Subgroups — C₁₃×#60773 #15747112

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3489	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3204	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3202	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3197	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3196	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3195	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₁₃	—	2	2	no	—
24	C₁₃×#548	—	2	2	no	—
25	C₁₃×#547	—	2	4	no	—
26	C₁₃×#547	—	2	2	no	—
27	C₁₃×#546	—	2	4	no	—
28	C₁₃×#546	—	2	2	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#537	C₂²	1	4	yes	—
31	C₁₃×#536	C₂²	1	2	yes	—
32	C₁₃×#536	C₂²	1	4	yes	—
33	C₁₃×#525	C₂²	1	2	yes	—
34	C₁₃×#525	C₂²	1	4	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₁₃×#520	C₂²	1	2	yes	—
38	C₁₃×#485	C₂²	1	4	yes	complemented
39	C₁₃×#485	C₂²	1	4	yes	complemented
40	C₁₃×#485	C₂²	1	4	yes	complemented
41	C₁₃×#484	C₂²	1	4	yes	complemented
42	C₁₃×#483	C₂²	1	4	yes	complemented
43	C₁₃×#483	C₂²	1	4	yes	complemented
44	C₁₃×#482	C₂²	1	4	yes	complemented
45	C₁₃×#481	C₂²	1	4	yes	complemented
46	C₁₃×#470	C₂²	1	2	yes	—
47	C₁₃×#470	C₂²	1	2	yes	—
48	C₁₃×#470	C₂²	1	1	yes	characteristic
49	C₁₃×#470	C₂²	1	4	yes	—
50	C₁₃×#470	C₂²	1	2	yes	complemented
51	C₁₃×#470	C₂²	1	2	yes	complemented
52	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#469	C₂²	1	1	yes	characteristic
54	C₁₃×#469	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#468	C₂²	1	2	yes	—
56	C₁₃×#468	C₂²	1	4	yes	—
57	C₁₃×#468	C₂²	1	2	yes	complemented
58	C₁₃×#467	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#452	C₂²	1	4	yes	complemented
61	C₁₃×#452	C₂²	1	4	yes	complemented
62	C₁₃×#452	C₂²	1	4	yes	complemented
63	C₁₃×#451	C₂²	1	4	yes	complemented
64	C₁₃×#451	C₂²	1	4	yes	complemented
65	C₁₃×#451	C₂²	1	4	yes	complemented
66	C₁₃×#449	C₂²	1	4	yes	complemented
67	C₁₃×#448	C₂²	1	4	yes	complemented
68	C₁₃×#428	C₂²	1	2	yes	complemented
69	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#419	C₂²	1	2	yes	complemented
72	C₁₃×#417	C₂²	1	2	yes	complemented
73	C₁₃×#416	C₂²	1	2	yes	complemented
74	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
75	C₁₃×#408	C₂²	1	2	yes	—
76	C₁₃×#408	C₂²	1	2	yes	—
77	C₁₃×#408	C₂²	1	2	yes	—
78	C₁₃×#408	C₂²	1	2	yes	—
79	C₁₃×#407	C₂²	1	2	yes	—
80	C₁₃×#407	C₂²	1	2	yes	—
81	C₁₃×2₋¹⁺⁴	—	4	4	no	—
82	C₁₃×2₋¹⁺⁴	—	4	4	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	2	no	—
85	C₂×C₁₃×#41	—	4	2	no	—
86	C₂×C₁₃×#41	—	4	2	no	—
87	C₂×C₁₃×#41	D₄	1	2	yes	—
88	C₂×C₁₃×#41	D₄	1	2	yes	—
89	C₂×C₁₃×#41	C₂³	1	2	yes	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂²×Q₈×C₁₃	—	2	2	no	—
94	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	D₄	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#137	—	4	4	no	—
102	C₁₃×#135	—	4	2	no	—
103	C₂×C₁₃×Q₁₆	—	4	2	no	—
104	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×M₁₆	—	4	2	no	—
112	C₂×C₁₃×M₁₆	—	4	2	no	—
113	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	—	2	2	no	—
123	C₁₃×C₄⋊Q₈	—	2	4	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	—	2	4	no	—
126	C₁₃×#123	—	2	4	no	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₁₃×#121	—	2	4	no	—
145	C₁₃×#121	—	2	4	no	—
146	C₁₃×#121	—	2	4	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	4	no	—
149	C₁₃×#121	C₂³	1	4	yes	—
150	C₁₃×#121	C₂³	1	2	yes	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#120	—	2	2	no	—
