Subgroups — C₁₃×#61329 #15747668

Order 3328.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	C₁₃×#559	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	Q₈²×C₁₃	C₂²	1	2	yes	complemented
25	C₁₃×#557	C₂²	1	2	yes	complemented
26	C₁₃×#554	—	2	2	no	—
27	C₁₃×#554	C₂²	1	2	yes	complemented
28	C₁₃×#550	C₂²	1	2	yes	—
29	C₁₃×#550	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₃	—	2	2	no	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
32	C₁₃×#546	—	2	2	no	—
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#544	—	2	2	no	—
35	C₁₃×#544	C₂²	1	2	yes	—
36	C₁₃×#540	—	2	2	no	—
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#533	—	2	1	no	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	—	2	1	no	—
42	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
45	C₁₃×#520	C₂²	1	2	yes	—
46	C₁₃×#518	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₁₃×#490	C₂²	1	4	yes	complemented
50	C₁₃×#489	C₂²	1	4	yes	complemented
51	C₁₃×#488	C₂²	1	4	yes	complemented
52	C₁₃×#486	C₂²	1	2	yes	—
53	C₁₃×#486	C₂²	1	2	yes	—
54	C₁₃×#486	C₂²	1	2	yes	—
55	C₁₃×#486	C₂²	1	2	yes	—
56	C₁₃×#486	C₂²	1	4	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	complemented
58	C₁₃×#478	C₂²	1	4	yes	complemented
59	C₁₃×#477	C₂²	1	2	yes	complemented
60	C₁₃×#476	C₂²	1	2	yes	complemented
61	C₁₃×#476	C₂²	1	4	yes	complemented
62	C₁₃×#475	C₂²	1	2	yes	complemented
63	C₁₃×#474	C₂²	1	2	yes	complemented
64	C₁₃×#474	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#460	C₂²	1	2	yes	—
68	C₁₃×#460	C₂²	1	2	yes	—
69	C₁₃×#460	C₂²	1	4	yes	complemented
70	C₁₃×#459	C₂²	1	2	yes	—
71	C₁₃×#459	C₂²	1	2	yes	—
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#446	C₂²	1	2	yes	complemented
74	C₁₃×#446	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
76	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
77	C₁₃×#442	C₂²	1	4	yes	complemented
78	C₁₃×#440	C₂²	1	4	yes	complemented
79	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
88	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#428	C₂²	1	2	yes	—
90	C₁₃×#427	C₂²	1	1	yes	characteristic
91	C₁₃×#424	C₂²	1	2	yes	—
92	C₁₃×#423	C₂²	1	1	yes	characteristic
93	C₁₃×#418	C₂²	1	2	yes	—
94	C₁₃×#417	C₂²	1	2	yes	—
95	C₁₃×#416	C₂²	1	1	yes	characteristic
96	C₁₃×#416	C₂²	1	1	yes	characteristic
97	C₂×C₁₃×#102	C₂²	1	2	yes	—
98	C₂×C₁₃×#102	C₂²	1	2	yes	—
99	C₁₃×#405	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
101	C₂×C₁₃×#41	—	2	2	no	—
102	C₂×C₁₃×#41	—	2	2	no	—
103	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₁₃	—	2	2	no	—
106	C₂²×Q₈×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	—	2	1	no	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₁₃×#135	—	2	4	no	—
112	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	—	2	2	no	—
122	C₁₃×C₄⋊Q₈	—	2	2	no	—
123	C₁₃×C₄⋊Q₈	—	2	2	no	—
124	C₁₃×C₄⋊Q₈	—	2	4	no	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
129	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#127	—	2	1	no	—
133	C₁₃×#127	—	2	1	no	—
134	C₁₃×#127	C₂³	1	2	yes	—
135	C₁₃×#127	C₂³	1	2	yes	—
136	C₁₃×#127	C₂³	1	4	yes	—
137	C₁₃×#125	—	2	2	no	—
138	C₁₃×#125	—	2	4	no	—
