Subgroups — C₁₃×#61057 #15747396

Order 3328.

2696 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3489	C₂	1	2	yes	maximal, complemented
4	D₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3283	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3269	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	2	yes	—
20	C₁₃×#578	—	2	8	no	—
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#135	—	2	8	no	—
25	C₂×C₁₃×#135	C₂²	1	2	yes	—
26	C₂×C₁₃×#135	C₂²	1	2	yes	—
27	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
32	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
34	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
36	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
40	C₁₃×#548	C₂²	1	4	yes	complemented
41	C₁₃×#547	—	2	4	no	—
42	C₁₃×#547	C₂²	1	4	yes	complemented
43	C₁₃×#546	—	2	4	no	—
44	C₁₃×#546	C₂²	1	4	yes	—
45	C₁₃×#537	—	2	2	no	—
46	C₁₃×#537	C₂²	1	2	yes	complemented
47	C₁₃×#536	—	2	2	no	—
48	C₁₃×#536	C₂²	1	2	yes	complemented
49	C₁₃×#525	—	2	2	no	—
50	C₁₃×#525	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
52	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
53	C₁₃×#520	C₂²	1	2	yes	complemented
54	C₁₃×#497	C₂²	1	4	yes	complemented
55	C₁₃×#495	C₂²	1	2	yes	complemented
56	C₁₃×#494	C₂²	1	2	yes	complemented
57	C₁₃×#468	C₂²	1	4	yes	complemented
58	C₁₃×#467	C₂²	1	2	yes	—
59	C₁₃×#467	C₂²	1	2	yes	—
60	C₁₃×#467	C₂²	1	2	yes	complemented
61	C₁₃×#467	C₂²	1	2	yes	complemented
62	C₁₃×#467	C₂²	1	2	yes	complemented
63	C₁₃×#466	C₂²	1	2	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#452	C₂²	1	4	yes	complemented
69	C₁₃×#452	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#451	C₂²	1	4	yes	—
72	C₁₃×#451	C₂²	1	4	yes	complemented
73	C₁₃×#450	C₂²	1	4	yes	—
74	C₁₃×#449	C₂²	1	4	yes	complemented
75	C₁₃×#448	C₂²	1	4	yes	complemented
76	C₁₃×#440	C₂²	1	4	yes	complemented
77	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
78	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
79	C₁₃×#435	C₂²	1	2	yes	—
80	C₁₃×#435	C₂²	1	2	yes	complemented
81	C₈×D₄×C₁₃	C₂²	1	2	yes	—
82	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#417	C₂²	1	2	yes	complemented
86	C₁₃×#417	C₂²	1	2	yes	complemented
87	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
88	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#407	C₂²	1	1	yes	characteristic
90	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×2₋¹⁺⁴	—	2	8	no	—
92	C₁₃×2₋¹⁺⁴	—	4	4	no	—
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	—	2	4	no	—
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	4	yes	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂×C₁₃×#41	C₂³	1	2	yes	—
104	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₁₃	—	2	2	no	—
106	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	—	2	2	no	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	—	2	2	no	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#137	—	2	8	no	—
114	C₁₃×#137	—	2	16	no	—
115	C₁₃×#137	—	4	4	no	—
116	C₁₃×#135	—	2	8	no	—
117	C₁₃×#135	—	2	4	no	—
118	C₁₃×#135	—	2	8	no	—
119	C₁₃×#135	—	2	4	no	—
120	C₁₃×#135	—	2	8	no	—
121	C₁₃×#135	—	2	4	no	—
122	C₁₃×#135	D₄	1	8	yes	complemented
123	C₂×C₁₃×Q₁₆	—	2	4	no	—
124	C₂×C₁₃×Q₁₆	—	2	8	no	—
125	C₂×C₁₃×Q₁₆	—	2	4	no	—
126	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
132	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×SD₁₆	—	2	8	no	—
134	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