153	C₁₃×#120	—	2	4	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	4	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	4	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	4	no	—
161	C₁₃×#117	C₂³	1	2	yes	—
162	C₁₃×#117	C₂³	1	4	yes	—
163	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×#107	C₂³	1	2	yes	—
170	C₁₃×#107	C₂³	1	4	yes	—
171	C₁₃×#106	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	2	yes	—
173	C₁₃×#106	C₂³	1	1	yes	characteristic
174	C₁₃×#106	C₂³	1	1	yes	characteristic
175	C₁₃×#106	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	2	yes	—
179	C₁₃×#103	C₂³	1	2	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	2	yes	—
184	C₁₃×#102	C₂³	1	2	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
190	#60773	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
193	C₁₃×#41	—	2	4	no	—
194	C₁₃×#41	—	2	4	no	—
195	C₁₃×#41	—	2	4	no	—
196	C₁₃×#41	—	2	4	no	—
197	C₁₃×#41	—	4	2	no	—
198	C₁₃×#41	—	4	2	no	—
199	C₁₃×#41	—	4	4	no	—
200	C₁₃×#41	—	4	4	no	—
201	C₁₃×#41	—	4	4	no	—
202	C₁₃×#41	—	4	4	no	—
203	C₁₃×#41	—	4	16	no	—
204	C₁₃×#41	—	4	8	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	4	no	—
208	C₂×Q₈×C₁₃	—	2	4	no	—
209	C₂×Q₈×C₁₃	—	4	2	no	—
210	C₂×Q₈×C₁₃	—	4	4	no	—
211	C₂×Q₈×C₁₃	—	4	4	no	—
212	C₂×Q₈×C₁₃	—	4	8	no	—
213	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
215	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
216	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	4	2	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
228	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₁₃×Q₁₆	—	4	2	no	—
249	C₁₃×Q₁₆	—	4	2	no	—
250	C₁₃×Q₁₆	—	4	1	no	—
251	C₁₃×Q₁₆	—	4	4	no	—
252	C₁₃×SD₁₆	—	4	2	no	—
253	C₁₃×SD₁₆	—	4	4	no	—
254	C₁₃×D₈	—	4	1	no	—
255	C₁₃×M₁₆	—	2	4	no	—
256	C₁₃×M₁₆	—	4	1	no	—
257	C₁₃×M₁₆	—	4	1	no	—
258	C₁₃×M₁₆	—	4	1	no	—
259	C₁₃×M₁₆	—	4	1	no	—
260	C₁₃×M₁₆	—	4	2	no	—
261	C₂×C₈×C₁₃	—	2	2	no	—
262	C₂×C₈×C₁₃	—	2	2	no	—
263	C₂×C₈×C₁₃	—	4	2	no	—
264	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₄²×C₁₃	—	2	4	no	—
294	C₄²×C₁₃	—	2	2	no	—
295	#3489	C₂×C₁₃	1	2	yes	complemented
296	#3204	C₂×C₁₃	1	2	yes	complemented
297	#3202	C₂×C₁₃	1	2	yes	complemented
298	#3201	C₂×C₁₃	1	4	yes	complemented
299	#3197	C₂×C₁₃	1	2	yes	complemented
300	#3196	C₂×C₁₃	1	4	yes	complemented
301	#3195	C₂×C₁₃	1	2	yes	complemented
302	#3099	C₂×C₁₃	1	2	yes	complemented
303	#3097	C₂×C₁₃	1	2	yes	complemented
304	#3056	C₂×C₁₃	1	2	yes	complemented
305	#3054	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#3013	C₂×C₁₃	1	2	yes	complemented
308	#3011	C₂×C₁₃	1	2	yes	complemented
309	#2879	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	4	2	no	—
313	C₂³×C₁₃	—	4	2	no	—
314	C₂³×C₁₃	—	4	4	no	—
315	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
316	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
318	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₁₃	—	2	4	no	—
320	Q₈×C₁₃	—	2	4	no	—
321	Q₈×C₁₃	—	2	2	no	—
322	Q₈×C₁₃	—	2	4	no	—
323	Q₈×C₁₃	—	2	2	no	—
324	Q₈×C₁₃	—	4	2	no	—
325	Q₈×C₁₃	—	4	8	no	—
326	Q₈×C₁₃	—	4	4	no	—
327	D₄×C₁₃	—	2	8	no	—
328	D₄×C₁₃	—	2	4	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	2	2	no	—
331	D₄×C₁₃	—	4	2	no	—
332	D₄×C₁₃	—	4	4	no	—
333	D₄×C₁₃	—	4	4	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	4	no	—
336	D₄×C₁₃	—	8	2	no	—
337	D₄×C₁₃	—	8	4	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	4	no	—
