Subgroups — C₁₃×#61254 #15747593

Order 3328.

1872 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3356	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3346	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3095	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3092	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
20	C₁₃×#556	C₂²	1	1	yes	characteristic
21	C₁₃×#555	C₂²	1	1	yes	characteristic
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#554	—	2	2	no	—
24	C₁₃×#554	—	2	1	no	—
25	C₁₃×#554	C₂²	1	2	yes	—
26	C₁₃×#554	C₂²	1	1	yes	characteristic
27	C₁₃×#554	C₂²	1	4	yes	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#553	C₂²	1	2	yes	—
30	C₁₃×#552	—	2	1	no	—
31	C₁₃×#552	C₂²	1	2	yes	—
32	C₁₃×#551	—	2	2	no	—
33	C₁₃×#547	C₂²	1	1	yes	characteristic
34	C₁₃×#546	—	2	1	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₁₃×#529	—	2	2	no	—
38	C₁₃×#529	—	2	1	no	—
39	C₂×C₁₃×#125	—	2	1	no	—
40	C₁₃×#525	C₂²	1	2	yes	—
41	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#117	C₂²	1	2	yes	—
49	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₁₃×#501	C₂²	1	4	yes	complemented
51	C₁₃×#500	C₂²	1	2	yes	complemented
52	C₁₃×#498	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	4	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#484	C₂²	1	4	yes	complemented
56	C₁₃×#484	C₂²	1	4	yes	complemented
57	C₁₃×#483	C₂²	1	4	yes	complemented
58	C₁₃×#483	C₂²	1	4	yes	complemented
59	C₁₃×#481	C₂²	1	4	yes	complemented
60	C₁₃×#480	C₂²	1	4	yes	complemented
61	C₁₃×#479	C₂²	1	4	yes	complemented
62	C₁₃×#477	C₂²	1	2	yes	complemented
63	C₁₃×#477	C₂²	1	2	yes	complemented
64	C₁₃×#476	C₂²	1	2	yes	complemented
65	C₁₃×#475	C₂²	1	2	yes	complemented
66	C₁₃×#475	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#470	C₂²	1	4	yes	complemented
69	C₁₃×#468	C₂²	1	4	yes	complemented
70	C₁₃×#467	C₂²	1	4	yes	complemented
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#441	C₂²	1	2	yes	complemented
73	C₁₃×#440	C₂²	1	2	yes	complemented
74	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
75	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
76	C₁₃×#436	C₂²	1	2	yes	—
77	C₁₃×#435	C₂²	1	4	yes	—
78	C₈×D₄×C₁₃	C₂²	1	2	yes	—
79	C₁₃×#428	C₂²	1	2	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	2	yes	—
82	C₁₃×#428	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	1	yes	characteristic
84	C₁₃×#428	C₂²	1	4	yes	complemented
85	C₁₃×#428	C₂²	1	4	yes	complemented
86	C₂×C₁₃×#107	C₂²	1	4	yes	complemented
87	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
88	C₁₃×#423	C₂²	1	1	yes	characteristic
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#419	C₂²	1	1	yes	characteristic
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₁₃×#407	C₂²	1	2	yes	—
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	—	2	2	no	—
101	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
102	C₁₃×#137	—	2	4	no	—
103	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×M₁₆	—	2	8	no	—
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#126	—	2	2	no	—
118	C₁₃×#126	—	2	2	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	1	no	—
125	C₁₃×#125	C₂³	1	2	yes	—
126	C₁₃×#124	—	2	1	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#123	—	2	2	no	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	1	no	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	2	yes	—
150	C₁₃×#120	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₁₃	—	2	4	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
170	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
