Subgroups — C₁₃×#61629 #15747968

Order 3328.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3294	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3265	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
25	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
26	C₁₃×#562	—	2	2	no	—
27	C₁₃×#554	C₂²	1	2	yes	complemented
28	C₁₃×#548	C₂²	1	2	yes	complemented
29	C₁₃×#547	C₂²	1	2	yes	complemented
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	—	2	1	no	—
32	C₁₃×#546	—	2	2	no	—
33	C₁₃×#546	C₂²	1	2	yes	—
34	C₁₃×#546	C₂²	1	2	yes	complemented
35	C₁₃×#546	C₂²	1	2	yes	complemented
36	D₄²×C₁₃	—	2	1	no	—
37	D₄²×C₁₃	—	2	1	no	—
38	D₄²×C₁₃	C₂²	1	2	yes	—
39	D₄²×C₁₃	C₂²	1	2	yes	complemented
40	C₁₃×#543	—	2	1	no	—
41	C₁₃×#542	C₂²	1	2	yes	complemented
42	C₁₃×#539	—	2	1	no	—
43	C₁₃×#538	—	2	1	no	—
44	C₁₃×#537	—	2	1	no	—
45	C₁₃×#537	C₂²	1	2	yes	complemented
46	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#534	—	2	2	no	—
49	C₁₃×#525	C₂²	1	1	yes	characteristic
50	C₁₃×#525	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×#120	—	2	2	no	—
54	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#496	C₂²	1	2	yes	complemented
56	C₁₃×#495	C₂²	1	2	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	complemented
58	C₁₃×#486	C₂²	1	2	yes	complemented
59	C₁₃×#485	C₂²	1	2	yes	complemented
60	C₁₃×#484	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#482	C₂²	1	2	yes	complemented
63	C₁₃×#481	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#481	C₂²	1	2	yes	complemented
65	C₁₃×#480	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#480	C₂²	1	2	yes	complemented
67	C₁₃×#476	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#469	C₂²	1	2	yes	complemented
70	C₁₃×#468	C₂²	1	2	yes	complemented
71	C₁₃×#467	C₂²	1	2	yes	complemented
72	C₁₃×#466	C₂²	1	2	yes	complemented
73	C₁₃×#466	C₂²	1	2	yes	complemented
74	C₁₃×#465	C₂²	1	2	yes	complemented
75	C₁₃×#465	C₂²	1	2	yes	complemented
76	C₁₃×#465	C₂²	1	2	yes	complemented
77	C₁₃×#464	C₂²	1	2	yes	complemented
78	C₁₃×#463	C₂²	1	2	yes	complemented
79	C₁₃×#463	C₂²	1	2	yes	complemented
80	C₁₃×#463	C₂²	1	2	yes	complemented
81	C₁₃×#460	C₂²	1	2	yes	complemented
82	C₁₃×#459	C₂²	1	2	yes	complemented
83	C₁₃×#452	C₂²	1	2	yes	complemented
84	C₁₃×#452	C₂²	1	2	yes	complemented
85	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#450	C₂²	1	2	yes	complemented
87	C₁₃×#450	C₂²	1	2	yes	complemented
88	C₁₃×#450	C₂²	1	2	yes	complemented
89	C₁₃×#450	C₂²	1	2	yes	complemented
90	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#450	C₂²	1	2	yes	complemented
92	C₁₃×#449	C₂²	1	2	yes	complemented
93	C₁₃×#449	C₂²	1	2	yes	complemented
94	C₁₃×#449	C₂²	1	2	yes	complemented
95	C₁₃×#449	C₂²	1	2	yes	complemented
96	C₁₃×#448	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#447	C₂²	1	2	yes	—
98	C₁₃×#447	C₂²	1	2	yes	complemented
99	C₁₃×#447	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	complemented
101	C₁₃×#447	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#447	C₂²	1	2	yes	complemented
103	C₁₃×#442	C₂²	1	2	yes	complemented
104	C₁₃×#440	C₂²	1	2	yes	complemented
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
106	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
107	C₁₃×#435	C₂²	1	2	yes	complemented
108	C₁₃×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
110	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
111	C₁₃×#433	C₂²	1	2	yes	complemented
112	C₁₃×#417	C₂²	1	2	yes	complemented
113	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
114	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
115	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
116	C₁₃×#408	C₂²	1	2	yes	complemented
117	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂⁵×C₁₃	—	2	1	no	—
120	C₁₃×H(5,𝔽₂)	—	4	4	no	—
121	C₂×C₁₃×#41	—	2	1	no	—
122	C₂×C₁₃×#41	—	2	2	no	—
123	C₂×C₁₃×#41	C₂³	1	2	yes	—
124	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×#41	C₂³	1	2	yes	complemented
127	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃	—	2	1	no	—
129	C₂²×D₄×C₁₃	—	2	2	no	—
130	C₂²×D₄×C₁₃	—	2	1	no	—
131	C₂²×D₄×C₁₃	—	2	2	no	—
132	C₂²×D₄×C₁₃	—	2	2	no	—
133	C₂²×D₄×C₁₃	—	2	1	no	—
134	C₂²×D₄×C₁₃	—	2	1	no	—
135	C₂²×D₄×C₁₃	—	2	1	no	—
136	C₂²×D₄×C₁₃	—	4	4	no	—
