Subgroups — C₁₃×#17592 #15703931

Order 3328.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 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×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1520	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1519	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1513	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1504	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#41	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	—	2	1	no	—
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	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
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	C₄	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
30	C₁₃×#407	—	2	1	no	—
31	C₁₃×#407	—	2	1	no	—
32	C₁₃×#407	C₂²	1	2	yes	complemented
33	C₁₃×#407	C₂²	1	2	yes	complemented
34	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₁₃×#380	—	2	1	no	—
37	C₁₃×#380	—	2	1	no	—
38	C₁₃×#380	C₂²	1	2	yes	—
39	C₁₃×#380	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
41	C₁₃×#328	C₂²	1	8	yes	complemented
42	C₁₃×#327	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	—
48	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
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	1	no	—
55	C₂³×C₄×C₁₃	—	2	2	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	—	2	2	no	—
73	C₂×C₁₃×M₁₆	—	4	4	no	—
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	complemented
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
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	complemented
93	C₁₃×#121	C₂×C₄	1	2	yes	complemented
94	C₁₃×#121	C₂³	1	2	yes	—
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	—
110	C₁₃×#117	C₂×C₄	1	2	yes	complemented
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	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×C₁₃×C₂²⋊C₄	—	2	2	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₁₃×C₂²⋊C₈	—	2	2	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
131	C₁₃×#95	—	2	2	no	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	#17592	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₂⁴×C₁₃	—	2	2	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	—	4	4	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	2	no	—
164	C₂×D₄×C₁₃	—	4	2	no	—
165	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	4	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	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	4	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	—	4	4	no	—
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	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₁₃×M₁₆	—	4	4	no	—
219	C₁₃×M₁₆	—	4	4	no	—
220	C₂×C₈×C₁₃	—	2	4	no	—
221	C₂×C₈×C₁₃	—	4	4	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	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	4	4	no	—
229	C₁₃×C₄⋊C₄	—	4	4	no	—
230	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
231	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	C₁₃×C₂²⋊C₄	—	2	2	no	—
242	C₁₃×C₂²⋊C₄	—	4	4	no	—
243	C₁₃×C₂²⋊C₄	—	4	4	no	—
244	C₄²×C₁₃	—	2	2	no	—
245	C₄²×C₁₃	—	2	2	no	—
246	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
247	C₂×#407	C₂×C₁₃	1	1	yes	characteristic, complemented
248	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1520	C₂×C₁₃	1	2	yes	complemented
250	#1519	C₂×C₁₃	1	2	yes	complemented
251	#1513	C₂×C₁₃	1	4	yes	complemented
252	#1504	C₂×C₁₃	1	4	yes	complemented
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	1	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	—	2	2	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	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	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	8	no	—
277	C₂³×C₁₃	—	4	8	no	—
278	C₂³×C₁₃	—	4	2	no	—
279	C₂³×C₁₃	—	4	2	no	—
280	C₂³×C₁₃	—	4	2	no	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
288	C₂³×C₁₃	#137	1	2	yes	—
289	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₁₃	—	4	2	no	—
291	Q₈×C₁₃	—	4	2	no	—
292	D₄×C₁₃	—	4	2	no	—
293	D₄×C₁₃	—	4	4	no	—
294	D₄×C₁₃	—	4	4	no	—
295	D₄×C₁₃	—	4	2	no	—
296	D₄×C₁₃	—	4	2	no	—
297	D₄×C₁₃	—	4	4	no	—
298	D₄×C₁₃	—	4	4	no	—
299	D₄×C₁₃	—	4	4	no	—
300	D₄×C₁₃	—	4	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	2	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	—	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	—	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	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	4	2	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	2	no	—
335	C₂×C₄×C₁₃	—	4	4	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	8	8	no	—
340	C₂×C₄×C₁₃	#99	1	4	yes	—
341	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₈×C₁₃	—	4	4	no	—
350	C₂²×#41	C₄×C₁₃	1	1	yes	characteristic, complemented
351	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
352	C₂²×M₁₆	—	2	1	no	—
353	#525	—	2	1	no	—
354	#525	—	2	1	no	—
355	#525	—	2	1	no	—
356	#525	—	2	1	no	—
357	#525	C₄×C₁₃	1	2	yes	complemented
358	#525	C₄×C₁₃	1	2	yes	complemented
359	#525	C₂²×C₁₃	1	2	yes	—
360	#525	C₂²×C₁₃	1	2	yes	—
