Subgroups — C₁₃×#60837 #15747176

Order 3328.

2008 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3223	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3156	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
23	D₄×Q₈×C₁₃	—	2	1	no	—
24	D₄×Q₈×C₁₃	—	2	1	no	—
25	C₁₃×#547	—	2	2	no	—
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#547	—	2	2	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#544	C₂²	1	1	yes	characteristic
30	C₁₃×#542	—	2	1	no	—
31	C₁₃×#542	C₂²	1	2	yes	—
32	C₁₃×#541	—	2	1	no	—
33	C₁₃×#541	C₂²	1	2	yes	—
34	C₁₃×#539	—	2	2	no	—
35	C₁₃×#537	C₂²	1	1	yes	characteristic
36	C₁₃×#536	C₂²	1	2	yes	—
37	C₁₃×#536	C₂²	1	1	yes	characteristic
38	C₁₃×#536	C₂²	1	4	yes	—
39	C₁₃×#536	C₂²	1	1	yes	characteristic
40	C₁₃×#533	—	2	1	no	—
41	C₁₃×#533	C₂²	1	2	yes	—
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₁₃×#532	C₂²	1	2	yes	—
44	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
46	C₁₃×#529	—	2	2	no	—
47	C₁₃×#529	—	2	1	no	—
48	C₁₃×#529	C₂²	1	2	yes	—
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
51	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	4	yes	—
53	C₁₃×#497	C₂²	1	4	yes	—
54	C₁₃×#495	C₂²	1	4	yes	—
55	C₁₃×#494	C₂²	1	4	yes	—
56	C₁₃×#491	C₂²	1	4	yes	—
57	C₁₃×#489	C₂²	1	4	yes	—
58	C₁₃×#488	C₂²	1	4	yes	—
59	C₁₃×#487	C₂²	1	4	yes	—
60	C₁₃×#464	C₂²	1	2	yes	—
61	C₁₃×#464	C₂²	1	4	yes	—
62	C₁₃×#463	C₂²	1	2	yes	—
63	C₁₃×#462	C₂²	1	2	yes	—
64	C₁₃×#462	C₂²	1	2	yes	—
65	C₁₃×#462	C₂²	1	4	yes	—
66	C₁₃×#462	C₂²	1	1	yes	characteristic
67	C₁₃×#462	C₂²	1	2	yes	—
68	C₁₃×#462	C₂²	1	2	yes	—
69	C₁₃×#462	C₂²	1	2	yes	—
70	C₁₃×#461	C₂²	1	1	yes	characteristic
71	C₁₃×#461	C₂²	1	2	yes	—
72	C₁₃×#461	C₂²	1	2	yes	—
73	C₁₃×#460	C₂²	1	1	yes	characteristic
74	C₁₃×#460	C₂²	1	2	yes	—
75	C₁₃×#459	C₂²	1	1	yes	characteristic
76	C₁₃×#452	C₂²	1	4	yes	—
77	C₁₃×#452	C₂²	1	4	yes	—
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#451	C₂²	1	4	yes	—
80	C₁₃×#451	C₂²	1	4	yes	—
81	C₁₃×#451	C₂²	1	4	yes	—
82	C₁₃×#449	C₂²	1	4	yes	—
83	C₁₃×#448	C₂²	1	4	yes	—
84	C₁₃×#433	C₂²	1	4	yes	—
85	C₁₃×#432	C₂²	1	2	yes	—
86	C₁₃×#431	C₂²	1	2	yes	—
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	2	yes	—
91	C₁₃×#416	C₂²	1	2	yes	—
92	C₂×C₁₃×#103	C₂²	1	2	yes	—
93	C₁₃×#408	C₂²	1	2	yes	—
94	C₁₃×#405	C₂²	1	2	yes	—
95	C₁₃×2₋¹⁺⁴	—	4	4	no	—
96	C₁₃×2₋¹⁺⁴	—	4	4	no	—
97	C₂×C₁₃×#41	—	2	4	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	4	yes	—
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	—	2	2	no	—
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
107	C₁₃×#137	—	4	4	no	—
108	C₁₃×#137	—	4	4	no	—
109	C₁₃×#135	—	4	4	no	—
110	C₂×C₁₃×Q₁₆	—	4	4	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×D₈	C₂³	1	2	yes	—
121	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
122	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	—	2	1	no	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	—	2	2	no	—
128	C₁₃×C₄⋊Q₈	—	2	2	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×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#127	C₂³	1	1	yes	characteristic
136	C₁₃×#126	—	2	2	no	—
137	C₁₃×#126	—	2	2	no	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#125	—	2	2	no	—
141	C₁₃×#125	—	2	1	no	—
142	C₁₃×#125	—	2	2	no	—
143	C₁₃×#125	—	2	2	no	—
144	C₁₃×#125	C₂³	1	2	yes	—
145	C₁₃×#124	—	2	1	no	—
146	C₁₃×#124	—	2	2	no	—
147	C₁₃×#124	C₂³	1	2	yes	—
148	C₁₃×#124	C₂³	1	4	yes	—