171	C₄×D₄×C₁₃	D₄	1	2	yes	—
172	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₁₃	C₂³	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
177	C₁₃×#117	—	2	2	no	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	1	no	—
180	C₁₃×#117	—	2	2	no	—
181	C₁₃×#117	—	2	1	no	—
182	C₁₃×#117	C₂³	1	1	yes	characteristic
183	C₁₃×#117	C₂³	1	2	yes	—
184	C₁₃×#117	C₂³	1	2	yes	—
185	C₁₃×#117	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
202	C₂×C₄²×C₁₃	—	2	2	no	—
203	C₂×C₄²×C₁₃	—	2	1	no	—
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₁₃×#107	C₂³	1	2	yes	—
207	C₁₃×#107	C₂³	1	4	yes	—
208	C₁₃×#107	C₂³	1	4	yes	—
209	C₁₃×#107	C₂³	1	4	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×#106	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×#106	C₂³	1	4	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₁₃×#97	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61254	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	8	2	no	—
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	8	4	no	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₁₃×Q₁₆	—	2	4	no	—
275	C₁₃×SD₁₆	—	2	4	no	—
276	C₁₃×M₁₆	—	2	4	no	—
277	C₁₃×M₁₆	—	2	2	no	—
278	C₁₃×M₁₆	—	2	8	no	—
279	C₁₃×M₁₆	#41	1	4	yes	complemented
280	C₂×C₈×C₁₃	—	2	8	no	—
281	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
283	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	#3475	C₂×C₁₃	1	1	yes	characteristic
342	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3357	C₂×C₁₃	1	2	yes	complemented
344	#3356	C₂×C₁₃	1	2	yes	complemented
345	#3346	C₂×C₁₃	1	4	yes	complemented
346	#3344	C₂×C₁₃	1	4	yes	complemented
347	#3338	C₂×C₁₃	1	2	yes	complemented
348	#3335	C₂×C₁₃	1	2	yes	complemented
349	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3095	C₂×C₁₃	1	2	yes	complemented
351	#3092	C₂×C₁₃	1	2	yes	complemented
352	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3056	C₂×C₁₃	1	2	yes	complemented
355	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
356	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#428	C₂×C₁₃	1	2	yes	complemented
358	C₂³×C₁₃	—	2	4	no	—
359	C₂³×C₁₃	—	2	4	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
363	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	1	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	1	no	—
369	Q₈×C₁₃	—	4	2	no	—
370	Q₈×C₁₃	—	4	2	no	—
371	Q₈×C₁₃	—	8	1	no	—
372	Q₈×C₁₃	—	8	2	no	—
373	Q₈×C₁₃	—	8	2	no	—
374	D₄×C₁₃	—	2	4	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	2	1	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	4	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	#137	1	4	yes	complemented
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	4	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	4	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	2	no	—
405	C₂×C₄×C₁₃	—	8	1	no	—
406	C₂×C₄×C₁₃	—	8	2	no	—
407	C₂×C₄×C₁₃	—	8	4	no	—
408	C₂×C₄×C₁₃	—	8	4	no	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
419	C₈×C₁₃	—	2	4	no	—
420	C₈×C₁₃	—	2	2	no	—
421	C₈×C₁₃	C₂×#41	1	4	yes	—
422	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
424	#556	C₂²×C₁₃	1	1	yes	characteristic
425	#555	C₂²×C₁₃	1	1	yes	characteristic
426	#554	—	2	1	no	—
427	#554	—	2	2	no	—
428	#554	—	2	1	no	—
429	#554	C₂²×C₁₃	1	2	yes	—
430	#554	C₂²×C₁₃	1	1	yes	characteristic
431	#554	C₂²×C₁₃	1	4	yes	—
432	#554	C₂²×C₁₃	1	2	yes	—
433	#553	C₂²×C₁₃	1	2	yes	—
434	#552	—	2	1	no	—
435	#552	C₂²×C₁₃	1	2	yes	—
436	#551	—	2	2	no	—
437	#547	C₂²×C₁₃	1	1	yes	characteristic
438	#546	—	2	1	no	—
439	#533	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
