Subgroups — C₁₃×#61166 #15747505

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3321	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3319	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3303	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3093	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
22	C₁₃×#555	—	2	1	no	—
23	C₁₃×#555	—	2	1	no	—
24	C₁₃×#555	—	2	2	no	—
25	C₁₃×#555	C₂²	1	2	yes	—
26	C₁₃×#555	C₂²	1	2	yes	complemented
27	C₁₃×#555	C₂²	1	4	yes	complemented
28	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#548	C₂²	1	2	yes	complemented
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	C₂²	1	2	yes	complemented
35	D₄²×C₁₃	—	2	1	no	—
36	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#532	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#124	—	2	2	no	—
41	C₁₃×#525	—	2	2	no	—
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×#121	—	2	1	no	—
44	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#117	—	2	1	no	—
50	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
51	C₁₃×#489	C₂²	1	4	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#485	C₂²	1	4	yes	complemented
56	C₁₃×#482	C₂²	1	4	yes	complemented
57	C₁₃×#482	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#474	C₂²	1	2	yes	complemented
62	C₁₃×#469	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#466	C₂²	1	4	yes	complemented
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	2	yes	complemented
68	C₁₃×#459	C₂²	1	2	yes	complemented
69	C₁₃×#449	C₂²	1	4	yes	complemented
70	C₁₃×#449	C₂²	1	4	yes	complemented
71	C₁₃×#448	C₂²	1	4	yes	complemented
72	C₁₃×#447	C₂²	1	4	yes	complemented
73	C₁₃×#442	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₁₃×#428	C₂²	1	2	yes	complemented
81	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#419	C₂²	1	4	yes	complemented
84	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#418	C₂²	1	4	yes	complemented
86	C₁₃×#417	C₂²	1	2	yes	—
87	C₁₃×#417	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	complemented
90	C₁₃×#417	C₂²	1	2	yes	complemented
91	C₁₃×#416	C₂²	1	4	yes	complemented
92	C₁₃×#416	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	complemented
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	8	no	—
98	C₂×C₁₃×#41	—	4	4	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	—	2	1	no	—
112	C₂³×C₄×C₁₃	—	2	2	no	—
113	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
114	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
115	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	2	yes	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	—	4	4	no	—
121	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
125	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	—	2	1	no	—
128	C₁₃×C₄⋊Q₈	—	2	1	no	—
129	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#127	—	2	1	no	—
133	C₁₃×#127	C₂³	1	1	yes	characteristic
134	C₁₃×#124	—	2	4	no	—
135	C₁₃×#124	—	2	4	no	—
136	C₁₃×#124	—	2	4	no	—
137	C₁₃×#124	—	2	4	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	C₂³	1	2	yes	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	4	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	C₂³	1	4	yes	—
160	C₁₃×#121	C₂³	1	4	yes	—
161	C₁₃×#121	C₂³	1	2	yes	—
162	C₁₃×#121	C₂³	1	2	yes	—
163	C₁₃×#120	—	2	2	no	—
164	C₁₃×#120	—	2	2	no	—
165	C₁₃×#120	—	2	2	no	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₁₃	—	2	1	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	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
180	C₄×D₄×C₁₃	D₄	1	2	yes	—
