Subgroups — C₁₃×#61415 #15747754

Order 3328.

1914 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2951	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂×C₁₃×#135	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	2	yes	—
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₁₃×#559	C₂²	1	4	yes	—
22	C₁₃×#559	C₂²	1	2	yes	complemented
23	C₁₃×#557	C₂²	1	2	yes	complemented
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	4	yes	complemented
27	C₁₃×#555	—	2	1	no	—
28	C₁₃×#554	—	2	1	no	—
29	C₁₃×#553	—	2	2	no	—
30	C₁₃×#552	—	2	2	no	—
31	C₁₃×#550	C₂²	1	2	yes	—
32	C₁₃×#547	—	2	1	no	—
33	C₁₃×#539	—	2	2	no	—
34	C₁₃×#538	—	2	2	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#535	C₂²	1	2	yes	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#529	—	2	2	no	—
41	C₁₃×#525	—	2	2	no	—
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₁₃×#520	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#497	C₂²	1	4	yes	—
47	C₁₃×#497	C₂²	1	2	yes	complemented
48	C₁₃×#497	C₂²	1	2	yes	complemented
49	C₁₃×#496	C₂²	1	4	yes	—
50	C₁₃×#496	C₂²	1	2	yes	complemented
51	C₁₃×#496	C₂²	1	2	yes	complemented
52	C₁₃×#495	C₂²	1	4	yes	—
53	C₁₃×#492	C₂²	1	4	yes	—
54	C₁₃×#464	C₂²	1	4	yes	—
55	C₁₃×#464	C₂²	1	4	yes	complemented
56	C₁₃×#464	C₂²	1	4	yes	complemented
57	C₁₃×#463	C₂²	1	4	yes	—
58	C₁₃×#463	C₂²	1	4	yes	—
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#462	C₂²	1	2	yes	complemented
61	C₁₃×#462	C₂²	1	4	yes	complemented
62	C₁₃×#461	C₂²	1	2	yes	—
63	C₁₃×#461	C₂²	1	4	yes	complemented
64	C₁₃×#460	C₂²	1	4	yes	—
65	C₁₃×#460	C₂²	1	2	yes	complemented
66	C₁₃×#459	C₂²	1	2	yes	—
67	C₁₃×#459	C₂²	1	4	yes	—
68	C₁₃×#446	C₂²	1	4	yes	complemented
69	C₁₃×#446	C₂²	1	4	yes	complemented
70	C₁₃×#440	C₂²	1	4	yes	—
71	C₁₃×#440	C₂²	1	4	yes	—
72	C₁₃×#440	C₂²	1	4	yes	complemented
73	C₁₃×#440	C₂²	1	4	yes	complemented
74	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
75	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
76	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
77	C₁₃×#424	C₂²	1	2	yes	—
78	C₁₃×#423	C₂²	1	1	yes	characteristic
79	C₁₃×#417	C₂²	1	2	yes	—
80	C₁₃×#417	C₂²	1	2	yes	—
81	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
83	C₁₃×#405	C₂²	1	2	yes	—
84	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	C₂³	1	2	yes	—
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	—	2	1	no	—
91	C₁₃×#137	—	4	4	no	—
92	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
93	C₁₃×#135	—	2	8	no	—
94	C₁₃×#135	—	4	4	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×SD₁₆	—	2	4	no	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×D₈	C₂³	1	2	yes	—
107	C₂×C₁₃×D₈	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	C₂³	1	2	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	4	yes	—
119	C₁₃×#127	C₂³	1	1	yes	characteristic
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#126	—	2	4	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	D₄	1	2	yes	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	C₂³	1	2	yes	—
129	C₁₃×#124	C₂³	1	4	yes	—
130	C₁₃×#124	C₂³	1	4	yes	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#123	—	2	4	no	—
133	C₁₃×#123	—	2	4	no	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₁₃×#121	—	2	1	no	—
143	C₁₃×#121	—	2	1	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	4	no	—
