Subgroups — C₁₃×#21000 #15707339

Order 3328.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1906	C₂	1	8	yes	maximal, complemented
7	C₂×C₁₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
11	C₁₃×#575	—	2	2	no	—
12	C₁₃×#575	—	2	2	no	—
13	C₁₃×#575	C₄	1	4	yes	complemented
14	C₁₃×#575	C₂²	1	4	yes	—
15	C₂×C₁₃×#137	—	2	1	no	—
16	C₂×C₁₃×#137	C₄	1	2	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
18	C₂×C₁₃×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
19	C₂×C₁₃×#135	—	2	2	no	—
20	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₁₃×#520	—	2	2	no	—
23	C₁₃×#520	—	2	2	no	—
24	C₁₃×#519	—	2	1	no	—
25	C₁₃×#518	—	2	1	no	—
26	C₁₃×#518	—	2	2	no	—
27	C₄×C₁₃×#41	—	2	2	no	—
28	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#117	—	2	2	no	—
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₁₃×#421	—	2	2	no	—
34	C₁₃×#421	—	2	2	no	—
35	C₁₃×#421	—	2	2	no	—
36	C₁₃×#421	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#104	—	2	2	no	—
38	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
39	C₁₃×#410	—	2	2	no	—
40	C₁₃×#410	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#99	—	2	2	no	—
42	C₁₃×#344	C₂²	1	4	yes	complemented
43	C₁₃×#339	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	—	2	1	no	—
52	C₂×C₁₃×#41	—	2	1	no	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂×C₁₃×#41	—	2	1	no	—
57	C₂×C₁₃×#41	—	2	1	no	—
58	C₂×C₁₃×#41	—	2	1	no	—
59	C₂×C₁₃×#41	—	2	1	no	—
60	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
63	C₂×C₁₃×#41	D₄	1	2	yes	—
64	C₂×C₁₃×#41	D₄	1	2	yes	—
65	C₂×C₁₃×#41	D₄	1	2	yes	—
66	C₂×C₁₃×#41	C₂³	1	2	yes	—
67	C₂×C₁₃×#41	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#137	—	2	4	no	—
78	C₁₃×#137	—	2	4	no	—
79	C₁₃×#137	—	2	4	no	—
80	C₁₃×#137	C₂×C₄	1	8	yes	complemented
81	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
82	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
83	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
84	C₁₃×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
85	C₁₃×#135	—	2	8	no	—
86	C₁₃×#135	—	2	8	no	—
87	C₂×C₁₃×Q₁₆	—	2	2	no	—
88	C₂×C₁₃×SD₁₆	—	2	2	no	—
89	C₂×C₁₃×SD₁₆	—	2	2	no	—
90	C₂×C₁₃×D₈	—	2	2	no	—
91	C₂×C₁₃×M₁₆	—	2	1	no	—
92	C₂×C₁₃×M₁₆	—	2	1	no	—
93	C₂×C₁₃×M₁₆	—	2	1	no	—
94	C₂×C₁₃×M₁₆	—	2	1	no	—
95	C₂×C₁₃×M₁₆	—	2	1	no	—
96	C₂×C₁₃×M₁₆	—	2	1	no	—
97	C₂×C₁₃×M₁₆	—	2	1	no	—
98	C₂×C₁₃×M₁₆	—	2	1	no	—
99	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	complemented
100	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	complemented
101	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₃	—	2	1	no	—
104	C₂²×C₈×C₁₃	—	2	1	no	—
105	C₄×Q₈×C₁₃	—	2	4	no	—
106	C₄×Q₈×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	8	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₁₃×#117	—	2	4	no	—
112	C₁₃×#117	—	2	4	no	—
113	C₁₃×#117	—	2	1	no	—
114	C₁₃×#117	—	2	1	no	—
115	C₁₃×#117	—	2	1	no	—
116	C₁₃×#117	—	2	1	no	—
117	C₁₃×#117	—	2	1	no	—
118	C₁₃×#117	—	2	4	no	—
119	C₁₃×#117	—	2	1	no	—
120	C₁₃×#117	—	2	1	no	—
121	C₁₃×#117	D₄	1	2	yes	—
122	C₁₃×#117	D₄	1	2	yes	—
123	C₁₃×#117	D₄	1	2	yes	—
124	C₁₃×#117	C₂³	1	2	yes	—
125	C₁₃×#117	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
134	C₂×C₄²×C₁₃	—	2	1	no	—
135	C₂×C₄²×C₁₃	—	2	4	no	—
136	C₂×C₄²×C₁₃	—	2	1	no	—
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₁₃×#104	—	2	8	no	—
139	C₁₃×#104	—	2	8	no	—
140	C₁₃×#99	—	2	8	no	—
