Subgroups — C₁₃×#61667 #15748006

Order 3328.

2064 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3331	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3330	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3283	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3013	C₂	1	4	yes	maximal, complemented
17	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	4	yes	—
20	C₂×C₁₃×#135	C₂²	1	4	yes	—
21	C₁₃×#562	—	2	2	no	—
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#550	—	2	1	no	—
25	C₁₃×#550	C₂²	1	2	yes	—
26	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#547	—	2	2	no	—
29	C₁₃×#547	—	2	2	no	—
30	C₁₃×#547	C₂²	1	2	yes	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#547	C₂²	1	2	yes	—
33	C₁₃×#547	C₂²	1	2	yes	—
34	C₁₃×#540	—	2	2	no	—
35	C₁₃×#537	—	2	2	no	—
36	C₁₃×#537	C₂²	1	4	yes	—
37	C₁₃×#536	—	2	2	no	—
38	C₁₃×#536	C₂²	1	2	yes	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₁₃×#494	C₂²	1	2	yes	—
47	C₁₃×#492	C₂²	1	2	yes	—
48	C₁₃×#487	C₂²	1	2	yes	—
49	C₁₃×#487	C₂²	1	2	yes	—
50	C₁₃×#485	C₂²	1	2	yes	—
51	C₁₃×#484	C₂²	1	4	yes	—
52	C₁₃×#483	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	2	yes	—
54	C₁₃×#477	C₂²	1	1	yes	characteristic
55	C₁₃×#476	C₂²	1	1	yes	characteristic
56	C₁₃×#475	C₂²	1	1	yes	characteristic
57	C₁₃×#474	C₂²	1	1	yes	characteristic
58	C₁₃×#470	C₂²	1	4	yes	—
59	C₁₃×#468	C₂²	1	4	yes	—
60	C₁₃×#467	C₂²	1	4	yes	—
61	C₁₃×#465	C₂²	1	4	yes	—
62	C₁₃×#462	C₂²	1	1	yes	characteristic
63	C₁₃×#462	C₂²	1	2	yes	—
64	C₁₃×#462	C₂²	1	2	yes	—
65	C₁₃×#461	C₂²	1	2	yes	—
66	C₁₃×#461	C₂²	1	1	yes	characteristic
67	C₁₃×#461	C₂²	1	2	yes	—
68	C₁₃×#460	C₂²	1	1	yes	characteristic
69	C₁₃×#459	C₂²	1	1	yes	characteristic
70	C₁₃×#452	C₂²	1	2	yes	—
71	C₁₃×#452	C₂²	1	4	yes	—
72	C₁₃×#452	C₂²	1	4	yes	—
73	C₁₃×#452	C₂²	1	4	yes	—
74	C₁₃×#451	C₂²	1	4	yes	—
75	C₁₃×#451	C₂²	1	4	yes	—
76	C₁₃×#449	C₂²	1	2	yes	—
77	C₁₃×#449	C₂²	1	4	yes	—
78	C₁₃×#448	C₂²	1	4	yes	—
79	C₁₃×#448	C₂²	1	4	yes	—
80	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
82	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
83	C₄×C₁₃×D₈	C₂²	1	2	yes	—
84	C₁₃×#436	C₂²	1	2	yes	—
85	C₁₃×#436	C₂²	1	2	yes	—
86	C₈×D₄×C₁₃	C₂²	1	2	yes	—
87	C₈×D₄×C₁₃	C₂²	1	2	yes	—
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#431	C₂²	1	1	yes	characteristic
90	C₁₃×#417	C₂²	1	4	yes	—
91	C₂×C₁₃×#103	C₂²	1	4	yes	—
92	C₁₃×#408	C₂²	1	4	yes	—
93	C₁₃×2₋¹⁺⁴	—	4	4	no	—
94	C₁₃×2₋¹⁺⁴	—	4	4	no	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	4	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×#41	C₂³	1	4	yes	—
101	C₂×C₁₃×#41	C₂³	1	4	yes	—
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂²×Q₈×C₁₃	—	2	2	no	—
104	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₁₃×#137	—	4	8	no	—
107	C₁₃×#135	—	4	8	no	—
108	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×D₈	C₂³	1	2	yes	—
116	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
117	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
118	C₁₃×C₄⋊Q₈	—	2	2	no	—
119	C₁₃×C₄⋊Q₈	—	2	2	no	—
120	C₁₃×C₄⋊Q₈	—	2	2	no	—
121	C₁₃×C₄⋊Q₈	—	2	1	no	—
122	C₁₃×C₄⋊Q₈	—	2	1	no	—
123	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
124	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₁₃×#127	—	2	2	no	—
130	C₁₃×#127	D₄	1	1	yes	characteristic
131	C₁₃×#127	C₂³	1	1	yes	characteristic
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	—	2	1	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	—	2	1	no	—
136	C₁₃×#124	D₄	1	2	yes	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×#123	—	2	4	no	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	4	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	4	no	—