150	C₁₃×#120	—	2	4	no	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×D₄×C₁₃	—	2	4	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₄×D₄×C₁₃	—	2	4	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	C₂³	1	4	yes	—
171	C₄×D₄×C₁₃	C₂³	1	4	yes	—
172	C₄×D₄×C₁₃	C₂³	1	2	yes	—
173	C₄×D₄×C₁₃	C₂³	1	2	yes	—
174	C₁₃×#117	—	2	2	no	—
175	C₁₃×#117	—	2	2	no	—
176	C₁₃×#117	—	2	2	no	—
177	C₁₃×#117	—	2	4	no	—
178	C₁₃×#117	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₄²×C₁₃	—	2	1	no	—
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₁₃×#107	C₂³	1	4	yes	—
188	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
191	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
192	C₁₃×#103	C₂³	1	4	yes	—
193	C₁₃×#103	C₂³	1	4	yes	—
194	C₁₃×#103	C₂³	1	4	yes	—
195	C₁₃×#102	C₂³	1	4	yes	—
196	C₁₃×#102	C₂³	1	4	yes	—
197	C₁₃×#102	C₂³	1	4	yes	—
198	C₁₃×#97	C₂³	1	2	yes	—
199	C₁₃×#97	C₂³	1	2	yes	—
200	C₁₃×#97	C₂³	1	4	yes	—
201	C₄×C₈×C₁₃	C₂³	1	4	yes	—
202	#61415	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂⁴×C₁₃	—	2	1	no	—
204	C₁₃×#41	—	2	4	no	—
205	C₁₃×#41	—	2	4	no	—
206	C₁₃×#41	—	2	4	no	—
207	C₁₃×#41	—	2	4	no	—
208	C₁₃×#41	—	8	4	no	—
209	C₂×Q₈×C₁₃	—	2	1	no	—
210	C₂×Q₈×C₁₃	—	2	2	no	—
211	C₂×Q₈×C₁₃	—	2	2	no	—
212	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	2	1	no	—
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	8	2	no	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₁₃×Q₁₆	—	2	4	no	—
245	C₁₃×Q₁₆	—	4	2	no	—
246	C₁₃×Q₁₆	—	4	4	no	—
247	C₁₃×SD₁₆	—	2	8	no	—
248	C₁₃×SD₁₆	—	2	4	no	—
249	C₁₃×SD₁₆	—	2	4	no	—
250	C₁₃×SD₁₆	—	4	2	no	—
251	C₁₃×SD₁₆	—	4	2	no	—
252	C₁₃×SD₁₆	—	4	4	no	—
253	C₁₃×SD₁₆	—	4	4	no	—
254	C₁₃×D₈	—	2	4	no	—
255	C₁₃×D₈	—	4	2	no	—
256	C₁₃×D₈	—	4	4	no	—
257	C₁₃×M₁₆	—	2	4	no	—
258	C₂×C₈×C₁₃	—	2	2	no	—
259	C₂×C₈×C₁₃	#41	1	4	yes	complemented
260	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	2	no	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂⁴	1	4	yes	—
303	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
305	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#3403	C₂×C₁₃	1	4	yes	complemented
308	#3402	C₂×C₁₃	1	4	yes	complemented
309	#3400	C₂×C₁₃	1	4	yes	complemented
310	#3397	C₂×C₁₃	1	4	yes	complemented
311	#3154	C₂×C₁₃	1	2	yes	complemented
312	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3046	C₂×C₁₃	1	2	yes	complemented
314	#3045	C₂×C₁₃	1	2	yes	complemented
315	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#2951	C₂×C₁₃	1	2	yes	complemented
319	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	4	2	no	—
324	C₂³×C₁₃	—	8	1	no	—
325	C₂³×C₁₃	—	8	1	no	—
326	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	2	2	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	4	2	no	—
334	Q₈×C₁₃	—	4	2	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	D₄×C₁₃	—	2	2	no	—
337	D₄×C₁₃	—	2	2	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	2	2	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	4	2	no	—
343	D₄×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	4	4	no	—
345	D₄×C₁₃	—	4	4	no	—
346	D₄×C₁₃	—	4	2	no	—
347	D₄×C₁₃	—	8	1	no	—
348	D₄×C₁₃	—	8	1	no	—
349	D₄×C₁₃	—	8	4	no	—
350	D₄×C₁₃	—	8	4	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	4	2	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	4	4	no	—
362	C₂×C₄×C₁₃	—	8	4	no	—
363	C₂×C₄×C₁₃	—	8	2	no	—
364	C₂×C₄×C₁₃	—	8	4	no	—
365	C₂×C₄×C₁₃	—	8	1	no	—
366	C₂×C₄×C₁₃	—	8	1	no	—
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
377	C₈×C₁₃	—	2	2	no	—
378	C₈×C₁₃	—	2	4	no	—