346	C₂×C₄×C₁₃	—	2	4	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	4	2	no	—
353	C₂×C₄×C₁₃	—	4	4	no	—
354	C₂×C₄×C₁₃	—	4	8	no	—
355	C₂×C₄×C₁₃	—	4	8	no	—
356	C₂×C₄×C₁₃	—	4	4	no	—
357	C₂×C₄×C₁₃	—	4	4	no	—
358	C₂×C₄×C₁₃	—	8	2	no	—
359	C₂×C₄×C₁₃	—	8	4	no	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
365	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
366	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
367	C₈×C₁₃	—	2	1	no	—
368	C₈×C₁₃	—	2	1	no	—
369	C₈×C₁₃	—	2	1	no	—
370	C₈×C₁₃	—	2	1	no	—
371	C₈×C₁₃	—	2	4	no	—
372	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
373	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
375	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
376	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
377	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
379	D₄×Q₈	—	2	2	no	—
380	#548	—	2	2	no	—
381	#547	—	2	4	no	—
382	#547	—	2	2	no	—
383	#546	—	2	4	no	—
384	#546	—	2	2	no	—
385	#537	C₂²×C₁₃	1	2	yes	—
386	#537	C₂²×C₁₃	1	4	yes	—
387	#536	C₂²×C₁₃	1	2	yes	—
388	#536	C₂²×C₁₃	1	4	yes	—
389	#525	C₂²×C₁₃	1	4	yes	—
390	#525	C₂²×C₁₃	1	2	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
393	#520	C₂²×C₁₃	1	2	yes	—
394	#485	C₂²×C₁₃	1	4	yes	complemented
395	#485	C₂²×C₁₃	1	4	yes	complemented
396	#485	C₂²×C₁₃	1	4	yes	complemented
397	#484	C₂²×C₁₃	1	4	yes	complemented
398	#483	C₂²×C₁₃	1	4	yes	complemented
399	#483	C₂²×C₁₃	1	4	yes	complemented
400	#482	C₂²×C₁₃	1	4	yes	complemented
401	#481	C₂²×C₁₃	1	4	yes	complemented
402	#470	C₂²×C₁₃	1	1	yes	characteristic
403	#470	C₂²×C₁₃	1	4	yes	—
404	#470	C₂²×C₁₃	1	2	yes	—
405	#470	C₂²×C₁₃	1	2	yes	—
406	#470	C₂²×C₁₃	1	2	yes	complemented
407	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	#470	C₂²×C₁₃	1	2	yes	complemented
409	#469	C₂²×C₁₃	1	1	yes	characteristic
410	#469	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	#468	C₂²×C₁₃	1	2	yes	—
412	#468	C₂²×C₁₃	1	4	yes	—
413	#468	C₂²×C₁₃	1	2	yes	complemented
414	#467	C₂²×C₁₃	1	4	yes	complemented
415	#465	C₂²×C₁₃	1	4	yes	complemented
416	#452	C₂²×C₁₃	1	4	yes	complemented
417	#452	C₂²×C₁₃	1	4	yes	complemented
418	#452	C₂²×C₁₃	1	4	yes	complemented
419	#451	C₂²×C₁₃	1	4	yes	complemented
420	#451	C₂²×C₁₃	1	4	yes	complemented
421	#451	C₂²×C₁₃	1	4	yes	complemented
422	#449	C₂²×C₁₃	1	4	yes	complemented
423	#448	C₂²×C₁₃	1	4	yes	complemented
424	#428	C₂²×C₁₃	1	2	yes	complemented
425	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#419	C₂²×C₁₃	1	2	yes	complemented
428	#417	C₂²×C₁₃	1	2	yes	complemented
429	#416	C₂²×C₁₃	1	2	yes	complemented
430	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
431	#408	C₂²×C₁₃	1	2	yes	—
432	#408	C₂²×C₁₃	1	2	yes	—
433	#408	C₂²×C₁₃	1	2	yes	—
434	#408	C₂²×C₁₃	1	2	yes	—
435	#407	C₂²×C₁₃	1	2	yes	—
436	#407	C₂²×C₁₃	1	2	yes	—
437	C₂²×C₁₃	—	2	2	no	—
438	C₂²×C₁₃	—	2	4	no	—
439	C₂²×C₁₃	—	2	2	no	—
440	C₂²×C₁₃	—	2	2	no	—
441	C₂²×C₁₃	—	2	4	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	4	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	4	2	no	—
448	C₂²×C₁₃	—	8	2	no	—
449	C₂²×C₁₃	—	8	4	no	—
450	C₂²×C₁₃	#534	1	2	yes	—
451	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₁₃	—	2	1	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	2	4	no	—
455	C₄×C₁₃	—	4	4	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	4	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	#534	1	2	yes	—
461	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	2₋¹⁺⁴	—	4	4	no	—