149	C₁₃×#124	C₂³	1	2	yes	—
150	C₁₃×#123	—	2	2	no	—
151	C₁₃×#123	—	2	2	no	—
152	C₁₃×#123	—	2	2	no	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×#123	—	2	4	no	—
155	C₁₃×#123	—	2	4	no	—
156	C₁₃×#123	—	2	4	no	—
157	C₁₃×C₂²⋊Q₈	—	2	1	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	1	no	—
160	C₁₃×C₂²⋊Q₈	—	2	1	no	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	4	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	4	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	1	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	1	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	C₂³	1	2	yes	—
177	C₄×Q₈×C₁₃	—	2	1	no	—
178	C₄×Q₈×C₁₃	—	2	1	no	—
179	C₄×Q₈×C₁₃	—	2	2	no	—
180	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
181	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
182	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
183	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
185	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	—	2	1	no	—
187	C₄×D₄×C₁₃	—	2	1	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	1	no	—
190	C₄×D₄×C₁₃	—	2	1	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
194	C₄×D₄×C₁₃	D₄	1	2	yes	—
195	C₄×D₄×C₁₃	D₄	1	2	yes	—
196	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
197	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
198	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×#117	—	2	2	no	—
200	C₁₃×#117	—	2	1	no	—
201	C₁₃×#117	—	2	2	no	—
202	C₁₃×#117	C₂³	1	1	yes	characteristic
203	C₁₃×#117	C₂³	1	1	yes	characteristic
204	C₁₃×#117	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃	—	2	1	no	—
212	C₂×C₄²×C₁₃	—	2	1	no	—
213	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#103	C₂³	1	4	yes	—
226	C₁₃×#103	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₁₃×#97	C₂³	1	4	yes	—
233	C₄×C₈×C₁₃	C₂³	1	4	yes	—
234	#60837	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	2	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	4	4	no	—
242	C₁₃×#41	—	4	4	no	—
243	C₁₃×#41	—	4	16	no	—
244	C₁₃×#41	—	4	8	no	—
245	C₂×Q₈×C₁₃	—	2	1	no	—
246	C₂×Q₈×C₁₃	—	2	4	no	—
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	—	2	2	no	—
252	C₂×Q₈×C₁₃	—	2	4	no	—
253	C₂×Q₈×C₁₃	—	4	4	no	—
254	C₂×Q₈×C₁₃	—	4	4	no	—
255	C₂×Q₈×C₁₃	—	4	8	no	—
256	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
258	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
259	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
260	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	1	no	—
267	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	1	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	1	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₁₃×Q₁₆	—	4	4	no	—
287	C₁₃×Q₁₆	—	4	4	no	—
288	C₁₃×Q₁₆	—	4	2	no	—
289	C₁₃×Q₁₆	—	4	4	no	—
290	C₁₃×Q₁₆	—	4	4	no	—
291	C₁₃×SD₁₆	—	4	2	no	—
292	C₁₃×SD₁₆	—	4	2	no	—
293	C₁₃×SD₁₆	—	4	4	no	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×D₈	—	4	2	no	—
296	C₁₃×M₁₆	—	2	4	no	—
297	C₂×C₈×C₁₃	—	2	4	no	—
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
300	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	4	no	—
310	C₁₃×C₄⋊C₄	—	2	4	no	—
311	C₁₃×C₄⋊C₄	—	2	1	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
323	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
324	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