137	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
145	C₁₃×#135	—	4	4	no	—
146	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	complemented
147	C₂×C₁₃×SD₁₆	—	4	4	no	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
154	C₂×C₁₃×D₈	—	4	4	no	—
155	C₂×C₁₃×D₈	C₂³	1	2	yes	—
156	C₂×C₁₃×D₈	C₂³	1	2	yes	—
157	C₂×C₁₃×D₈	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	2	yes	—
159	C₂×C₁₃×D₈	C₂³	1	2	yes	complemented
160	C₂×C₁₃×M₁₆	C₂³	1	2	yes	complemented
161	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
163	C₂²×C₈×C₁₃	C₂³	1	2	yes	complemented
164	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
165	C₁₃×#127	—	2	1	no	—
166	C₁₃×#127	C₂³	1	2	yes	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#124	—	2	1	no	—
170	C₁₃×#124	—	2	2	no	—
171	C₁₃×#124	—	2	2	no	—
172	C₁₃×#124	C₂³	1	2	yes	—
173	C₁₃×#124	C₂³	1	2	yes	complemented
174	C₁₃×#123	—	2	1	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	D₄	1	2	yes	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	1	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
191	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
192	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	D₄	1	1	yes	characteristic
211	C₁₃×#121	D₄	1	1	yes	characteristic
212	C₁₃×#121	C₂³	1	2	yes	—
213	C₁₃×#121	C₂³	1	2	yes	—
214	C₁₃×#121	C₂³	1	1	yes	characteristic
215	C₁₃×#121	C₂³	1	1	yes	characteristic
216	C₁₃×#121	C₂³	1	2	yes	—
217	C₁₃×#121	C₂³	1	2	yes	—
218	C₁₃×#121	C₂³	1	2	yes	complemented
219	C₁₃×#120	—	2	1	no	—
220	C₁₃×#120	—	2	2	no	—
221	C₁₃×#120	—	2	2	no	—
222	C₁₃×#120	—	2	2	no	—
223	C₁₃×#120	—	2	2	no	—
224	C₁₃×#120	—	2	2	no	—
225	C₁₃×#120	—	2	2	no	—
226	C₁₃×#120	—	2	2	no	—
227	C₁₃×#120	—	2	2	no	—
228	C₁₃×#120	—	2	2	no	—
229	C₁₃×#120	D₄	1	2	yes	—
230	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	2	yes	—
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
242	C₁₃×#117	C₂³	1	1	yes	characteristic
243	C₁₃×#117	C₂³	1	1	yes	characteristic
244	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
248	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
254	C₁₃×#107	C₂³	1	2	yes	complemented
255	C₁₃×#107	C₂³	1	2	yes	complemented
256	C₁₃×#106	C₂³	1	2	yes	complemented
257	C₁₃×#106	C₂³	1	2	yes	complemented
258	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
260	C₁₃×#103	C₂³	1	2	yes	complemented
261	C₁₃×#103	C₂³	1	2	yes	complemented
262	C₁₃×#103	C₂³	1	2	yes	complemented
263	C₁₃×#103	C₂³	1	2	yes	complemented
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×#102	C₂³	1	2	yes	—
271	C₁₃×#102	C₂³	1	2	yes	—
272	C₁₃×#102	C₂³	1	2	yes	complemented
273	C₁₃×#102	C₂³	1	2	yes	complemented
274	C₁₃×#102	C₂³	1	2	yes	complemented
275	C₁₃×#102	C₂³	1	2	yes	complemented
276	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
283	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
284	C₁₃×#97	C₂³	1	2	yes	complemented
285	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
286	#61629	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂⁴×C₁₃	—	2	1	no	—
288	C₂⁴×C₁₃	—	2	2	no	—
289	C₂⁴×C₁₃	—	2	2	no	—
290	C₂⁴×C₁₃	—	2	1	no	—
291	C₂⁴×C₁₃	—	2	1	no	—
292	C₂⁴×C₁₃	—	2	2	no	—
293	C₂⁴×C₁₃	—	4	4	no	—
294	C₂⁴×C₁₃	—	8	2	no	—
295	C₂⁴×C₁₃	—	8	2	no	—
296	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₁₃×#41	—	2	4	no	—
298	C₁₃×#41	—	4	2	no	—
299	C₁₃×#41	—	4	2	no	—
300	C₁₃×#41	—	4	2	no	—
301	C₁₃×#41	—	4	2	no	—
302	C₁₃×#41	—	4	2	no	—
303	C₁₃×#41	—	4	4	no	—
304	C₁₃×#41	—	8	4	no	—
305	C₂×Q₈×C₁₃	—	2	1	no	—
306	C₂×Q₈×C₁₃	—	2	2	no	—
307	C₂×Q₈×C₁₃	—	4	2	no	—
308	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
311	C₂×D₄×C₁₃	—	2	4	no	—
312	C₂×D₄×C₁₃	—	2	4	no	—
313	C₂×D₄×C₁₃	—	2	4	no	—
314	C₂×D₄×C₁₃	—	2	4	no	—
315	C₂×D₄×C₁₃	—	2	1	no	—
316	C₂×D₄×C₁₃	—	2	1	no	—
317	C₂×D₄×C₁₃	—	2	2	no	—
318	C₂×D₄×C₁₃	—	2	1	no	—
319	C₂×D₄×C₁₃	—	2	2	no	—
320	C₂×D₄×C₁₃	—	2	2	no	—
321	C₂×D₄×C₁₃	—	2	2	no	—
322	C₂×D₄×C₁₃	—	2	2	no	—
323	C₂×D₄×C₁₃	—	2	2	no	—
324	C₂×D₄×C₁₃	—	2	2	no	—
325	C₂×D₄×C₁₃	—	2	1	no	—
326	C₂×D₄×C₁₃	—	2	2	no	—
327	C₂×D₄×C₁₃	—	2	2	no	—
328	C₂×D₄×C₁₃	—	2	2	no	—
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	4	2	no	—
334	C₂×D₄×C₁₃	—	4	2	no	—
335	C₂×D₄×C₁₃	—	4	2	no	—
336	C₂×D₄×C₁₃	—	4	2	no	—
337	C₂×D₄×C₁₃	—	4	2	no	—
338	C₂×D₄×C₁₃	—	4	4	no	—
339	C₂×D₄×C₁₃	—	4	4	no	—
340	C₂×D₄×C₁₃	—	4	4	no	—
341	C₂×D₄×C₁₃	—	4	4	no	—
