Subgroups — C₁₃×#61596 #15747935

Order 3328.

2168 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	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3317	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3271	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3194	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3187	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
21	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#552	C₂²	1	2	yes	complemented
24	C₁₃×#551	—	2	2	no	—
25	C₁₃×#550	—	2	1	no	—
26	C₁₃×#550	—	2	2	no	—
27	C₁₃×#550	—	2	1	no	—
28	C₁₃×#550	C₂²	1	4	yes	—
29	C₁₃×#550	C₂²	1	2	yes	—
30	C₁₃×#550	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#548	C₂²	1	2	yes	complemented
33	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#546	—	2	1	no	—
36	C₁₃×#542	—	2	1	no	—
37	C₁₃×#539	—	2	2	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#127	—	2	1	no	—
40	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
41	C₁₃×#529	C₂²	1	1	yes	characteristic
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₁₃×#121	—	2	2	no	—
45	C₂×C₁₃×#121	C₂²	1	2	yes	—
46	C₁₃×#520	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#496	C₂²	1	2	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#490	C₂²	1	2	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#483	C₂²	1	1	yes	characteristic
55	C₁₃×#483	C₂²	1	2	yes	—
56	C₁₃×#482	C₂²	1	4	yes	complemented
57	C₁₃×#481	C₂²	1	4	yes	complemented
58	C₁₃×#480	C₂²	1	1	yes	characteristic
59	C₁₃×#479	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#469	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#465	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	2	yes	complemented
67	C₁₃×#460	C₂²	1	4	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#459	C₂²	1	2	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#452	C₂²	1	4	yes	complemented
73	C₁₃×#451	C₂²	1	1	yes	characteristic
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#450	C₂²	1	2	yes	—
76	C₁₃×#450	C₂²	1	2	yes	—
77	C₁₃×#450	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	4	yes	complemented
80	C₁₃×#448	C₂²	1	1	yes	characteristic
81	C₁₃×#448	C₂²	1	4	yes	complemented
82	C₁₃×#447	C₂²	1	2	yes	—
83	C₁₃×#441	C₂²	1	4	yes	complemented
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₁₃×#436	C₂²	1	2	yes	complemented
87	C₁₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#417	C₂²	1	4	yes	complemented
92	C₁₃×#416	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	4	8	no	—
99	C₂×C₁₃×#41	C₂³	1	4	yes	—
100	C₂×C₁₃×#41	C₂³	1	4	yes	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	—	2	2	no	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×#137	—	4	8	no	—
113	C₁₃×#135	—	4	8	no	—
114	C₂×C₁₃×Q₁₆	C₂³	1	2	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	4	yes	—
120	C₂×C₁₃×D₈	C₂³	1	4	yes	—
121	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
122	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×#127	—	2	2	no	—
127	C₁₃×#127	—	2	2	no	—
128	C₁₃×#127	—	2	4	no	—
129	C₁₃×#127	—	2	1	no	—
130	C₁₃×#127	—	2	1	no	—
131	C₁₃×#127	C₂³	1	2	yes	—
132	C₁₃×#127	C₂³	1	2	yes	—
133	C₁₃×#126	—	2	2	no	—
134	C₁₃×#126	—	2	2	no	—
135	C₁₃×#126	—	2	1	no	—
136	C₁₃×#125	—	2	2	no	—
137	C₁₃×#125	—	2	1	no	—
138	C₁₃×#125	C₂³	1	1	yes	characteristic
139	C₁₃×#124	—	2	1	no	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#124	C₂³	1	1	yes	characteristic
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	1	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	4	no	—
163	C₁₃×#121	—	2	4	no	—