181	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₁₃×#117	—	2	2	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	4	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	C₂³	1	4	yes	—
196	C₁₃×#117	C₂³	1	4	yes	—
197	C₁₃×#117	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
208	C₂×C₄²×C₁₃	—	2	2	no	—
209	C₂×C₄²×C₁₃	—	2	1	no	—
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	2	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	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	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₁₃	C₂³	1	2	yes	—
233	#61166	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	—	2	1	no	—
235	C₂⁴×C₁₃	—	2	2	no	—
236	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	4	no	—
242	C₁₃×#41	—	4	8	no	—
243	C₁₃×#41	—	4	2	no	—
244	C₁₃×#41	—	4	2	no	—
245	C₁₃×#41	—	4	8	no	—
246	C₁₃×#41	#41	1	4	yes	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	4	no	—
251	C₂×Q₈×C₁₃	—	4	2	no	—
252	C₂×Q₈×C₁₃	—	8	2	no	—
253	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
254	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	4	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	2	1	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	1	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	4	2	no	—
271	C₂×D₄×C₁₃	—	4	2	no	—
272	C₂×D₄×C₁₃	—	4	8	no	—
273	C₂×D₄×C₁₃	—	4	4	no	—
274	C₂×D₄×C₁₃	—	8	4	no	—
275	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	4	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	1	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	1	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	1	no	—
294	C₂²×C₄×C₁₃	—	4	8	no	—
295	C₂²×C₄×C₁₃	—	4	4	no	—
296	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×SD₁₆	—	2	4	no	—
305	C₁₃×SD₁₆	—	4	4	no	—
306	C₁₃×D₈	—	2	4	no	—
307	C₁₃×D₈	—	4	4	no	—
308	C₁₃×M₁₆	—	2	2	no	—
309	C₁₃×M₁₆	—	2	2	no	—
310	C₁₃×M₁₆	—	2	4	no	—
311	C₁₃×M₁₆	—	4	4	no	—
312	C₂×C₈×C₁₃	—	4	4	no	—
313	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	1	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	1	no	—
323	C₁₃×C₄⋊C₄	—	2	1	no	—
324	C₁₃×C₄⋊C₄	—	2	1	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
327	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
332	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	2	2	no	—
336	C₁₃×C₂²⋊C₄	—	2	1	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	4	no	—
339	C₁₃×C₂²⋊C₄	—	2	4	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	1	no	—
345	C₁₃×C₂²⋊C₄	—	2	1	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
349	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
350	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
351	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
352	C₄²×C₁₃	—	2	4	no	—
353	C₄²×C₁₃	—	2	4	no	—
354	C₄²×C₁₃	—	2	1	no	—
355	C₄²×C₁₃	—	2	1	no	—
356	C₄²×C₁₃	—	2	1	no	—
357	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
358	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
359	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
362	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3329	C₂×C₁₃	1	2	yes	complemented
364	#3325	C₂×C₁₃	1	2	yes	complemented
365	#3321	C₂×C₁₃	1	4	yes	complemented
366	#3319	C₂×C₁₃	1	4	yes	complemented
367	#3305	C₂×C₁₃	1	2	yes	complemented
368	#3303	C₂×C₁₃	1	2	yes	complemented
369	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#3093	C₂×C₁₃	1	2	yes	complemented
371	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#3055	C₂×C₁₃	1	2	yes	complemented
373	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
374	#3006	C₂×C₁₃	1	2	yes	complemented
375	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