342	C₂×D₄×C₁₃	—	4	8	no	—
343	C₂×D₄×C₁₃	—	8	4	no	—
344	C₂×D₄×C₁₃	—	8	4	no	—
345	C₂×D₄×C₁₃	—	8	2	no	—
346	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
351	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	2	2	no	—
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	1	no	—
360	C₂²×C₄×C₁₃	—	2	2	no	—
361	C₂²×C₄×C₁₃	—	2	2	no	—
362	C₂²×C₄×C₁₃	—	2	2	no	—
363	C₂²×C₄×C₁₃	—	2	2	no	—
364	C₂²×C₄×C₁₃	—	4	2	no	—
365	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
372	C₁₃×Q₁₆	—	4	2	no	—
373	C₁₃×SD₁₆	—	2	4	no	—
374	C₁₃×SD₁₆	—	2	4	no	—
375	C₁₃×SD₁₆	—	4	2	no	—
376	C₁₃×SD₁₆	—	4	2	no	—
377	C₁₃×SD₁₆	—	4	2	no	—
378	C₁₃×SD₁₆	—	4	2	no	—
379	C₁₃×D₈	—	2	4	no	—
380	C₁₃×D₈	—	2	4	no	—
381	C₁₃×D₈	—	4	2	no	—
382	C₁₃×D₈	—	4	2	no	—
383	C₁₃×D₈	—	4	2	no	—
384	C₁₃×M₁₆	—	4	2	no	—
385	C₂×C₈×C₁₃	—	4	2	no	—
386	C₂×C₈×C₁₃	—	4	2	no	—
387	C₂×C₈×C₁₃	—	4	2	no	—
388	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
390	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
391	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	1	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₄²×C₁₃	—	2	1	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	C₂⁴	1	2	yes	—
438	#3536	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#3484	C₂×C₁₃	1	1	yes	characteristic, complemented
440	#3314	C₂×C₁₃	1	2	yes	complemented
441	#3306	C₂×C₁₃	1	2	yes	complemented
442	#3295	C₂×C₁₃	1	2	yes	complemented
443	#3294	C₂×C₁₃	1	2	yes	complemented
444	#3282	C₂×C₁₃	1	2	yes	complemented
445	#3280	C₂×C₁₃	1	2	yes	complemented
446	#3265	C₂×C₁₃	1	2	yes	complemented
447	#3264	C₂×C₁₃	1	2	yes	complemented
448	#3224	C₂×C₁₃	1	2	yes	complemented
449	#3198	C₂×C₁₃	1	2	yes	complemented
450	#3190	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3188	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3118	C₂×C₁₃	1	2	yes	complemented
453	#3012	C₂×C₁₃	1	2	yes	complemented
454	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
455	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#2977	C₂×C₁₃	1	1	yes	characteristic, complemented
457	C₂³×C₁₃	—	2	4	no	—
458	C₂³×C₁₃	—	2	2	no	—
459	C₂³×C₁₃	—	2	2	no	—
460	C₂³×C₁₃	—	2	2	no	—
461	C₂³×C₁₃	—	2	2	no	—
462	C₂³×C₁₃	—	2	2	no	—
463	C₂³×C₁₃	—	2	1	no	—
464	C₂³×C₁₃	—	4	1	no	—
465	C₂³×C₁₃	—	4	4	no	—
466	C₂³×C₁₃	—	4	4	no	—
467	C₂³×C₁₃	—	4	4	no	—
468	C₂³×C₁₃	—	4	2	no	—
469	C₂³×C₁₃	—	4	4	no	—
470	C₂³×C₁₃	—	4	4	no	—
471	C₂³×C₁₃	—	4	2	no	—
472	C₂³×C₁₃	—	8	2	no	—
473	C₂³×C₁₃	—	8	2	no	—
474	C₂³×C₁₃	—	8	1	no	—
475	C₂³×C₁₃	—	8	1	no	—
476	C₂³×C₁₃	—	8	1	no	—
477	C₂³×C₁₃	—	8	1	no	—
478	C₂³×C₁₃	—	8	1	no	—
479	C₂³×C₁₃	—	8	1	no	—
480	C₂³×C₁₃	—	8	2	no	—
481	C₂³×C₁₃	—	8	2	no	—
482	C₂³×C₁₃	—	8	16	no	—
483	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
487	Q₈×C₁₃	—	2	2	no	—
488	Q₈×C₁₃	—	2	2	no	—
489	Q₈×C₁₃	—	2	2	no	—
490	Q₈×C₁₃	—	4	1	no	—
491	Q₈×C₁₃	—	8	1	no	—
492	Q₈×C₁₃	—	8	2	no	—
493	D₄×C₁₃	—	2	4	no	—
494	D₄×C₁₃	—	2	4	no	—
495	D₄×C₁₃	—	2	4	no	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	2	2	no	—
498	D₄×C₁₃	—	2	2	no	—
499	D₄×C₁₃	—	2	2	no	—
500	D₄×C₁₃	—	2	2	no	—
501	D₄×C₁₃	—	2	2	no	—
502	D₄×C₁₃	—	4	1	no	—
503	D₄×C₁₃	—	4	2	no	—
504	D₄×C₁₃	—	4	4	no	—
505	D₄×C₁₃	—	4	4	no	—
506	D₄×C₁₃	—	4	4	no	—
507	D₄×C₁₃	—	4	2	no	—
508	D₄×C₁₃	—	4	4	no	—
509	D₄×C₁₃	—	4	2	no	—
510	D₄×C₁₃	—	4	2	no	—
511	D₄×C₁₃	—	4	4	no	—
512	D₄×C₁₃	—	4	2	no	—
513	D₄×C₁₃	—	8	1	no	—
514	D₄×C₁₃	—	8	2	no	—
515	D₄×C₁₃	—	8	2	no	—
516	D₄×C₁₃	—	8	2	no	—
517	D₄×C₁₃	—	8	2	no	—
518	D₄×C₁₃	—	8	2	no	—
519	D₄×C₁₃	—	8	2	no	—
520	D₄×C₁₃	—	8	2	no	—
521	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	2	no	—
524	C₂×C₄×C₁₃	—	2	2	no	—
525	C₂×C₄×C₁₃	—	2	2	no	—
526	C₂×C₄×C₁₃	—	2	2	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	2	no	—
530	C₂×C₄×C₁₃	—	2	2	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	2	2	no	—
533	C₂×C₄×C₁₃	—	4	1	no	—
534	C₂×C₄×C₁₃	—	4	1	no	—
535	C₂×C₄×C₁₃	—	4	1	no	—
536	C₂×C₄×C₁₃	—	4	4	no	—
537	C₂×C₄×C₁₃	—	4	2	no	—
538	C₂×C₄×C₁₃	—	4	2	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	—	8	1	no	—
544	C₂×C₄×C₁₃	—	8	1	no	—
545	C₂×C₄×C₁₃	—	8	2	no	—
546	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
553	C₈×C₁₃	—	2	2	no	—
554	C₈×C₁₃	—	2	2	no	—
555	C₈×C₁₃	—	2	2	no	—
556	C₈×C₁₃	—	2	2	no	—
557	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