135	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
136	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
137	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
139	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×D₈	—	2	4	no	—
141	C₂×C₁₃×D₈	C₂³	1	2	yes	—
142	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
144	C₁₃×#131	—	2	4	no	—
145	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
148	C₂²×C₈×C₁₃	—	2	4	no	—
149	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	—	2	4	no	—
157	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
158	C₁₃×#124	—	2	4	no	—
159	C₁₃×#124	C₂³	1	4	yes	—
160	C₁₃×#123	—	2	4	no	—
161	C₁₃×#123	—	2	4	no	—
162	C₁₃×#123	—	2	4	no	—
163	C₁₃×#123	—	2	4	no	—
164	C₁₃×#123	D₄	1	2	yes	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	4	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	4	no	—
172	C₁₃×C₂²⋊Q₈	—	2	4	no	—
173	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
174	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
175	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	4	no	—
180	C₁₃×#121	—	2	4	no	—
181	C₁₃×#121	—	2	4	no	—
182	C₁₃×#121	—	2	4	no	—
183	C₁₃×#121	D₄	1	1	yes	characteristic
184	C₁₃×#121	D₄	1	1	yes	characteristic
185	C₁₃×#121	C₂³	1	4	yes	—
186	C₁₃×#120	—	2	4	no	—
187	C₁₃×#120	D₄	1	2	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
189	C₄×D₄×C₁₃	—	2	4	no	—
190	C₄×D₄×C₁₃	—	2	4	no	—
191	C₄×D₄×C₁₃	—	2	4	no	—
192	C₄×D₄×C₁₃	C₂³	1	4	yes	—
193	C₄×D₄×C₁₃	C₂³	1	2	yes	—
194	C₄×D₄×C₁₃	C₂³	1	2	yes	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
206	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
207	C₁₃×#103	C₂³	1	4	yes	—
208	C₁₃×#103	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	4	yes	—
211	C₁₃×#102	C₂³	1	4	yes	—
212	C₁₃×#102	C₂³	1	4	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#97	C₂³	1	2	yes	—
218	C₄×C₈×C₁₃	C₂³	1	2	yes	—
219	#61057	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂⁴×C₁₃	—	2	2	no	—
221	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₁₃×#41	—	2	2	no	—
223	C₁₃×#41	—	2	4	no	—
224	C₁₃×#41	—	2	2	no	—
225	C₁₃×#41	—	2	4	no	—
226	C₁₃×#41	—	2	4	no	—
227	C₁₃×#41	—	2	8	no	—
228	C₁₃×#41	—	2	4	no	—
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	4	8	no	—
231	C₁₃×#41	—	4	2	no	—
232	C₁₃×#41	—	4	2	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₁₃×#41	—	4	8	no	—
235	C₁₃×#41	—	4	8	no	—
236	C₁₃×#41	—	4	16	no	—
237	C₁₃×#41	C₂×D₄	1	8	yes	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	8	no	—
243	C₂×Q₈×C₁₃	—	2	4	no	—
244	C₂×Q₈×C₁₃	—	2	4	no	—
245	C₂×Q₈×C₁₃	—	4	2	no	—
246	C₂×Q₈×C₁₃	—	4	4	no	—
247	C₂×Q₈×C₁₃	—	4	8	no	—
248	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	4	2	no	—
261	C₂×D₄×C₁₃	—	4	8	no	—
262	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	2	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	4	no	—
280	C₂²×C₄×C₁₃	—	4	8	no	—
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₁₃×Q₁₆	—	2	4	no	—
289	C₁₃×Q₁₆	—	2	8	no	—
290	C₁₃×Q₁₆	—	2	4	no	—
291	C₁₃×Q₁₆	—	2	2	no	—
292	C₁₃×Q₁₆	—	2	4	no	—
293	C₁₃×Q₁₆	—	4	4	no	—
294	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
295	C₁₃×SD₁₆	—	2	4	no	—
296	C₁₃×SD₁₆	—	2	4	no	—
297	C₁₃×SD₁₆	—	2	8	no	—
298	C₁₃×SD₁₆	—	2	4	no	—
299	C₁₃×SD₁₆	—	4	4	no	—
300	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
301	C₁₃×D₈	—	2	4	no	—
302	C₁₃×D₈	—	2	2	no	—
303	C₁₃×D₈	C₂×D₄	1	4	yes	—
304	C₁₃×M₁₆	—	2	2	no	—