376	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#2896	C₂×C₁₃	1	2	yes	complemented
378	C₂³×C₁₃	—	2	1	no	—
379	C₂³×C₁₃	—	2	4	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	4	2	no	—
383	C₂³×C₁₃	—	4	2	no	—
384	C₂³×C₁₃	—	4	4	no	—
385	C₂³×C₁₃	—	4	2	no	—
386	C₂³×C₁₃	—	4	4	no	—
387	C₂³×C₁₃	—	4	2	no	—
388	C₂³×C₁₃	—	4	2	no	—
389	C₂³×C₁₃	—	8	2	no	—
390	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
391	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	Q₈×C₁₃	—	2	1	no	—
394	Q₈×C₁₃	—	2	2	no	—
395	Q₈×C₁₃	—	2	2	no	—
396	Q₈×C₁₃	—	4	4	no	—
397	Q₈×C₁₃	—	8	2	no	—
398	Q₈×C₁₃	—	8	2	no	—
399	Q₈×C₁₃	C₂×#41	1	2	yes	—
400	D₄×C₁₃	—	2	4	no	—
401	D₄×C₁₃	—	2	2	no	—
402	D₄×C₁₃	—	2	2	no	—
403	D₄×C₁₃	—	2	2	no	—
404	D₄×C₁₃	—	2	2	no	—
405	D₄×C₁₃	—	2	1	no	—
406	D₄×C₁₃	—	2	2	no	—
407	D₄×C₁₃	—	2	2	no	—
408	D₄×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	4	4	no	—
410	D₄×C₁₃	—	4	4	no	—
411	D₄×C₁₃	—	4	4	no	—
412	D₄×C₁₃	—	4	4	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	2	no	—
415	D₄×C₁₃	—	4	2	no	—
416	D₄×C₁₃	—	8	1	no	—
417	D₄×C₁₃	—	8	2	no	—
418	D₄×C₁₃	—	8	4	no	—
419	D₄×C₁₃	—	8	4	no	—
420	D₄×C₁₃	C₂×#41	1	2	yes	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	4	no	—
424	C₂×C₄×C₁₃	—	2	4	no	—
425	C₂×C₄×C₁₃	—	2	4	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	4	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	4	1	no	—
437	C₂×C₄×C₁₃	—	4	4	no	—
438	C₂×C₄×C₁₃	—	4	4	no	—
439	C₂×C₄×C₁₃	—	4	4	no	—
440	C₂×C₄×C₁₃	—	4	4	no	—
441	C₂×C₄×C₁₃	—	4	2	no	—
442	C₂×C₄×C₁₃	—	4	4	no	—
443	C₂×C₄×C₁₃	—	4	4	no	—
444	C₂×C₄×C₁₃	—	4	4	no	—
445	C₂×C₄×C₁₃	—	4	2	no	—
446	C₂×C₄×C₁₃	—	8	1	no	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
455	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
456	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
457	C₈×C₁₃	—	2	2	no	—
458	C₈×C₁₃	—	2	2	no	—
459	C₈×C₁₃	—	2	4	no	—
460	C₂²×#41	C₂²×C₁₃	1	2	yes	—
461	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
463	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
464	#555	—	2	1	no	—
465	#555	—	2	1	no	—
466	#555	—	2	2	no	—
467	#555	C₂²×C₁₃	1	2	yes	—
468	#555	C₂²×C₁₃	1	2	yes	complemented
469	#555	C₂²×C₁₃	1	4	yes	complemented
470	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	#548	C₂²×C₁₃	1	2	yes	complemented
473	#547	—	2	1	no	—
474	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#546	—	2	2	no	—
476	#546	C₂²×C₁₃	1	2	yes	complemented
477	D₄²	—	2	1	no	—
478	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	#532	—	2	1	no	—
480	#532	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂×#124	—	2	2	no	—
483	#525	—	2	2	no	—
484	#525	C₂²×C₁₃	1	2	yes	—
485	C₂×#121	—	2	1	no	—
486	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
487	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×C₄×D₄	—	2	1	no	—
489	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	C₂×#117	—	2	1	no	—
492	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
493	#489	C₂²×C₁₃	1	4	yes	complemented
494	#487	C₂²×C₁₃	1	2	yes	complemented
495	#486	C₂²×C₁₃	1	2	yes	complemented
496	#485	C₂²×C₁₃	1	4	yes	complemented
497	#485	C₂²×C₁₃	1	4	yes	complemented
498	#482	C₂²×C₁₃	1	4	yes	complemented
499	#482	C₂²×C₁₃	1	4	yes	complemented
500	#477	C₂²×C₁₃	1	2	yes	complemented
501	#476	C₂²×C₁₃	1	2	yes	complemented
502	#475	C₂²×C₁₃	1	2	yes	complemented
503	#474	C₂²×C₁₃	1	2	yes	complemented
504	#469	C₂²×C₁₃	1	4	yes	complemented
505	#468	C₂²×C₁₃	1	4	yes	complemented
506	#466	C₂²×C₁₃	1	4	yes	complemented
507	#465	C₂²×C₁₃	1	4	yes	complemented
508	#463	C₂²×C₁₃	1	4	yes	complemented
509	#461	C₂²×C₁₃	1	2	yes	complemented
510	#459	C₂²×C₁₃	1	2	yes	complemented