559	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
560	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
561	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
562	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
563	#562	—	2	2	no	—
564	#554	C₂²×C₁₃	1	2	yes	complemented
565	#548	C₂²×C₁₃	1	2	yes	complemented
566	#547	C₂²×C₁₃	1	2	yes	complemented
567	#546	—	2	1	no	—
568	#546	—	2	1	no	—
569	#546	—	2	2	no	—
570	#546	C₂²×C₁₃	1	2	yes	—
571	#546	C₂²×C₁₃	1	2	yes	complemented
572	#546	C₂²×C₁₃	1	2	yes	complemented
573	D₄²	—	2	1	no	—
574	D₄²	—	2	1	no	—
575	D₄²	C₂²×C₁₃	1	2	yes	—
576	D₄²	C₂²×C₁₃	1	2	yes	complemented
577	#543	—	2	1	no	—
578	#542	C₂²×C₁₃	1	2	yes	complemented
579	#539	—	2	1	no	—
580	#538	—	2	1	no	—
581	#537	—	2	1	no	—
582	#537	C₂²×C₁₃	1	2	yes	complemented
583	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
585	#534	—	2	2	no	—
586	#525	C₂²×C₁₃	1	1	yes	characteristic
587	#525	C₂²×C₁₃	1	1	yes	characteristic
588	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
590	C₂×#120	—	2	2	no	—
591	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	#496	C₂²×C₁₃	1	2	yes	complemented
593	#495	C₂²×C₁₃	1	2	yes	complemented
594	#489	C₂²×C₁₃	1	2	yes	complemented
595	#486	C₂²×C₁₃	1	2	yes	complemented
596	#485	C₂²×C₁₃	1	2	yes	complemented
597	#484	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#483	C₂²×C₁₃	1	1	yes	characteristic, complemented
599	#482	C₂²×C₁₃	1	2	yes	complemented
600	#481	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#481	C₂²×C₁₃	1	2	yes	complemented
602	#480	C₂²×C₁₃	1	1	yes	characteristic, complemented
603	#480	C₂²×C₁₃	1	2	yes	complemented
604	#476	C₂²×C₁₃	1	2	yes	complemented
605	#474	C₂²×C₁₃	1	2	yes	complemented
606	#469	C₂²×C₁₃	1	2	yes	complemented
607	#468	C₂²×C₁₃	1	2	yes	complemented
608	#467	C₂²×C₁₃	1	2	yes	complemented
609	#466	C₂²×C₁₃	1	2	yes	complemented
610	#466	C₂²×C₁₃	1	2	yes	complemented
611	#465	C₂²×C₁₃	1	2	yes	complemented
612	#465	C₂²×C₁₃	1	2	yes	complemented
613	#465	C₂²×C₁₃	1	2	yes	complemented
614	#464	C₂²×C₁₃	1	2	yes	complemented
615	#463	C₂²×C₁₃	1	2	yes	complemented
616	#463	C₂²×C₁₃	1	2	yes	complemented
617	#463	C₂²×C₁₃	1	2	yes	complemented
618	#460	C₂²×C₁₃	1	2	yes	complemented
619	#459	C₂²×C₁₃	1	2	yes	complemented
620	#452	C₂²×C₁₃	1	2	yes	complemented
621	#452	C₂²×C₁₃	1	2	yes	complemented
622	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	#450	C₂²×C₁₃	1	2	yes	complemented
624	#450	C₂²×C₁₃	1	2	yes	complemented
625	#450	C₂²×C₁₃	1	2	yes	complemented
626	#450	C₂²×C₁₃	1	2	yes	complemented
627	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#450	C₂²×C₁₃	1	2	yes	complemented
629	#449	C₂²×C₁₃	1	2	yes	complemented
630	#449	C₂²×C₁₃	1	2	yes	complemented
631	#449	C₂²×C₁₃	1	2	yes	complemented
632	#449	C₂²×C₁₃	1	2	yes	complemented
633	#448	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#447	C₂²×C₁₃	1	2	yes	—
635	#447	C₂²×C₁₃	1	2	yes	complemented
636	#447	C₂²×C₁₃	1	2	yes	complemented
637	#447	C₂²×C₁₃	1	2	yes	complemented
638	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#447	C₂²×C₁₃	1	2	yes	complemented
640	#442	C₂²×C₁₃	1	2	yes	complemented
641	#440	C₂²×C₁₃	1	2	yes	complemented
642	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
643	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
644	#435	C₂²×C₁₃	1	2	yes	complemented
645	#435	C₂²×C₁₃	1	2	yes	complemented
646	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
647	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
648	#433	C₂²×C₁₃	1	2	yes	complemented
649	#417	C₂²×C₁₃	1	2	yes	complemented
650	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
651	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
652	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
653	#408	C₂²×C₁₃	1	2	yes	complemented
654	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	C₂²×C₁₃	—	2	1	no	—
657	C₂²×C₁₃	—	2	1	no	—
658	C₂²×C₁₃	—	2	1	no	—
659	C₂²×C₁₃	—	2	1	no	—
660	C₂²×C₁₃	—	2	1	no	—
661	C₂²×C₁₃	—	2	2	no	—
662	C₂²×C₁₃	—	2	4	no	—
663	C₂²×C₁₃	—	2	2	no	—
664	C₂²×C₁₃	—	2	1	no	—
665	C₂²×C₁₃	—	2	2	no	—
666	C₂²×C₁₃	—	2	1	no	—
667	C₂²×C₁₃	—	4	4	no	—
668	C₂²×C₁₃	—	4	2	no	—
669	C₂²×C₁₃	—	4	2	no	—
670	C₂²×C₁₃	—	4	1	no	—
671	C₂²×C₁₃	—	4	2	no	—
672	C₂²×C₁₃	—	4	2	no	—
673	C₂²×C₁₃	—	4	2	no	—
