Subgroups — C₁₃×#61576 #15747915

Order 3328.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3319	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3311	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3268	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3267	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3003	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#556	C₂²	1	2	yes	complemented
22	C₁₃×#555	C₂²	1	2	yes	complemented
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	C₁₃×#547	C₂²	1	2	yes	complemented
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	2	no	—
28	C₁₃×#546	C₂²	1	4	yes	—
29	C₁₃×#546	C₂²	1	4	yes	—
30	C₁₃×#538	—	2	1	no	—
31	C₁₃×#538	—	2	1	no	—
32	C₁₃×#535	—	2	1	no	—
33	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
36	C₁₃×#525	C₂²	1	2	yes	—
37	C₁₃×#525	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#123	—	2	1	no	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#121	—	2	1	no	—
41	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#120	—	2	1	no	—
43	C₁₃×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
47	C₁₃×#497	C₂²	1	2	yes	complemented
48	C₁₃×#496	C₂²	1	2	yes	complemented
49	C₁₃×#489	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#484	C₂²	1	2	yes	complemented
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#481	C₂²	1	2	yes	complemented
55	C₁₃×#476	C₂²	1	2	yes	complemented
56	C₁₃×#474	C₂²	1	2	yes	complemented
57	C₁₃×#470	C₂²	1	4	yes	complemented
58	C₁₃×#468	C₂²	1	4	yes	complemented
59	C₁₃×#466	C₂²	1	4	yes	complemented
60	C₁₃×#465	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#461	C₂²	1	2	yes	complemented
64	C₁₃×#459	C₂²	1	2	yes	complemented
65	C₁₃×#452	C₂²	1	4	yes	complemented
66	C₁₃×#452	C₂²	1	4	yes	complemented
67	C₁₃×#451	C₂²	1	2	yes	complemented
68	C₁₃×#450	C₂²	1	2	yes	—
69	C₁₃×#450	C₂²	1	2	yes	—
70	C₁₃×#450	C₂²	1	4	yes	complemented
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#449	C₂²	1	4	yes	complemented
73	C₁₃×#448	C₂²	1	2	yes	complemented
74	C₁₃×#447	C₂²	1	2	yes	—
75	C₁₃×#447	C₂²	1	2	yes	—
76	C₁₃×#447	C₂²	1	4	yes	complemented
77	C₁₃×#442	C₂²	1	4	yes	complemented
78	C₁₃×#440	C₂²	1	4	yes	complemented
79	C₁₃×#435	C₂²	1	4	yes	complemented
80	C₁₃×#435	C₂²	1	4	yes	complemented
81	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#418	C₂²	1	4	yes	complemented
84	C₁₃×#416	C₂²	1	4	yes	complemented
85	C₁₃×#407	C₂²	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂⁵×C₁₃	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	—	4	4	no	—
91	C₂×C₁₃×#41	C₂³	1	4	yes	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂×C₁₃×#41	C₂³	1	2	yes	complemented
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	—	2	1	no	—
96	C₂²×D₄×C₁₃	—	2	1	no	—
97	C₂²×D₄×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	2	no	—
99	C₂²×D₄×C₁₃	—	4	4	no	—
100	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	—	2	1	no	—
105	C₂³×C₄×C₁₃	—	2	1	no	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
109	C₁₃×#135	—	4	8	no	—
110	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×D₈	C₂³	1	4	yes	—
116	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
117	C₂²×C₈×C₁₃	C₂³	1	4	yes	complemented
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
121	C₁₃×#127	—	2	2	no	—
122	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#125	—	2	1	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	C₂³	1	2	yes	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	C₂³	1	2	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	complemented
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	4	no	—
