1	no	—
13	C₁₃×#525	—	2	1	no	—
14	C₁₃×#525	—	2	1	no	—
15	C₁₃×#525	C₄	1	2	yes	complemented
16	C₁₃×#525	C₄	1	2	yes	complemented
17	C₁₃×#525	C₂²	1	2	yes	—
18	C₁₃×#525	C₂²	1	2	yes	—
19	C₂×C₁₃×#123	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#121	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#121	C₄	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#120	—	2	1	no	—
25	C₂×C₄×D₄×C₁₃	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	—	2	1	no	—
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
29	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#104	C₂²	1	8	yes	complemented
31	C₁₃×#407	—	2	1	no	—
32	C₁₃×#407	—	2	1	no	—
33	C₁₃×#407	C₂²	1	2	yes	—
34	C₁₃×#407	C₂²	1	2	yes	complemented
35	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
36	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
37	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#95	—	2	1	no	—
42	C₁₃×#339	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
48	C₂×C₁₃×#41	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₃	—	4	4	no	—
57	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	4	4	no	—
73	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
74	C₂²×C₈×C₁₃	—	2	2	no	—
75	C₁₃×#123	—	2	2	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×#123	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
84	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	C₂×C₄	1	2	yes	—
92	C₁₃×#121	C₂×C₄	1	2	yes	—
93	C₁₃×#121	C₂×C₄	1	2	yes	complemented
94	C₁₃×#121	C₂×C₄	1	2	yes	complemented
95	C₁₃×#120	—	2	2	no	—
96	C₁₃×#120	—	2	2	no	—
97	C₁₃×#120	—	2	2	no	—
98	C₁₃×#120	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₁₃×#117	—	2	1	no	—
108	C₁₃×#117	—	2	1	no	—
109	C₁₃×#117	C₂×C₄	1	2	yes	complemented
110	C₁₃×#117	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
114	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
115	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	—	2	2	no	—
125	C₂×C₄²×C₁₃	—	4	4	no	—
126	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
127	C₁₃×#104	—	4	8	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	—	2	2	no	—
131	C₁₃×C₂²⋊C₈	—	2	2	no	—
132	C₁₃×#95	—	2	2	no	—
133	C₁₃×#95	—	2	2	no	—
134	#21773	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	—	2	4	no	—
136	C₂⁴×C₁₃	—	2	1	no	—
137	C₂⁴×C₁₃	—	4	2	no	—
138	C₂⁴×C₁₃	—	4	2	no	—
139	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
140	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
142	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×#41	—	2	8	no	—
147	C₁₃×#41	—	4	4	no	—
148	C₁₃×#41	—	4	4	no	—
149	C₁₃×#41	—	4	4	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	4	2	no	—
152	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	2	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	4	2	no	—
161	C₂×D₄×C₁₃	—	4	4	no	—
162	C₂×D₄×C₁₃	—	4	4	no	—
163	C₂×D₄×C₁₃	—	4	4	no	—
164	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	—	4	2	no	—
182	C₂²×C₄×C₁₃	—	4	2	no	—
183	C₂²×C₄×C₁₃	—	4	2	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	2	no	—
186	C₂²×C₄×C₁₃	—	4	4	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×M₁₆	—	2	8	no	—
218	C₁₃×M₁₆	—	4	4	no	—
219	C₂×C₈×C₁₃	—	2	4	no	—
220	C₂×C₈×C₁₃	—	4	4	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
228	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	—	2	8	no	—
231	C₁₃×C₂²⋊C₄	—	2	2	no	—
232	C₁₃×C₂²⋊C₄	—	2	2	no	—
233	C₁₃×C₂²⋊C₄	—	2	2	no	—
234	C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₁₃×C₂²⋊C₄	—	2	2	no	—
236	C₁₃×C₂²⋊C₄	—	2	2	no	—
237	C₁₃×C₂²⋊C₄	—	2	2	no	—
238	C₁₃×C₂²⋊C₄	—	2	2	no	—
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	—	2	2	no	—
241	C₄²×C₁₃	—	2	2	no	—
242	C₄²×C₁₃	—	2	2	no	—
243	C₄²×C₁₃	—	2	8	no	—
244	C₄²×C₁₃	—	4	4	no	—
245	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
246	C₂×#407	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1896	C₂×C₁₃	1	4	yes	complemented
249	#1871	C₂×C₁₃	1	4	yes	complemented
250	#1826	C₂×C₁₃	1	2	yes	complemented
251	#1789	C₂×C₁₃	1	2	yes	complemented
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	16	no	—