464	2₋¹⁺⁴	—	4	4	no	—
465	C₂×#41	—	2	4	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	4	2	no	—
468	C₂×#41	—	4	2	no	—
469	C₂×#41	D₄×C₁₃	1	2	yes	—
470	C₂×#41	D₄×C₁₃	1	2	yes	—
471	C₂×#41	C₂³×C₁₃	1	2	yes	—
472	C₂×#41	C₂³×C₁₃	1	4	yes	—
473	C₂×#41	C₂³×C₁₃	1	2	yes	—
474	C₂×#41	C₂³×C₁₃	1	2	yes	—
475	C₂²×Q₈	—	2	2	no	—
476	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
478	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
479	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
480	C₂²×D₄	D₄×C₁₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
483	#137	—	4	4	no	—
484	#135	—	4	2	no	—
485	C₂×Q₁₆	—	4	2	no	—
486	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
487	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
488	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
491	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
492	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×M₁₆	—	4	2	no	—
494	C₂×M₁₆	—	4	2	no	—
495	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
496	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
498	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
499	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	4	no	—
506	#124	—	2	2	no	—
507	#124	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	—	2	2	no	—
512	#123	—	2	4	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
520	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
521	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
522	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
523	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
524	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
525	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	—	2	2	no	—
530	#121	—	2	4	no	—
531	#121	C₂³×C₁₃	1	2	yes	—
532	#121	C₂³×C₁₃	1	4	yes	—
533	#121	C₂³×C₁₃	1	2	yes	—
534	#120	—	2	2	no	—
535	#120	—	2	4	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	4	no	—
543	#117	C₂³×C₁₃	1	2	yes	—
544	#117	C₂³×C₁₃	1	4	yes	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₂²⋊C₄	—	2	4	no	—
551	#107	C₂³×C₁₃	1	2	yes	—
552	#107	C₂³×C₁₃	1	4	yes	—
553	#106	C₂³×C₁₃	1	2	yes	—
554	#106	C₂³×C₁₃	1	2	yes	—
555	#106	C₂³×C₁₃	1	1	yes	characteristic
556	#106	C₂³×C₁₃	1	1	yes	characteristic
557	#106	C₂³×C₁₃	1	4	yes	—
558	#103	C₂³×C₁₃	1	4	yes	—
559	#103	C₂³×C₁₃	1	4	yes	—
560	#103	C₂³×C₁₃	1	2	yes	—
561	#103	C₂³×C₁₃	1	2	yes	—
562	#103	C₂³×C₁₃	1	4	yes	—
563	#103	C₂³×C₁₃	1	4	yes	—
564	#103	C₂³×C₁₃	1	4	yes	—
565	#102	C₂³×C₁₃	1	2	yes	—
566	#102	C₂³×C₁₃	1	2	yes	—
567	#102	C₂³×C₁₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
572	C₂×C₁₃	—	2	2	no	—
573	C₂×C₁₃	—	4	4	no	—
574	C₂×C₁₃	—	4	1	no	—
575	C₂×C₁₃	—	4	1	no	—
576	C₂×C₁₃	—	8	2	no	—
577	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
578	C₂×C₁₃	#3586	1	2	yes	—
579	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
581	#41	—	2	4	no	—
582	#41	—	2	4	no	—
583	#41	—	2	4	no	—
584	#41	—	2	4	no	—
585	#41	—	4	2	no	—
586	#41	—	4	2	no	—
587	#41	—	4	4	no	—
588	#41	—	4	4	no	—
589	#41	—	4	4	no	—
590	#41	—	4	4	no	—
591	#41	—	4	16	no	—
592	#41	—	4	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	4	2	no	—
598	C₂×Q₈	—	4	4	no	—
599	C₂×Q₈	—	4	4	no	—
600	C₂×Q₈	—	4	8	no	—
601	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
602	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
603	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