151	C₁₃×#121	—	2	4	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	C₂³	1	2	yes	—
155	C₁₃×#121	C₂³	1	2	yes	—
156	C₁₃×#121	C₂³	1	4	yes	—
157	C₁₃×#121	C₂³	1	2	yes	complemented
158	C₁₃×#120	—	2	2	no	—
159	C₁₃×#120	—	2	2	no	—
160	C₁₃×#120	—	2	4	no	—
161	C₁₃×#120	—	2	4	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	D₄	1	2	yes	—
174	C₄×D₄×C₁₃	D₄	1	2	yes	—
175	C₄×D₄×C₁₃	C₂³	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	2	yes	—
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
180	C₁₃×#117	—	2	1	no	—
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	C₂³	1	2	yes	—
183	C₁₃×#117	C₂³	1	2	yes	complemented
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₁₃×#107	C₂³	1	4	yes	complemented
199	C₁₃×#106	C₂³	1	4	yes	complemented
200	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
202	C₁₃×#103	C₂³	1	4	yes	complemented
203	C₁₃×#103	C₂³	1	4	yes	complemented
204	C₁₃×#103	C₂³	1	4	yes	complemented
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	complemented
210	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
214	C₁₃×#97	C₂³	1	2	yes	complemented
215	C₁₃×#97	C₂³	1	2	yes	complemented
216	#61576	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂⁴×C₁₃	—	2	1	no	—
218	C₂⁴×C₁₃	—	2	1	no	—
219	C₂⁴×C₁₃	—	2	4	no	—
220	C₂⁴×C₁₃	—	4	4	no	—
221	C₂⁴×C₁₃	—	4	4	no	—
222	C₂⁴×C₁₃	—	8	2	no	—
223	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₁₃×#41	—	2	8	no	—
226	C₁₃×#41	—	4	4	no	—
227	C₁₃×#41	—	4	4	no	—
228	C₁₃×#41	—	4	4	no	—
229	C₁₃×#41	—	4	4	no	—
230	C₁₃×#41	—	4	8	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	8	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	4	4	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	—	4	2	no	—
254	C₂×D₄×C₁₃	—	4	8	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	8	2	no	—
258	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	4	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	2	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	2	no	—
273	C₂²×C₄×C₁₃	—	4	4	no	—
274	C₂²×C₄×C₁₃	—	8	2	no	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₁₃×Q₁₆	—	4	4	no	—
285	C₁₃×SD₁₆	—	2	8	no	—
286	C₁₃×SD₁₆	—	4	4	no	—
287	C₁₃×SD₁₆	—	4	4	no	—
288	C₁₃×D₈	—	2	8	no	—
289	C₁₃×D₈	—	4	4	no	—
290	C₁₃×M₁₆	—	4	4	no	—
291	C₂×C₈×C₁₃	—	4	4	no	—
292	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
293	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	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	2	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	2	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	C₂×D₄	1	2	yes	—
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	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
337	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3319	C₂×C₁₃	1	4	yes	complemented
340	#3311	C₂×C₁₃	1	4	yes	complemented
341	#3268	C₂×C₁₃	1	4	yes	complemented
342	#3267	C₂×C₁₃	1	4	yes	complemented
343	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3196	C₂×C₁₃	1	2	yes	complemented
346	#3188	C₂×C₁₃	1	2	yes	complemented
347	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3003	C₂×C₁₃	1	2	yes	complemented
350	#3002	C₂×C₁₃	1	2	yes	complemented
351	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂³×C₁₃	—	2	4	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	4	1	no	—
361	C₂³×C₁₃	—	4	1	no	—
362	C₂³×C₁₃	—	4	8	no	—
363	C₂³×C₁₃	—	4	2	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	—	4	2	no	—
366	C₂³×C₁₃	—	4	8	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	4	2	no	—
369	C₂³×C₁₃	—	8	4	no	—
370	C₂³×C₁₃	—	8	16	no	—
371	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	Q₈×C₁₃	—	2	4	no	—