155	C₁₃×#121	—	2	4	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	4	no	—
160	C₁₃×#121	D₄	1	2	yes	—
161	C₁₃×#121	D₄	1	2	yes	—
162	C₁₃×#121	C₂³	1	2	yes	—
163	C₁₃×#121	C₂³	1	4	yes	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	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	1	no	—
175	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₁₃×#117	—	2	1	no	—
181	C₁₃×#117	—	2	1	no	—
182	C₁₃×#117	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₄²×C₁₃	—	2	1	no	—
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₁₃×#107	C₂³	1	2	yes	—
192	C₁₃×#107	C₂³	1	2	yes	—
193	C₁₃×#106	C₂³	1	2	yes	—
194	C₁₃×#106	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
196	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
197	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	2	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
215	C₄×C₈×C₁₃	C₂³	1	2	yes	—
216	C₄×C₈×C₁₃	C₂³	1	2	yes	—
217	#61667	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₁₃×#41	—	2	2	no	—
219	C₁₃×#41	—	2	2	no	—
220	C₁₃×#41	—	2	8	no	—
221	C₁₃×#41	—	4	2	no	—
222	C₁₃×#41	—	4	2	no	—
223	C₁₃×#41	—	4	4	no	—
224	C₁₃×#41	—	4	8	no	—
225	C₁₃×#41	—	4	4	no	—
226	C₁₃×#41	—	4	4	no	—
227	C₁₃×#41	—	4	16	no	—
228	C₁₃×#41	—	8	2	no	—
229	C₁₃×#41	—	8	4	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	2	4	no	—
232	C₂×Q₈×C₁₃	—	2	2	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	8	no	—
235	C₂×Q₈×C₁₃	—	4	4	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	2	no	—
238	C₂×Q₈×C₁₃	—	4	8	no	—
239	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
269	C₁₃×Q₁₆	—	2	4	no	—
270	C₁₃×Q₁₆	—	4	4	no	—
271	C₁₃×Q₁₆	—	4	4	no	—
272	C₁₃×SD₁₆	—	2	4	no	—
273	C₁₃×SD₁₆	—	2	4	no	—
274	C₁₃×SD₁₆	—	4	4	no	—
275	C₁₃×SD₁₆	—	4	4	no	—
276	C₁₃×D₈	—	2	4	no	—
277	C₁₃×M₁₆	—	4	4	no	—
278	C₂×C₈×C₁₃	—	4	4	no	—
279	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
281	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	1	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	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
316	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
317	C₄²×C₁₃	—	2	1	no	—
318	C₄²×C₁₃	—	2	1	no	—
319	C₄²×C₁₃	—	2	1	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
325	#3548	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3331	C₂×C₁₃	1	2	yes	complemented
328	#3330	C₂×C₁₃	1	2	yes	complemented
329	#3299	C₂×C₁₃	1	2	yes	complemented
330	#3298	C₂×C₁₃	1	2	yes	complemented
331	#3284	C₂×C₁₃	1	2	yes	complemented
332	#3283	C₂×C₁₃	1	2	yes	complemented
333	#3278	C₂×C₁₃	1	2	yes	complemented
334	#3276	C₂×C₁₃	1	2	yes	complemented
335	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3201	C₂×C₁₃	1	4	yes	complemented
338	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3013	C₂×C₁₃	1	4	yes	complemented
341	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
345	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₁₃	—	2	1	no	—
347	Q₈×C₁₃	—	2	2	no	—
348	Q₈×C₁₃	—	2	4	no	—
349	Q₈×C₁₃	—	2	4	no	—
350	Q₈×C₁₃	—	2	2	no	—
351	Q₈×C₁₃	—	4	2	no	—
352	Q₈×C₁₃	—	4	8	no	—
353	Q₈×C₁₃	—	4	4	no	—
354	Q₈×C₁₃	—	4	2	no	—
355	Q₈×C₁₃	—	8	1	no	—
356	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
357	D₄×C₁₃	—	2	4	no	—
358	D₄×C₁₃	—	2	4	no	—
359	D₄×C₁₃	—	2	4	no	—
360	D₄×C₁₃	—	2	1	no	—
361	D₄×C₁₃	—	2	2	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	4	2	no	—
364	D₄×C₁₃	—	4	4	no	—
365	D₄×C₁₃	—	4	8	no	—
366	D₄×C₁₃	—	4	2	no	—
367	D₄×C₁₃	—	8	1	no	—
368	D₄×C₁₃	—	8	4	no	—
369	D₄×C₁₃	—	8	2	no	—
370	D₄×C₁₃	—	8	4	no	—
371	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