325	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	1	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	1	no	—
334	C₁₃×C₂²⋊C₄	—	2	1	no	—
335	C₁₃×C₂²⋊C₄	—	2	2	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	4	no	—
340	C₁₃×C₂²⋊C₄	—	2	4	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	1	no	—
347	C₄²×C₁₃	—	2	1	no	—
348	C₄²×C₁₃	—	2	1	no	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₁₃	C₂×D₄	1	2	yes	—
353	C₄²×C₁₃	C₂×D₄	1	2	yes	—
354	C₄²×C₁₃	C₂⁴	1	2	yes	—
355	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
357	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3461	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3225	C₂×C₁₃	1	4	yes	complemented
360	#3223	C₂×C₁₃	1	4	yes	complemented
361	#3218	C₂×C₁₃	1	2	yes	complemented
362	#3216	C₂×C₁₃	1	2	yes	complemented
363	#3212	C₂×C₁₃	1	2	yes	complemented
364	#3209	C₂×C₁₃	1	2	yes	complemented
365	#3156	C₂×C₁₃	1	2	yes	complemented
366	#3137	C₂×C₁₃	1	2	yes	complemented
367	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#3013	C₂×C₁₃	1	2	yes	complemented
372	#3011	C₂×C₁₃	1	2	yes	complemented
373	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
374	C₂³×C₁₃	—	2	1	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	Q₈×C₁₃	—	2	2	no	—
379	Q₈×C₁₃	—	2	2	no	—
380	Q₈×C₁₃	—	2	1	no	—
381	Q₈×C₁₃	—	2	4	no	—
382	Q₈×C₁₃	—	2	2	no	—
383	Q₈×C₁₃	—	2	2	no	—
384	Q₈×C₁₃	—	2	1	no	—
385	Q₈×C₁₃	—	2	4	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	4	8	no	—
388	Q₈×C₁₃	—	4	2	no	—
389	Q₈×C₁₃	—	4	4	no	—
390	Q₈×C₁₃	—	8	2	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	2	no	—
393	D₄×C₁₃	—	2	1	no	—
394	D₄×C₁₃	—	2	2	no	—
395	D₄×C₁₃	—	2	1	no	—
396	D₄×C₁₃	—	2	2	no	—
397	D₄×C₁₃	—	4	2	no	—
398	D₄×C₁₃	—	4	8	no	—
399	D₄×C₁₃	—	4	2	no	—
400	D₄×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	4	2	no	—
402	D₄×C₁₃	—	8	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	4	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	4	1	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	8	no	—
417	C₂×C₄×C₁₃	—	4	8	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	4	no	—
420	C₂×C₄×C₁₃	—	4	4	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	2	no	—
423	C₂×C₄×C₁₃	—	8	1	no	—
424	C₂×C₄×C₁₃	—	8	1	no	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
434	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
436	C₈×C₁₃	—	2	2	no	—
437	C₈×C₁₃	—	2	2	no	—
438	C₈×C₁₃	—	2	4	no	—
439	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
440	C₂×#137	C₂²×C₁₃	1	2	yes	—
441	C₂×#137	C₂²×C₁₃	1	2	yes	—
442	C₂×#135	C₂²×C₁₃	1	2	yes	—
443	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
444	D₄×Q₈	—	2	1	no	—
445	D₄×Q₈	—	2	1	no	—
446	#547	—	2	2	no	—
447	#547	—	2	1	no	—
448	#547	—	2	2	no	—
449	#547	—	2	1	no	—
450	#544	C₂²×C₁₃	1	1	yes	characteristic
451	#542	—	2	1	no	—
452	#542	C₂²×C₁₃	1	2	yes	—
453	#541	—	2	1	no	—
454	#541	C₂²×C₁₃	1	2	yes	—
455	#539	—	2	2	no	—
456	#537	C₂²×C₁₃	1	1	yes	characteristic
457	#536	C₂²×C₁₃	1	2	yes	—
458	#536	C₂²×C₁₃	1	1	yes	characteristic
459	#536	C₂²×C₁₃	1	4	yes	—
460	#536	C₂²×C₁₃	1	1	yes	characteristic
461	#533	—	2	1	no	—
462	#533	C₂²×C₁₃	1	2	yes	—
463	#532	C₂²×C₁₃	1	2	yes	—
464	#532	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
466	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
467	#529	—	2	2	no	—
468	#529	—	2	1	no	—
469	#529	C₂²×C₁₃	1	2	yes	—
470	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