375	Q₈×C₁₃	—	2	4	no	—
376	Q₈×C₁₃	—	4	2	no	—
377	Q₈×C₁₃	—	4	2	no	—
378	Q₈×C₁₃	—	8	1	no	—
379	D₄×C₁₃	—	2	4	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	4	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	4	8	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	4	8	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	8	1	no	—
391	D₄×C₁₃	—	8	2	no	—
392	D₄×C₁₃	—	8	2	no	—
393	D₄×C₁₃	—	8	4	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	2	no	—
396	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	1	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	1	no	—
411	C₂×C₄×C₁₃	—	4	8	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	8	2	no	—
416	C₂×C₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	—	8	2	no	—
418	C₂×C₄×C₁₃	—	8	2	no	—
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
427	C₈×C₁₃	—	2	4	no	—
428	C₈×C₁₃	—	2	4	no	—
429	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
430	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
432	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
433	#559	—	2	2	no	—
434	#556	C₂²×C₁₃	1	2	yes	complemented
435	#555	C₂²×C₁₃	1	2	yes	complemented
436	#553	—	2	2	no	—
437	#550	C₂²×C₁₃	1	2	yes	complemented
438	#547	C₂²×C₁₃	1	2	yes	complemented
439	#546	—	2	2	no	—
440	#546	—	2	2	no	—
441	#546	C₂²×C₁₃	1	4	yes	—
442	#546	C₂²×C₁₃	1	4	yes	—
443	#538	—	2	1	no	—
444	#538	—	2	1	no	—
445	#535	—	2	1	no	—
446	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
449	#525	C₂²×C₁₃	1	2	yes	—
450	#525	C₂²×C₁₃	1	2	yes	complemented
451	C₂×#123	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×#121	—	2	1	no	—
454	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#120	—	2	1	no	—
456	#520	—	2	1	no	—
457	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
459	C₂²×C₂²⋊C₄	—	2	1	no	—
460	#497	C₂²×C₁₃	1	2	yes	complemented
461	#496	C₂²×C₁₃	1	2	yes	complemented
462	#489	C₂²×C₁₃	1	2	yes	complemented
463	#489	C₂²×C₁₃	1	2	yes	complemented
464	#485	C₂²×C₁₃	1	4	yes	complemented
465	#484	C₂²×C₁₃	1	2	yes	complemented
466	#482	C₂²×C₁₃	1	4	yes	complemented
467	#481	C₂²×C₁₃	1	2	yes	complemented
468	#476	C₂²×C₁₃	1	2	yes	complemented
469	#474	C₂²×C₁₃	1	2	yes	complemented
470	#470	C₂²×C₁₃	1	4	yes	complemented
471	#468	C₂²×C₁₃	1	4	yes	complemented
472	#466	C₂²×C₁₃	1	4	yes	complemented
473	#465	C₂²×C₁₃	1	4	yes	complemented
474	#464	C₂²×C₁₃	1	4	yes	complemented
475	#463	C₂²×C₁₃	1	4	yes	complemented
476	#461	C₂²×C₁₃	1	2	yes	complemented
477	#459	C₂²×C₁₃	1	2	yes	complemented
478	#452	C₂²×C₁₃	1	4	yes	complemented
479	#452	C₂²×C₁₃	1	4	yes	complemented
480	#451	C₂²×C₁₃	1	2	yes	complemented
481	#450	C₂²×C₁₃	1	2	yes	—
482	#450	C₂²×C₁₃	1	2	yes	—
483	#450	C₂²×C₁₃	1	4	yes	complemented
484	#449	C₂²×C₁₃	1	4	yes	complemented
485	#449	C₂²×C₁₃	1	4	yes	complemented
486	#448	C₂²×C₁₃	1	2	yes	complemented
487	#447	C₂²×C₁₃	1	2	yes	—
488	#447	C₂²×C₁₃	1	2	yes	—
489	#447	C₂²×C₁₃	1	4	yes	complemented
490	#442	C₂²×C₁₃	1	4	yes	complemented
491	#440	C₂²×C₁₃	1	4	yes	complemented
492	#435	C₂²×C₁₃	1	4	yes	complemented
493	#435	C₂²×C₁₃	1	4	yes	complemented
494	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#418	C₂²×C₁₃	1	4	yes	complemented
497	#416	C₂²×C₁₃	1	4	yes	complemented
498	#407	C₂²×C₁₃	1	2	yes	—
499	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	4	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	4	8	no	—
510	C₂²×C₁₃	—	4	4	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	8	2	no	—
520	C₂²×C₁₃	—	8	4	no	—
521	C₂²×C₁₃	—	8	16	no	—
522	C₂²×C₁₃	#575	1	2	yes	—
523	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	2	1	no	—
528	C₄×C₁₃	—	2	2	no	—
