Subgroups — C₁₃×#61954 #15748293

Order 3328.

1868 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3301	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3285	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	4	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	C₂²	1	1	yes	characteristic
22	C₁₃×#557	C₂²	1	1	yes	characteristic
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#556	C₂²	1	1	yes	characteristic
26	C₁₃×#555	—	2	1	no	—
27	C₁₃×#554	—	2	1	no	—
28	C₁₃×#553	—	2	2	no	—
29	C₁₃×#553	—	2	2	no	—
30	C₁₃×#553	C₂²	1	2	yes	—
31	C₁₃×#550	C₂²	1	1	yes	characteristic
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#548	C₂²	1	4	yes	—
34	C₁₃×#547	C₂²	1	2	yes	—
35	C₁₃×#542	—	2	2	no	—
36	C₁₃×#537	—	2	1	no	—
37	C₁₃×#533	C₂²	1	2	yes	—
38	C₁₃×#532	—	2	1	no	—
39	C₁₃×#532	C₂²	1	2	yes	—
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×#529	—	2	2	no	—
44	C₁₃×#529	C₂²	1	2	yes	—
45	C₁₃×#520	—	2	1	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#495	C₂²	1	4	yes	—
51	C₁₃×#492	C₂²	1	2	yes	—
52	C₁₃×#488	C₂²	1	4	yes	—
53	C₁₃×#487	C₂²	1	2	yes	—
54	C₁₃×#485	C₂²	1	4	yes	—
55	C₁₃×#481	C₂²	1	2	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#475	C₂²	1	1	yes	characteristic
58	C₁₃×#475	C₂²	1	1	yes	characteristic
59	C₁₃×#474	C₂²	1	2	yes	—
60	C₁₃×#474	C₂²	1	2	yes	—
61	C₁₃×#467	C₂²	1	4	yes	—
62	C₁₃×#466	C₂²	1	4	yes	—
63	C₁₃×#465	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#464	C₂²	1	4	yes	—
66	C₁₃×#463	C₂²	1	4	yes	—
67	C₁₃×#462	C₂²	1	2	yes	—
68	C₁₃×#462	C₂²	1	2	yes	—
69	C₁₃×#462	C₂²	1	2	yes	—
70	C₁₃×#462	C₂²	1	2	yes	—
71	C₁₃×#461	C₂²	1	2	yes	—
72	C₁₃×#461	C₂²	1	2	yes	—
73	C₁₃×#460	C₂²	1	1	yes	characteristic
74	C₁₃×#460	C₂²	1	1	yes	characteristic
75	C₁₃×#459	C₂²	1	2	yes	—
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	4	yes	—
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#449	C₂²	1	4	yes	—
80	C₁₃×#448	C₂²	1	2	yes	—
81	C₁₃×#448	C₂²	1	4	yes	—
82	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
83	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
87	C₈×D₄×C₁₃	C₂²	1	2	yes	—
88	C₈×D₄×C₁₃	C₂²	1	4	yes	—
89	C₁₃×#431	C₂²	1	1	yes	characteristic
90	C₁₃×#431	C₂²	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	4	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂×C₁₃×#41	C₂³	1	4	yes	—
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
102	C₁₃×#135	—	4	8	no	—
103	C₂×C₁₃×Q₁₆	—	4	4	no	—
104	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	1	no	—
121	C₁₃×#127	C₂³	1	1	yes	characteristic
122	C₁₃×#127	C₂³	1	1	yes	characteristic
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	4	no	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	—	2	1	no	—
136	C₁₃×#124	C₂³	1	4	yes	—
137	C₁₃×#124	C₂³	1	2	yes	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	4	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	4	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	D₄	1	2	yes	—
186	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	D₄	1	1	yes	characteristic
197	C₁₃×#117	D₄	1	2	yes	—
198	C₁₃×#117	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	2	2	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	4	yes	—
230	#61954	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	4	2	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	4	1	no	—
244	C₂×Q₈×C₁₃	—	4	2	no	—
245	C₂×Q₈×C₁₃	—	4	2	no	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₁₃×Q₁₆	—	2	8	no	—
278	C₁₃×Q₁₆	—	4	4	no	—
279	C₁₃×SD₁₆	—	2	4	no	—
280	C₁₃×SD₁₆	—	4	4	no	—
281	C₁₃×SD₁₆	—	4	2	no	—
282	C₁₃×SD₁₆	—	4	4	no	—
283	C₁₃×D₈	—	4	4	no	—
284	C₂×C₈×C₁₃	—	4	2	no	—