141	#21000	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂⁴×C₁₃	—	2	1	no	—
144	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₁₃×#41	—	2	2	no	—
146	C₁₃×#41	—	2	2	no	—
147	C₁₃×#41	—	2	2	no	—
148	C₁₃×#41	—	2	2	no	—
149	C₁₃×#41	—	2	2	no	—
150	C₁₃×#41	—	2	2	no	—
151	C₁₃×#41	—	2	2	no	—
152	C₁₃×#41	—	2	2	no	—
153	C₁₃×#41	—	2	2	no	—
154	C₁₃×#41	—	2	2	no	—
155	C₁₃×#41	—	2	2	no	—
156	C₁₃×#41	—	2	2	no	—
157	C₁₃×#41	—	2	2	no	—
158	C₁₃×#41	—	2	2	no	—
159	C₁₃×#41	—	2	2	no	—
160	C₁₃×#41	—	2	2	no	—
161	C₁₃×#41	—	2	2	no	—
162	C₁₃×#41	—	2	2	no	—
163	C₁₃×#41	—	2	2	no	—
164	C₁₃×#41	—	2	2	no	—
165	C₁₃×#41	—	4	1	no	—
166	C₁₃×#41	—	4	1	no	—
167	C₁₃×#41	—	4	1	no	—
168	C₁₃×#41	—	4	1	no	—
169	C₁₃×#41	—	4	1	no	—
170	C₁₃×#41	—	4	1	no	—
171	C₁₃×#41	—	4	1	no	—
172	C₁₃×#41	—	4	1	no	—
173	C₁₃×#41	C₂²⋊C₄	1	4	yes	—
174	C₁₃×#41	C₂²⋊C₄	1	4	yes	—
175	C₁₃×#41	C₂²×C₄	1	4	yes	—
176	C₁₃×#41	C₂×D₄	1	4	yes	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
186	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
187	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
188	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₁₃	—	2	2	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	4	1	no	—
206	C₂×D₄×C₁₃	—	4	1	no	—
207	C₂×D₄×C₁₃	—	4	1	no	—
208	C₂×D₄×C₁₃	—	4	1	no	—
209	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
210	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
211	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
212	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	8	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	4	1	no	—
227	C₂²×C₄×C₁₃	—	4	1	no	—
228	C₂²×C₄×C₁₃	—	4	1	no	—
229	C₂²×C₄×C₁₃	—	4	1	no	—
230	C₂²×C₄×C₁₃	—	4	1	no	—
231	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×Q₁₆	—	2	8	no	—
246	C₁₃×SD₁₆	—	2	8	no	—
247	C₁₃×SD₁₆	—	2	8	no	—
248	C₁₃×D₈	—	2	8	no	—
249	C₁₃×M₁₆	—	2	2	no	—
250	C₁₃×M₁₆	—	2	2	no	—
251	C₁₃×M₁₆	—	2	2	no	—
252	C₁₃×M₁₆	—	2	2	no	—
253	C₁₃×M₁₆	—	2	2	no	—
254	C₁₃×M₁₆	—	4	1	no	—
255	C₁₃×M₁₆	—	4	1	no	—
256	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
257	C₂×C₈×C₁₃	—	2	2	no	—
258	C₂×C₈×C₁₃	—	2	2	no	—
259	C₂×C₈×C₁₃	—	2	2	no	—
260	C₂×C₈×C₁₃	—	2	2	no	—
261	C₂×C₈×C₁₃	—	4	1	no	—
262	C₂×C₈×C₁₃	—	4	1	no	—
263	C₁₃×C₄⋊C₄	—	2	8	no	—
264	C₁₃×C₄⋊C₄	—	2	2	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	4	1	no	—
270	C₁₃×C₂²⋊C₄	—	2	8	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	1	no	—
276	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
277	C₄²×C₁₃	—	2	8	no	—
278	C₄²×C₁₃	—	2	2	no	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	4	1	no	—
283	C₄²×C₁₃	C₂×D₄	1	4	yes	—
284	C₂×#575	C₂×C₁₃	1	1	yes	characteristic
285	#3428	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#421	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#421	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#410	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1906	C₂×C₁₃	1	8	yes	complemented
290	C₂×#344	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#1733	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	4	1	no	—
297	C₂³×C₁₃	—	4	1	no	—
298	C₂³×C₁₃	—	8	1	no	—
299	C₂³×C₁₃	—	8	2	no	—
300	C₂³×C₁₃	—	8	2	no	—
301	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
302	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
303	C₂³×C₁₃	#120	1	1	yes	characteristic
304	C₂³×C₁₃	#120	1	1	yes	characteristic