674	C₂²×C₁₃	—	4	1	no	—
675	C₂²×C₁₃	—	4	2	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	2	no	—
678	C₂²×C₁₃	—	4	2	no	—
679	C₂²×C₁₃	—	8	8	no	—
680	C₂²×C₁₃	—	8	8	no	—
681	C₂²×C₁₃	—	8	4	no	—
682	C₂²×C₁₃	—	8	4	no	—
683	C₂²×C₁₃	—	16	2	no	—
684	C₂²×C₁₃	—	16	4	no	—
685	C₂²×C₁₃	#576	1	2	yes	—
686	C₂²×C₁₃	#577	1	2	yes	—
687	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
688	C₄×C₁₃	—	2	1	no	—
689	C₄×C₁₃	—	2	2	no	—
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	1	no	—
692	C₄×C₁₃	—	2	2	no	—
693	C₄×C₁₃	—	2	2	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	2	no	—
696	C₄×C₁₃	—	4	2	no	—
697	C₄×C₁₃	—	4	1	no	—
698	C₄×C₁₃	—	4	2	no	—
699	C₄×C₁₃	—	4	1	no	—
700	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
701	C₂⁵	—	2	1	no	—
702	H(5,𝔽₂)	—	4	4	no	—
703	C₂×#41	—	2	1	no	—
704	C₂×#41	—	2	2	no	—
705	C₂×#41	C₂³×C₁₃	1	2	yes	—
706	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
707	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×#41	C₂³×C₁₃	1	2	yes	complemented
709	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
710	C₂²×D₄	—	2	1	no	—
711	C₂²×D₄	—	2	2	no	—
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	—	2	2	no	—
714	C₂²×D₄	—	2	2	no	—
715	C₂²×D₄	—	2	1	no	—
716	C₂²×D₄	—	2	1	no	—
717	C₂²×D₄	—	2	1	no	—
718	C₂²×D₄	—	4	4	no	—
719	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
720	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
721	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
722	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
723	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
724	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
726	AGL(1,ℤ/8)	—	4	4	no	—
727	#135	—	4	4	no	—
728	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	complemented
729	C₂×SD₁₆	—	4	4	no	—
730	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
735	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
736	C₂×D₈	—	4	4	no	—
737	C₂×D₈	C₂³×C₁₃	1	2	yes	—
738	C₂×D₈	C₂³×C₁₃	1	2	yes	—
739	C₂×D₈	C₂³×C₁₃	1	2	yes	—
740	C₂×D₈	C₂³×C₁₃	1	2	yes	—
741	C₂×D₈	C₂³×C₁₃	1	2	yes	complemented
742	C₂×M₁₆	C₂³×C₁₃	1	2	yes	complemented
743	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
744	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
745	C₂²×C₈	C₂³×C₁₃	1	2	yes	complemented
746	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
747	#127	—	2	1	no	—
748	#127	C₂³×C₁₃	1	2	yes	—
749	#126	—	2	2	no	—
750	#125	—	2	2	no	—
751	#124	—	2	1	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	C₂³×C₁₃	1	2	yes	—
755	#124	C₂³×C₁₃	1	2	yes	complemented
756	#123	—	2	1	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	D₄×C₁₃	1	2	yes	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
773	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	D₄×C₁₃	1	1	yes	characteristic
793	#121	D₄×C₁₃	1	1	yes	characteristic
794	#121	C₂³×C₁₃	1	2	yes	—
795	#121	C₂³×C₁₃	1	2	yes	—
796	#121	C₂³×C₁₃	1	1	yes	characteristic
797	#121	C₂³×C₁₃	1	1	yes	characteristic
798	#121	C₂³×C₁₃	1	2	yes	—
799	#121	C₂³×C₁₃	1	2	yes	—
800	#121	C₂³×C₁₃	1	2	yes	complemented
801	#120	—	2	1	no	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	D₄×C₁₃	1	2	yes	—
812	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	C₂³×C₁₃	1	2	yes	—
820	C₄×D₄	C₂³×C₁₃	1	2	yes	—
821	C₄×D₄	C₂³×C₁₃	1	2	yes	—
822	C₄×D₄	C₂³×C₁₃	1	2	yes	—
823	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
824	#117	C₂³×C₁₃	1	1	yes	characteristic
825	#117	C₂³×C₁₃	1	1	yes	characteristic
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₂²⋊C₄	—	2	2	no	—
834	C₂×C₂²⋊C₄	—	2	2	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	#107	C₂³×C₁₃	1	2	yes	complemented
837	#107	C₂³×C₁₃	1	2	yes	complemented
838	#106	C₂³×C₁₃	1	2	yes	complemented
839	#106	C₂³×C₁₃	1	2	yes	complemented
840	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
841	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
842	#103	C₂³×C₁₃	1	2	yes	complemented
843	#103	C₂³×C₁₃	1	2	yes	complemented
844	#103	C₂³×C₁₃	1	2	yes	complemented
845	#103	C₂³×C₁₃	1	2	yes	complemented
846	#102	C₂³×C₁₃	1	2	yes	—
847	#102	C₂³×C₁₃	1	2	yes	—
848	#102	C₂³×C₁₃	1	2	yes	—
849	#102	C₂³×C₁₃	1	2	yes	—
850	#102	C₂³×C₁₃	1	2	yes	—
851	#102	C₂³×C₁₃	1	2	yes	—
852	#102	C₂³×C₁₃	1	2	yes	—
853	#102	C₂³×C₁₃	1	2	yes	—