139	C₁₃×#125	D₄	1	2	yes	—
140	C₁₃×#125	C₂³	1	4	yes	—
141	C₁₃×#124	—	2	2	no	—
142	C₁₃×#124	—	2	2	no	—
143	C₁₃×#124	C₂³	1	4	yes	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×#123	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	—	2	4	no	—
151	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#120	—	2	4	no	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	4	no	—
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	4	yes	—
183	C₄×D₄×C₁₃	C₂³	1	4	yes	—
184	C₄×D₄×C₁₃	C₂³	1	4	yes	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	C₂³	1	1	yes	characteristic
189	C₁₃×#117	C₂³	1	1	yes	characteristic
190	C₁₃×#117	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₄²×C₁₃	—	2	1	no	—
197	C₂×C₄²×C₁₃	—	2	1	no	—
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×#107	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	1	yes	characteristic
201	C₁₃×#107	C₂³	1	4	yes	—
202	C₁₃×#106	C₂³	1	1	yes	characteristic
203	C₁₃×#106	C₂³	1	1	yes	characteristic
204	C₁₃×#106	C₂³	1	4	yes	—
205	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
206	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	1	yes	characteristic
210	C₁₃×#103	C₂³	1	1	yes	characteristic
211	C₁₃×#103	C₂³	1	1	yes	characteristic
212	C₁₃×#103	C₂³	1	1	yes	characteristic
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#102	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	1	yes	characteristic
219	C₁₃×#102	C₂³	1	1	yes	characteristic
220	C₁₃×#102	C₂³	1	1	yes	characteristic
221	C₁₃×#102	C₂³	1	1	yes	characteristic
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₁₃	C₂³	1	4	yes	—
231	#61329	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	8	4	no	—
237	C₁₃×#41	—	8	4	no	—
238	C₁₃×#41	#41	1	4	yes	complemented
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	8	2	no	—
243	C₂×Q₈×C₁₃	—	8	4	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	8	2	no	—
260	C₂×D₄×C₁₃	—	8	2	no	—
261	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₁₃×Q₁₆	—	2	2	no	—
278	C₁₃×SD₁₆	—	2	2	no	—
279	C₁₃×SD₁₆	—	2	8	no	—
280	C₁₃×SD₁₆	—	2	2	no	—
281	C₁₃×D₈	—	2	2	no	—
282	C₁₃×D₈	—	2	8	no	—
283	C₁₃×M₁₆	—	2	4	no	—
284	C₂×C₈×C₁₃	—	2	2	no	—
285	C₂×C₈×C₁₃	—	2	2	no	—
286	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	4	no	—
332	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₁₃	C₂⁴	1	4	yes	—
337	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3375	C₂×C₁₃	1	2	yes	complemented
340	#3373	C₂×C₁₃	1	2	yes	complemented
341	#3368	C₂×C₁₃	1	2	yes	complemented
342	#3366	C₂×C₁₃	1	2	yes	complemented
343	#3365	C₂×C₁₃	1	2	yes	complemented
344	#3362	C₂×C₁₃	1	2	yes	complemented
345	#3361	C₂×C₁₃	1	2	yes	complemented
346	#3358	C₂×C₁₃	1	2	yes	complemented
347	#3136	C₂×C₁₃	1	2	yes	complemented
348	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3081	C₂×C₁₃	1	2	yes	complemented
350	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3045	C₂×C₁₃	1	2	yes	complemented
352	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2946	C₂×C₁₃	1	2	yes	complemented
355	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₂³×C₁₃	—	2	1	no	—