529	C₄×C₁₃	—	2	1	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	4	2	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
537	C₂⁵	—	2	1	no	—
538	C₂×#41	—	2	1	no	—
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	4	4	no	—
541	C₂×#41	C₂³×C₁₃	1	4	yes	—
542	C₂×#41	C₂³×C₁₃	1	2	yes	—
543	C₂×#41	C₂³×C₁₃	1	2	yes	complemented
544	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	—	4	4	no	—
550	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
553	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	—	2	1	no	—
556	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
558	AGL(1,ℤ/8)	—	4	8	no	—
559	#135	—	4	8	no	—
560	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
561	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
562	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
564	C₂×D₈	C₂³×C₁₃	1	4	yes	—
565	C₂×D₈	C₂³×C₁₃	1	4	yes	—
566	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂²×C₈	C₂³×C₁₃	1	4	yes	complemented
568	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
569	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
570	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
571	#127	—	2	2	no	—
572	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
573	#126	—	2	2	no	—
574	#126	—	2	2	no	—
575	#125	—	2	1	no	—
576	#124	—	2	2	no	—
577	#124	—	2	2	no	—
578	#124	—	2	2	no	—
579	#124	—	2	1	no	—
580	#124	—	2	1	no	—
581	#124	—	2	1	no	—
582	#124	C₂³×C₁₃	1	2	yes	—
583	#124	C₂³×C₁₃	1	2	yes	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	4	no	—
587	#123	—	2	4	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	2	2	no	—
599	#121	—	2	1	no	—
600	#121	—	2	4	no	—
601	#121	—	2	4	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	C₂³×C₁₃	1	4	yes	—
605	#121	C₂³×C₁₃	1	2	yes	—
606	#121	C₂³×C₁₃	1	2	yes	—
607	#121	C₂³×C₁₃	1	2	yes	complemented
608	#120	—	2	2	no	—
609	#120	—	2	2	no	—
610	#120	—	2	4	no	—
611	#120	—	2	4	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	D₄×C₁₃	1	2	yes	—
624	C₄×D₄	D₄×C₁₃	1	2	yes	—
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	2	yes	—
629	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
630	#117	—	2	1	no	—
631	#117	—	2	2	no	—
632	#117	C₂³×C₁₃	1	2	yes	—
633	#117	C₂³×C₁₃	1	2	yes	complemented
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	4	no	—
644	C₂×C₂²⋊C₄	—	2	4	no	—
645	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
648	#107	C₂³×C₁₃	1	4	yes	complemented
649	#106	C₂³×C₁₃	1	4	yes	complemented
650	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
651	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
652	#103	C₂³×C₁₃	1	4	yes	complemented
653	#103	C₂³×C₁₃	1	4	yes	complemented
654	#103	C₂³×C₁₃	1	4	yes	complemented
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	4	yes	—
657	#102	C₂³×C₁₃	1	4	yes	—
658	#102	C₂³×C₁₃	1	4	yes	—
659	#102	C₂³×C₁₃	1	4	yes	complemented
660	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
663	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
664	#97	C₂³×C₁₃	1	2	yes	complemented
665	#97	C₂³×C₁₃	1	2	yes	complemented
666	C₂×C₁₃	—	2	2	no	—
667	C₂×C₁₃	—	4	2	no	—
668	C₂×C₁₃	—	4	2	no	—
669	C₂×C₁₃	—	4	4	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	—	8	2	no	—
672	C₂×C₁₃	#3484	1	1	yes	characteristic
673	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
674	C₂×C₁₃	#3585	1	1	yes	characteristic
675	C₂⁴	—	2	1	no	—
676	C₂⁴	—	2	1	no	—
677	C₂⁴	—	2	4	no	—
678	C₂⁴	—	4	4	no	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	—	8	2	no	—
681	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
683	#41	—	2	8	no	—