854	#102	C₂³×C₁₃	1	2	yes	complemented
855	#102	C₂³×C₁₃	1	2	yes	complemented
856	#102	C₂³×C₁₃	1	2	yes	complemented
857	#102	C₂³×C₁₃	1	2	yes	complemented
858	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	complemented
865	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	complemented
866	#97	C₂³×C₁₃	1	2	yes	complemented
867	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
868	C₂×C₁₃	—	2	2	no	—
869	C₂×C₁₃	—	2	2	no	—
870	C₂×C₁₃	—	4	1	no	—
871	C₂×C₁₃	—	4	2	no	—
872	C₂×C₁₃	—	4	4	no	—
873	C₂×C₁₃	—	8	2	no	—
874	C₂×C₁₃	—	8	2	no	—
875	C₂×C₁₃	—	8	1	no	—
876	C₂×C₁₃	#3484	1	1	yes	characteristic
877	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
878	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
879	C₂⁴	—	2	1	no	—
880	C₂⁴	—	2	2	no	—
881	C₂⁴	—	2	2	no	—
882	C₂⁴	—	2	1	no	—
883	C₂⁴	—	2	1	no	—
884	C₂⁴	—	2	2	no	—
885	C₂⁴	—	4	4	no	—
886	C₂⁴	—	8	2	no	—
887	C₂⁴	—	8	2	no	—
888	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
889	#41	—	2	4	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	4	no	—
896	#41	—	8	4	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	4	2	no	—
900	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
903	C₂×D₄	—	2	4	no	—
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	4	no	—
906	C₂×D₄	—	2	4	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	4	no	—
931	C₂×D₄	—	4	4	no	—
932	C₂×D₄	—	4	4	no	—
933	C₂×D₄	—	4	4	no	—
934	C₂×D₄	—	4	8	no	—
935	C₂×D₄	—	8	4	no	—
936	C₂×D₄	—	8	4	no	—
937	C₂×D₄	—	8	2	no	—
938	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
939	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
943	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
945	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	4	2	no	—
957	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
959	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
964	Q₁₆	—	4	2	no	—
965	SD₁₆	—	2	4	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	D₈	—	2	4	no	—
972	D₈	—	2	4	no	—
973	D₈	—	4	2	no	—
974	D₈	—	4	2	no	—
975	D₈	—	4	2	no	—
976	M₁₆	—	4	2	no	—
977	C₂×C₈	—	4	2	no	—
978	C₂×C₈	—	4	2	no	—
979	C₂×C₈	—	4	2	no	—
980	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
981	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
982	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
983	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂⁴×C₁₃	1	2	yes	—
1030	C₁₃	#61629	1	1	yes	characteristic, direct product factor, Sylow
1031	C₂³	—	2	4	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	4	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	4	4	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	4	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	1	no	—
1051	C₂³	—	8	1	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	8	1	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	16	no	—
1057	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1058	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1059	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1060	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	2	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	8	1	no	—
1066	Q₈	—	8	2	no	—
1067	D₄	—	2	4	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	4	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1126	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₈	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	4	no	—
1142	C₂²	—	4	4	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	8	8	no	—
1155	C₂²	—	8	8	no	—
1156	C₂²	—	8	4	no	—
1157	C₂²	—	8	4	no	—
1158	C₂²	—	16	2	no	—
1159	C₂²	—	16	4	no	—
1160	C₂²	C₁₃×#576	1	2	yes	—
1161	C₂²	C₁₃×#577	1	2	yes	—
1162	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	1	no	—
1168	C₄	—	2	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	2	no	—
1175	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1176	C₂	—	2	2	no	—
1177	C₂	—	2	2	no	—
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	4	4	no	—
1181	C₂	—	8	2	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	2	no	—
1184	C₂	C₁₃×#3484	1	1	yes	characteristic
1185	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1186	C₂	C₂×C₁₃×#577	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3536	C₂	semidirect
2. C₁₃×#3484	C₂	semidirect
3. C₁₃×#3314	C₂	semidirect