305	C₂³×C₁₃	#121	1	1	yes	characteristic
306	C₂³×C₁₃	#121	1	1	yes	characteristic
307	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	2	2	no	—
310	Q₈×C₁₃	—	2	2	no	—
311	Q₈×C₁₃	—	2	2	no	—
312	Q₈×C₁₃	—	2	2	no	—
313	Q₈×C₁₃	—	4	1	no	—
314	Q₈×C₁₃	—	4	1	no	—
315	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	4	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	2	4	no	—
320	D₄×C₁₃	—	2	2	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	4	2	no	—
326	D₄×C₁₃	—	4	2	no	—
327	D₄×C₁₃	—	4	2	no	—
328	D₄×C₁₃	—	4	2	no	—
329	D₄×C₁₃	—	4	1	no	—
330	D₄×C₁₃	—	4	1	no	—
331	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	2	no	—
345	C₂×C₄×C₁₃	—	4	2	no	—
346	C₂×C₄×C₁₃	—	4	2	no	—
347	C₂×C₄×C₁₃	—	4	2	no	—
348	C₂×C₄×C₁₃	—	4	2	no	—
349	C₂×C₄×C₁₃	—	8	2	no	—
350	C₂×C₄×C₁₃	—	8	2	no	—
351	C₂×C₄×C₁₃	—	8	8	no	—
352	C₂×C₄×C₁₃	—	8	2	no	—
353	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
364	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
365	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
366	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
367	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
368	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
369	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
370	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
371	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
372	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
373	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
374	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
381	C₈×C₁₃	—	2	4	no	—
382	C₈×C₁₃	—	4	2	no	—
383	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
385	#575	—	2	2	no	—
386	#575	—	2	2	no	—
387	#575	C₄×C₁₃	1	4	yes	complemented
388	#575	C₂²×C₁₃	1	4	yes	—
389	C₂×#137	—	2	1	no	—
390	C₂×#137	C₄×C₁₃	1	2	yes	complemented
391	C₂×AGL(1,ℤ/8)	—	2	1	no	—
392	C₂×AGL(1,ℤ/8)	C₄×C₁₃	1	2	yes	complemented
393	C₂×#135	—	2	2	no	—
394	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
396	#520	—	2	2	no	—
397	#520	—	2	2	no	—
398	#519	—	2	1	no	—
399	#518	—	2	1	no	—
400	#518	—	2	2	no	—
401	C₄×#41	—	2	2	no	—
402	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
403	C₂×#117	—	2	2	no	—
404	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
407	#421	—	2	2	no	—
408	#421	—	2	2	no	—
409	#421	—	2	2	no	—
410	#421	C₂²×C₁₃	1	4	yes	complemented
411	C₂×#104	—	2	2	no	—
412	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
413	#410	—	2	2	no	—
414	#410	C₂²×C₁₃	1	4	yes	complemented
415	C₂×#99	—	2	2	no	—
416	#344	C₂²×C₁₃	1	4	yes	complemented
417	#339	C₂²×C₁₃	1	4	yes	complemented
418	C₂²×C₁₃	—	2	4	no	—
419	C₂²×C₁₃	—	4	1	no	—
420	C₂²×C₁₃	—	4	1	no	—
421	C₂²×C₁₃	—	4	1	no	—
422	C₂²×C₁₃	—	4	1	no	—
423	C₂²×C₁₃	—	4	1	no	—
424	C₂²×C₁₃	—	4	1	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	4	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	8	2	no	—
429	C₂²×C₁₃	—	8	2	no	—
430	C₂²×C₁₃	—	8	2	no	—
431	C₂²×C₁₃	—	8	2	no	—
432	C₂²×C₁₃	—	8	2	no	—
433	C₂²×C₁₃	#386	1	1	yes	characteristic
434	C₂²×C₁₃	#386	1	1	yes	characteristic
435	C₂²×C₁₃	#386	1	1	yes	characteristic
436	C₂²×C₁₃	#386	1	1	yes	characteristic
437	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
438	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
439	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
440	C₄×C₁₃	—	2	4	no	—