684	#41	—	4	4	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	8	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
694	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	8	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	8	2	no	—
716	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
717	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
720	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	8	2	no	—
733	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	Q₁₆	—	4	4	no	—
743	SD₁₆	—	2	8	no	—
744	SD₁₆	—	4	4	no	—
745	SD₁₆	—	4	4	no	—
746	D₈	—	2	8	no	—
747	D₈	—	4	4	no	—
748	M₁₆	—	4	4	no	—
749	C₂×C₈	—	4	4	no	—
750	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
751	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
787	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
792	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
793	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₁₃	#61576	1	1	yes	characteristic, direct product factor, Sylow
796	C₂³	—	2	4	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	8	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	16	no	—
815	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	Q₈	—	2	4	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	8	1	no	—
823	D₄	—	2	4	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	1	no	—
835	D₄	—	8	4	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
870	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
871	C₈	—	2	4	no	—
872	C₈	—	2	4	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	4	8	no	—
883	C₂²	—	4	4	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	8	2	no	—
893	C₂²	—	8	4	no	—
894	C₂²	—	8	16	no	—
895	C₂²	C₁₃×#575	1	2	yes	—
896	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
897	C₄	—	2	1	no	—
898	C₄	—	2	1	no	—
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₁₃×#3484	1	1	yes	characteristic
917	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
918	C₂	C₁₃×#3585	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3319	C₂	semidirect
4. C₁₃×#3311	C₂	semidirect
5. C₁₃×#3268	C₂	semidirect
6. C₁₃×#3267	C₂	semidirect
7. C₁₃×#3215	C₂	semidirect
8. C₁₃×#3213	C₂	semidirect
9. C₁₃×#3196	C₂	semidirect
10. C₁₃×#3188	C₂	semidirect
11. C₁₃×#3110	C₂	semidirect
12. C₁₃×#3109	C₂	semidirect
13. C₁₃×#3003	C₂	semidirect
14. C₁₃×#3002	C₂	semidirect
15. C₁₃×#2973	C₂	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#555	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
33. C₁₃×#533	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
37. C₁₃×#525	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
48. C₁₃×#496	C₂²	semidirect
49. C₁₃×#489	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
52. C₁₃×#484	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
54. C₁₃×#481	C₂²	semidirect
55. C₁₃×#476	C₂²	semidirect
56. C₁₃×#474	C₂²	semidirect
57. C₁₃×#470	C₂²	semidirect
58. C₁₃×#468	C₂²	semidirect
59. C₁₃×#466	C₂²	semidirect
60. C₁₃×#465	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#461	C₂²	semidirect
64. C₁₃×#459	C₂²	semidirect
65. C₁₃×#452	C₂²	semidirect
66. C₁₃×#452	C₂²	semidirect
67. C₁₃×#451	C₂²	semidirect
70. C₁₃×#450	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#449	C₂²	semidirect
73. C₁₃×#448	C₂²	semidirect
76. C₁₃×#447	C₂²	semidirect
77. C₁₃×#442	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₁₃×#435	C₂²	semidirect
80. C₁₃×#435	C₂²	semidirect
81. C₁₃×#432	C₂²	semidirect
82. C₁₃×#432	C₂²	semidirect
83. C₁₃×#418	C₂²	semidirect
84. C₁₃×#416	C₂²	semidirect
86. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
93. C₂×C₁₃×#41	C₂³	semidirect
110. C₂×C₁₃×Q₁₆	C₂³	semidirect