471	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
473	#497	C₂²×C₁₃	1	4	yes	—
474	#497	C₂²×C₁₃	1	4	yes	—
475	#495	C₂²×C₁₃	1	4	yes	—
476	#494	C₂²×C₁₃	1	4	yes	—
477	#491	C₂²×C₁₃	1	4	yes	—
478	#489	C₂²×C₁₃	1	4	yes	—
479	#488	C₂²×C₁₃	1	4	yes	—
480	#487	C₂²×C₁₃	1	4	yes	—
481	#464	C₂²×C₁₃	1	2	yes	—
482	#464	C₂²×C₁₃	1	4	yes	—
483	#463	C₂²×C₁₃	1	2	yes	—
484	#462	C₂²×C₁₃	1	1	yes	characteristic
485	#462	C₂²×C₁₃	1	2	yes	—
486	#462	C₂²×C₁₃	1	2	yes	—
487	#462	C₂²×C₁₃	1	2	yes	—
488	#462	C₂²×C₁₃	1	2	yes	—
489	#462	C₂²×C₁₃	1	2	yes	—
490	#462	C₂²×C₁₃	1	4	yes	—
491	#461	C₂²×C₁₃	1	2	yes	—
492	#461	C₂²×C₁₃	1	1	yes	characteristic
493	#461	C₂²×C₁₃	1	2	yes	—
494	#460	C₂²×C₁₃	1	2	yes	—
495	#460	C₂²×C₁₃	1	1	yes	characteristic
496	#459	C₂²×C₁₃	1	1	yes	characteristic
497	#452	C₂²×C₁₃	1	4	yes	—
498	#452	C₂²×C₁₃	1	4	yes	—
499	#452	C₂²×C₁₃	1	4	yes	—
500	#451	C₂²×C₁₃	1	4	yes	—
501	#451	C₂²×C₁₃	1	4	yes	—
502	#451	C₂²×C₁₃	1	4	yes	—
503	#449	C₂²×C₁₃	1	4	yes	—
504	#448	C₂²×C₁₃	1	4	yes	—
505	#433	C₂²×C₁₃	1	4	yes	—
506	#432	C₂²×C₁₃	1	2	yes	—
507	#431	C₂²×C₁₃	1	2	yes	—
508	#423	C₂²×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
510	#419	C₂²×C₁₃	1	2	yes	—
511	#417	C₂²×C₁₃	1	2	yes	—
512	#416	C₂²×C₁₃	1	2	yes	—
513	C₂×#103	C₂²×C₁₃	1	2	yes	—
514	#408	C₂²×C₁₃	1	2	yes	—
515	#405	C₂²×C₁₃	1	2	yes	—
516	C₂²×C₁₃	—	2	1	no	—
517	C₂²×C₁₃	—	2	1	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	4	1	no	—
522	C₂²×C₁₃	—	4	2	no	—
523	C₂²×C₁₃	—	4	2	no	—
524	C₂²×C₁₃	—	4	1	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	#535	1	2	yes	—
528	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₁₃	—	2	1	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	1	no	—
534	C₄×C₁₃	—	2	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	4	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	—	4	1	no	—
540	C₄×C₁₃	—	4	2	no	—
541	C₄×C₁₃	—	4	1	no	—
542	C₄×C₁₃	#535	1	2	yes	—
543	C₄×C₁₃	#578	1	2	yes	—
544	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
545	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	2₋¹⁺⁴	—	4	4	no	—
547	2₋¹⁺⁴	—	4	4	no	—
548	C₂×#41	—	2	4	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×#41	C₂³×C₁₃	1	2	yes	—
552	C₂×#41	C₂³×C₁₃	1	4	yes	—
553	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
554	C₂²×Q₈	—	2	2	no	—
555	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
557	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
558	#137	—	4	4	no	—
559	#137	—	4	4	no	—
560	#135	—	4	4	no	—
561	C₂×Q₁₆	—	4	4	no	—
562	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
564	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
565	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
568	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
569	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
571	C₂×D₈	C₂³×C₁₃	1	2	yes	—
572	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
573	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
574	C₄⋊Q₈	—	2	1	no	—
575	C₄⋊Q₈	—	2	1	no	—
576	C₄⋊Q₈	—	2	1	no	—
577	C₄⋊Q₈	—	2	2	no	—
578	C₄⋊Q₈	—	2	1	no	—
579	C₄⋊Q₈	—	2	2	no	—
580	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
584	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
585	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
586	#127	C₂³×C₁₃	1	1	yes	characteristic
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#125	—	2	2	no	—
592	#125	—	2	1	no	—
593	#125	—	2	2	no	—
594	#125	—	2	2	no	—