441	#529	—	2	2	no	—
442	#529	—	2	1	no	—
443	C₂×#125	—	2	1	no	—
444	#525	C₂²×C₁₃	1	2	yes	—
445	C₂×C₂²⋊Q₈	—	2	2	no	—
446	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
447	C₄×#41	—	2	1	no	—
448	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×C₄×D₄	—	2	1	no	—
451	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#117	C₂²×C₁₃	1	2	yes	—
453	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
454	#501	C₂²×C₁₃	1	4	yes	complemented
455	#500	C₂²×C₁₃	1	2	yes	complemented
456	#498	C₂²×C₁₃	1	2	yes	complemented
457	#485	C₂²×C₁₃	1	4	yes	complemented
458	#485	C₂²×C₁₃	1	4	yes	complemented
459	#484	C₂²×C₁₃	1	4	yes	complemented
460	#484	C₂²×C₁₃	1	4	yes	complemented
461	#483	C₂²×C₁₃	1	4	yes	complemented
462	#483	C₂²×C₁₃	1	4	yes	complemented
463	#481	C₂²×C₁₃	1	4	yes	complemented
464	#480	C₂²×C₁₃	1	4	yes	complemented
465	#479	C₂²×C₁₃	1	4	yes	complemented
466	#477	C₂²×C₁₃	1	2	yes	complemented
467	#477	C₂²×C₁₃	1	2	yes	complemented
468	#476	C₂²×C₁₃	1	2	yes	complemented
469	#475	C₂²×C₁₃	1	2	yes	complemented
470	#475	C₂²×C₁₃	1	2	yes	complemented
471	#474	C₂²×C₁₃	1	2	yes	complemented
472	#470	C₂²×C₁₃	1	4	yes	complemented
473	#468	C₂²×C₁₃	1	4	yes	complemented
474	#467	C₂²×C₁₃	1	4	yes	complemented
475	#465	C₂²×C₁₃	1	4	yes	complemented
476	#441	C₂²×C₁₃	1	2	yes	complemented
477	#440	C₂²×C₁₃	1	2	yes	complemented
478	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
479	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
480	#436	C₂²×C₁₃	1	2	yes	—
481	#435	C₂²×C₁₃	1	4	yes	—
482	C₈×D₄	C₂²×C₁₃	1	2	yes	—
483	#428	C₂²×C₁₃	1	2	yes	—
484	#428	C₂²×C₁₃	1	2	yes	—
485	#428	C₂²×C₁₃	1	2	yes	—
486	#428	C₂²×C₁₃	1	2	yes	—
487	#428	C₂²×C₁₃	1	1	yes	characteristic
488	#428	C₂²×C₁₃	1	4	yes	complemented
489	#428	C₂²×C₁₃	1	4	yes	complemented
490	C₂×#107	C₂²×C₁₃	1	4	yes	complemented
491	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
492	#423	C₂²×C₁₃	1	1	yes	characteristic
493	#419	C₂²×C₁₃	1	2	yes	—
494	#419	C₂²×C₁₃	1	1	yes	characteristic
495	#417	C₂²×C₁₃	1	2	yes	—
496	#417	C₂²×C₁₃	1	1	yes	characteristic
497	#407	C₂²×C₁₃	1	2	yes	—
498	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	2	no	—
501	C₂²×C₁₃	—	2	2	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	4	8	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	#547	1	2	yes	—
511	C₂²×C₁₃	C₂×#137	1	4	yes	—
512	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	4	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	#547	1	2	yes	—
527	C₄×C₁₃	C₂×#137	1	2	yes	—
528	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
529	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₂×#41	—	2	1	no	—
531	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×Q₈	—	2	1	no	—
533	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
535	C₂³×C₄	—	2	2	no	—
536	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
537	#137	—	2	4	no	—
538	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
540	C₂×M₁₆	—	2	8	no	—
541	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
542	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
543	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	—	2	2	no	—
557	#125	—	2	4	no	—
558	#125	—	2	2	no	—
559	#125	—	2	1	no	—
560	#125	C₂³×C₁₃	1	2	yes	—
561	#124	—	2	1	no	—
562	#124	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	4	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
578	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
579	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
580	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