372	C₂×C₄×C₁₃	—	2	4	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	4	8	no	—
387	C₂×C₄×C₁₃	—	4	8	no	—
388	C₂×C₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	8	4	no	—
393	C₂×C₄×C₁₃	—	8	4	no	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
401	C₈×C₁₃	—	2	2	no	—
402	C₈×C₁₃	—	2	2	no	—
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	2	2	no	—
405	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
406	C₂×#137	C₂²×C₁₃	1	4	yes	—
407	C₂×#135	C₂²×C₁₃	1	4	yes	—
408	#562	—	2	2	no	—
409	#554	—	2	1	no	—
410	#554	C₂²×C₁₃	1	2	yes	—
411	#550	—	2	1	no	—
412	#550	C₂²×C₁₃	1	2	yes	—
413	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
414	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
415	#547	—	2	2	no	—
416	#547	—	2	2	no	—
417	#547	C₂²×C₁₃	1	2	yes	—
418	#547	C₂²×C₁₃	1	2	yes	—
419	#547	C₂²×C₁₃	1	2	yes	—
420	#547	C₂²×C₁₃	1	2	yes	—
421	#540	—	2	2	no	—
422	#537	—	2	2	no	—
423	#537	C₂²×C₁₃	1	4	yes	—
424	#536	—	2	2	no	—
425	#536	C₂²×C₁₃	1	2	yes	—
426	#533	C₂²×C₁₃	1	1	yes	characteristic
427	#532	—	2	1	no	—
428	#532	C₂²×C₁₃	1	1	yes	characteristic
429	#532	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	—	2	1	no	—
431	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
432	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
433	#494	C₂²×C₁₃	1	2	yes	—
434	#492	C₂²×C₁₃	1	2	yes	—
435	#487	C₂²×C₁₃	1	2	yes	—
436	#487	C₂²×C₁₃	1	2	yes	—
437	#485	C₂²×C₁₃	1	2	yes	—
438	#484	C₂²×C₁₃	1	4	yes	—
439	#483	C₂²×C₁₃	1	4	yes	—
440	#482	C₂²×C₁₃	1	2	yes	—
441	#477	C₂²×C₁₃	1	1	yes	characteristic
442	#476	C₂²×C₁₃	1	1	yes	characteristic
443	#475	C₂²×C₁₃	1	1	yes	characteristic
444	#474	C₂²×C₁₃	1	1	yes	characteristic
445	#470	C₂²×C₁₃	1	4	yes	—
446	#468	C₂²×C₁₃	1	4	yes	—
447	#467	C₂²×C₁₃	1	4	yes	—
448	#465	C₂²×C₁₃	1	4	yes	—
449	#462	C₂²×C₁₃	1	2	yes	—
450	#462	C₂²×C₁₃	1	1	yes	characteristic
451	#462	C₂²×C₁₃	1	2	yes	—
452	#461	C₂²×C₁₃	1	2	yes	—
453	#461	C₂²×C₁₃	1	1	yes	characteristic
454	#461	C₂²×C₁₃	1	2	yes	—
455	#460	C₂²×C₁₃	1	1	yes	characteristic
456	#459	C₂²×C₁₃	1	1	yes	characteristic
457	#452	C₂²×C₁₃	1	4	yes	—
458	#452	C₂²×C₁₃	1	2	yes	—
459	#452	C₂²×C₁₃	1	4	yes	—
460	#452	C₂²×C₁₃	1	4	yes	—
461	#451	C₂²×C₁₃	1	4	yes	—
462	#451	C₂²×C₁₃	1	4	yes	—
463	#449	C₂²×C₁₃	1	4	yes	—
464	#449	C₂²×C₁₃	1	2	yes	—
465	#448	C₂²×C₁₃	1	4	yes	—
466	#448	C₂²×C₁₃	1	4	yes	—
467	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
468	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
469	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
470	C₄×D₈	C₂²×C₁₃	1	2	yes	—
471	#436	C₂²×C₁₃	1	2	yes	—
472	#436	C₂²×C₁₃	1	2	yes	—
473	C₈×D₄	C₂²×C₁₃	1	2	yes	—
474	C₈×D₄	C₂²×C₁₃	1	2	yes	—
475	#431	C₂²×C₁₃	1	1	yes	characteristic
476	#431	C₂²×C₁₃	1	1	yes	characteristic
477	#417	C₂²×C₁₃	1	4	yes	—
478	C₂×#103	C₂²×C₁₃	1	4	yes	—
479	#408	C₂²×C₁₃	1	4	yes	—
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	2	2	no	—
482	C₂²×C₁₃	—	2	4	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	4	no	—
485	C₂²×C₁₃	—	2	1	no	—
486	C₂²×C₁₃	—	2	4	no	—
487	C₂²×C₁₃	—	4	1	no	—
488	C₂²×C₁₃	—	4	1	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	4	2	no	—
492	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	2	4	no	—
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	4	4	no	—
499	C₄×C₁₃	—	4	2	no	—
500	C₄×C₁₃	—	4	1	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	1	no	—
504	C₄×C₁₃	#577	1	2	yes	—
505	C₄×C₁₃	#578	1	2	yes	—
506	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	2₋¹⁺⁴	—	4	4	no	—
509	2₋¹⁺⁴	—	4	4	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	4	no	—
512	C₂×#41	—	2	2	no	—