285	C₂×C₈×C₁₃	—	4	4	no	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
288	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	2	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	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	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	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	—	2	1	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	1	no	—
336	C₄²×C₁₃	—	2	4	no	—
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂×D₄	1	2	yes	—
339	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
344	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3394	C₂×C₁₃	1	2	yes	complemented
347	#3364	C₂×C₁₃	1	2	yes	complemented
348	#3302	C₂×C₁₃	1	2	yes	complemented
349	#3301	C₂×C₁₃	1	4	yes	complemented
350	#3285	C₂×C₁₃	1	4	yes	complemented
351	#3284	C₂×C₁₃	1	2	yes	complemented
352	#3248	C₂×C₁₃	1	2	yes	complemented
353	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3212	C₂×C₁₃	1	2	yes	complemented
355	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3107	C₂×C₁₃	1	2	yes	complemented
357	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3035	C₂×C₁₃	1	2	yes	complemented
359	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
364	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	1	no	—
367	Q₈×C₁₃	—	2	4	no	—
368	Q₈×C₁₃	—	2	1	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	4	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	4	2	no	—
374	Q₈×C₁₃	—	8	2	no	—
375	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
376	D₄×C₁₃	—	2	4	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	4	4	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	4	4	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	8	1	no	—
389	D₄×C₁₃	—	8	2	no	—
390	D₄×C₁₃	—	8	4	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	4	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	4	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	8	2	no	—
410	C₂×C₄×C₁₃	—	8	4	no	—
411	C₂×C₄×C₁₃	—	8	1	no	—
412	C₂×C₄×C₁₃	—	8	2	no	—
413	C₂×C₄×C₁₃	#135	1	4	yes	complemented
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
423	C₈×C₁₃	—	2	4	no	—
424	C₈×C₁₃	—	2	2	no	—
425	C₈×C₁₃	—	2	2	no	—
426	C₂×#135	C₂²×C₁₃	1	4	yes	—
427	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
428	#559	—	2	1	no	—
429	#559	C₂²×C₁₃	1	1	yes	characteristic
430	#557	C₂²×C₁₃	1	1	yes	characteristic
431	#556	—	2	1	no	—
432	#556	C₂²×C₁₃	1	2	yes	—
433	#556	C₂²×C₁₃	1	1	yes	characteristic
434	#555	—	2	1	no	—
435	#554	—	2	1	no	—
436	#553	—	2	2	no	—
437	#553	—	2	2	no	—
438	#553	C₂²×C₁₃	1	2	yes	—
439	#550	C₂²×C₁₃	1	1	yes	characteristic
440	#548	C₂²×C₁₃	1	2	yes	—
441	#548	C₂²×C₁₃	1	4	yes	—
442	#547	C₂²×C₁₃	1	2	yes	—
443	#542	—	2	2	no	—
444	#537	—	2	1	no	—
445	#533	C₂²×C₁₃	1	2	yes	—
446	#532	—	2	1	no	—
447	#532	C₂²×C₁₃	1	2	yes	—
448	#532	C₂²×C₁₃	1	1	yes	characteristic
449	#532	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	#529	—	2	2	no	—
452	#529	C₂²×C₁₃	1	2	yes	—
453	#520	—	2	1	no	—
454	C₄×#41	—	2	1	no	—
455	C₄×#41	C₂²×C₁₃	1	2	yes	—
456	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
458	#495	C₂²×C₁₃	1	4	yes	—
459	#492	C₂²×C₁₃	1	2	yes	—
460	#488	C₂²×C₁₃	1	4	yes	—
461	#487	C₂²×C₁₃	1	2	yes	—
462	#485	C₂²×C₁₃	1	4	yes	—
463	#481	C₂²×C₁₃	1	2	yes	—
464	#479	C₂²×C₁₃	1	4	yes	—
465	#475	C₂²×C₁₃	1	1	yes	characteristic
466	#475	C₂²×C₁₃	1	1	yes	characteristic
467	#474	C₂²×C₁₃	1	2	yes	—
468	#474	C₂²×C₁₃	1	2	yes	—
469	#467	C₂²×C₁₃	1	4	yes	—
470	#466	C₂²×C₁₃	1	4	yes	—
471	#465	C₂²×C₁₃	1	4	yes	—
472	#464	C₂²×C₁₃	1	4	yes	—
473	#464	C₂²×C₁₃	1	4	yes	—
474	#463	C₂²×C₁₃	1	4	yes	—
475	#462	C₂²×C₁₃	1	2	yes	—
476	#462	C₂²×C₁₃	1	2	yes	—