581	#121	—	2	2	no	—
582	#121	—	2	1	no	—
583	#121	C₂³×C₁₃	1	2	yes	—
584	#121	C₂³×C₁₃	1	2	yes	—
585	#120	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
605	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
606	C₄×D₄	D₄×C₁₃	1	2	yes	—
607	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	#117	—	2	2	no	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	—	2	2	no	—
616	#117	—	2	1	no	—
617	#117	C₂³×C₁₃	1	1	yes	characteristic
618	#117	C₂³×C₁₃	1	2	yes	—
619	#117	C₂³×C₁₃	1	2	yes	—
620	#117	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	2	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	2	no	—
627	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
641	#107	C₂³×C₁₃	1	2	yes	—
642	#107	C₂³×C₁₃	1	4	yes	—
643	#107	C₂³×C₁₃	1	4	yes	—
644	#107	C₂³×C₁₃	1	4	yes	—
645	#107	C₂³×C₁₃	1	4	yes	—
646	#106	C₂³×C₁₃	1	2	yes	—
647	#106	C₂³×C₁₃	1	4	yes	—
648	#106	C₂³×C₁₃	1	4	yes	—
649	#106	C₂³×C₁₃	1	4	yes	—
650	#106	C₂³×C₁₃	1	4	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
652	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
653	#103	C₂³×C₁₃	1	2	yes	—
654	#103	C₂³×C₁₃	1	4	yes	—
655	#103	C₂³×C₁₃	1	2	yes	—
656	#103	C₂³×C₁₃	1	2	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#102	C₂³×C₁₃	1	2	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
662	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
663	#97	C₂³×C₁₃	1	2	yes	—
664	C₄×C₈	C₂³×C₁₃	1	2	yes	—
665	C₂×C₁₃	—	2	2	no	—
666	C₂×C₁₃	—	2	4	no	—
667	C₂×C₁₃	—	4	2	no	—
668	C₂×C₁₃	—	8	1	no	—
669	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
670	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
671	C₂×C₁₃	#3585	1	1	yes	characteristic
672	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
673	#41	—	2	2	no	—
674	#41	—	2	2	no	—
675	#41	—	4	4	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	8	2	no	—
684	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	8	4	no	—
707	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
709	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
715	Q₁₆	—	2	4	no	—
716	SD₁₆	—	2	4	no	—
717	M₁₆	—	2	4	no	—
718	M₁₆	—	2	2	no	—
719	M₁₆	—	2	8	no	—
720	M₁₆	C₁₃×#41	1	4	yes	complemented
721	C₂×C₈	—	2	8	no	—
722	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
723	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
724	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₁₃	#61254	1	1	yes	characteristic, direct product factor, Sylow
783	C₂³	—	2	4	no	—
784	C₂³	—	2	4	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
788	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	1	no	—
794	Q₈	—	4	2	no	—
795	Q₈	—	4	2	no	—
796	Q₈	—	8	2	no	—
797	Q₈	—	8	2	no	—
798	Q₈	—	8	1	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	1	no	—
802	D₄	—	2	1	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	4	no	—
805	D₄	—	8	2	no	—
806	D₄	C₁₃×#137	1	4	yes	complemented
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	8	1	no	—
831	C₂×C₄	—	8	4	no	—
832	C₂×C₄	—	8	4	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
842	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
843	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
844	C₈	—	2	4	no	—
845	C₈	—	2	2	no	—
846	C₈	C₂×C₁₃×#41	1	4	yes	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	8	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	C₁₃×#547	1	2	yes	—
859	C₂²	C₂×C₁₃×#137	1	4	yes	—
860	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	4	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	C₁₃×#547	1	2	yes	—
875	C₄	C₂×C₁₃×#137	1	2	yes	—