361	C₂×#123	—	2	1	no	—
362	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
363	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#121	C₄×C₁₃	1	1	yes	characteristic, complemented
365	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#120	—	2	1	no	—
367	C₂×C₄×D₄	—	2	1	no	—
368	C₂×C₄×D₄	—	2	1	no	—
369	C₂×#117	C₄×C₁₃	1	1	yes	characteristic, complemented
370	C₂²×C₄⋊C₄	—	2	1	no	—
371	C₂²×C₂²⋊C₄	—	2	1	no	—
372	#407	—	2	1	no	—
373	#407	—	2	1	no	—
374	#407	C₂²×C₁₃	1	2	yes	complemented
375	#407	C₂²×C₁₃	1	2	yes	complemented
376	C₂×C₂²⋊C₈	—	2	1	no	—
377	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
378	#380	—	2	1	no	—
379	#380	—	2	1	no	—
380	#380	C₂²×C₁₃	1	2	yes	—
381	#380	C₂²×C₁₃	1	2	yes	complemented
382	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
383	#328	C₂²×C₁₃	1	8	yes	complemented
384	#327	C₂²×C₁₃	1	8	yes	complemented
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	2	4	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	—	2	1	no	—
397	C₂²×C₁₃	—	2	1	no	—
398	C₂²×C₁₃	—	2	1	no	—
399	C₂²×C₁₃	—	2	1	no	—
400	C₂²×C₁₃	—	2	1	no	—
401	C₂²×C₁₃	—	2	1	no	—
402	C₂²×C₁₃	—	2	1	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	—	4	2	no	—
405	C₂²×C₁₃	—	4	4	no	—
406	C₂²×C₁₃	—	4	4	no	—
407	C₂²×C₁₃	—	4	4	no	—
408	C₂²×C₁₃	—	4	4	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	8	4	no	—
415	C₂²×C₁₃	C₂×#99	1	2	yes	—
416	C₂²×C₁₃	#417	1	2	yes	—
417	C₂²×C₁₃	#417	1	2	yes	—
418	C₂²×C₁₃	#421	1	2	yes	—
419	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂²×C₁₃	C₂×#137	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	—	4	2	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	—	4	2	no	—
431	C₄×C₁₃	—	8	4	no	—
432	C₄×C₁₃	C₂×#99	1	2	yes	—
433	C₄×C₁₃	C₂×#99	1	2	yes	—
434	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
435	C₂×#41	—	2	1	no	—
436	C₂×#41	—	2	1	no	—
437	C₂×#41	—	4	4	no	—
438	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
439	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
440	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	2	no	—
447	C₂³×C₄	—	4	4	no	—
448	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
449	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
450	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
451	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
452	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
453	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
454	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
455	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
456	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
457	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
458	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×M₁₆	—	2	2	no	—
463	C₂×M₁₆	—	2	2	no	—
464	C₂×M₁₆	—	4	4	no	—
465	C₂²×C₈	—	2	2	no	—
466	#123	—	2	2	no	—
467	#123	—	2	2	no	—
468	#123	—	2	2	no	—
469	#123	—	2	2	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
475	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
476	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
477	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	C₂×C₄×C₁₃	1	2	yes	—
483	#121	C₂×C₄×C₁₃	1	2	yes	complemented
484	#121	C₂×C₄×C₁₃	1	2	yes	complemented
485	#121	C₂³×C₁₃	1	2	yes	—
486	#120	—	2	2	no	—
487	#120	—	2	2	no	—
488	#120	—	2	2	no	—
489	#120	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	#117	—	2	1	no	—
499	#117	—	2	1	no	—
500	#117	C₂×C₄×C₁₃	1	2	yes	—
501	#117	C₂×C₄×C₁₃	1	2	yes	complemented
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	4	4	no	—
507	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
508	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	2	no	—
515	C₂×C₂²⋊C₄	—	2	2	no	—
516	C₂×C₂²⋊C₄	—	4	4	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂²⋊C₈	—	2	2	no	—
519	C₂²⋊C₈	—	2	2	no	—
520	C₂²⋊C₈	—	2	2	no	—
521	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
522	#95	—	2	2	no	—
523	#95	C₂³×C₁₃	1	4	yes	—
524	C₂×C₁₃	—	2	1	no	—
525	C₂×C₁₃	—	2	1	no	—
526	C₂×C₁₃	—	2	2	no	—
527	C₂×C₁₃	—	2	2	no	—
528	C₂×C₁₃	—	2	2	no	—
529	C₂×C₁₃	—	2	2	no	—
530	C₂×C₁₃	—	4	1	no	—
531	C₂×C₁₃	—	4	1	no	—
532	C₂×C₁₃	—	8	2	no	—
533	C₂×C₁₃	C₂²×#99	1	1	yes	characteristic
534	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
535	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	2	1	no	—
539	C₂⁴	—	4	2	no	—
540	C₂⁴	—	4	2	no	—
541	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
542	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
543	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
544	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
545	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
548	#41	—	4	4	no	—
549	#41	—	4	4	no	—
550	#41	—	4	4	no	—
551	#41	—	4	4	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	4	2	no	—
554	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
593	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
594	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
595	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
596	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