441	C₄×C₁₃	—	4	4	no	—
442	C₄×C₁₃	—	4	4	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	8	2	no	—
445	C₄×C₁₃	#386	1	1	yes	characteristic
446	C₄×C₁₃	#386	1	1	yes	characteristic
447	C₄×C₁₃	#386	1	1	yes	characteristic
448	C₄×C₁₃	#386	1	1	yes	characteristic
449	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
450	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
451	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
452	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
470	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
471	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
472	C₂×#41	D₄×C₁₃	1	2	yes	—
473	C₂×#41	D₄×C₁₃	1	2	yes	—
474	C₂×#41	D₄×C₁₃	1	2	yes	—
475	C₂×#41	C₂³×C₁₃	1	2	yes	—
476	C₂×#41	C₂³×C₁₃	1	2	yes	—
477	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
478	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
482	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
486	#137	—	2	4	no	—
487	#137	—	2	4	no	—
488	#137	—	2	4	no	—
489	#137	C₂×C₄×C₁₃	1	8	yes	complemented
490	AGL(1,ℤ/8)	—	2	4	no	—
491	AGL(1,ℤ/8)	—	2	4	no	—
492	AGL(1,ℤ/8)	—	2	4	no	—
493	AGL(1,ℤ/8)	C₂×C₄×C₁₃	1	8	yes	complemented
494	#135	—	2	8	no	—
495	#135	—	2	8	no	—
496	C₂×Q₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×D₈	—	2	2	no	—
500	C₂×M₁₆	—	2	1	no	—
501	C₂×M₁₆	—	2	1	no	—
502	C₂×M₁₆	—	2	1	no	—
503	C₂×M₁₆	—	2	1	no	—
504	C₂×M₁₆	—	2	1	no	—
505	C₂×M₁₆	—	2	1	no	—
506	C₂×M₁₆	—	2	1	no	—
507	C₂×M₁₆	—	2	1	no	—
508	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	complemented
509	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	complemented
510	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
511	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
512	C₂²×C₈	—	2	1	no	—
513	C₂²×C₈	—	2	1	no	—
514	C₄×Q₈	—	2	4	no	—
515	C₄×Q₈	—	2	4	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	8	no	—
520	#117	—	2	4	no	—
521	#117	—	2	4	no	—
522	#117	—	2	1	no	—
523	#117	—	2	1	no	—
524	#117	—	2	1	no	—
525	#117	—	2	1	no	—
526	#117	—	2	1	no	—
527	#117	—	2	4	no	—
528	#117	—	2	1	no	—
529	#117	—	2	1	no	—
530	#117	D₄×C₁₃	1	2	yes	—
531	#117	D₄×C₁₃	1	2	yes	—
532	#117	D₄×C₁₃	1	2	yes	—
533	#117	C₂³×C₁₃	1	2	yes	—
534	#117	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	4	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	—	2	4	no	—
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
547	#104	—	2	8	no	—
548	#104	—	2	8	no	—
549	#99	—	2	8	no	—
550	C₂×C₁₃	—	2	1	no	—
551	C₂×C₁₃	—	2	1	no	—
552	C₂×C₁₃	—	2	1	no	—
553	C₂×C₁₃	—	2	1	no	—
554	C₂×C₁₃	—	2	1	no	—
555	C₂×C₁₃	—	2	1	no	—
556	C₂×C₁₃	—	2	1	no	—
557	C₂×C₁₃	—	4	4	no	—
558	C₂×C₁₃	—	8	2	no	—
559	C₂×C₁₃	C₂×#386	1	1	yes	characteristic
560	C₂⁴	—	2	1	no	—
561	C₂⁴	—	2	1	no	—
562	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	2	2	no	—
572	#41	—	2	2	no	—
573	#41	—	2	2	no	—
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	2	2	no	—
579	#41	—	2	2	no	—
580	#41	—	2	2	no	—
581	#41	—	2	2	no	—
582	#41	—	2	2	no	—
583	#41	—	4	1	no	—
584	#41	—	4	1	no	—
585	#41	—	4	1	no	—
586	#41	—	4	1	no	—
587	#41	—	4	1	no	—
588	#41	—	4	1	no	—
589	#41	—	4	1	no	—
590	#41	—	4	1	no	—
591	#41	C₁₃×C₂²⋊C₄	1	4	yes	—
592	#41	C₁₃×C₂²⋊C₄	1	4	yes	—
593	#41	C₂²×C₄×C₁₃	1	4	yes	—
594	#41	C₂×D₄×C₁₃	1	4	yes	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
604	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