511	#449	C₂²×C₁₃	1	4	yes	complemented
512	#449	C₂²×C₁₃	1	4	yes	complemented
513	#448	C₂²×C₁₃	1	4	yes	complemented
514	#447	C₂²×C₁₃	1	4	yes	complemented
515	#442	C₂²×C₁₃	1	2	yes	complemented
516	#440	C₂²×C₁₃	1	2	yes	complemented
517	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
518	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
519	#436	C₂²×C₁₃	1	2	yes	complemented
520	#435	C₂²×C₁₃	1	4	yes	complemented
521	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
522	#428	C₂²×C₁₃	1	2	yes	complemented
523	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	#419	C₂²×C₁₃	1	4	yes	complemented
526	#418	C₂²×C₁₃	1	4	yes	complemented
527	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	#417	C₂²×C₁₃	1	2	yes	—
529	#417	C₂²×C₁₃	1	1	yes	characteristic
530	#417	C₂²×C₁₃	1	2	yes	complemented
531	#417	C₂²×C₁₃	1	2	yes	complemented
532	#417	C₂²×C₁₃	1	2	yes	complemented
533	#416	C₂²×C₁₃	1	4	yes	complemented
534	#416	C₂²×C₁₃	1	4	yes	complemented
535	#407	C₂²×C₁₃	1	2	yes	complemented
536	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	C₂²×C₁₃	—	2	1	no	—
538	C₂²×C₁₃	—	2	1	no	—
539	C₂²×C₁₃	—	2	2	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	2	no	—
542	C₂²×C₁₃	—	2	2	no	—
543	C₂²×C₁₃	—	2	2	no	—
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	2	2	no	—
546	C₂²×C₁₃	—	4	1	no	—
547	C₂²×C₁₃	—	4	1	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	4	2	no	—
550	C₂²×C₁₃	—	4	2	no	—
551	C₂²×C₁₃	—	4	2	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	8	4	no	—
555	C₂²×C₁₃	—	8	4	no	—
556	C₂²×C₁₃	—	8	8	no	—
557	C₂²×C₁₃	#546	1	2	yes	—
558	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₁₃	—	2	1	no	—
560	C₄×C₁₃	—	2	1	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	2	2	no	—
564	C₄×C₁₃	—	2	1	no	—
565	C₄×C₁₃	—	4	4	no	—
566	C₄×C₁₃	—	4	1	no	—
567	C₄×C₁₃	—	4	2	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	1	no	—
570	C₄×C₁₃	#546	1	2	yes	—
571	C₄×C₁₃	#575	1	2	yes	—
572	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
573	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	2	2	no	—
576	C₂×#41	—	2	8	no	—
577	C₂×#41	—	4	4	no	—
578	C₂×#41	C₂³×C₁₃	1	2	yes	—
579	C₂×#41	C₂³×C₁₃	1	2	yes	—
580	C₂×#41	C₂³×C₁₃	1	2	yes	—
581	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
582	C₂²×Q₈	—	2	1	no	—
583	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	2	no	—
586	C₂²×D₄	—	2	1	no	—
587	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
590	C₂³×C₄	—	2	1	no	—
591	C₂³×C₄	—	2	2	no	—
592	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
593	AGL(1,ℤ/8)	—	2	4	no	—
594	AGL(1,ℤ/8)	—	4	4	no	—
595	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
596	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
597	C₂×D₈	C₂³×C₁₃	1	2	yes	—
598	C₂×D₈	C₂³×C₁₃	1	4	yes	—
599	C₂×M₁₆	—	4	4	no	—
600	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
602	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
604	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
605	C₄⋊Q₈	—	2	1	no	—
606	C₄⋊Q₈	—	2	1	no	—
607	C₄⋊Q₈	—	2	1	no	—
608	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
610	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
611	#127	—	2	1	no	—
612	#127	C₂³×C₁₃	1	1	yes	characteristic
613	#124	—	2	4	no	—
614	#124	—	2	4	no	—
615	#124	—	2	4	no	—
616	#124	—	2	4	no	—
617	#124	—	2	2	no	—
618	#124	C₂³×C₁₃	1	2	yes	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
626	#121	—	2	2	no	—
627	#121	—	2	2	no	—
628	#121	—	2	4	no	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	2	no	—
632	#121	—	2	2	no	—
633	#121	—	2	1	no	—
634	#121	—	2	1	no	—