379	C₈×C₁₃	C₂×#41	1	4	yes	—
380	C₂×#137	C₂²×C₁₃	1	2	yes	—
381	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
382	C₂×#135	C₂²×C₁₃	1	2	yes	—
383	C₂×#135	C₂²×C₁₃	1	2	yes	—
384	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
385	#559	C₂²×C₁₃	1	4	yes	—
386	#559	C₂²×C₁₃	1	2	yes	complemented
387	#557	C₂²×C₁₃	1	2	yes	complemented
388	#556	—	2	1	no	—
389	#556	C₂²×C₁₃	1	2	yes	—
390	#556	C₂²×C₁₃	1	4	yes	complemented
391	#555	—	2	1	no	—
392	#554	—	2	1	no	—
393	#553	—	2	2	no	—
394	#552	—	2	2	no	—
395	#550	C₂²×C₁₃	1	2	yes	—
396	#547	—	2	1	no	—
397	#539	—	2	2	no	—
398	#538	—	2	2	no	—
399	#536	C₂²×C₁₃	1	2	yes	—
400	#535	C₂²×C₁₃	1	2	yes	—
401	#533	C₂²×C₁₃	1	1	yes	characteristic
402	#532	C₂²×C₁₃	1	1	yes	characteristic
403	#532	C₂²×C₁₃	1	1	yes	characteristic
404	#529	—	2	2	no	—
405	#525	—	2	2	no	—
406	#520	C₂²×C₁₃	1	2	yes	—
407	#520	C₂²×C₁₃	1	2	yes	—
408	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	#497	C₂²×C₁₃	1	4	yes	—
411	#497	C₂²×C₁₃	1	2	yes	complemented
412	#497	C₂²×C₁₃	1	2	yes	complemented
413	#496	C₂²×C₁₃	1	4	yes	—
414	#496	C₂²×C₁₃	1	2	yes	complemented
415	#496	C₂²×C₁₃	1	2	yes	complemented
416	#495	C₂²×C₁₃	1	4	yes	—
417	#492	C₂²×C₁₃	1	4	yes	—
418	#464	C₂²×C₁₃	1	4	yes	—
419	#464	C₂²×C₁₃	1	4	yes	complemented
420	#464	C₂²×C₁₃	1	4	yes	complemented
421	#463	C₂²×C₁₃	1	4	yes	—
422	#463	C₂²×C₁₃	1	4	yes	—
423	#463	C₂²×C₁₃	1	4	yes	complemented
424	#462	C₂²×C₁₃	1	4	yes	complemented
425	#462	C₂²×C₁₃	1	2	yes	complemented
426	#461	C₂²×C₁₃	1	2	yes	—
427	#461	C₂²×C₁₃	1	4	yes	complemented
428	#460	C₂²×C₁₃	1	4	yes	—
429	#460	C₂²×C₁₃	1	2	yes	complemented
430	#459	C₂²×C₁₃	1	4	yes	—
431	#459	C₂²×C₁₃	1	2	yes	—
432	#446	C₂²×C₁₃	1	4	yes	complemented
433	#446	C₂²×C₁₃	1	4	yes	complemented
434	#440	C₂²×C₁₃	1	4	yes	—
435	#440	C₂²×C₁₃	1	4	yes	—
436	#440	C₂²×C₁₃	1	4	yes	complemented
437	#440	C₂²×C₁₃	1	4	yes	complemented
438	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
439	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
440	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
441	#424	C₂²×C₁₃	1	2	yes	—
442	#423	C₂²×C₁₃	1	1	yes	characteristic
443	#417	C₂²×C₁₃	1	2	yes	—
444	#417	C₂²×C₁₃	1	2	yes	—
445	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
447	#405	C₂²×C₁₃	1	2	yes	—
448	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	8	4	no	—
461	C₂²×C₁₃	#550	1	2	yes	—
462	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
463	C₄×C₁₃	—	2	1	no	—
464	C₄×C₁₃	—	2	1	no	—
465	C₄×C₁₃	—	2	4	no	—
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	4	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	2	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	#550	1	2	yes	—
475	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
476	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×#41	—	2	2	no	—
478	C₂×#41	C₂³×C₁₃	1	2	yes	—
479	C₂×#41	C₂³×C₁₃	1	2	yes	—
480	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂³×C₄	—	2	1	no	—
483	#137	—	4	4	no	—
484	AGL(1,ℤ/8)	—	4	4	no	—
485	#135	—	2	8	no	—
486	#135	—	4	4	no	—
487	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
488	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
489	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
490	C₂×SD₁₆	—	2	4	no	—
491	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
493	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
498	C₂×D₈	C₂³×C₁₃	1	2	yes	—
499	C₂×D₈	C₂³×C₁₃	1	2	yes	—
500	C₂×D₈	C₂³×C₁₃	1	4	yes	—