305	C₁₃×M₁₆	—	2	2	no	—
306	C₁₃×M₁₆	—	2	4	no	—
307	C₂×C₈×C₁₃	—	2	2	no	—
308	C₂×C₈×C₁₃	—	2	2	no	—
309	C₂×C₈×C₁₃	—	2	2	no	—
310	C₂×C₈×C₁₃	—	2	2	no	—
311	C₂×C₈×C₁₃	—	2	2	no	—
312	C₂×C₈×C₁₃	—	2	4	no	—
313	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	—	2	4	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	4	no	—
323	C₁₃×C₄⋊C₄	—	2	4	no	—
324	C₁₃×C₄⋊C₄	—	2	4	no	—
325	C₁₃×C₄⋊C₄	—	2	4	no	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	4	no	—
337	C₁₃×C₂²⋊C₄	—	2	4	no	—
338	C₁₃×C₂²⋊C₄	—	2	4	no	—
339	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₄²×C₁₃	—	2	4	no	—
345	C₄²×C₁₃	C₂⁴	1	2	yes	—
346	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
347	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3489	C₂×C₁₃	1	2	yes	complemented
349	D₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
350	#3285	C₂×C₁₃	1	2	yes	complemented
351	#3283	C₂×C₁₃	1	2	yes	complemented
352	#3280	C₂×C₁₃	1	2	yes	complemented
353	#3269	C₂×C₁₃	1	4	yes	complemented
354	#3266	C₂×C₁₃	1	4	yes	complemented
355	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3046	C₂×C₁₃	1	2	yes	complemented
359	#3013	C₂×C₁₃	1	2	yes	complemented
360	#3007	C₂×C₁₃	1	2	yes	complemented
361	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	4	1	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	4	4	no	—
370	C₂³×C₁₃	—	8	2	no	—
371	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	2	4	no	—
379	Q₈×C₁₃	—	2	4	no	—
380	Q₈×C₁₃	—	2	2	no	—
381	Q₈×C₁₃	—	4	8	no	—
382	Q₈×C₁₃	—	4	4	no	—
383	Q₈×C₁₃	—	4	4	no	—
384	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
385	D₄×C₁₃	—	2	8	no	—
386	D₄×C₁₃	—	2	4	no	—
387	D₄×C₁₃	—	2	4	no	—
388	D₄×C₁₃	—	2	2	no	—
389	D₄×C₁₃	—	2	2	no	—
390	D₄×C₁₃	—	2	2	no	—
391	D₄×C₁₃	—	2	2	no	—
392	D₄×C₁₃	—	4	2	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	4	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	8	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	8	4	no	—
399	D₄×C₁₃	C₂²×D₄	1	4	yes	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	8	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	4	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	8	no	—
418	C₂×C₄×C₁₃	—	4	8	no	—
419	C₂×C₄×C₁₃	—	4	4	no	—
420	C₂×C₄×C₁₃	—	4	4	no	—
421	C₂×C₄×C₁₃	—	8	4	no	—
422	C₂×C₄×C₁₃	—	8	2	no	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
432	C₈×C₁₃	—	2	1	no	—
433	C₈×C₁₃	—	2	1	no	—
434	C₈×C₁₃	—	2	2	no	—
435	C₈×C₁₃	—	2	2	no	—
436	C₈×C₁₃	C₂²×D₄	1	2	yes	—
437	C₈×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
439	C₂²×#41	C₂²×C₁₃	1	2	yes	—
440	#578	—	2	8	no	—
441	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
442	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
443	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
444	C₂×#135	—	2	8	no	—
445	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#135	C₂²×C₁₃	1	2	yes	—
447	C₂×#135	C₂²×C₁₃	1	2	yes	—
448	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
452	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
453	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
455	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
456	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
459	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
460	#548	C₂²×C₁₃	1	4	yes	complemented
461	#547	—	2	4	no	—
462	#547	C₂²×C₁₃	1	4	yes	complemented
463	#546	—	2	4	no	—
464	#546	C₂²×C₁₃	1	4	yes	—
465	#537	—	2	2	no	—
466	#537	C₂²×C₁₃	1	2	yes	complemented