605	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
606	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	4	1	no	—
624	C₂×D₄	—	4	1	no	—
625	C₂×D₄	—	4	1	no	—
626	C₂×D₄	—	4	1	no	—
627	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
628	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
629	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
630	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
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	1	no	—
639	C₂²×C₄	—	2	8	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	1	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
659	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
660	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
661	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
663	Q₁₆	—	2	8	no	—
664	SD₁₆	—	2	8	no	—
665	SD₁₆	—	2	8	no	—
666	D₈	—	2	8	no	—
667	M₁₆	—	2	2	no	—
668	M₁₆	—	2	2	no	—
669	M₁₆	—	2	2	no	—
670	M₁₆	—	2	2	no	—
671	M₁₆	—	2	2	no	—
672	M₁₆	—	4	1	no	—
673	M₁₆	—	4	1	no	—
674	M₁₆	C₂²×C₄×C₁₃	1	4	yes	—
675	C₂×C₈	—	2	2	no	—
676	C₂×C₈	—	2	2	no	—
677	C₂×C₈	—	2	2	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	4	1	no	—
680	C₂×C₈	—	4	1	no	—
681	C₄⋊C₄	—	2	8	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
695	C₄²	—	2	8	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	4	1	no	—
701	C₄²	C₂×D₄×C₁₃	1	4	yes	—
702	C₁₃	#21000	1	1	yes	characteristic, direct product factor, Sylow
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	—	8	2	no	—
711	C₂³	—	8	2	no	—
712	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
713	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
714	C₂³	C₁₃×#120	1	1	yes	characteristic
715	C₂³	C₁₃×#120	1	1	yes	characteristic
716	C₂³	C₁₃×#121	1	1	yes	characteristic
717	C₂³	C₁₃×#121	1	1	yes	characteristic
718	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	4	1	no	—
725	Q₈	—	4	1	no	—
726	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	4	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	2	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	8	2	no	—
761	C₂×C₄	—	8	2	no	—
762	C₂×C₄	—	8	8	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
765	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
766	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
767	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
768	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
769	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
770	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
771	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
772	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
773	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
775	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
776	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
777	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
778	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
779	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
780	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
781	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
782	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
783	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
784	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
785	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
786	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