501	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
502	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
504	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
505	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
509	#127	C₂³×C₁₃	1	1	yes	characteristic
510	#127	C₂³×C₁₃	1	1	yes	characteristic
511	#127	C₂³×C₁₃	1	4	yes	—
512	#126	—	2	4	no	—
513	#126	—	2	4	no	—
514	#126	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	—	2	4	no	—
517	#125	D₄×C₁₃	1	2	yes	—
518	#124	—	2	2	no	—
519	#124	—	2	4	no	—
520	#124	C₂³×C₁₃	1	2	yes	—
521	#124	C₂³×C₁₃	1	2	yes	—
522	#124	C₂³×C₁₃	1	4	yes	—
523	#124	C₂³×C₁₃	1	4	yes	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
533	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
534	#121	—	2	1	no	—
535	#121	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	—	2	1	no	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	4	no	—
542	#120	—	2	4	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
549	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
550	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
551	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄×D₄	—	2	4	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₁₃	1	2	yes	—
563	C₄×D₄	C₂³×C₁₃	1	2	yes	—
564	C₄×D₄	C₂³×C₁₃	1	4	yes	—
565	C₄×D₄	C₂³×C₁₃	1	4	yes	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	—	2	4	no	—
570	#117	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	2	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₄²	—	2	1	no	—
578	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
579	#107	C₂³×C₁₃	1	4	yes	—
580	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
581	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
582	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
583	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
584	#103	C₂³×C₁₃	1	4	yes	—
585	#103	C₂³×C₁₃	1	4	yes	—
586	#103	C₂³×C₁₃	1	4	yes	—
587	#102	C₂³×C₁₃	1	4	yes	—
588	#102	C₂³×C₁₃	1	4	yes	—
589	#102	C₂³×C₁₃	1	4	yes	—
590	#97	C₂³×C₁₃	1	2	yes	—
591	#97	C₂³×C₁₃	1	2	yes	—
592	#97	C₂³×C₁₃	1	4	yes	—
593	C₄×C₈	C₂³×C₁₃	1	4	yes	—
594	C₂×C₁₃	—	2	2	no	—
595	C₂×C₁₃	—	8	2	no	—
596	C₂×C₁₃	—	8	2	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
599	C₂×C₁₃	#3585	1	1	yes	characteristic
600	C₂×C₁₃	#3586	1	1	yes	characteristic
601	C₂⁴	—	2	1	no	—
602	#41	—	2	4	no	—
603	#41	—	2	4	no	—
604	#41	—	2	4	no	—
605	#41	—	2	4	no	—
606	#41	—	8	4	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
611	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
627	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	8	2	no	—
639	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
642	Q₁₆	—	2	4	no	—
643	Q₁₆	—	4	2	no	—
644	Q₁₆	—	4	4	no	—
645	SD₁₆	—	2	8	no	—
646	SD₁₆	—	2	4	no	—
647	SD₁₆	—	2	4	no	—
648	SD₁₆	—	4	2	no	—
649	SD₁₆	—	4	2	no	—
650	SD₁₆	—	4	4	no	—
651	SD₁₆	—	4	4	no	—
652	D₈	—	2	4	no	—
653	D₈	—	4	2	no	—
654	D₈	—	4	4	no	—
655	M₁₆	—	2	4	no	—
656	C₂×C₈	—	2	2	no	—
657	C₂×C₈	C₁₃×#41	1	4	yes	complemented
658	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
659	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
660	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	—	2	4	no	—
698	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₄²	C₂⁴×C₁₃	1	4	yes	—
701	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₁₃	#61415	1	1	yes	characteristic, direct product factor, Sylow