164	C₁₃×#121	—	2	4	no	—
165	C₁₃×#121	—	2	4	no	—
166	C₁₃×#121	C₂³	1	1	yes	characteristic
167	C₁₃×#121	C₂³	1	4	yes	—
168	C₁₃×#121	C₂³	1	2	yes	—
169	C₁₃×#121	C₂³	1	4	yes	—
170	C₁₃×#120	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	1	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	—	2	1	no	—
174	C₄×Q₈×C₁₃	—	2	1	no	—
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	4	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	D₄	1	2	yes	—
189	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₁₃	C₂³	1	2	yes	—
193	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	C₂³	1	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
207	C₂×C₄²×C₁₃	—	2	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×#106	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₁₃	C₂³	1	2	yes	—
231	#61596	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
234	C₁₃×#41	—	2	8	no	—
235	C₁₃×#41	—	2	8	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	4	4	no	—
240	C₁₃×#41	—	4	8	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	2	1	no	—
244	C₂×Q₈×C₁₃	—	2	1	no	—
245	C₂×Q₈×C₁₃	—	2	2	no	—
246	C₂×Q₈×C₁₃	—	4	4	no	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	4	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	4	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	4	2	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	4	4	no	—
265	C₂×D₄×C₁₃	—	4	8	no	—
266	C₂×D₄×C₁₃	—	8	2	no	—
267	C₂×D₄×C₁₃	—	8	4	no	—
268	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
272	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	—	2	1	no	—
274	C₂²×C₄×C₁₃	—	2	1	no	—
275	C₂²×C₄×C₁₃	—	2	2	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	—	2	4	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	4	4	no	—
282	C₂²×C₄×C₁₃	—	4	8	no	—
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₁₃×Q₁₆	—	2	8	no	—
292	C₁₃×Q₁₆	—	2	4	no	—
293	C₁₃×SD₁₆	—	2	4	no	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×SD₁₆	—	4	4	no	—
296	C₁₃×SD₁₆	—	4	4	no	—
297	C₁₃×D₈	—	4	4	no	—
298	C₁₃×M₁₆	—	4	4	no	—
299	C₂×C₈×C₁₃	—	4	4	no	—
300	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
301	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
302	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	1	no	—
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	1	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	1	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	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	2	1	no	—
348	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
352	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3332	C₂×C₁₃	1	2	yes	complemented
355	#3317	C₂×C₁₃	1	4	yes	complemented
356	#3304	C₂×C₁₃	1	2	yes	complemented
357	#3284	C₂×C₁₃	1	2	yes	complemented
358	#3278	C₂×C₁₃	1	2	yes	complemented
359	#3271	C₂×C₁₃	1	4	yes	complemented
360	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3194	C₂×C₁₃	1	2	yes	complemented
363	#3187	C₂×C₁₃	1	2	yes	complemented
364	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3007	C₂×C₁₃	1	2	yes	complemented
367	#3002	C₂×C₁₃	1	2	yes	complemented
368	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
369	C₂³×C₁₃	—	2	4	no	—
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	2	4	no	—
372	C₂³×C₁₃	—	4	2	no	—
373	C₂³×C₁₃	—	4	2	no	—
374	C₂³×C₁₃	—	4	4	no	—
375	C₂³×C₁₃	—	4	4	no	—
376	C₂³×C₁₃	—	4	4	no	—
377	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
379	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	Q₈×C₁₃	—	2	4	no	—
381	Q₈×C₁₃	—	2	2	no	—