595	#125	C₂³×C₁₃	1	2	yes	—
596	#124	—	2	1	no	—
597	#124	—	2	2	no	—
598	#124	C₂³×C₁₃	1	2	yes	—
599	#124	C₂³×C₁₃	1	2	yes	—
600	#124	C₂³×C₁₃	1	4	yes	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	4	no	—
606	#123	—	2	4	no	—
607	#123	—	2	4	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	4	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	4	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
619	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
620	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
621	#121	—	2	2	no	—
622	#121	—	2	1	no	—
623	#121	—	2	1	no	—
624	#121	—	2	2	no	—
625	#121	—	2	1	no	—
626	#121	—	2	2	no	—
627	#121	C₂³×C₁₃	1	2	yes	—
628	C₄×Q₈	—	2	1	no	—
629	C₄×Q₈	—	2	1	no	—
630	C₄×Q₈	—	2	2	no	—
631	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
632	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
633	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
634	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
635	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
636	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
645	C₄×D₄	D₄×C₁₃	1	2	yes	—
646	C₄×D₄	D₄×C₁₃	1	2	yes	—
647	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
648	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
649	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
650	#117	—	2	2	no	—
651	#117	—	2	1	no	—
652	#117	—	2	2	no	—
653	#117	C₂³×C₁₃	1	1	yes	characteristic
654	#117	C₂³×C₁₃	1	1	yes	characteristic
655	#117	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	2	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	2	no	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
667	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
670	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
671	#103	C₂³×C₁₃	1	4	yes	—
672	#103	C₂³×C₁₃	1	4	yes	—
673	#103	C₂³×C₁₃	1	2	yes	—
674	#103	C₂³×C₁₃	1	2	yes	—
675	#103	C₂³×C₁₃	1	4	yes	—
676	#103	C₂³×C₁₃	1	4	yes	—
677	#103	C₂³×C₁₃	1	4	yes	—
678	#102	C₂³×C₁₃	1	2	yes	—
679	#102	C₂³×C₁₃	1	2	yes	—
680	#102	C₂³×C₁₃	1	4	yes	—
681	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
682	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
683	#97	C₂³×C₁₃	1	4	yes	—
684	C₄×C₈	C₂³×C₁₃	1	4	yes	—
685	C₂×C₁₃	—	2	2	no	—
686	C₂×C₁₃	—	4	2	no	—
687	C₂×C₁₃	—	8	1	no	—
688	C₂×C₁₃	—	8	2	no	—
689	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
690	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
691	C₂×C₁₃	#3586	1	1	yes	characteristic
692	#41	—	2	2	no	—
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	2	4	no	—
696	#41	—	2	2	no	—
697	#41	—	2	4	no	—
698	#41	—	4	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	16	no	—
701	#41	—	4	8	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	4	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	4	4	no	—
711	C₂×Q₈	—	4	4	no	—
712	C₂×Q₈	—	4	8	no	—
713	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
714	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
715	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
717	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
743	Q₁₆	—	4	4	no	—
744	Q₁₆	—	4	4	no	—
745	Q₁₆	—	4	2	no	—
746	Q₁₆	—	4	4	no	—
747	Q₁₆	—	4	4	no	—
748	SD₁₆	—	4	2	no	—
749	SD₁₆	—	4	2	no	—
750	SD₁₆	—	4	4	no	—
751	SD₁₆	—	4	4	no	—
752	D₈	—	4	2	no	—
753	M₁₆	—	2	4	no	—
754	C₂×C₈	—	2	4	no	—
755	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