357	C₂³×C₁₃	—	2	4	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	4	4	no	—
360	C₂³×C₁₃	—	8	2	no	—
361	C₂³×C₁₃	—	8	2	no	—
362	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₁₃	—	2	4	no	—
364	Q₈×C₁₃	—	2	4	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	—	2	1	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	4	4	no	—
369	Q₈×C₁₃	—	8	2	no	—
370	Q₈×C₁₃	—	8	4	no	—
371	Q₈×C₁₃	C₂×#41	1	2	yes	—
372	D₄×C₁₃	—	2	4	no	—
373	D₄×C₁₃	—	2	4	no	—
374	D₄×C₁₃	—	2	1	no	—
375	D₄×C₁₃	—	2	1	no	—
376	D₄×C₁₃	—	2	4	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	4	no	—
380	D₄×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	4	4	no	—
382	D₄×C₁₃	—	8	2	no	—
383	D₄×C₁₃	—	8	2	no	—
384	D₄×C₁₃	—	8	4	no	—
385	D₄×C₁₃	—	8	4	no	—
386	D₄×C₁₃	C₂×#41	1	2	yes	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	4	2	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	8	4	no	—
403	C₂×C₄×C₁₃	—	8	4	no	—
404	C₂×C₄×C₁₃	—	8	4	no	—
405	C₂×C₄×C₁₃	—	8	2	no	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
416	C₈×C₁₃	—	2	1	no	—
417	C₈×C₁₃	—	2	1	no	—
418	C₈×C₁₃	—	2	4	no	—
419	C₈×C₁₃	—	2	1	no	—
420	C₈×C₁₃	—	2	1	no	—
421	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
422	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
423	#559	C₂²×C₁₃	1	2	yes	—
424	#559	C₂²×C₁₃	1	2	yes	—
425	Q₈²	C₂²×C₁₃	1	2	yes	complemented
426	#557	C₂²×C₁₃	1	2	yes	complemented
427	#554	—	2	2	no	—
428	#554	C₂²×C₁₃	1	2	yes	complemented
429	#550	C₂²×C₁₃	1	2	yes	—
430	#550	C₂²×C₁₃	1	2	yes	—
431	D₄×Q₈	—	2	2	no	—
432	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
433	#546	—	2	2	no	—
434	#546	—	2	2	no	—
435	#544	—	2	2	no	—
436	#544	C₂²×C₁₃	1	2	yes	—
437	#540	—	2	2	no	—
438	#535	C₂²×C₁₃	1	2	yes	—
439	#533	—	2	1	no	—
440	#533	C₂²×C₁₃	1	1	yes	characteristic
441	#532	—	2	1	no	—
442	#532	—	2	1	no	—
443	C₂×C₄⋊Q₈	—	2	1	no	—
444	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
446	#520	C₂²×C₁₃	1	2	yes	—
447	#518	C₂²×C₁₃	1	2	yes	—
448	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
449	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
450	#490	C₂²×C₁₃	1	4	yes	complemented
451	#489	C₂²×C₁₃	1	4	yes	complemented
452	#488	C₂²×C₁₃	1	4	yes	complemented
453	#486	C₂²×C₁₃	1	2	yes	—
454	#486	C₂²×C₁₃	1	2	yes	—
455	#486	C₂²×C₁₃	1	2	yes	—
456	#486	C₂²×C₁₃	1	2	yes	—
457	#486	C₂²×C₁₃	1	4	yes	complemented
458	#478	C₂²×C₁₃	1	4	yes	complemented
459	#478	C₂²×C₁₃	1	4	yes	complemented
460	#477	C₂²×C₁₃	1	2	yes	complemented
461	#476	C₂²×C₁₃	1	2	yes	complemented
462	#476	C₂²×C₁₃	1	4	yes	complemented
463	#475	C₂²×C₁₃	1	2	yes	complemented
464	#474	C₂²×C₁₃	1	2	yes	complemented
465	#474	C₂²×C₁₃	1	4	yes	complemented
466	#464	C₂²×C₁₃	1	4	yes	complemented
467	#463	C₂²×C₁₃	1	4	yes	complemented
468	#460	C₂²×C₁₃	1	2	yes	—
469	#460	C₂²×C₁₃	1	2	yes	—
470	#460	C₂²×C₁₃	1	4	yes	complemented
471	#459	C₂²×C₁₃	1	2	yes	—
472	#459	C₂²×C₁₃	1	2	yes	—
473	#459	C₂²×C₁₃	1	4	yes	complemented
474	#446	C₂²×C₁₃	1	2	yes	complemented
475	#446	C₂²×C₁₃	1	2	yes	complemented
476	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
477	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