467	#536	—	2	2	no	—
468	#536	C₂²×C₁₃	1	2	yes	complemented
469	#525	—	2	2	no	—
470	#525	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₂²⋊Q₈	—	2	2	no	—
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
473	#520	C₂²×C₁₃	1	2	yes	complemented
474	#497	C₂²×C₁₃	1	4	yes	complemented
475	#495	C₂²×C₁₃	1	2	yes	complemented
476	#494	C₂²×C₁₃	1	2	yes	complemented
477	#468	C₂²×C₁₃	1	4	yes	complemented
478	#467	C₂²×C₁₃	1	2	yes	—
479	#467	C₂²×C₁₃	1	2	yes	—
480	#467	C₂²×C₁₃	1	2	yes	complemented
481	#467	C₂²×C₁₃	1	2	yes	complemented
482	#467	C₂²×C₁₃	1	2	yes	complemented
483	#466	C₂²×C₁₃	1	2	yes	complemented
484	#464	C₂²×C₁₃	1	4	yes	complemented
485	#463	C₂²×C₁₃	1	4	yes	complemented
486	#462	C₂²×C₁₃	1	4	yes	complemented
487	#461	C₂²×C₁₃	1	4	yes	complemented
488	#452	C₂²×C₁₃	1	4	yes	complemented
489	#452	C₂²×C₁₃	1	4	yes	complemented
490	#452	C₂²×C₁₃	1	4	yes	complemented
491	#451	C₂²×C₁₃	1	4	yes	—
492	#451	C₂²×C₁₃	1	4	yes	complemented
493	#450	C₂²×C₁₃	1	4	yes	—
494	#449	C₂²×C₁₃	1	4	yes	complemented
495	#448	C₂²×C₁₃	1	4	yes	complemented
496	#440	C₂²×C₁₃	1	4	yes	complemented
497	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
498	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
499	#435	C₂²×C₁₃	1	2	yes	—
500	#435	C₂²×C₁₃	1	2	yes	complemented
501	C₈×D₄	C₂²×C₁₃	1	2	yes	—
502	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
503	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	#417	C₂²×C₁₃	1	2	yes	complemented
506	#417	C₂²×C₁₃	1	2	yes	complemented
507	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
508	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#407	C₂²×C₁₃	1	1	yes	characteristic
510	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	2	1	no	—
514	C₂²×C₁₃	—	2	1	no	—
515	C₂²×C₁₃	—	2	1	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	1	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	4	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	1	no	—
522	C₂²×C₁₃	—	4	4	no	—
523	C₂²×C₁₃	—	4	2	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	8	8	no	—
529	C₂²×C₁₃	D₄²	1	2	yes	—
530	C₂²×C₁₃	#578	1	2	yes	complemented
531	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	1	no	—
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	2	4	no	—
536	C₄×C₁₃	—	2	2	no	—
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	4	4	no	—
539	C₄×C₁₃	—	4	2	no	—
540	C₄×C₁₃	—	4	4	no	—
541	C₄×C₁₃	D₄²	1	2	yes	—
542	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	2₋¹⁺⁴	—	2	8	no	—
545	2₋¹⁺⁴	—	4	4	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	4	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	8	no	—
551	C₂×#41	—	4	4	no	—
552	C₂×#41	C₂³×C₁₃	1	2	yes	—
553	C₂×#41	C₂³×C₁₃	1	4	yes	—
554	C₂×#41	C₂³×C₁₃	1	2	yes	—
555	C₂×#41	C₂³×C₁₃	1	2	yes	—
556	C₂×#41	C₂³×C₁₃	1	2	yes	—
557	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
558	C₂²×Q₈	—	2	2	no	—
559	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
560	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
561	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
564	C₂³×C₄	—	2	2	no	—
565	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
566	#137	—	2	8	no	—
567	#137	—	2	16	no	—
568	#137	—	4	4	no	—
569	#135	—	2	8	no	—
570	#135	—	2	4	no	—
571	#135	—	2	8	no	—
572	#135	—	2	4	no	—
573	#135	—	2	8	no	—
574	#135	—	2	4	no	—
575	#135	D₄×C₁₃	1	8	yes	complemented
576	C₂×Q₁₆	—	2	4	no	—
577	C₂×Q₁₆	—	2	8	no	—
578	C₂×Q₁₆	—	2	4	no	—