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	8	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	2	no	—
731	D₄	—	8	1	no	—
732	D₄	—	8	1	no	—
733	D₄	—	8	4	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	1	no	—
751	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
759	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
760	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
761	C₈	—	2	2	no	—
762	C₈	—	2	4	no	—
763	C₈	C₂×C₁₃×#41	1	4	yes	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₁₃×#550	1	2	yes	—
777	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	4	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	C₁₃×#550	1	2	yes	—
790	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
791	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂	—	2	2	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
797	C₂	C₁₃×#3585	1	1	yes	characteristic
798	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₁₃×#3506	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3402	C₂	semidirect
5. C₁₃×#3400	C₂	semidirect
6. C₁₃×#3397	C₂	semidirect
7. C₁₃×#3154	C₂	semidirect
8. C₁₃×#3150	C₂	semidirect
9. C₁₃×#3046	C₂	semidirect
10. C₁₃×#3045	C₂	semidirect
11. C₁₃×#3037	C₂	semidirect
12. C₁₃×#3036	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2951	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
22. C₁₃×#559	C₂²	semidirect
23. C₁₃×#557	C₂²	semidirect
26. C₁₃×#556	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
48. C₁₃×#497	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
55. C₁₃×#464	C₂²	semidirect
56. C₁₃×#464	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#462	C₂²	semidirect
61. C₁₃×#462	C₂²	semidirect
63. C₁₃×#461	C₂²	semidirect
65. C₁₃×#460	C₂²	semidirect
68. C₁₃×#446	C₂²	semidirect
69. C₁₃×#446	C₂²	semidirect
72. C₁₃×#440	C₂²	semidirect
73. C₁₃×#440	C₂²	semidirect
74. C₄×C₁₃×Q₁₆	C₂²	semidirect
75. C₄×C₁₃×D₈	C₂²	semidirect
202. #61415	C₁₃	direct (N × H)
259. C₂×C₈×C₁₃	#41	semidirect
305. #3507	C₂×C₁₃	semidirect
306. #3506	C₂×C₁₃	semidirect
307. #3403	C₂×C₁₃	semidirect
308. #3402	C₂×C₁₃	semidirect
309. #3400	C₂×C₁₃	semidirect
310. #3397	C₂×C₁₃	semidirect
311. #3154	C₂×C₁₃	semidirect
312. #3150	C₂×C₁₃	semidirect
313. #3046	C₂×C₁₃	semidirect
314. #3045	C₂×C₁₃	semidirect
315. #3037	C₂×C₁₃	semidirect
316. #3036	C₂×C₁₃	semidirect
317. #2961	C₂×C₁₃	semidirect
318. #2951	C₂×C₁₃	semidirect
319. C₂×#440	C₂×C₁₃	semidirect
386. #559	C₂²×C₁₃	semidirect
387. #557	C₂²×C₁₃	semidirect
390. #556	C₂²×C₁₃	semidirect
411. #497	C₂²×C₁₃	semidirect
412. #497	C₂²×C₁₃	semidirect
414. #496	C₂²×C₁₃	semidirect
415. #496	C₂²×C₁₃	semidirect
419. #464	C₂²×C₁₃	semidirect
420. #464	C₂²×C₁₃	semidirect
423. #463	C₂²×C₁₃	semidirect
424. #462	C₂²×C₁₃	semidirect
425. #462	C₂²×C₁₃	semidirect
427. #461	C₂²×C₁₃	semidirect
429. #460	C₂²×C₁₃	semidirect
432. #446	C₂²×C₁₃	semidirect
433. #446	C₂²×C₁₃	semidirect
436. #440	C₂²×C₁₃	semidirect
437. #440	C₂²×C₁₃	semidirect
438. C₄×Q₁₆	C₂²×C₁₃	semidirect
439. C₄×D₈	C₂²×C₁₃	semidirect
657. C₂×C₈	C₁₃×#41	semidirect
703. C₁₃	#61415	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×#3507	2
C₁₃×#3506	2
C₁₃×#3403	2
C₁₃×#3402	2
C₁₃×#3400	2
C₁₃×#3397	2
C₁₃×#3154	2
C₁₃×#3150	2
C₁₃×#3046	2
C₁₃×#3045	2
C₁₃×#3037	2
C₁₃×#3036	2
C₁₃×#2961	2
C₁₃×#2951	2
C₂×C₁₃×#440	2
#61415	13

Subgroups — C13×#61415 #15747754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61415 #15747754