756	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
757	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	1	no	—
804	C₄²	—	2	1	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	2	no	—
807	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₁₃	1	2	yes	—
810	C₄²	C₂×D₄×C₁₃	1	2	yes	—
811	C₄²	C₂⁴×C₁₃	1	2	yes	—
812	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₁₃	#60837	1	1	yes	characteristic, direct product factor, Sylow
815	C₂³	—	2	1	no	—
816	C₂³	—	2	2	no	—
817	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	2	4	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	4	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	4	8	no	—
829	Q₈	—	4	4	no	—
830	Q₈	—	4	2	no	—
831	Q₈	—	8	2	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	1	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	1	no	—
837	D₄	—	2	2	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	2	no	—
843	D₄	—	8	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	8	1	no	—
865	C₂×C₄	—	8	1	no	—
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	2	yes	—
870	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
875	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
876	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	4	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	C₁₃×#535	1	2	yes	—
892	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
893	C₄	—	2	1	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	4	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	C₁₃×#535	1	2	yes	—
907	C₄	C₁₃×#578	1	2	yes	—
908	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
909	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂	—	2	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	8	1	no	—
913	C₂	—	8	2	no	—
914	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
915	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
916	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3499	C₂	semidirect
2. C₁₃×#3461	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3223	C₂	semidirect
5. C₁₃×#3218	C₂	semidirect
6. C₁₃×#3216	C₂	semidirect
7. C₁₃×#3212	C₂	semidirect
8. C₁₃×#3209	C₂	semidirect
9. C₁₃×#3156	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3039	C₂	semidirect
12. C₁₃×#3037	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#462	C₂	semidirect
15. C₁₃×#3013	C₂	semidirect
16. C₁₃×#3011	C₂	semidirect
17. C₁₃×#2925	C₂	semidirect
234. #60837	C₁₃	direct (N × H)
357. #3499	C₂×C₁₃	semidirect
358. #3461	C₂×C₁₃	semidirect
359. #3225	C₂×C₁₃	semidirect
360. #3223	C₂×C₁₃	semidirect
361. #3218	C₂×C₁₃	semidirect
362. #3216	C₂×C₁₃	semidirect
363. #3212	C₂×C₁₃	semidirect
364. #3209	C₂×C₁₃	semidirect
365. #3156	C₂×C₁₃	semidirect
366. #3137	C₂×C₁₃	semidirect
367. #3039	C₂×C₁₃	semidirect
368. #3037	C₂×C₁₃	semidirect
369. #3035	C₂×C₁₃	semidirect
370. C₂×#462	C₂×C₁₃	semidirect
371. #3013	C₂×C₁₃	semidirect
372. #3011	C₂×C₁₃	semidirect
373. #2925	C₂×C₁₃	semidirect
814. C₁₃	#60837	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×#3499	2
C₁₃×#3461	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3218	2
C₁₃×#3216	2
C₁₃×#3212	2
C₁₃×#3209	2
C₁₃×#3156	2
C₁₃×#3137	2
C₁₃×#3039	2
C₁₃×#3037	2
C₁₃×#3035	2
C₂×C₁₃×#462	2
C₁₃×#3013	2
C₁₃×#3011	2
C₁₃×#2925	2
#60837	13

Subgroups — C13×#60837 #15747176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60837 #15747176