597	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
598	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
599	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
600	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
601	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
602	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
603	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
604	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
620	M₁₆	—	4	4	no	—
621	M₁₆	—	4	4	no	—
622	C₂×C₈	—	2	4	no	—
623	C₂×C₈	—	4	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	4	4	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
633	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₁₃	#17592	1	1	yes	characteristic, direct product factor, Sylow
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	4	8	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	4	2	no	—
676	C₂³	—	4	2	no	—
677	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
678	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
679	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
680	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
681	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
682	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
683	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
684	C₂³	C₁₃×#137	1	2	yes	—
685	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
686	Q₈	—	4	2	no	—
687	Q₈	—	4	2	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	4	no	—
690	D₄	—	4	4	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	8	8	no	—
736	C₂×C₄	C₁₃×#99	1	4	yes	—
737	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
738	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
739	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
740	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
741	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
742	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
743	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₈	—	4	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₂×C₁₃×#99	1	2	yes	—
777	C₂²	C₁₃×#417	1	2	yes	—
778	C₂²	C₁₃×#417	1	2	yes	—
779	C₂²	C₁₃×#421	1	2	yes	—
780	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
781	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
782	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	8	4	no	—
793	C₄	C₂×C₁₃×#99	1	2	yes	—
794	C₄	C₂×C₁₃×#99	1	2	yes	—
795	C₂	—	2	1	no	—
796	C₂	—	2	2	no	—
797	C₂	—	2	2	no	—
798	C₂	—	2	1	no	—
799	C₂	—	2	2	no	—
800	C₂	—	2	2	no	—
801	C₂	—	4	1	no	—
802	C₂	—	4	1	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂²×C₁₃×#99	1	1	yes	characteristic
805	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
806	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×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×C₁₃×#380	C₂	semidirect
4. C₁₃×#1520	C₂	semidirect
5. C₁₃×#1519	C₂	semidirect
6. C₁₃×#1513	C₂	semidirect
7. C₁₃×#1504	C₂	semidirect
8. C₂²×C₁₃×#41	C₄	semidirect
15. C₁₃×#525	C₄	semidirect
16. C₁₃×#525	C₄	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
22. C₂×C₁₃×#121	C₄	semidirect
27. C₂×C₁₃×#117	C₄	semidirect
32. C₁₃×#407	C₂²	semidirect
33. C₁₃×#407	C₂²	semidirect
39. C₁₃×#380	C₂²	semidirect
40. C₂×C₁₃×#95	C₂²	semidirect
41. C₁₃×#328	C₂²	semidirect
42. C₁₃×#327	C₂²	semidirect
48. C₂×C₁₃×#41	C₂×C₄	semidirect
49. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
53. C₂²×D₄×C₁₃	C₂×C₄	semidirect
84. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
85. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
92. C₁₃×#121	C₂×C₄	semidirect
93. C₁₃×#121	C₂×C₄	semidirect
110. C₁₃×#117	C₂×C₄	semidirect
116. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
117. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
133. #17592	C₁₃	direct (N × H)
247. C₂×#407	C₂×C₁₃	semidirect
248. C₂×#380	C₂×C₁₃	semidirect
249. #1520	C₂×C₁₃	semidirect
250. #1519	C₂×C₁₃	semidirect
251. #1513	C₂×C₁₃	semidirect
252. #1504	C₂×C₁₃	semidirect
350. C₂²×#41	C₄×C₁₃	semidirect
357. #525	C₄×C₁₃	semidirect
358. #525	C₄×C₁₃	semidirect
362. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
364. C₂×#121	C₄×C₁₃	semidirect
369. C₂×#117	C₄×C₁₃	semidirect
374. #407	C₂²×C₁₃	semidirect
375. #407	C₂²×C₁₃	semidirect
381. #380	C₂²×C₁₃	semidirect
382. C₂×#95	C₂²×C₁₃	semidirect
383. #328	C₂²×C₁₃	semidirect
384. #327	C₂²×C₁₃	semidirect
439. C₂×#41	C₂×C₄×C₁₃	semidirect
440. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
444. C₂²×D₄	C₂×C₄×C₁₃	semidirect
475. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
476. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
483. #121	C₂×C₄×C₁₃	semidirect
484. #121	C₂×C₄×C₁₃	semidirect
501. #117	C₂×C₄×C₁₃	semidirect
507. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
508. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
648. C₁₃	#17592	direct (N × H)

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×C₁₃×#380	2
C₁₃×#1520	2
C₁₃×#1519	2
C₁₃×#1513	2
C₁₃×#1504	2
#17592	13

Subgroups — C13×#17592 #15703931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17592 #15703931