274	C₂³×C₁₃	—	4	2	no	—
275	C₂³×C₁₃	—	4	2	no	—
276	C₂³×C₁₃	—	4	2	no	—
277	C₂³×C₁₃	#104	1	4	yes	complemented
278	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₁₃	—	2	4	no	—
286	Q₈×C₁₃	—	4	2	no	—
287	D₄×C₁₃	—	2	4	no	—
288	D₄×C₁₃	—	4	2	no	—
289	D₄×C₁₃	—	4	4	no	—
290	D₄×C₁₃	—	4	4	no	—
291	D₄×C₁₃	—	4	4	no	—
292	D₄×C₁₃	—	4	4	no	—
293	D₄×C₁₃	—	4	4	no	—
294	D₄×C₁₃	—	4	4	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	8	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	4	no	—
327	C₂×C₄×C₁₃	—	4	16	no	—
328	C₂×C₄×C₁₃	—	4	4	no	—
329	C₂×C₄×C₁₃	—	4	2	no	—
330	C₂×C₄×C₁₃	—	4	2	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	4	2	no	—
333	C₂×C₄×C₁₃	—	4	4	no	—
334	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
343	C₈×C₁₃	—	4	4	no	—
344	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
345	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
347	#525	—	2	1	no	—
348	#525	—	2	1	no	—
349	#525	—	2	1	no	—
350	#525	—	2	1	no	—
351	#525	C₄×C₁₃	1	2	yes	complemented
352	#525	C₄×C₁₃	1	2	yes	complemented
353	#525	C₂²×C₁₃	1	2	yes	—
354	#525	C₂²×C₁₃	1	2	yes	—
355	C₂×#123	—	2	1	no	—
356	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
357	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#121	C₄×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#121	C₄×C₁₃	1	1	yes	characteristic, complemented
360	C₂×#120	—	2	1	no	—
361	C₂×C₄×D₄	—	2	1	no	—
362	C₂×C₄×D₄	—	2	1	no	—
363	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	—	2	1	no	—
365	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
366	C₂×#104	C₂²×C₁₃	1	8	yes	complemented
367	#407	—	2	1	no	—
368	#407	—	2	1	no	—
369	#407	C₂²×C₁₃	1	2	yes	—
370	#407	C₂²×C₁₃	1	2	yes	complemented
371	C₂×C₂²⋊C₈	—	2	1	no	—
372	C₂×C₂²⋊C₈	—	2	1	no	—
373	C₄×C₂²⋊C₄	—	2	1	no	—
374	C₄×C₂²⋊C₄	—	2	1	no	—
375	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
377	C₂×#95	—	2	1	no	—
378	#339	C₂²×C₁₃	1	8	yes	complemented
379	C₂²×C₁₃	—	2	8	no	—
380	C₂²×C₁₃	—	2	1	no	—
381	C₂²×C₁₃	—	2	1	no	—
382	C₂²×C₁₃	—	2	1	no	—
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	2	1	no	—
385	C₂²×C₁₃	—	2	1	no	—
386	C₂²×C₁₃	—	2	1	no	—
387	C₂²×C₁₃	—	2	1	no	—
388	C₂²×C₁₃	—	2	1	no	—
389	C₂²×C₁₃	—	2	1	no	—
390	C₂²×C₁₃	—	2	1	no	—
391	C₂²×C₁₃	—	2	1	no	—
392	C₂²×C₁₃	—	2	1	no	—
393	C₂²×C₁₃	—	2	1	no	—
394	C₂²×C₁₃	—	2	1	no	—
395	C₂²×C₁₃	—	2	1	no	—
396	C₂²×C₁₃	—	4	4	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	4	no	—
399	C₂²×C₁₃	—	4	4	no	—
400	C₂²×C₁₃	—	4	4	no	—
401	C₂²×C₁₃	—	4	4	no	—
402	C₂²×C₁₃	—	4	2	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	—	4	2	no	—
405	C₂²×C₁₃	—	8	4	no	—
406	C₂²×C₁₃	C₂×#104	1	2	yes	—
407	C₂²×C₁₃	C₂×#104	1	2	yes	—
408	C₂²×C₁₃	C₂×#104	1	2	yes	—
409	C₂²×C₁₃	#421	1	2	yes	—
410	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
411	C₂²×C₁₃	#534	1	2	yes	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	2	1	no	—
414	C₄×C₁₃	—	2	1	no	—
415	C₄×C₁₃	—	2	1	no	—
416	C₄×C₁₃	—	2	1	no	—
417	C₄×C₁₃	—	2	1	no	—
418	C₄×C₁₃	—	4	8	no	—
419	C₄×C₁₃	—	4	2	no	—
420	C₄×C₁₃	—	4	2	no	—
421	C₄×C₁₃	—	4	2	no	—
422	C₄×C₁₃	#518	1	2	yes	—
423	C₄×C₁₃	#534	1	2	yes	—
424	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
425	C₂×#41	—	2	1	no	—
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	4	4	no	—
428	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
429	C₂×#41	C₂³×C₁₃	1	2	yes	—
430	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
435	C₂³×C₄	—	2	2	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	—	4	4	no	—
438	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
439	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
440	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
441	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
442	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
445	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
446	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
448	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×M₁₆	—	2	2	no	—
453	C₂×M₁₆	—	4	4	no	—
454	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
455	C₂²×C₈	—	2	2	no	—
456	#123	—	2	2	no	—