382	Q₈×C₁₃	—	2	2	no	—
383	Q₈×C₁₃	—	2	4	no	—
384	Q₈×C₁₃	—	4	2	no	—
385	Q₈×C₁₃	—	8	2	no	—
386	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	2	no	—
389	D₄×C₁₃	—	2	2	no	—
390	D₄×C₁₃	—	2	4	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	4	2	no	—
393	D₄×C₁₃	—	4	8	no	—
394	D₄×C₁₃	—	4	8	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	4	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	2	no	—
399	D₄×C₁₃	—	4	4	no	—
400	D₄×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	8	2	no	—
402	D₄×C₁₃	—	8	4	no	—
403	D₄×C₁₃	—	8	4	no	—
404	D₄×C₁₃	—	8	2	no	—
405	C₂×C₄×C₁₃	—	2	4	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	4	no	—
410	C₂×C₄×C₁₃	—	2	4	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	2	no	—
421	C₂×C₄×C₁₃	—	4	8	no	—
422	C₂×C₄×C₁₃	—	4	8	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	—	4	2	no	—
425	C₂×C₄×C₁₃	—	4	2	no	—
426	C₂×C₄×C₁₃	—	8	2	no	—
427	C₂×C₄×C₁₃	—	8	2	no	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
436	C₈×C₁₃	—	2	2	no	—
437	C₈×C₁₃	—	2	4	no	—
438	C₈×C₁₃	—	2	2	no	—
439	C₂²×#41	C₂²×C₁₃	1	2	yes	—
440	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
441	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
442	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	#554	—	2	1	no	—
444	#552	C₂²×C₁₃	1	2	yes	complemented
445	#551	—	2	2	no	—
446	#550	—	2	1	no	—
447	#550	—	2	2	no	—
448	#550	—	2	1	no	—
449	#550	C₂²×C₁₃	1	2	yes	—
450	#550	C₂²×C₁₃	1	4	yes	—
451	#550	C₂²×C₁₃	1	2	yes	—
452	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#548	C₂²×C₁₃	1	2	yes	complemented
454	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#546	—	2	1	no	—
457	#542	—	2	1	no	—
458	#539	—	2	2	no	—
459	#533	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#127	—	2	1	no	—
461	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
462	#529	C₂²×C₁₃	1	1	yes	characteristic
463	#525	C₂²×C₁₃	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
465	C₂×#121	—	2	2	no	—
466	C₂×#121	C₂²×C₁₃	1	2	yes	—
467	#520	—	2	1	no	—
468	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×D₄	—	2	1	no	—
470	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
471	#496	C₂²×C₁₃	1	2	yes	complemented
472	#492	C₂²×C₁₃	1	2	yes	complemented
473	#490	C₂²×C₁₃	1	2	yes	complemented
474	#486	C₂²×C₁₃	1	2	yes	complemented
475	#483	C₂²×C₁₃	1	1	yes	characteristic
476	#483	C₂²×C₁₃	1	2	yes	—
477	#482	C₂²×C₁₃	1	4	yes	complemented
478	#481	C₂²×C₁₃	1	4	yes	complemented
479	#480	C₂²×C₁₃	1	1	yes	characteristic
480	#479	C₂²×C₁₃	1	2	yes	complemented
481	#475	C₂²×C₁₃	1	2	yes	complemented
482	#469	C₂²×C₁₃	1	4	yes	complemented
483	#468	C₂²×C₁₃	1	4	yes	complemented
484	#465	C₂²×C₁₃	1	4	yes	complemented
485	#465	C₂²×C₁₃	1	4	yes	complemented
486	#464	C₂²×C₁₃	1	2	yes	complemented
487	#462	C₂²×C₁₃	1	2	yes	complemented
488	#460	C₂²×C₁₃	1	4	yes	complemented
489	#460	C₂²×C₁₃	1	2	yes	complemented
490	#459	C₂²×C₁₃	1	2	yes	complemented
491	#452	C₂²×C₁₃	1	4	yes	complemented
492	#452	C₂²×C₁₃	1	4	yes	complemented
493	#452	C₂²×C₁₃	1	4	yes	complemented
494	#451	C₂²×C₁₃	1	1	yes	characteristic
495	#451	C₂²×C₁₃	1	2	yes	—
496	#450	C₂²×C₁₃	1	2	yes	—
497	#450	C₂²×C₁₃	1	2	yes	—
498	#450	C₂²×C₁₃	1	2	yes	—
499	#449	C₂²×C₁₃	1	4	yes	complemented
500	#449	C₂²×C₁₃	1	4	yes	complemented
501	#448	C₂²×C₁₃	1	1	yes	characteristic
502	#448	C₂²×C₁₃	1	4	yes	complemented
503	#447	C₂²×C₁₃	1	2	yes	—
504	#441	C₂²×C₁₃	1	4	yes	complemented
505	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
506	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