477	#462	C₂²×C₁₃	1	2	yes	—
478	#462	C₂²×C₁₃	1	2	yes	—
479	#461	C₂²×C₁₃	1	2	yes	—
480	#461	C₂²×C₁₃	1	2	yes	—
481	#460	C₂²×C₁₃	1	1	yes	characteristic
482	#460	C₂²×C₁₃	1	1	yes	characteristic
483	#459	C₂²×C₁₃	1	2	yes	—
484	#459	C₂²×C₁₃	1	2	yes	—
485	#452	C₂²×C₁₃	1	4	yes	—
486	#452	C₂²×C₁₃	1	4	yes	—
487	#449	C₂²×C₁₃	1	4	yes	—
488	#448	C₂²×C₁₃	1	2	yes	—
489	#448	C₂²×C₁₃	1	4	yes	—
490	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
491	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
492	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
493	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
494	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
495	C₈×D₄	C₂²×C₁₃	1	2	yes	—
496	C₈×D₄	C₂²×C₁₃	1	4	yes	—
497	#431	C₂²×C₁₃	1	1	yes	characteristic
498	#431	C₂²×C₁₃	1	2	yes	—
499	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
501	#416	C₂²×C₁₃	1	4	yes	—
502	C₂×#103	C₂²×C₁₃	1	2	yes	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	C₂×#135	1	2	yes	—
515	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	4	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	C₂×#135	1	2	yes	—
530	C₄×C₁₃	C₂×#135	1	2	yes	—
531	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₄×C₁₃	#585	1	1	yes	characteristic
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	1	no	—
535	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
536	C₂×#41	C₂³×C₁₃	1	2	yes	—
537	C₂×#41	C₂³×C₁₃	1	4	yes	—
538	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
540	#135	—	4	8	no	—
541	C₂×Q₁₆	—	4	4	no	—
542	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
543	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
546	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
548	C₂×D₈	C₂³×C₁₃	1	4	yes	—
549	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
550	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	#127	—	2	1	no	—
559	#127	C₂³×C₁₃	1	1	yes	characteristic
560	#127	C₂³×C₁₃	1	1	yes	characteristic
561	#126	—	2	2	no	—
562	#126	—	2	4	no	—
563	#126	—	2	2	no	—
564	#126	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	—	2	2	no	—
567	#125	C₂³×C₁₃	1	2	yes	—
568	#124	—	2	1	no	—
569	#124	—	2	1	no	—
570	#124	—	2	2	no	—
571	#124	—	2	4	no	—
572	#124	—	2	1	no	—
573	#124	—	2	1	no	—
574	#124	C₂³×C₁₃	1	2	yes	—
575	#124	C₂³×C₁₃	1	4	yes	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	4	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	C₂³×C₁₃	1	2	yes	—
596	#121	C₂³×C₁₃	1	2	yes	—
597	#121	C₂³×C₁₃	1	2	yes	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
609	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
610	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	4	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	D₄×C₁₃	1	2	yes	—
624	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₁₃	1	2	yes	—
626	C₄×D₄	C₂³×C₁₃	1	2	yes	—
627	C₄×D₄	C₂³×C₁₃	1	2	yes	—
628	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₁₃	1	2	yes	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	D₄×C₁₃	1	1	yes	characteristic
635	#117	D₄×C₁₃	1	2	yes	—
636	#117	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	2	no	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	2	no	—
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	#107	C₂³×C₁₃	1	4	yes	—
647	#106	C₂³×C₁₃	1	2	yes	—
648	#106	C₂³×C₁₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
652	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
654	#103	C₂³×C₁₃	1	4	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	2	yes	—
658	#103	C₂³×C₁₃	1	2	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	2	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	#102	C₂³×C₁₃	1	2	yes	—