635	#121	—	2	1	no	—
636	#121	—	2	2	no	—
637	#121	—	2	2	no	—
638	#121	C₂³×C₁₃	1	4	yes	—
639	#121	C₂³×C₁₃	1	4	yes	—
640	#121	C₂³×C₁₃	1	2	yes	—
641	#121	C₂³×C₁₃	1	2	yes	—
642	#120	—	2	2	no	—
643	#120	—	2	2	no	—
644	#120	—	2	2	no	—
645	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
646	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
659	C₄×D₄	D₄×C₁₃	1	2	yes	—
660	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₁₃	1	2	yes	—
662	C₄×D₄	C₂³×C₁₃	1	2	yes	—
663	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
666	C₄×D₄	C₂³×C₁₃	1	2	yes	—
667	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
668	#117	—	2	2	no	—
669	#117	—	2	2	no	—
670	#117	—	2	2	no	—
671	#117	—	2	2	no	—
672	#117	—	2	4	no	—
673	#117	—	2	1	no	—
674	#117	C₂³×C₁₃	1	4	yes	—
675	#117	C₂³×C₁₃	1	4	yes	—
676	#117	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	—	2	1	no	—
678	C₂×C₄⋊C₄	—	2	1	no	—
679	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₂²⋊C₄	—	2	2	no	—
683	C₂×C₂²⋊C₄	—	2	2	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	2	no	—
686	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
687	C₂×C₄²	—	2	2	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
690	#107	C₂³×C₁₃	1	2	yes	—
691	#107	C₂³×C₁₃	1	4	yes	—
692	#106	C₂³×C₁₃	1	2	yes	—
693	#106	C₂³×C₁₃	1	4	yes	—
694	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
695	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
696	#103	C₂³×C₁₃	1	2	yes	—
697	#103	C₂³×C₁₃	1	4	yes	—
698	#103	C₂³×C₁₃	1	4	yes	—
699	#103	C₂³×C₁₃	1	4	yes	—
700	#103	C₂³×C₁₃	1	4	yes	—
701	#102	C₂³×C₁₃	1	2	yes	—
702	#102	C₂³×C₁₃	1	4	yes	—
703	#102	C₂³×C₁₃	1	4	yes	—
704	#102	C₂³×C₁₃	1	4	yes	—
705	#102	C₂³×C₁₃	1	4	yes	—
706	#102	C₂³×C₁₃	1	2	yes	—
707	#102	C₂³×C₁₃	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
709	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
710	#97	C₂³×C₁₃	1	2	yes	—
711	C₄×C₈	C₂³×C₁₃	1	2	yes	—
712	C₂×C₁₃	—	2	2	no	—
713	C₂×C₁₃	—	4	2	no	—
714	C₂×C₁₃	—	4	2	no	—
715	C₂×C₁₃	—	4	2	no	—
716	C₂×C₁₃	—	8	2	no	—
717	C₂×C₁₃	—	8	2	no	—
718	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
719	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
720	C₂×C₁₃	#3585	1	1	yes	characteristic
721	C₂⁴	—	2	1	no	—
722	C₂⁴	—	2	2	no	—
723	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
724	#41	—	2	2	no	—
725	#41	—	2	4	no	—
726	#41	—	2	4	no	—
727	#41	—	2	4	no	—
728	#41	—	2	4	no	—
729	#41	—	4	8	no	—
730	#41	—	4	2	no	—
731	#41	—	4	2	no	—
732	#41	—	4	8	no	—
733	#41	C₁₃×#41	1	4	yes	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	4	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	8	2	no	—
740	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
741	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	4	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	8	no	—
760	C₂×D₄	—	4	4	no	—
761	C₂×D₄	—	8	4	no	—
762	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	2	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	1	no	—
781	C₂²×C₄	—	4	8	no	—
782	C₂²×C₄	—	4	4	no	—
783	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	SD₁₆	—	2	4	no	—
792	SD₁₆	—	4	4	no	—
793	D₈	—	2	4	no	—
794	D₈	—	4	4	no	—
795	M₁₆	—	2	2	no	—
796	M₁₆	—	2	2	no	—
797	M₁₆	—	2	4	no	—
798	M₁₆	—	4	4	no	—
799	C₂×C₈	—	4	4	no	—
800	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
801	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
814	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
818	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	1	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
836	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