4. C₁₃×#3306	C₂	semidirect
5. C₁₃×#3295	C₂	semidirect
6. C₁₃×#3294	C₂	semidirect
7. C₁₃×#3282	C₂	semidirect
8. C₁₃×#3280	C₂	semidirect
9. C₁₃×#3265	C₂	semidirect
10. C₁₃×#3264	C₂	semidirect
11. C₁₃×#3224	C₂	semidirect
12. C₁₃×#3198	C₂	semidirect
13. C₁₃×#3190	C₂	semidirect
14. C₁₃×#3188	C₂	semidirect
15. C₁₃×#3118	C₂	semidirect
16. C₁₃×#3012	C₂	semidirect
17. C₂×C₁₃×#450	C₂	semidirect
18. C₂×C₁₃×#447	C₂	semidirect
19. C₁₃×#2977	C₂	semidirect
20. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₁₃×#135	C₂²	semidirect
24. C₂²×C₁₃×SD₁₆	C₂²	semidirect
25. C₂²×C₁₃×D₈	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#548	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
34. C₁₃×#546	C₂²	semidirect
35. C₁₃×#546	C₂²	semidirect
39. D₄²×C₁₃	C₂²	semidirect
41. C₁₃×#542	C₂²	semidirect
45. C₁₃×#537	C₂²	semidirect
46. C₁₃×#535	C₂²	semidirect
47. C₁₃×#535	C₂²	semidirect
51. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₁₃×#121	C₂²	semidirect
54. C₁₃×#518	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
56. C₁₃×#495	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#486	C₂²	semidirect
59. C₁₃×#485	C₂²	semidirect
60. C₁₃×#484	C₂²	semidirect
61. C₁₃×#483	C₂²	semidirect
62. C₁₃×#482	C₂²	semidirect
63. C₁₃×#481	C₂²	semidirect
64. C₁₃×#481	C₂²	semidirect
65. C₁₃×#480	C₂²	semidirect
66. C₁₃×#480	C₂²	semidirect
67. C₁₃×#476	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#469	C₂²	semidirect
70. C₁₃×#468	C₂²	semidirect
71. C₁₃×#467	C₂²	semidirect
72. C₁₃×#466	C₂²	semidirect
73. C₁₃×#466	C₂²	semidirect
74. C₁₃×#465	C₂²	semidirect
75. C₁₃×#465	C₂²	semidirect
76. C₁₃×#465	C₂²	semidirect
77. C₁₃×#464	C₂²	semidirect
78. C₁₃×#463	C₂²	semidirect
79. C₁₃×#463	C₂²	semidirect
80. C₁₃×#463	C₂²	semidirect
81. C₁₃×#460	C₂²	semidirect
82. C₁₃×#459	C₂²	semidirect
83. C₁₃×#452	C₂²	semidirect
84. C₁₃×#452	C₂²	semidirect
85. C₁₃×#451	C₂²	semidirect
86. C₁₃×#450	C₂²	semidirect
87. C₁₃×#450	C₂²	semidirect
88. C₁₃×#450	C₂²	semidirect
89. C₁₃×#450	C₂²	semidirect
90. C₁₃×#450	C₂²	semidirect
91. C₁₃×#450	C₂²	semidirect
92. C₁₃×#449	C₂²	semidirect
93. C₁₃×#449	C₂²	semidirect
94. C₁₃×#449	C₂²	semidirect
95. C₁₃×#449	C₂²	semidirect
96. C₁₃×#448	C₂²	semidirect
98. C₁₃×#447	C₂²	semidirect
99. C₁₃×#447	C₂²	semidirect
100. C₁₃×#447	C₂²	semidirect
101. C₁₃×#447	C₂²	semidirect
102. C₁₃×#447	C₂²	semidirect
103. C₁₃×#442	C₂²	semidirect
104. C₁₃×#440	C₂²	semidirect
105. C₄×C₁₃×SD₁₆	C₂²	semidirect
106. C₄×C₁₃×D₈	C₂²	semidirect
107. C₁₃×#435	C₂²	semidirect
108. C₁₃×#435	C₂²	semidirect
109. C₈×D₄×C₁₃	C₂²	semidirect
110. C₈×D₄×C₁₃	C₂²	semidirect
111. C₁₃×#433	C₂²	semidirect
112. C₁₃×#417	C₂²	semidirect
113. C₂×C₁₃×#102	C₂²	semidirect
114. C₂×C₁₃×#102	C₂²	semidirect
115. C₂×C₁₃×#102	C₂²	semidirect
116. C₁₃×#408	C₂²	semidirect
117. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
118. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
126. C₂×C₁₃×#41	C₂³	semidirect
146. C₂×C₁₃×Q₁₆	C₂³	semidirect
152. C₂×C₁₃×SD₁₆	C₂³	semidirect
153. C₂×C₁₃×SD₁₆	C₂³	semidirect
159. C₂×C₁₃×D₈	C₂³	semidirect
160. C₂×C₁₃×M₁₆	C₂³	semidirect
163. C₂²×C₈×C₁₃	C₂³	semidirect
164. C₁₃×C₄⋊Q₈	C₂³	semidirect
173. C₁₃×#124	C₂³	semidirect
196. C₁₃×C₂²⋊Q₈	C₂³	semidirect
218. C₁₃×#121	C₂³	semidirect
230. C₄×Q₈×C₁₃	C₂³	semidirect
241. C₄×D₄×C₁₃	C₂³	semidirect
247. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
254. C₁₃×#107	C₂³	semidirect
255. C₁₃×#107	C₂³	semidirect
256. C₁₃×#106	C₂³	semidirect
257. C₁₃×#106	C₂³	semidirect
258. C₁₃×C₄⋊C₈	C₂³	semidirect
259. C₁₃×C₄⋊C₈	C₂³	semidirect
260. C₁₃×#103	C₂³	semidirect
261. C₁₃×#103	C₂³	semidirect
262. C₁₃×#103	C₂³	semidirect
263. C₁₃×#103	C₂³	semidirect
272. C₁₃×#102	C₂³	semidirect
273. C₁₃×#102	C₂³	semidirect
274. C₁₃×#102	C₂³	semidirect
275. C₁₃×#102	C₂³	semidirect
282. C₁₃×C₂²⋊C₈	C₂³	semidirect
283. C₁₃×C₂²⋊C₈	C₂³	semidirect
284. C₁₃×#97	C₂³	semidirect
285. C₄×C₈×C₁₃	C₂³	semidirect
286. #61629	C₁₃	direct (N × H)
438. #3536	C₂×C₁₃	semidirect
439. #3484	C₂×C₁₃	semidirect
440. #3314	C₂×C₁₃	semidirect
441. #3306	C₂×C₁₃	semidirect
442. #3295	C₂×C₁₃	semidirect
443. #3294	C₂×C₁₃	semidirect
444. #3282	C₂×C₁₃	semidirect
445. #3280	C₂×C₁₃	semidirect
446. #3265	C₂×C₁₃	semidirect
447. #3264	C₂×C₁₃	semidirect