457	#123	—	2	2	no	—
458	#123	—	2	2	no	—
459	#123	—	2	2	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	—	2	1	no	—
463	C₂²⋊Q₈	—	2	1	no	—
464	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
465	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
466	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
467	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
468	#121	—	2	1	no	—
469	#121	—	2	1	no	—
470	#121	—	2	1	no	—
471	#121	—	2	1	no	—
472	#121	C₂×C₄×C₁₃	1	2	yes	—
473	#121	C₂×C₄×C₁₃	1	2	yes	—
474	#121	C₂×C₄×C₁₃	1	2	yes	complemented
475	#121	C₂×C₄×C₁₃	1	2	yes	complemented
476	#120	—	2	2	no	—
477	#120	—	2	2	no	—
478	#120	—	2	2	no	—
479	#120	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	#117	—	2	1	no	—
489	#117	—	2	1	no	—
490	#117	C₂×C₄×C₁₃	1	2	yes	complemented
491	#117	C₂³×C₁₃	1	2	yes	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
495	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
496	C₂×C₂²⋊C₄	—	2	8	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	2	no	—
500	C₂×C₂²⋊C₄	—	2	2	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	2	no	—
506	C₂×C₄²	—	4	4	no	—
507	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
508	#104	—	4	8	no	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	—	2	2	no	—
511	C₂²⋊C₈	—	2	2	no	—
512	C₂²⋊C₈	—	2	2	no	—
513	#95	—	2	2	no	—
514	#95	—	2	2	no	—
515	C₂×C₁₃	—	2	2	no	—
516	C₂×C₁₃	—	2	2	no	—
517	C₂×C₁₃	—	2	2	no	—
518	C₂×C₁₃	—	2	2	no	—
519	C₂×C₁₃	—	2	2	no	—
520	C₂×C₁₃	—	4	1	no	—
521	C₂×C₁₃	—	4	1	no	—
522	C₂×C₁₃	—	8	2	no	—
523	C₂×C₁₃	#2308	1	1	yes	characteristic
524	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
525	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	1	no	—
528	C₂⁴	—	4	2	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
531	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
532	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
533	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
534	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
537	#41	—	2	8	no	—
538	#41	—	4	4	no	—
539	#41	—	4	4	no	—
540	#41	—	4	4	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	4	2	no	—
543	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	8	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	4	4	no	—
579	C₂²×C₄	—	4	4	no	—
580	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
581	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
582	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
583	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
584	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
585	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
586	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
587	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
588	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
589	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
590	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
591	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
592	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
593	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×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	M₁₆	—	2	8	no	—
609	M₁₆	—	4	4	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	4	4	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
619	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	8	no	—
635	C₄²	—	4	4	no	—
636	C₁₃	#21773	1	1	yes	characteristic, direct product factor, Sylow
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	16	no	—
659	C₂³	—	4	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	C₁₃×#104	1	4	yes	complemented
663	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
664	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
665	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
666	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
667	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
668	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
669	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	Q₈	—	2	4	no	—