507	#436	C₂²×C₁₃	1	2	yes	complemented
508	#435	C₂²×C₁₃	1	4	yes	complemented
509	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
510	#432	C₂²×C₁₃	1	1	yes	characteristic
511	#431	C₂²×C₁₃	1	1	yes	characteristic
512	#417	C₂²×C₁₃	1	4	yes	complemented
513	#416	C₂²×C₁₃	1	4	yes	complemented
514	#407	C₂²×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₈	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	—	2	2	no	—
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	2	2	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	—	4	1	no	—
527	C₂²×C₁₃	—	4	4	no	—
528	C₂²×C₁₃	—	4	1	no	—
529	C₂²×C₁₃	—	4	4	no	—
530	C₂²×C₁₃	—	8	4	no	—
531	C₂²×C₁₃	—	8	8	no	—
532	C₂²×C₁₃	#577	1	2	yes	—
533	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
534	C₄×C₁₃	—	2	4	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	2	no	—
537	C₄×C₁₃	—	2	1	no	—
538	C₄×C₁₃	—	2	1	no	—
539	C₄×C₁₃	—	2	1	no	—
540	C₄×C₁₃	—	2	1	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	1	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₄×C₁₃	—	4	1	no	—
547	C₄×C₁₃	#575	1	2	yes	—
548	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
549	C₂×#41	—	2	1	no	—
550	C₂×#41	—	2	2	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	—	4	8	no	—
553	C₂×#41	C₂³×C₁₃	1	4	yes	—
554	C₂×#41	C₂³×C₁₃	1	4	yes	—
555	C₂×#41	C₂³×C₁₃	1	2	yes	—
556	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	2	2	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
564	C₂³×C₄	—	2	2	no	—
565	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
566	#137	—	4	8	no	—
567	#135	—	4	8	no	—
568	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
569	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
570	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
571	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
574	C₂×D₈	C₂³×C₁₃	1	4	yes	—
575	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
576	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
577	C₄⋊Q₈	—	2	1	no	—
578	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
580	#127	—	2	2	no	—
581	#127	—	2	2	no	—
582	#127	—	2	4	no	—
583	#127	—	2	1	no	—
584	#127	—	2	1	no	—
585	#127	C₂³×C₁₃	1	2	yes	—
586	#127	C₂³×C₁₃	1	2	yes	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#126	—	2	1	no	—
590	#125	—	2	2	no	—
591	#125	—	2	1	no	—
592	#125	C₂³×C₁₃	1	1	yes	characteristic
593	#124	—	2	1	no	—
594	#124	—	2	2	no	—
595	#124	C₂³×C₁₃	1	1	yes	characteristic
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	1	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
609	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
610	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	4	no	—
617	#121	—	2	4	no	—
618	#121	—	2	4	no	—
619	#121	—	2	4	no	—
620	#121	C₂³×C₁₃	1	4	yes	—
621	#121	C₂³×C₁₃	1	4	yes	—
622	#121	C₂³×C₁₃	1	1	yes	characteristic
623	#121	C₂³×C₁₃	1	2	yes	—
624	#120	—	2	2	no	—
625	C₄×Q₈	—	2	1	no	—
626	C₄×Q₈	—	2	1	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	—	2	1	no	—
629	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
630	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
631	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	4	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
642	C₄×D₄	D₄×C₁₃	1	2	yes	—
643	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
645	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₄×D₄	C₂³×C₁₃	1	2	yes	—
648	#117	—	2	1	no	—
649	#117	—	2	2	no	—
650	#117	—	2	1	no	—