876	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
877	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂	—	2	2	no	—
879	C₂	—	2	4	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	1	no	—
882	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
883	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
884	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3357	C₂	semidirect
4. C₁₃×#3356	C₂	semidirect
5. C₁₃×#3346	C₂	semidirect
6. C₁₃×#3344	C₂	semidirect
7. C₁₃×#3338	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3095	C₂	semidirect
11. C₁₃×#3092	C₂	semidirect
12. C₁₃×#3079	C₂	semidirect
13. C₁₃×#3078	C₂	semidirect
14. C₁₃×#3056	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₂×C₁₃×#428	C₂	semidirect
50. C₁₃×#501	C₂²	semidirect
51. C₁₃×#500	C₂²	semidirect
52. C₁₃×#498	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#484	C₂²	semidirect
56. C₁₃×#484	C₂²	semidirect
57. C₁₃×#483	C₂²	semidirect
58. C₁₃×#483	C₂²	semidirect
59. C₁₃×#481	C₂²	semidirect
60. C₁₃×#480	C₂²	semidirect
61. C₁₃×#479	C₂²	semidirect
62. C₁₃×#477	C₂²	semidirect
63. C₁₃×#477	C₂²	semidirect
64. C₁₃×#476	C₂²	semidirect
65. C₁₃×#475	C₂²	semidirect
66. C₁₃×#475	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#470	C₂²	semidirect
69. C₁₃×#468	C₂²	semidirect
70. C₁₃×#467	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
72. C₁₃×#441	C₂²	semidirect
73. C₁₃×#440	C₂²	semidirect
74. C₄×C₁₃×Q₁₆	C₂²	semidirect
75. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₁₃×#428	C₂²	semidirect
85. C₁₃×#428	C₂²	semidirect
86. C₂×C₁₃×#107	C₂²	semidirect
87. C₂×C₁₃×#106	C₂²	semidirect
230. #61254	C₁₃	direct (N × H)
279. C₁₃×M₁₆	#41	semidirect
342. C₂×#554	C₂×C₁₃	semidirect
343. #3357	C₂×C₁₃	semidirect
344. #3356	C₂×C₁₃	semidirect
345. #3346	C₂×C₁₃	semidirect
346. #3344	C₂×C₁₃	semidirect
347. #3338	C₂×C₁₃	semidirect
348. #3335	C₂×C₁₃	semidirect
349. #3165	C₂×C₁₃	semidirect
350. #3095	C₂×C₁₃	semidirect
351. #3092	C₂×C₁₃	semidirect
352. #3079	C₂×C₁₃	semidirect
353. #3078	C₂×C₁₃	semidirect
354. #3056	C₂×C₁₃	semidirect
355. C₄×#137	C₂×C₁₃	semidirect
356. D₄×M₁₆	C₂×C₁₃	semidirect
357. C₂×#428	C₂×C₁₃	semidirect
381. D₄×C₁₃	#137	semidirect
454. #501	C₂²×C₁₃	semidirect
455. #500	C₂²×C₁₃	semidirect
456. #498	C₂²×C₁₃	semidirect
457. #485	C₂²×C₁₃	semidirect
458. #485	C₂²×C₁₃	semidirect
459. #484	C₂²×C₁₃	semidirect
460. #484	C₂²×C₁₃	semidirect
461. #483	C₂²×C₁₃	semidirect
462. #483	C₂²×C₁₃	semidirect
463. #481	C₂²×C₁₃	semidirect
464. #480	C₂²×C₁₃	semidirect
465. #479	C₂²×C₁₃	semidirect
466. #477	C₂²×C₁₃	semidirect
467. #477	C₂²×C₁₃	semidirect
468. #476	C₂²×C₁₃	semidirect
469. #475	C₂²×C₁₃	semidirect
470. #475	C₂²×C₁₃	semidirect
471. #474	C₂²×C₁₃	semidirect
472. #470	C₂²×C₁₃	semidirect
473. #468	C₂²×C₁₃	semidirect
474. #467	C₂²×C₁₃	semidirect
475. #465	C₂²×C₁₃	semidirect
476. #441	C₂²×C₁₃	semidirect
477. #440	C₂²×C₁₃	semidirect
478. C₄×Q₁₆	C₂²×C₁₃	semidirect
479. C₄×SD₁₆	C₂²×C₁₃	semidirect
488. #428	C₂²×C₁₃	semidirect
489. #428	C₂²×C₁₃	semidirect
490. C₂×#107	C₂²×C₁₃	semidirect
491. C₂×#106	C₂²×C₁₃	semidirect
720. M₁₆	C₁₃×#41	semidirect
782. C₁₃	#61254	direct (N × H)
806. D₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3475	2
C₂×C₁₃×#554	2
C₁₃×#3357	2
C₁₃×#3356	2
C₁₃×#3346	2
C₁₃×#3344	2
C₁₃×#3338	2
C₁₃×#3335	2
C₁₃×#3165	2
C₁₃×#3095	2
C₁₃×#3092	2
C₁₃×#3079	2
C₁₃×#3078	2
C₁₃×#3056	2
C₄×C₁₃×#137	2
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#428	2
#61254	13

Subgroups — C13×#61254 #15747593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61254 #15747593