790	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
791	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
792	C₈	—	2	4	no	—
793	C₈	—	4	2	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	8	2	no	—
805	C₂²	—	8	2	no	—
806	C₂²	—	8	2	no	—
807	C₂²	—	8	2	no	—
808	C₂²	—	8	2	no	—
809	C₂²	C₁₃×#386	1	1	yes	characteristic
810	C₂²	C₁₃×#386	1	1	yes	characteristic
811	C₂²	C₁₃×#386	1	1	yes	characteristic
812	C₂²	C₁₃×#386	1	1	yes	characteristic
813	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
814	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
815	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
816	C₄	—	2	4	no	—
817	C₄	—	4	4	no	—
818	C₄	—	4	4	no	—
819	C₄	—	4	2	no	—
820	C₄	—	8	2	no	—
821	C₄	C₁₃×#386	1	1	yes	characteristic
822	C₄	C₁₃×#386	1	1	yes	characteristic
823	C₄	C₁₃×#386	1	1	yes	characteristic
824	C₄	C₁₃×#386	1	1	yes	characteristic
825	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
826	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
827	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
828	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
829	C₂	—	2	1	no	—
830	C₂	—	2	1	no	—
831	C₂	—	2	1	no	—
832	C₂	—	2	1	no	—
833	C₂	—	2	1	no	—
834	C₂	—	2	1	no	—
835	C₂	—	2	1	no	—
836	C₂	—	4	4	no	—
837	C₂	—	8	2	no	—
838	C₂	C₂×C₁₃×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#386
prime radical	C₂×C₁₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3428	C₂	semidirect
3. C₂×C₁₃×#421	C₂	semidirect
4. C₂×C₁₃×#421	C₂	semidirect
5. C₂×C₁₃×#410	C₂	semidirect
6. C₁₃×#1906	C₂	semidirect
7. C₂×C₁₃×#344	C₂	semidirect
8. C₁₃×#1733	C₂	semidirect
13. C₁₃×#575	C₄	semidirect
16. C₂×C₁₃×#137	C₄	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₄	semidirect
28. C₄×C₁₃×#41	C₂²	semidirect
36. C₁₃×#421	C₂²	semidirect
38. C₂×C₁₃×#104	C₂²	semidirect
40. C₁₃×#410	C₂²	semidirect
42. C₁₃×#344	C₂²	semidirect
43. C₁₃×#339	C₂²	semidirect
62. C₂×C₁₃×#41	C₂×C₄	semidirect
68. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
72. C₂²×D₄×C₁₃	C₂×C₄	semidirect
80. C₁₃×#137	C₂×C₄	semidirect
84. C₁₃×AGL(1,ℤ/8)	C₂×C₄	semidirect
99. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
100. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
141. #21000	C₁₃	direct (N × H)
285. #3428	C₂×C₁₃	semidirect
286. C₂×#421	C₂×C₁₃	semidirect
287. C₂×#421	C₂×C₁₃	semidirect
288. C₂×#410	C₂×C₁₃	semidirect
289. #1906	C₂×C₁₃	semidirect
290. C₂×#344	C₂×C₁₃	semidirect
291. #1733	C₂×C₁₃	semidirect
387. #575	C₄×C₁₃	semidirect
390. C₂×#137	C₄×C₁₃	semidirect
392. C₂×AGL(1,ℤ/8)	C₄×C₁₃	semidirect
402. C₄×#41	C₂²×C₁₃	semidirect
410. #421	C₂²×C₁₃	semidirect
412. C₂×#104	C₂²×C₁₃	semidirect
414. #410	C₂²×C₁₃	semidirect
416. #344	C₂²×C₁₃	semidirect
417. #339	C₂²×C₁₃	semidirect
471. C₂×#41	C₂×C₄×C₁₃	semidirect
477. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
481. C₂²×D₄	C₂×C₄×C₁₃	semidirect
489. #137	C₂×C₄×C₁₃	semidirect
493. AGL(1,ℤ/8)	C₂×C₄×C₁₃	semidirect
508. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
509. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
702. C₁₃	#21000	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×#575	2
C₁₃×#3428	2
C₂×C₁₃×#421	2
C₂×C₁₃×#410	2
C₁₃×#1906	2
C₂×C₁₃×#344	2
C₁₃×#1733	2
#21000	13

Subgroups — C13×#21000 #15707339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21000 #15707339