651	#117	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	2	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	#107	C₂³×C₁₃	1	2	yes	—
664	#106	C₂³×C₁₃	1	2	yes	—
665	#106	C₂³×C₁₃	1	4	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
668	#103	C₂³×C₁₃	1	2	yes	—
669	#103	C₂³×C₁₃	1	4	yes	—
670	#103	C₂³×C₁₃	1	2	yes	—
671	#103	C₂³×C₁₃	1	2	yes	—
672	#103	C₂³×C₁₃	1	4	yes	—
673	#102	C₂³×C₁₃	1	4	yes	—
674	#102	C₂³×C₁₃	1	4	yes	—
675	#102	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	4	yes	—
677	#102	C₂³×C₁₃	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
679	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
681	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
682	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
683	#97	C₂³×C₁₃	1	2	yes	—
684	C₄×C₈	C₂³×C₁₃	1	2	yes	—
685	C₂×C₁₃	—	2	2	no	—
686	C₂×C₁₃	—	4	2	no	—
687	C₂×C₁₃	—	4	2	no	—
688	C₂×C₁₃	—	8	1	no	—
689	C₂×C₁₃	—	8	4	no	—
690	C₂×C₁₃	#3484	1	1	yes	characteristic
691	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
692	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
693	C₂⁴	—	2	2	no	—
694	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
695	#41	—	2	8	no	—
696	#41	—	2	8	no	—
697	#41	—	4	4	no	—
698	#41	—	4	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	8	no	—
702	#41	—	4	8	no	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	8	no	—
726	C₂×D₄	—	4	4	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	—	8	4	no	—
729	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
732	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
733	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	4	4	no	—
743	C₂²×C₄	—	4	8	no	—
744	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
748	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
752	Q₁₆	—	2	8	no	—
753	Q₁₆	—	2	4	no	—
754	SD₁₆	—	2	4	no	—
755	SD₁₆	—	4	4	no	—
756	SD₁₆	—	4	4	no	—
757	SD₁₆	—	4	4	no	—
758	D₈	—	4	4	no	—
759	M₁₆	—	4	4	no	—
760	C₂×C₈	—	4	4	no	—
761	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
762	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
763	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
782	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
783	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
785	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	1	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	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	1	no	—
809	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
811	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
812	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₁₃	#61596	1	1	yes	characteristic, direct product factor, Sylow
814	C₂³	—	2	4	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
823	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
824	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	Q₈	—	2	4	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	8	2	no	—
831	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
832	D₄	—	2	2	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	2	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	8	2	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	2	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
880	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	4	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	8	4	no	—
899	C₂²	—	8	8	no	—
900	C₂²	C₁₃×#577	1	2	yes	—
901	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	C₁₃×#575	1	2	yes	—
916	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
917	C₂	—	2	2	no	—