113. C₂×C₁₃×SD₁₆	C₂³	semidirect
117. C₂²×C₈×C₁₃	C₂³	semidirect
118. C₁₃×C₄⋊Q₈	C₂³	semidirect
119. C₁₃×C₄⋊Q₈	C₂³	semidirect
120. C₁₃×C₄⋊Q₈	C₂³	semidirect
122. C₁₃×#127	C₂³	semidirect
145. C₁₃×C₂²⋊Q₈	C₂³	semidirect
157. C₁₃×#121	C₂³	semidirect
164. C₄×Q₈×C₁₃	C₂³	semidirect
179. C₄×D₄×C₁₃	C₂³	semidirect
183. C₁₃×#117	C₂³	semidirect
198. C₁₃×#107	C₂³	semidirect
199. C₁₃×#106	C₂³	semidirect
200. C₁₃×C₄⋊C₈	C₂³	semidirect
201. C₁₃×C₄⋊C₈	C₂³	semidirect
202. C₁₃×#103	C₂³	semidirect
203. C₁₃×#103	C₂³	semidirect
204. C₁₃×#103	C₂³	semidirect
209. C₁₃×#102	C₂³	semidirect
213. C₁₃×C₂²⋊C₈	C₂³	semidirect
214. C₁₃×#97	C₂³	semidirect
215. C₁₃×#97	C₂³	semidirect
216. #61576	C₁₃	direct (N × H)
337. #3506	C₂×C₁₃	semidirect
338. C₂×#546	C₂×C₁₃	semidirect
339. #3319	C₂×C₁₃	semidirect
340. #3311	C₂×C₁₃	semidirect
341. #3268	C₂×C₁₃	semidirect
342. #3267	C₂×C₁₃	semidirect
343. #3215	C₂×C₁₃	semidirect
344. #3213	C₂×C₁₃	semidirect
345. #3196	C₂×C₁₃	semidirect
346. #3188	C₂×C₁₃	semidirect
347. #3110	C₂×C₁₃	semidirect
348. #3109	C₂×C₁₃	semidirect
349. #3003	C₂×C₁₃	semidirect
350. #3002	C₂×C₁₃	semidirect
351. #2973	C₂×C₁₃	semidirect
431. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
432. C₂×#135	C₂²×C₁₃	semidirect
434. #556	C₂²×C₁₃	semidirect
435. #555	C₂²×C₁₃	semidirect
437. #550	C₂²×C₁₃	semidirect
438. #547	C₂²×C₁₃	semidirect
446. #533	C₂²×C₁₃	semidirect
447. #532	C₂²×C₁₃	semidirect
450. #525	C₂²×C₁₃	semidirect
460. #497	C₂²×C₁₃	semidirect
461. #496	C₂²×C₁₃	semidirect
462. #489	C₂²×C₁₃	semidirect
463. #489	C₂²×C₁₃	semidirect
464. #485	C₂²×C₁₃	semidirect
465. #484	C₂²×C₁₃	semidirect
466. #482	C₂²×C₁₃	semidirect
467. #481	C₂²×C₁₃	semidirect
468. #476	C₂²×C₁₃	semidirect
469. #474	C₂²×C₁₃	semidirect
470. #470	C₂²×C₁₃	semidirect
471. #468	C₂²×C₁₃	semidirect
472. #466	C₂²×C₁₃	semidirect
473. #465	C₂²×C₁₃	semidirect
474. #464	C₂²×C₁₃	semidirect
475. #463	C₂²×C₁₃	semidirect
476. #461	C₂²×C₁₃	semidirect
477. #459	C₂²×C₁₃	semidirect
478. #452	C₂²×C₁₃	semidirect
479. #452	C₂²×C₁₃	semidirect
480. #451	C₂²×C₁₃	semidirect
483. #450	C₂²×C₁₃	semidirect
484. #449	C₂²×C₁₃	semidirect
485. #449	C₂²×C₁₃	semidirect
486. #448	C₂²×C₁₃	semidirect
489. #447	C₂²×C₁₃	semidirect
490. #442	C₂²×C₁₃	semidirect
491. #440	C₂²×C₁₃	semidirect
492. #435	C₂²×C₁₃	semidirect
493. #435	C₂²×C₁₃	semidirect
494. #432	C₂²×C₁₃	semidirect
495. #432	C₂²×C₁₃	semidirect
496. #418	C₂²×C₁₃	semidirect
497. #416	C₂²×C₁₃	semidirect
499. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
543. C₂×#41	C₂³×C₁₃	semidirect
560. C₂×Q₁₆	C₂³×C₁₃	semidirect
563. C₂×SD₁₆	C₂³×C₁₃	semidirect
567. C₂²×C₈	C₂³×C₁₃	semidirect
568. C₄⋊Q₈	C₂³×C₁₃	semidirect
569. C₄⋊Q₈	C₂³×C₁₃	semidirect
570. C₄⋊Q₈	C₂³×C₁₃	semidirect
572. #127	C₂³×C₁₃	semidirect
595. C₂²⋊Q₈	C₂³×C₁₃	semidirect
607. #121	C₂³×C₁₃	semidirect
614. C₄×Q₈	C₂³×C₁₃	semidirect
629. C₄×D₄	C₂³×C₁₃	semidirect
633. #117	C₂³×C₁₃	semidirect
648. #107	C₂³×C₁₃	semidirect
649. #106	C₂³×C₁₃	semidirect
650. C₄⋊C₈	C₂³×C₁₃	semidirect
651. C₄⋊C₈	C₂³×C₁₃	semidirect
652. #103	C₂³×C₁₃	semidirect
653. #103	C₂³×C₁₃	semidirect
654. #103	C₂³×C₁₃	semidirect
659. #102	C₂³×C₁₃	semidirect
663. C₂²⋊C₈	C₂³×C₁₃	semidirect
664. #97	C₂³×C₁₃	semidirect
665. #97	C₂³×C₁₃	semidirect
795. C₁₃	#61576	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×#3506	2
C₂×C₁₃×#546	2
C₁₃×#3319	2
C₁₃×#3311	2
C₁₃×#3268	2
C₁₃×#3267	2
C₁₃×#3215	2
C₁₃×#3213	2
C₁₃×#3196	2
C₁₃×#3188	2
C₁₃×#3110	2
C₁₃×#3109	2
C₁₃×#3003	2
C₁₃×#3002	2
C₁₃×#2973	2
#61576	13

Subgroups — C13×#61576 #15747915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61576 #15747915