579	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
580	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
582	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
583	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
584	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
585	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×SD₁₆	—	2	8	no	—
587	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
590	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
593	C₂×D₈	—	2	4	no	—
594	C₂×D₈	C₂³×C₁₃	1	2	yes	—
595	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
597	#131	—	2	4	no	—
598	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²×C₈	—	2	4	no	—
602	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
603	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
607	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
608	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₄⋊Q₈	—	2	4	no	—
610	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
611	#124	—	2	4	no	—
612	#124	C₂³×C₁₃	1	4	yes	—
613	#123	—	2	4	no	—
614	#123	—	2	4	no	—
615	#123	—	2	4	no	—
616	#123	—	2	4	no	—
617	#123	D₄×C₁₃	1	2	yes	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	4	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	4	no	—
626	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
627	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
628	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
629	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
630	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
631	#121	—	2	2	no	—
632	#121	—	2	4	no	—
633	#121	—	2	4	no	—
634	#121	—	2	4	no	—
635	#121	—	2	4	no	—
636	#121	D₄×C₁₃	1	1	yes	characteristic
637	#121	D₄×C₁₃	1	1	yes	characteristic
638	#121	C₂³×C₁₃	1	4	yes	—
639	#120	—	2	4	no	—
640	#120	D₄×C₁₃	1	2	yes	—
641	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	4	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	C₂³×C₁₃	1	4	yes	—
646	C₄×D₄	C₂³×C₁₃	1	2	yes	—
647	C₄×D₄	C₂³×C₁₃	1	2	yes	—
648	#117	—	2	2	no	—
649	#117	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	—	2	2	no	—
651	C₂×C₄⋊C₄	—	2	2	no	—
652	C₂×C₄⋊C₄	—	2	4	no	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	—	2	2	no	—
655	C₂×C₂²⋊C₄	—	2	4	no	—
656	#107	C₂³×C₁₃	1	2	yes	—
657	#107	C₂³×C₁₃	1	2	yes	—
658	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
659	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
660	#103	C₂³×C₁₃	1	4	yes	—
661	#103	C₂³×C₁₃	1	4	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#103	C₂³×C₁₃	1	4	yes	—
664	#102	C₂³×C₁₃	1	4	yes	—
665	#102	C₂³×C₁₃	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
670	#97	C₂³×C₁₃	1	2	yes	—
671	C₄×C₈	C₂³×C₁₃	1	2	yes	—
672	C₂×C₁₃	—	2	2	no	—
673	C₂×C₁₃	—	2	2	no	—
674	C₂×C₁₃	—	4	2	no	—
675	C₂×C₁₃	—	4	1	no	—
676	C₂×C₁₃	—	4	4	no	—
677	C₂×C₁₃	—	8	2	no	—
678	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
679	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
680	C₂×C₁₃	#3584	1	1	yes	characteristic
681	C₂⁴	—	2	2	no	—
682	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
683	#41	—	2	2	no	—
684	#41	—	2	4	no	—
685	#41	—	2	2	no	—
686	#41	—	2	4	no	—
687	#41	—	2	4	no	—
688	#41	—	2	8	no	—
689	#41	—	2	4	no	—
690	#41	—	2	4	no	—
691	#41	—	4	8	no	—
692	#41	—	4	2	no	—
693	#41	—	4	2	no	—
694	#41	—	4	4	no	—
695	#41	—	4	8	no	—
696	#41	—	4	8	no	—
697	#41	—	4	16	no	—