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	4	no	—
921	C₂	—	8	1	no	—
922	C₂	C₁₃×#3484	1	1	yes	characteristic
923	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
924	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3520	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3317	C₂	semidirect
5. C₁₃×#3304	C₂	semidirect
6. C₁₃×#3284	C₂	semidirect
7. C₁₃×#3278	C₂	semidirect
8. C₁₃×#3271	C₂	semidirect
9. C₁₃×#3217	C₂	semidirect
10. C₁₃×#3208	C₂	semidirect
11. C₁₃×#3194	C₂	semidirect
12. C₁₃×#3187	C₂	semidirect
13. C₁₃×#3113	C₂	semidirect
14. C₁₃×#3108	C₂	semidirect
15. C₁₃×#3007	C₂	semidirect
16. C₁₃×#3002	C₂	semidirect
17. C₁₃×#2974	C₂	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×#135	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#548	C₂²	semidirect
33. C₁₃×#547	C₂²	semidirect
34. C₁₃×#547	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
56. C₁₃×#482	C₂²	semidirect
57. C₁₃×#481	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#465	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#460	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#452	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
81. C₁₃×#448	C₂²	semidirect
83. C₁₃×#441	C₂²	semidirect
84. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₁₃×#436	C₂²	semidirect
87. C₁₃×#435	C₂²	semidirect
88. C₈×D₄×C₁₃	C₂²	semidirect
91. C₁₃×#417	C₂²	semidirect
92. C₁₃×#416	C₂²	semidirect
231. #61596	C₁₃	direct (N × H)
352. #3520	C₂×C₁₃	semidirect
353. C₂×#550	C₂×C₁₃	semidirect
354. #3332	C₂×C₁₃	semidirect
355. #3317	C₂×C₁₃	semidirect
356. #3304	C₂×C₁₃	semidirect
357. #3284	C₂×C₁₃	semidirect
358. #3278	C₂×C₁₃	semidirect
359. #3271	C₂×C₁₃	semidirect
360. #3217	C₂×C₁₃	semidirect
361. #3208	C₂×C₁₃	semidirect
362. #3194	C₂×C₁₃	semidirect
363. #3187	C₂×C₁₃	semidirect
364. #3113	C₂×C₁₃	semidirect
365. #3108	C₂×C₁₃	semidirect
366. #3007	C₂×C₁₃	semidirect
367. #3002	C₂×C₁₃	semidirect
368. #2974	C₂×C₁₃	semidirect
440. C₂×#137	C₂²×C₁₃	semidirect
441. C₂×#135	C₂²×C₁₃	semidirect
442. #556	C₂²×C₁₃	semidirect
444. #552	C₂²×C₁₃	semidirect
452. D₄×Q₈	C₂²×C₁₃	semidirect
453. #548	C₂²×C₁₃	semidirect
454. #547	C₂²×C₁₃	semidirect
455. #547	C₂²×C₁₃	semidirect
471. #496	C₂²×C₁₃	semidirect
472. #492	C₂²×C₁₃	semidirect
473. #490	C₂²×C₁₃	semidirect
474. #486	C₂²×C₁₃	semidirect
477. #482	C₂²×C₁₃	semidirect
478. #481	C₂²×C₁₃	semidirect
480. #479	C₂²×C₁₃	semidirect
481. #475	C₂²×C₁₃	semidirect
482. #469	C₂²×C₁₃	semidirect
483. #468	C₂²×C₁₃	semidirect
484. #465	C₂²×C₁₃	semidirect
485. #465	C₂²×C₁₃	semidirect
486. #464	C₂²×C₁₃	semidirect
487. #462	C₂²×C₁₃	semidirect
488. #460	C₂²×C₁₃	semidirect
489. #460	C₂²×C₁₃	semidirect
490. #459	C₂²×C₁₃	semidirect
491. #452	C₂²×C₁₃	semidirect
492. #452	C₂²×C₁₃	semidirect
493. #452	C₂²×C₁₃	semidirect
499. #449	C₂²×C₁₃	semidirect
500. #449	C₂²×C₁₃	semidirect
502. #448	C₂²×C₁₃	semidirect
504. #441	C₂²×C₁₃	semidirect
505. C₄×Q₁₆	C₂²×C₁₃	semidirect
506. C₄×SD₁₆	C₂²×C₁₃	semidirect
507. #436	C₂²×C₁₃	semidirect
508. #435	C₂²×C₁₃	semidirect
509. C₈×D₄	C₂²×C₁₃	semidirect
512. #417	C₂²×C₁₃	semidirect
513. #416	C₂²×C₁₃	semidirect
813. C₁₃	#61596	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×#3520	2
C₂×C₁₃×#550	2
C₁₃×#3332	2
C₁₃×#3317	2
C₁₃×#3304	2
C₁₃×#3284	2
C₁₃×#3278	2
C₁₃×#3271	2
C₁₃×#3217	2
C₁₃×#3208	2
C₁₃×#3194	2
C₁₃×#3187	2
C₁₃×#3113	2
C₁₃×#3108	2
C₁₃×#3007	2
C₁₃×#3002	2
C₁₃×#2974	2
#61596	13

Subgroups — C13×#61596 #15747935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61596 #15747935