478	#442	C₂²×C₁₃	1	4	yes	complemented
479	#440	C₂²×C₁₃	1	4	yes	complemented
480	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
485	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
489	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#428	C₂²×C₁₃	1	2	yes	—
491	#427	C₂²×C₁₃	1	1	yes	characteristic
492	#424	C₂²×C₁₃	1	2	yes	—
493	#423	C₂²×C₁₃	1	1	yes	characteristic
494	#418	C₂²×C₁₃	1	2	yes	—
495	#417	C₂²×C₁₃	1	2	yes	—
496	#416	C₂²×C₁₃	1	1	yes	characteristic
497	#416	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×#102	C₂²×C₁₃	1	2	yes	—
499	C₂×#102	C₂²×C₁₃	1	2	yes	—
500	#405	C₂²×C₁₃	1	2	yes	—
501	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	4	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	4	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	4	no	—
513	C₂²×C₁₃	—	16	4	no	—
514	C₂²×C₁₃	#548	1	2	yes	—
515	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	2	4	no	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	4	no	—
521	C₄×C₁₃	—	4	1	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	—	4	4	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	#548	1	2	yes	—
528	C₄×C₁₃	#576	1	2	yes	—
529	C₄×C₁₃	#577	1	2	yes	—
530	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
531	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×Q₈	—	2	2	no	—
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
541	AGL(1,ℤ/8)	—	2	8	no	—
542	#135	—	2	4	no	—
543	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×D₈	C₂³×C₁₃	1	4	yes	—
549	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
550	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	2	2	no	—
554	C₄⋊Q₈	—	2	2	no	—
555	C₄⋊Q₈	—	2	4	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
559	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
563	#127	—	2	1	no	—
564	#127	—	2	1	no	—
565	#127	C₂³×C₁₃	1	2	yes	—
566	#127	C₂³×C₁₃	1	2	yes	—
567	#127	C₂³×C₁₃	1	4	yes	—
568	#125	—	2	2	no	—
569	#125	—	2	4	no	—
570	#125	D₄×C₁₃	1	2	yes	—
571	#125	C₂³×C₁₃	1	4	yes	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₁₃	1	4	yes	—
575	#123	—	2	4	no	—
576	#123	—	2	4	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
583	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	4	no	—
590	#120	—	2	4	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
598	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₁₃	1	4	yes	—
614	C₄×D₄	C₂³×C₁₃	1	4	yes	—
615	C₄×D₄	C₂³×C₁₃	1	4	yes	—
616	#117	—	2	2	no	—
617	#117	—	2	1	no	—
618	#117	—	2	1	no	—
619	#117	C₂³×C₁₃	1	1	yes	characteristic
620	#117	C₂³×C₁₃	1	1	yes	characteristic
621	#117	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	—	2	4	no	—
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
630	#107	C₂³×C₁₃	1	1	yes	characteristic
631	#107	C₂³×C₁₃	1	1	yes	characteristic
632	#107	C₂³×C₁₃	1	4	yes	—
633	#106	C₂³×C₁₃	1	1	yes	characteristic
634	#106	C₂³×C₁₃	1	1	yes	characteristic
635	#106	C₂³×C₁₃	1	4	yes	—
636	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	1	yes	characteristic
641	#103	C₂³×C₁₃	1	1	yes	characteristic
642	#103	C₂³×C₁₃	1	1	yes	characteristic
643	#103	C₂³×C₁₃	1	1	yes	characteristic