698	#41	C₂×D₄×C₁₃	1	8	yes	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	4	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	—	4	8	no	—
709	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
711	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
712	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	8	no	—
723	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	4	8	no	—
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	Q₁₆	—	2	4	no	—
750	Q₁₆	—	2	8	no	—
751	Q₁₆	—	2	4	no	—
752	Q₁₆	—	2	2	no	—
753	Q₁₆	—	2	4	no	—
754	Q₁₆	—	4	4	no	—
755	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
756	SD₁₆	—	2	4	no	—
757	SD₁₆	—	2	4	no	—
758	SD₁₆	—	2	8	no	—
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	4	4	no	—
761	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
762	D₈	—	2	4	no	—
763	D₈	—	2	2	no	—
764	D₈	C₂×D₄×C₁₃	1	4	yes	—
765	M₁₆	—	2	2	no	—
766	M₁₆	—	2	2	no	—
767	M₁₆	—	2	4	no	—
768	C₂×C₈	—	2	2	no	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	—	2	4	no	—
774	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
775	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
776	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
777	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₄²	—	2	4	no	—
806	C₄²	C₂⁴×C₁₃	1	2	yes	—
807	C₁₃	#61057	1	1	yes	characteristic, direct product factor, Sylow
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	4	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	4	8	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	4	no	—
829	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
830	D₄	—	2	8	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	4	2	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	4	no	—
844	D₄	C₂²×D₄×C₁₃	1	4	yes	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	8	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	8	4	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	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	1	no	—
878	C₈	—	2	1	no	—
879	C₈	—	2	2	no	—
880	C₈	—	2	2	no	—
881	C₈	C₂²×D₄×C₁₃	1	2	yes	—
882	C₈	C₂²×D₄×C₁₃	1	2	yes	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	8	8	no	—
901	C₂²	D₄²×C₁₃	1	2	yes	—
902	C₂²	C₁₃×#578	1	2	yes	complemented
903	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	4	4	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	4	no	—
913	C₄	D₄²×C₁₃	1	2	yes	—
914	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
915	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂	—	2	2	no	—
917	C₂	—	2	2	no	—
918	C₂	—	4	1	no	—
919	C₂	—	4	2	no	—
920	C₂	—	4	4	no	—
921	C₂	—	8	2	no	—
922	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
923	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
924	C₂	C₁₃×#3584	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. C₂×C₁₃×#578	C₂	semidirect
2. C₂²×C₁₃×#135	C₂	semidirect
3. C₁₃×#3489	C₂	semidirect
4. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#3285	C₂	semidirect
6. C₁₃×#3283	C₂	semidirect
7. C₁₃×#3280	C₂	semidirect
8. C₁₃×#3269	C₂	semidirect
9. C₁₃×#3266	C₂	semidirect
10. C₁₃×#3156	C₂	semidirect
11. C₁₃×#3061	C₂	semidirect
12. C₂×C₁₃×#467	C₂	semidirect
13. C₁₃×#3046	C₂	semidirect
14. C₁₃×#3013	C₂	semidirect
15. C₁₃×#3007	C₂	semidirect
16. C₁₃×#2951	C₂	semidirect
17. C₁₃×#2929	C₂	semidirect
18. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
23. C₂×C₁₃×#137	C₂²	semidirect
31. C₂×C₁₃×#135	C₂²	semidirect
33. C₂²×C₁₃×Q₁₆	C₂²	semidirect