663	#102	C₂³×C₁₃	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
666	C₄×C₈	C₂³×C₁₃	1	2	yes	—
667	C₄×C₈	C₂³×C₁₃	1	4	yes	—
668	C₂×C₁₃	—	2	2	no	—
669	C₂×C₁₃	—	4	2	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	—	8	2	no	—
672	C₂×C₁₃	#3488	1	1	yes	characteristic
673	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
674	C₂×C₁₃	#3586	1	1	yes	characteristic
675	#41	—	2	4	no	—
676	#41	—	2	4	no	—
677	#41	—	4	2	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	1	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
692	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
706	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	Q₁₆	—	2	8	no	—
722	Q₁₆	—	4	4	no	—
723	SD₁₆	—	2	4	no	—
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	2	no	—
727	D₈	—	4	4	no	—
728	C₂×C₈	—	4	2	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
732	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	1	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	4	no	—
781	C₄²	C₂×D₄×C₁₃	1	2	yes	—
782	C₄²	C₂×D₄×C₁₃	1	2	yes	—
783	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
784	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₁₃	1	2	yes	—
787	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₁₃	#61954	1	1	yes	characteristic, direct product factor, Sylow
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
792	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	4	no	—
799	Q₈	—	4	2	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	4	2	no	—
802	Q₈	—	8	2	no	—
803	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	8	1	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₁₃×#135	1	4	yes	complemented
842	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	C₂×C₁₃×#135	1	2	yes	—
866	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	4	no	—
880	C₄	C₂×C₁₃×#135	1	2	yes	—
881	C₄	C₂×C₁₃×#135	1	2	yes	—
882	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
883	C₄	C₁₃×#585	1	1	yes	characteristic
884	C₂	—	2	2	no	—
885	C₂	—	4	2	no	—
886	C₂	—	8	2	no	—
887	C₂	—	8	2	no	—
888	C₂	C₁₃×#3488	1	1	yes	characteristic
889	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
890	C₂	C₁₃×#3586	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3394	C₂	semidirect
4. C₁₃×#3364	C₂	semidirect
5. C₁₃×#3302	C₂	semidirect
6. C₁₃×#3301	C₂	semidirect
7. C₁₃×#3285	C₂	semidirect
8. C₁₃×#3284	C₂	semidirect
9. C₁₃×#3248	C₂	semidirect
10. C₁₃×#3245	C₂	semidirect
11. C₁₃×#3212	C₂	semidirect
12. C₁₃×#3206	C₂	semidirect
13. C₁₃×#3107	C₂	semidirect
14. C₁₃×#3103	C₂	semidirect
15. C₁₃×#3035	C₂	semidirect
16. C₂×C₁₃×#462	C₂	semidirect
17. C₁₃×#2988	C₂	semidirect
230. #61954	C₁₃	direct (N × H)
344. #3511	C₂×C₁₃	semidirect
345. #3480	C₂×C₁₃	semidirect
346. #3394	C₂×C₁₃	semidirect
347. #3364	C₂×C₁₃	semidirect
348. #3302	C₂×C₁₃	semidirect
349. #3301	C₂×C₁₃	semidirect
350. #3285	C₂×C₁₃	semidirect
351. #3284	C₂×C₁₃	semidirect
352. #3248	C₂×C₁₃	semidirect
353. #3245	C₂×C₁₃	semidirect
354. #3212	C₂×C₁₃	semidirect
355. #3206	C₂×C₁₃	semidirect
356. #3107	C₂×C₁₃	semidirect
357. #3103	C₂×C₁₃	semidirect
358. #3035	C₂×C₁₃	semidirect
359. C₂×#462	C₂×C₁₃	semidirect
360. #2988	C₂×C₁₃	semidirect
413. C₂×C₄×C₁₃	#135	semidirect
788. C₁₃	#61954	direct (N × H)
841. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3480	2
C₁₃×#3394	2
C₁₃×#3364	2
C₁₃×#3302	2
C₁₃×#3301	2
C₁₃×#3285	2
C₁₃×#3284	2
C₁₃×#3248	2
C₁₃×#3245	2
C₁₃×#3212	2
C₁₃×#3206	2
C₁₃×#3107	2
C₁₃×#3103	2
C₁₃×#3035	2
C₂×C₁₃×#462	2
C₁₃×#2988	2
#61954	13

Subgroups — C13×#61954 #15748293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61954 #15748293