837	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
839	C₄²	—	2	4	no	—
840	C₄²	—	2	4	no	—
841	C₄²	—	2	1	no	—
842	C₄²	—	2	1	no	—
843	C₄²	—	2	1	no	—
844	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
845	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
846	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
847	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
848	C₁₃	#61166	1	1	yes	characteristic, direct product factor, Sylow
849	C₂³	—	2	1	no	—
850	C₂³	—	2	4	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	4	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	2	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	8	2	no	—
861	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
862	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
863	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
864	Q₈	—	2	1	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	4	4	no	—
868	Q₈	—	8	2	no	—
869	Q₈	—	8	2	no	—
870	Q₈	C₂×C₁₃×#41	1	2	yes	—
871	D₄	—	2	4	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	1	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	2	no	—
879	D₄	—	4	2	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	4	4	no	—
884	D₄	—	4	4	no	—
885	D₄	—	4	2	no	—
886	D₄	—	4	2	no	—
887	D₄	—	8	1	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	2	no	—
891	D₄	C₂×C₁₃×#41	1	2	yes	—
892	C₂×C₄	—	2	4	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	2	4	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	2	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	8	1	no	—
918	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
919	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
920	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
921	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
925	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
926	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
927	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
928	C₈	—	2	2	no	—
929	C₈	—	2	2	no	—
930	C₈	—	2	4	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	8	4	no	—
949	C₂²	—	8	4	no	—
950	C₂²	—	8	8	no	—
951	C₂²	C₁₃×#546	1	2	yes	—
952	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	4	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	C₁₃×#546	1	2	yes	—
965	C₄	C₁₃×#575	1	2	yes	—
966	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
967	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
968	C₂	—	2	2	no	—
969	C₂	—	4	2	no	—
970	C₂	—	4	2	no	—
971	C₂	—	4	2	no	—
972	C₂	—	8	2	no	—
973	C₂	—	8	2	no	—
974	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
975	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
976	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. C₂×C₁₃×#555	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3325	C₂	semidirect
5. C₁₃×#3321	C₂	semidirect
6. C₁₃×#3319	C₂	semidirect
7. C₁₃×#3305	C₂	semidirect
8. C₁₃×#3303	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3093	C₂	semidirect
11. C₁₃×#3079	C₂	semidirect
12. C₁₃×#3055	C₂	semidirect
13. C₁₃×#3036	C₂	semidirect
14. C₁₃×#3006	C₂	semidirect
15. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#2896	C₂	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂²×C₁₃×M₁₆	C₂²	semidirect
26. C₁₃×#555	C₂²	semidirect
27. C₁₃×#555	C₂²	semidirect
28. C₁₃×#550	C₂²	semidirect
29. D₄×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×#548	C₂²	semidirect
32. C₁₃×#547	C₂²	semidirect
34. C₁₃×#546	C₂²	semidirect
36. D₄²×C₁₃	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₁₃×#121	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₂×C₁₃×#117	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#485	C₂²	semidirect