448. #3224	C₂×C₁₃	semidirect
449. #3198	C₂×C₁₃	semidirect
450. #3190	C₂×C₁₃	semidirect
451. #3188	C₂×C₁₃	semidirect
452. #3118	C₂×C₁₃	semidirect
453. #3012	C₂×C₁₃	semidirect
454. C₂×#450	C₂×C₁₃	semidirect
455. C₂×#447	C₂×C₁₃	semidirect
456. #2977	C₂×C₁₃	semidirect
557. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
559. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
560. C₂×#135	C₂²×C₁₃	semidirect
561. C₂²×SD₁₆	C₂²×C₁₃	semidirect
562. C₂²×D₈	C₂²×C₁₃	semidirect
564. #554	C₂²×C₁₃	semidirect
565. #548	C₂²×C₁₃	semidirect
566. #547	C₂²×C₁₃	semidirect
571. #546	C₂²×C₁₃	semidirect
572. #546	C₂²×C₁₃	semidirect
576. D₄²	C₂²×C₁₃	semidirect
578. #542	C₂²×C₁₃	semidirect
582. #537	C₂²×C₁₃	semidirect
583. #535	C₂²×C₁₃	semidirect
584. #535	C₂²×C₁₃	semidirect
588. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
589. C₂×#121	C₂²×C₁₃	semidirect
591. #518	C₂²×C₁₃	semidirect
592. #496	C₂²×C₁₃	semidirect
593. #495	C₂²×C₁₃	semidirect
594. #489	C₂²×C₁₃	semidirect
595. #486	C₂²×C₁₃	semidirect
596. #485	C₂²×C₁₃	semidirect
597. #484	C₂²×C₁₃	semidirect
598. #483	C₂²×C₁₃	semidirect
599. #482	C₂²×C₁₃	semidirect
600. #481	C₂²×C₁₃	semidirect
601. #481	C₂²×C₁₃	semidirect
602. #480	C₂²×C₁₃	semidirect
603. #480	C₂²×C₁₃	semidirect
604. #476	C₂²×C₁₃	semidirect
605. #474	C₂²×C₁₃	semidirect
606. #469	C₂²×C₁₃	semidirect
607. #468	C₂²×C₁₃	semidirect
608. #467	C₂²×C₁₃	semidirect
609. #466	C₂²×C₁₃	semidirect
610. #466	C₂²×C₁₃	semidirect
611. #465	C₂²×C₁₃	semidirect
612. #465	C₂²×C₁₃	semidirect
613. #465	C₂²×C₁₃	semidirect
614. #464	C₂²×C₁₃	semidirect
615. #463	C₂²×C₁₃	semidirect
616. #463	C₂²×C₁₃	semidirect
617. #463	C₂²×C₁₃	semidirect
618. #460	C₂²×C₁₃	semidirect
619. #459	C₂²×C₁₃	semidirect
620. #452	C₂²×C₁₃	semidirect
621. #452	C₂²×C₁₃	semidirect
622. #451	C₂²×C₁₃	semidirect
623. #450	C₂²×C₁₃	semidirect
624. #450	C₂²×C₁₃	semidirect
625. #450	C₂²×C₁₃	semidirect
626. #450	C₂²×C₁₃	semidirect
627. #450	C₂²×C₁₃	semidirect
628. #450	C₂²×C₁₃	semidirect
629. #449	C₂²×C₁₃	semidirect
630. #449	C₂²×C₁₃	semidirect
631. #449	C₂²×C₁₃	semidirect
632. #449	C₂²×C₁₃	semidirect
633. #448	C₂²×C₁₃	semidirect
635. #447	C₂²×C₁₃	semidirect
636. #447	C₂²×C₁₃	semidirect
637. #447	C₂²×C₁₃	semidirect
638. #447	C₂²×C₁₃	semidirect
639. #447	C₂²×C₁₃	semidirect
640. #442	C₂²×C₁₃	semidirect
641. #440	C₂²×C₁₃	semidirect
642. C₄×SD₁₆	C₂²×C₁₃	semidirect
643. C₄×D₈	C₂²×C₁₃	semidirect
644. #435	C₂²×C₁₃	semidirect
645. #435	C₂²×C₁₃	semidirect
646. C₈×D₄	C₂²×C₁₃	semidirect
647. C₈×D₄	C₂²×C₁₃	semidirect
648. #433	C₂²×C₁₃	semidirect
649. #417	C₂²×C₁₃	semidirect
650. C₂×#102	C₂²×C₁₃	semidirect
651. C₂×#102	C₂²×C₁₃	semidirect
652. C₂×#102	C₂²×C₁₃	semidirect
653. #408	C₂²×C₁₃	semidirect
654. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
655. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
708. C₂×#41	C₂³×C₁₃	semidirect
728. C₂×Q₁₆	C₂³×C₁₃	semidirect
734. C₂×SD₁₆	C₂³×C₁₃	semidirect
735. C₂×SD₁₆	C₂³×C₁₃	semidirect
741. C₂×D₈	C₂³×C₁₃	semidirect
742. C₂×M₁₆	C₂³×C₁₃	semidirect
745. C₂²×C₈	C₂³×C₁₃	semidirect
746. C₄⋊Q₈	C₂³×C₁₃	semidirect
755. #124	C₂³×C₁₃	semidirect
778. C₂²⋊Q₈	C₂³×C₁₃	semidirect
800. #121	C₂³×C₁₃	semidirect
812. C₄×Q₈	C₂³×C₁₃	semidirect
823. C₄×D₄	C₂³×C₁₃	semidirect
829. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
836. #107	C₂³×C₁₃	semidirect
837. #107	C₂³×C₁₃	semidirect
838. #106	C₂³×C₁₃	semidirect
839. #106	C₂³×C₁₃	semidirect
840. C₄⋊C₈	C₂³×C₁₃	semidirect
841. C₄⋊C₈	C₂³×C₁₃	semidirect
842. #103	C₂³×C₁₃	semidirect
843. #103	C₂³×C₁₃	semidirect
844. #103	C₂³×C₁₃	semidirect
845. #103	C₂³×C₁₃	semidirect
854. #102	C₂³×C₁₃	semidirect
855. #102	C₂³×C₁₃	semidirect
856. #102	C₂³×C₁₃	semidirect
857. #102	C₂³×C₁₃	semidirect
864. C₂²⋊C₈	C₂³×C₁₃	semidirect
865. C₂²⋊C₈	C₂³×C₁₃	semidirect
866. #97	C₂³×C₁₃	semidirect
867. C₄×C₈	C₂³×C₁₃	semidirect
1030. C₁₃	#61629	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×#3536	2
C₁₃×#3484	2
C₁₃×#3314	2
C₁₃×#3306	2
C₁₃×#3295	2
C₁₃×#3294	2
C₁₃×#3282	2
C₁₃×#3280	2
C₁₃×#3265	2
C₁₃×#3264	2
C₁₃×#3224	2
C₁₃×#3198	2
C₁₃×#3190	2
C₁₃×#3188	2
C₁₃×#3118	2
C₁₃×#3012	2
C₂×C₁₃×#450	2
C₂×C₁₃×#447	2
C₁₃×#2977	2
#61629	13

Subgroups — C13×#61629 #15747968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61629 #15747968