513	C₂×#41	—	2	1	no	—
514	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×#41	C₂³×C₁₃	1	4	yes	—
516	C₂×#41	C₂³×C₁₃	1	4	yes	—
517	C₂×#41	C₂³×C₁₃	1	2	yes	—
518	C₂²×Q₈	—	2	2	no	—
519	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
520	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
521	#137	—	4	8	no	—
522	#135	—	4	8	no	—
523	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
525	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
526	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
527	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
529	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
530	C₂×D₈	C₂³×C₁₃	1	2	yes	—
531	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
532	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	2	2	no	—
535	C₄⋊Q₈	—	2	2	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
544	#127	—	2	2	no	—
545	#127	D₄×C₁₃	1	1	yes	characteristic
546	#127	C₂³×C₁₃	1	1	yes	characteristic
547	#125	—	2	2	no	—
548	#125	—	2	1	no	—
549	#124	—	2	2	no	—
550	#124	—	2	1	no	—
551	#124	D₄×C₁₃	1	2	yes	—
552	#123	—	2	4	no	—
553	#123	—	2	4	no	—
554	#123	—	2	4	no	—
555	#123	—	2	4	no	—
556	#123	—	2	4	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
564	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
565	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
566	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	—	2	4	no	—
570	#121	—	2	4	no	—
571	#121	—	2	2	no	—
572	#121	—	2	4	no	—
573	#121	—	2	1	no	—
574	#121	—	2	4	no	—
575	#121	D₄×C₁₃	1	2	yes	—
576	#121	D₄×C₁₃	1	2	yes	—
577	#121	C₂³×C₁₃	1	2	yes	—
578	#121	C₂³×C₁₃	1	4	yes	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
582	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×D₄	C₂³×C₁₃	1	2	yes	—
593	C₄×D₄	C₂³×C₁₃	1	2	yes	—
594	C₄×D₄	C₂³×C₁₃	1	2	yes	—
595	#117	—	2	1	no	—
596	#117	—	2	1	no	—
597	#117	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
604	C₂×C₄²	—	2	1	no	—
605	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
606	#107	C₂³×C₁₃	1	2	yes	—
607	#107	C₂³×C₁₃	1	2	yes	—
608	#106	C₂³×C₁₃	1	2	yes	—
609	#106	C₂³×C₁₃	1	2	yes	—
610	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
614	#103	C₂³×C₁₃	1	2	yes	—
615	#103	C₂³×C₁₃	1	2	yes	—
616	#103	C₂³×C₁₃	1	4	yes	—
617	#103	C₂³×C₁₃	1	4	yes	—
618	#103	C₂³×C₁₃	1	4	yes	—
619	#103	C₂³×C₁₃	1	4	yes	—
620	#103	C₂³×C₁₃	1	2	yes	—
621	#103	C₂³×C₁₃	1	2	yes	—
622	#102	C₂³×C₁₃	1	2	yes	—
623	#102	C₂³×C₁₃	1	2	yes	—
624	#102	C₂³×C₁₃	1	2	yes	—
625	#102	C₂³×C₁₃	1	2	yes	—
626	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
627	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
628	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
629	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
630	C₄×C₈	C₂³×C₁₃	1	2	yes	—
631	C₄×C₈	C₂³×C₁₃	1	2	yes	—
632	C₂×C₁₃	—	4	1	no	—
633	C₂×C₁₃	—	4	4	no	—
634	C₂×C₁₃	—	4	2	no	—
635	C₂×C₁₃	—	8	2	no	—
636	C₂×C₁₃	#3484	1	1	yes	characteristic
637	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
638	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
639	#41	—	2	2	no	—
640	#41	—	2	2	no	—
641	#41	—	2	8	no	—
642	#41	—	4	2	no	—
643	#41	—	4	2	no	—
644	#41	—	4	4	no	—
645	#41	—	4	8	no	—
646	#41	—	4	4	no	—
647	#41	—	4	4	no	—
648	#41	—	4	16	no	—
649	#41	—	8	2	no	—
650	#41	—	8	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	8	no	—
656	C₂×Q₈	—	4	4	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	8	no	—
660	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
661	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
662	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