34. C₂²×C₁₃×Q₁₆	C₂²	semidirect
37. C₂×C₁₃×#131	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
42. C₁₃×#547	C₂²	semidirect
46. C₁₃×#537	C₂²	semidirect
48. C₁₃×#536	C₂²	semidirect
53. C₁₃×#520	C₂²	semidirect
54. C₁₃×#497	C₂²	semidirect
55. C₁₃×#495	C₂²	semidirect
56. C₁₃×#494	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
60. C₁₃×#467	C₂²	semidirect
61. C₁₃×#467	C₂²	semidirect
62. C₁₃×#467	C₂²	semidirect
63. C₁₃×#466	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#452	C₂²	semidirect
69. C₁₃×#452	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
72. C₁₃×#451	C₂²	semidirect
74. C₁₃×#449	C₂²	semidirect
75. C₁₃×#448	C₂²	semidirect
76. C₁₃×#440	C₂²	semidirect
77. C₄×C₁₃×Q₁₆	C₂²	semidirect
78. C₄×C₁₃×D₈	C₂²	semidirect
80. C₁₃×#435	C₂²	semidirect
82. C₈×D₄×C₁₃	C₂²	semidirect
83. C₂×C₁₃×#107	C₂²	semidirect
84. C₁₃×#424	C₂²	semidirect
85. C₁₃×#417	C₂²	semidirect
86. C₁₃×#417	C₂²	semidirect
87. C₂×C₁₃×#103	C₂²	semidirect
88. C₁₃×#408	C₂²	semidirect
90. C₁₃×#405	C₂²	semidirect
122. C₁₃×#135	D₄	semidirect
219. #61057	C₁₃	direct (N × H)
346. C₂×#578	C₂×C₁₃	semidirect
347. C₂²×#135	C₂×C₁₃	semidirect
348. #3489	C₂×C₁₃	semidirect
349. D₄×Q₁₆	C₂×C₁₃	semidirect
350. #3285	C₂×C₁₃	semidirect
351. #3283	C₂×C₁₃	semidirect
352. #3280	C₂×C₁₃	semidirect
353. #3269	C₂×C₁₃	semidirect
354. #3266	C₂×C₁₃	semidirect
355. #3156	C₂×C₁₃	semidirect
356. #3061	C₂×C₁₃	semidirect
357. C₂×#467	C₂×C₁₃	semidirect
358. #3046	C₂×C₁₃	semidirect
359. #3013	C₂×C₁₃	semidirect
360. #3007	C₂×C₁₃	semidirect
361. #2951	C₂×C₁₃	semidirect
362. #2929	C₂×C₁₃	semidirect
438. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
441. C₂×#137	C₂²×C₁₃	semidirect
442. C₂×#137	C₂²×C₁₃	semidirect
443. C₂×#137	C₂²×C₁₃	semidirect
451. C₂×#135	C₂²×C₁₃	semidirect
453. C₂²×Q₁₆	C₂²×C₁₃	semidirect
454. C₂²×Q₁₆	C₂²×C₁₃	semidirect
457. C₂×#131	C₂²×C₁₃	semidirect
460. #548	C₂²×C₁₃	semidirect
462. #547	C₂²×C₁₃	semidirect
466. #537	C₂²×C₁₃	semidirect
468. #536	C₂²×C₁₃	semidirect
473. #520	C₂²×C₁₃	semidirect
474. #497	C₂²×C₁₃	semidirect
475. #495	C₂²×C₁₃	semidirect
476. #494	C₂²×C₁₃	semidirect
477. #468	C₂²×C₁₃	semidirect
480. #467	C₂²×C₁₃	semidirect
481. #467	C₂²×C₁₃	semidirect
482. #467	C₂²×C₁₃	semidirect
483. #466	C₂²×C₁₃	semidirect
484. #464	C₂²×C₁₃	semidirect
485. #463	C₂²×C₁₃	semidirect
486. #462	C₂²×C₁₃	semidirect
487. #461	C₂²×C₁₃	semidirect
488. #452	C₂²×C₁₃	semidirect
489. #452	C₂²×C₁₃	semidirect
490. #452	C₂²×C₁₃	semidirect
492. #451	C₂²×C₁₃	semidirect
494. #449	C₂²×C₁₃	semidirect
495. #448	C₂²×C₁₃	semidirect
496. #440	C₂²×C₁₃	semidirect
497. C₄×Q₁₆	C₂²×C₁₃	semidirect
498. C₄×D₈	C₂²×C₁₃	semidirect
500. #435	C₂²×C₁₃	semidirect
502. C₈×D₄	C₂²×C₁₃	semidirect
503. C₂×#107	C₂²×C₁₃	semidirect
504. #424	C₂²×C₁₃	semidirect
505. #417	C₂²×C₁₃	semidirect
506. #417	C₂²×C₁₃	semidirect
507. C₂×#103	C₂²×C₁₃	semidirect
508. #408	C₂²×C₁₃	semidirect
510. #405	C₂²×C₁₃	semidirect
530. C₂²×C₁₃	#578	semidirect
575. #135	D₄×C₁₃	semidirect
807. C₁₃	#61057	direct (N × H)
902. C₂²	C₁₃×#578	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#578	2
C₂²×C₁₃×#135	2
C₁₃×#3489	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3283	2
C₁₃×#3280	2
C₁₃×#3269	2
C₁₃×#3266	2
C₁₃×#3156	2
C₁₃×#3061	2
C₂×C₁₃×#467	2
C₁₃×#3046	2
C₁₃×#3013	2
C₁₃×#3007	2
C₁₃×#2951	2
C₁₃×#2929	2
#61057	13

Subgroups — C13×#61057 #15747396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61057 #15747396