671	Q₈	—	4	2	no	—
672	D₄	—	2	4	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	4	no	—
679	D₄	—	4	4	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	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	16	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
720	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
721	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
722	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
723	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
724	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
725	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
727	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
728	C₈	—	4	4	no	—
729	C₂²	—	2	8	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	4	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	8	4	no	—
756	C₂²	C₂×C₁₃×#104	1	2	yes	—
757	C₂²	C₂×C₁₃×#104	1	2	yes	—
758	C₂²	C₂×C₁₃×#104	1	2	yes	—
759	C₂²	C₁₃×#421	1	2	yes	—
760	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
761	C₂²	C₁₃×#534	1	2	yes	—
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	4	8	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	C₁₃×#518	1	2	yes	—
773	C₄	C₁₃×#534	1	2	yes	—
774	C₂	—	2	2	no	—
775	C₂	—	2	2	no	—
776	C₂	—	2	2	no	—
777	C₂	—	2	2	no	—
778	C₂	—	2	2	no	—
779	C₂	—	4	1	no	—
780	C₂	—	4	1	no	—
781	C₂	—	8	2	no	—
782	C₂	C₁₃×#2308	1	1	yes	characteristic
783	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
784	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#407	C₂	semidirect
3. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#1896	C₂	semidirect
5. C₁₃×#1871	C₂	semidirect
6. C₁₃×#1826	C₂	semidirect
7. C₁₃×#1789	C₂	semidirect
10. C₂²×C₁₃×M₁₆	C₂²	semidirect
15. C₁₃×#525	C₄	semidirect
16. C₁₃×#525	C₄	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
21. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
22. C₂×C₁₃×#121	C₄	semidirect
23. C₂×C₁₃×#121	C₄	semidirect
29. C₂²×C₄²×C₁₃	C₂²	semidirect
30. C₂×C₁₃×#104	C₂²	semidirect
34. C₁₃×#407	C₂²	semidirect
40. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₁₃×#339	C₂²	semidirect
47. C₂×C₁₃×#41	C₂×C₄	semidirect
49. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
53. C₂²×D₄×C₁₃	C₂×C₄	semidirect
85. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
86. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
93. C₁₃×#121	C₂×C₄	semidirect
94. C₁₃×#121	C₂×C₄	semidirect
109. C₁₃×#117	C₂×C₄	semidirect
113. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
114. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
134. #21773	C₁₃	direct (N × H)
246. C₂×#407	C₂×C₁₃	semidirect
247. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
248. #1896	C₂×C₁₃	semidirect
249. #1871	C₂×C₁₃	semidirect
250. #1826	C₂×C₁₃	semidirect
251. #1789	C₂×C₁₃	semidirect
277. C₂³×C₁₃	#104	semidirect
346. C₂²×M₁₆	C₂²×C₁₃	semidirect
351. #525	C₄×C₁₃	semidirect
352. #525	C₄×C₁₃	semidirect
356. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
357. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
358. C₂×#121	C₄×C₁₃	semidirect
359. C₂×#121	C₄×C₁₃	semidirect
365. C₂²×C₄²	C₂²×C₁₃	semidirect
366. C₂×#104	C₂²×C₁₃	semidirect
370. #407	C₂²×C₁₃	semidirect
376. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
378. #339	C₂²×C₁₃	semidirect
428. C₂×#41	C₂×C₄×C₁₃	semidirect
430. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
434. C₂²×D₄	C₂×C₄×C₁₃	semidirect
466. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
467. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
474. #121	C₂×C₄×C₁₃	semidirect
475. #121	C₂×C₄×C₁₃	semidirect
490. #117	C₂×C₄×C₁₃	semidirect
494. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
495. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
636. C₁₃	#21773	direct (N × H)
662. C₂³	C₁₃×#104	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#525	2
C₂×C₁₃×#407	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₁₃×#1896	2
C₁₃×#1871	2
C₁₃×#1826	2
C₁₃×#1789	2
#21773	13

Subgroups — C13×#21773 #15708112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21773 #15708112