663	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
672	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
673	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
674	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
690	Q₁₆	—	2	4	no	—
691	Q₁₆	—	4	4	no	—
692	Q₁₆	—	4	4	no	—
693	SD₁₆	—	2	4	no	—
694	SD₁₆	—	2	4	no	—
695	SD₁₆	—	4	4	no	—
696	SD₁₆	—	4	4	no	—
697	D₈	—	2	4	no	—
698	M₁₆	—	4	4	no	—
699	C₂×C₈	—	4	4	no	—
700	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
701	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
702	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
703	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
737	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
738	C₄²	—	2	1	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	2	no	—
742	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₁₃	#61667	1	1	yes	characteristic, direct product factor, Sylow
747	C₂³	—	2	1	no	—
748	C₂³	—	2	2	no	—
749	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
750	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	Q₈	—	2	1	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	4	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	4	8	no	—
758	Q₈	—	4	4	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	8	1	no	—
761	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	4	no	—
765	D₄	—	2	1	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	4	2	no	—
769	D₄	—	4	4	no	—
770	D₄	—	4	8	no	—
771	D₄	—	4	2	no	—
772	D₄	—	8	1	no	—
773	D₄	—	8	4	no	—
774	D₄	—	8	2	no	—
775	D₄	—	8	4	no	—
776	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
803	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	4	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	4	no	—
833	C₄	—	4	2	no	—
834	C₄	C₁₃×#577	1	2	yes	—
835	C₄	C₁₃×#578	1	2	yes	—
836	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
837	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
838	C₂	—	4	1	no	—
839	C₂	—	4	4	no	—
840	C₂	—	4	2	no	—
841	C₂	—	8	2	no	—
842	C₂	C₁₃×#3484	1	1	yes	characteristic
843	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
844	C₂	C₂×C₁₃×#578	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3548	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3331	C₂	semidirect
4. C₁₃×#3330	C₂	semidirect
5. C₁₃×#3299	C₂	semidirect
6. C₁₃×#3298	C₂	semidirect
7. C₁₃×#3284	C₂	semidirect
8. C₁₃×#3283	C₂	semidirect
9. C₁₃×#3278	C₂	semidirect
10. C₁₃×#3276	C₂	semidirect
11. C₁₃×#3209	C₂	semidirect
12. C₁₃×#3206	C₂	semidirect
13. C₁₃×#3201	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3106	C₂	semidirect
16. C₁₃×#3013	C₂	semidirect
17. C₁₃×#2979	C₂	semidirect
217. #61667	C₁₃	direct (N × H)
325. #3548	C₂×C₁₃	semidirect
326. #3499	C₂×C₁₃	semidirect
327. #3331	C₂×C₁₃	semidirect
328. #3330	C₂×C₁₃	semidirect
329. #3299	C₂×C₁₃	semidirect
330. #3298	C₂×C₁₃	semidirect
331. #3284	C₂×C₁₃	semidirect
332. #3283	C₂×C₁₃	semidirect
333. #3278	C₂×C₁₃	semidirect
334. #3276	C₂×C₁₃	semidirect
335. #3209	C₂×C₁₃	semidirect
336. #3206	C₂×C₁₃	semidirect
337. #3201	C₂×C₁₃	semidirect
338. #3107	C₂×C₁₃	semidirect
339. #3106	C₂×C₁₃	semidirect
340. #3013	C₂×C₁₃	semidirect
341. #2979	C₂×C₁₃	semidirect
746. C₁₃	#61667	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×#3548	2
C₁₃×#3499	2
C₁₃×#3331	2
C₁₃×#3330	2
C₁₃×#3299	2
C₁₃×#3298	2
C₁₃×#3284	2
C₁₃×#3283	2
C₁₃×#3278	2
C₁₃×#3276	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3201	2
C₁₃×#3107	2
C₁₃×#3106	2
C₁₃×#3013	2
C₁₃×#2979	2
#61667	13

Subgroups — C13×#61667 #15748006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61667 #15748006