56. C₁₃×#482	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#469	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#466	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
69. C₁₃×#449	C₂²	semidirect
70. C₁₃×#449	C₂²	semidirect
71. C₁₃×#448	C₂²	semidirect
72. C₁₃×#447	C₂²	semidirect
73. C₁₃×#442	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×SD₁₆	C₂²	semidirect
76. C₄×C₁₃×D₈	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#428	C₂²	semidirect
81. C₁₃×#428	C₂²	semidirect
82. C₁₃×#423	C₂²	semidirect
83. C₁₃×#419	C₂²	semidirect
84. C₁₃×#418	C₂²	semidirect
85. C₁₃×#418	C₂²	semidirect
88. C₁₃×#417	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₁₃×#416	C₂²	semidirect
92. C₁₃×#416	C₂²	semidirect
93. C₁₃×#407	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
233. #61166	C₁₃	direct (N × H)
361. C₂×#555	C₂×C₁₃	semidirect
362. D₄×#41	C₂×C₁₃	semidirect
363. #3329	C₂×C₁₃	semidirect
364. #3325	C₂×C₁₃	semidirect
365. #3321	C₂×C₁₃	semidirect
366. #3319	C₂×C₁₃	semidirect
367. #3305	C₂×C₁₃	semidirect
368. #3303	C₂×C₁₃	semidirect
369. #3141	C₂×C₁₃	semidirect
370. #3093	C₂×C₁₃	semidirect
371. #3079	C₂×C₁₃	semidirect
372. #3055	C₂×C₁₃	semidirect
373. #3036	C₂×C₁₃	semidirect
374. #3006	C₂×C₁₃	semidirect
375. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
376. D₄×M₁₆	C₂×C₁₃	semidirect
377. #2896	C₂×C₁₃	semidirect
462. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
463. C₂²×M₁₆	C₂²×C₁₃	semidirect
468. #555	C₂²×C₁₃	semidirect
469. #555	C₂²×C₁₃	semidirect
470. #550	C₂²×C₁₃	semidirect
471. D₄×Q₈	C₂²×C₁₃	semidirect
472. #548	C₂²×C₁₃	semidirect
474. #547	C₂²×C₁₃	semidirect
476. #546	C₂²×C₁₃	semidirect
478. D₄²	C₂²×C₁₃	semidirect
481. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
486. C₂×#121	C₂²×C₁₃	semidirect
490. C₂×C₄×D₄	C₂²×C₁₃	semidirect
492. C₂×#117	C₂²×C₁₃	semidirect
493. #489	C₂²×C₁₃	semidirect
494. #487	C₂²×C₁₃	semidirect
495. #486	C₂²×C₁₃	semidirect
496. #485	C₂²×C₁₃	semidirect
497. #485	C₂²×C₁₃	semidirect
498. #482	C₂²×C₁₃	semidirect
499. #482	C₂²×C₁₃	semidirect
500. #477	C₂²×C₁₃	semidirect
501. #476	C₂²×C₁₃	semidirect
502. #475	C₂²×C₁₃	semidirect
503. #474	C₂²×C₁₃	semidirect
504. #469	C₂²×C₁₃	semidirect
505. #468	C₂²×C₁₃	semidirect
506. #466	C₂²×C₁₃	semidirect
507. #465	C₂²×C₁₃	semidirect
508. #463	C₂²×C₁₃	semidirect
509. #461	C₂²×C₁₃	semidirect
510. #459	C₂²×C₁₃	semidirect
511. #449	C₂²×C₁₃	semidirect
512. #449	C₂²×C₁₃	semidirect
513. #448	C₂²×C₁₃	semidirect
514. #447	C₂²×C₁₃	semidirect
515. #442	C₂²×C₁₃	semidirect
516. #440	C₂²×C₁₃	semidirect
517. C₄×SD₁₆	C₂²×C₁₃	semidirect
518. C₄×D₈	C₂²×C₁₃	semidirect
519. #436	C₂²×C₁₃	semidirect
520. #435	C₂²×C₁₃	semidirect
521. C₈×D₄	C₂²×C₁₃	semidirect
522. #428	C₂²×C₁₃	semidirect
523. #428	C₂²×C₁₃	semidirect
524. #423	C₂²×C₁₃	semidirect
525. #419	C₂²×C₁₃	semidirect
526. #418	C₂²×C₁₃	semidirect
527. #418	C₂²×C₁₃	semidirect
530. #417	C₂²×C₁₃	semidirect
531. #417	C₂²×C₁₃	semidirect
532. #417	C₂²×C₁₃	semidirect
533. #416	C₂²×C₁₃	semidirect
534. #416	C₂²×C₁₃	semidirect
535. #407	C₂²×C₁₃	semidirect
536. C₄×M₁₆	C₂²×C₁₃	semidirect
848. C₁₃	#61166	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#555	2
D₄×C₁₃×#41	2
C₁₃×#3329	2
C₁₃×#3325	2
C₁₃×#3321	2
C₁₃×#3319	2
C₁₃×#3305	2
C₁₃×#3303	2
C₁₃×#3141	2
C₁₃×#3093	2
C₁₃×#3079	2
C₁₃×#3055	2
C₁₃×#3036	2
C₁₃×#3006	2
C₄×C₁₃×AGL(1,ℤ/8)	2
D₄×C₁₃×M₁₆	2
C₁₃×#2896	2
#61166	13

Subgroups — C13×#61166 #15747505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61166 #15747505