644	#103	C₂³×C₁₃	1	4	yes	—
645	#102	C₂³×C₁₃	1	4	yes	—
646	#102	C₂³×C₁₃	1	4	yes	—
647	#102	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	4	yes	—
649	#102	C₂³×C₁₃	1	1	yes	characteristic
650	#102	C₂³×C₁₃	1	1	yes	characteristic
651	#102	C₂³×C₁₃	1	1	yes	characteristic
652	#102	C₂³×C₁₃	1	1	yes	characteristic
653	#102	C₂³×C₁₃	1	4	yes	—
654	#102	C₂³×C₁₃	1	4	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#97	C₂³×C₁₃	1	4	yes	—
657	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
658	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
659	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
660	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
661	C₄×C₈	C₂³×C₁₃	1	4	yes	—
662	C₂×C₁₃	—	2	2	no	—
663	C₂×C₁₃	—	4	2	no	—
664	C₂×C₁₃	—	8	1	no	—
665	C₂×C₁₃	—	8	4	no	—
666	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
667	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
668	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
669	C₂⁴	—	2	2	no	—
670	#41	—	2	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	8	4	no	—
674	#41	—	8	4	no	—
675	#41	C₁₃×#41	1	4	yes	complemented
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	8	2	no	—
680	C₂×Q₈	—	8	4	no	—
681	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
682	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	8	2	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
699	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
714	Q₁₆	—	2	2	no	—
715	SD₁₆	—	2	2	no	—
716	SD₁₆	—	2	8	no	—
717	SD₁₆	—	2	2	no	—
718	D₈	—	2	2	no	—
719	D₈	—	2	8	no	—
720	M₁₆	—	2	4	no	—
721	C₂×C₈	—	2	2	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
744	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	4	no	—
769	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₄²	C₂⁴×C₁₃	1	4	yes	—
774	C₁₃	#61329	1	1	yes	characteristic, direct product factor, Sylow
775	C₂³	—	2	1	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	4	4	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	4	no	—
790	Q₈	C₂×C₁₃×#41	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	1	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	2	no	—
803	D₄	—	8	4	no	—
804	D₄	—	8	4	no	—
805	D₄	C₂×C₁₃×#41	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
833	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
834	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	4	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	16	4	no	—
852	C₂²	C₁₃×#548	1	2	yes	—
853	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
854	C₄	—	2	1	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	C₁₃×#548	1	2	yes	—
866	C₄	C₁₃×#576	1	2	yes	—
867	C₄	C₁₃×#577	1	2	yes	—
868	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
869	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	4	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
875	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
876	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3365	C₂	semidirect
8. C₁₃×#3362	C₂	semidirect
9. C₁₃×#3361	C₂	semidirect
10. C₁₃×#3358	C₂	semidirect
11. C₁₃×#3136	C₂	semidirect
12. C₂×C₁₃×#486	C₂	semidirect
13. C₁₃×#3081	C₂	semidirect
14. C₁₃×#3079	C₂	semidirect
15. C₁₃×#3045	C₂	semidirect
16. C₁₃×#3038	C₂	semidirect
17. C₁₃×#2960	C₂	semidirect
18. C₁₃×#2946	C₂	semidirect
19. C₄×C₁₃×#135	C₂	semidirect
24. Q₈²×C₁₃	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
49. C₁₃×#490	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
56. C₁₃×#486	C₂²	semidirect
57. C₁₃×#478	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
60. C₁₃×#476	C₂²	semidirect
61. C₁₃×#476	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#474	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₁₃×#446	C₂²	semidirect
75. C₈×Q₈×C₁₃	C₂²	semidirect
76. C₈×Q₈×C₁₃	C₂²	semidirect
77. C₁₃×#442	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₄×C₁₃×Q₁₆	C₂²	semidirect
80. C₄×C₁₃×Q₁₆	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₄×C₁₃×D₈	C₂²	semidirect
87. C₄×C₁₃×D₈	C₂²	semidirect
88. C₄×C₁₃×D₈	C₂²	semidirect
231. #61329	C₁₃	direct (N × H)
238. C₁₃×#41	#41	semidirect
337. #3508	C₂×C₁₃	semidirect
338. #3503	C₂×C₁₃	semidirect
339. #3375	C₂×C₁₃	semidirect
340. #3373	C₂×C₁₃	semidirect
341. #3368	C₂×C₁₃	semidirect
342. #3366	C₂×C₁₃	semidirect
343. #3365	C₂×C₁₃	semidirect
344. #3362	C₂×C₁₃	semidirect
345. #3361	C₂×C₁₃	semidirect
346. #3358	C₂×C₁₃	semidirect
347. #3136	C₂×C₁₃	semidirect
348. C₂×#486	C₂×C₁₃	semidirect
349. #3081	C₂×C₁₃	semidirect
350. #3079	C₂×C₁₃	semidirect
351. #3045	C₂×C₁₃	semidirect
352. #3038	C₂×C₁₃	semidirect
353. #2960	C₂×C₁₃	semidirect
354. #2946	C₂×C₁₃	semidirect
355. C₄×#135	C₂×C₁₃	semidirect
425. Q₈²	C₂²×C₁₃	semidirect
426. #557	C₂²×C₁₃	semidirect
428. #554	C₂²×C₁₃	semidirect
432. D₄×Q₈	C₂²×C₁₃	semidirect
450. #490	C₂²×C₁₃	semidirect
451. #489	C₂²×C₁₃	semidirect
452. #488	C₂²×C₁₃	semidirect
457. #486	C₂²×C₁₃	semidirect
458. #478	C₂²×C₁₃	semidirect
459. #478	C₂²×C₁₃	semidirect
460. #477	C₂²×C₁₃	semidirect
461. #476	C₂²×C₁₃	semidirect
462. #476	C₂²×C₁₃	semidirect
463. #475	C₂²×C₁₃	semidirect
464. #474	C₂²×C₁₃	semidirect
465. #474	C₂²×C₁₃	semidirect
466. #464	C₂²×C₁₃	semidirect
467. #463	C₂²×C₁₃	semidirect
470. #460	C₂²×C₁₃	semidirect
473. #459	C₂²×C₁₃	semidirect
474. #446	C₂²×C₁₃	semidirect
475. #446	C₂²×C₁₃	semidirect
476. C₈×Q₈	C₂²×C₁₃	semidirect
477. C₈×Q₈	C₂²×C₁₃	semidirect
478. #442	C₂²×C₁₃	semidirect
479. #440	C₂²×C₁₃	semidirect
480. C₄×Q₁₆	C₂²×C₁₃	semidirect
481. C₄×Q₁₆	C₂²×C₁₃	semidirect
482. C₄×SD₁₆	C₂²×C₁₃	semidirect
483. C₄×SD₁₆	C₂²×C₁₃	semidirect
484. C₄×SD₁₆	C₂²×C₁₃	semidirect
485. C₄×SD₁₆	C₂²×C₁₃	semidirect
486. C₄×SD₁₆	C₂²×C₁₃	semidirect
487. C₄×D₈	C₂²×C₁₃	semidirect
488. C₄×D₈	C₂²×C₁₃	semidirect
489. C₄×D₈	C₂²×C₁₃	semidirect
675. #41	C₁₃×#41	semidirect
774. C₁₃	#61329	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3508	2
C₁₃×#3503	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3368	2
C₁₃×#3366	2
C₁₃×#3365	2
C₁₃×#3362	2
C₁₃×#3361	2
C₁₃×#3358	2
C₁₃×#3136	2
C₂×C₁₃×#486	2
C₁₃×#3081	2
C₁₃×#3079	2
C₁₃×#3045	2
C₁₃×#3038	2
C₁₃×#2960	2
C₁₃×#2946	2
C₄×C₁₃×#135	2
#61329	13

Subgroups — C13×#61329 #15747668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61329 #15747668