604	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
613	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
614	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
615	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
616	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
636	Q₁₆	—	4	2	no	—
637	Q₁₆	—	4	2	no	—
638	Q₁₆	—	4	1	no	—
639	Q₁₆	—	4	4	no	—
640	SD₁₆	—	4	2	no	—
641	SD₁₆	—	4	4	no	—
642	D₈	—	4	1	no	—
643	M₁₆	—	2	4	no	—
644	M₁₆	—	4	1	no	—
645	M₁₆	—	4	1	no	—
646	M₁₆	—	4	1	no	—
647	M₁₆	—	4	1	no	—
648	M₁₆	—	4	2	no	—
649	C₂×C₈	—	2	2	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	—	4	2	no	—
652	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
655	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
656	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	2	no	—
683	C₁₃	#60773	1	1	yes	characteristic, direct product factor, Sylow
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	4	no	—
689	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
690	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
691	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
692	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
693	Q₈	—	2	4	no	—
694	Q₈	—	2	4	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	4	8	no	—
700	Q₈	—	4	4	no	—
701	D₄	—	2	8	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	4	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	4	no	—
710	D₄	—	8	2	no	—
711	D₄	—	8	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
738	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
739	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
740	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
741	C₈	—	2	1	no	—
742	C₈	—	2	1	no	—
743	C₈	—	2	1	no	—
744	C₈	—	2	1	no	—
745	C₈	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	8	2	no	—
758	C₂²	—	8	4	no	—
759	C₂²	C₁₃×#534	1	2	yes	—
760	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	4	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	2	no	—
769	C₄	C₁₃×#534	1	2	yes	—
770	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
771	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂	—	2	2	no	—
773	C₂	—	4	1	no	—
774	C₂	—	4	4	no	—
775	C₂	—	4	1	no	—
776	C₂	—	8	2	no	—
777	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
778	C₂	C₁₃×#3586	1	2	yes	—

	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 ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3489	C₂	semidirect
2. C₁₃×#3204	C₂	semidirect
3. C₁₃×#3202	C₂	semidirect
4. C₁₃×#3201	C₂	semidirect
5. C₁₃×#3197	C₂	semidirect
6. C₁₃×#3196	C₂	semidirect
7. C₁₃×#3195	C₂	semidirect
8. C₁₃×#3099	C₂	semidirect
9. C₁₃×#3097	C₂	semidirect
10. C₁₃×#3056	C₂	semidirect
11. C₁₃×#3054	C₂	semidirect
12. C₂×C₁₃×#470	C₂	semidirect
13. C₁₃×#3013	C₂	semidirect
14. C₁₃×#3011	C₂	semidirect
15. C₁₃×#2879	C₂	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
20. C₂²×C₁₃×Q₁₆	C₂²	semidirect
38. C₁₃×#485	C₂²	semidirect
39. C₁₃×#485	C₂²	semidirect
40. C₁₃×#485	C₂²	semidirect
41. C₁₃×#484	C₂²	semidirect
42. C₁₃×#483	C₂²	semidirect
43. C₁₃×#483	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
45. C₁₃×#481	C₂²	semidirect
50. C₁₃×#470	C₂²	semidirect
51. C₁₃×#470	C₂²	semidirect
52. C₁₃×#470	C₂²	semidirect
54. C₁₃×#469	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
58. C₁₃×#467	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#452	C₂²	semidirect
61. C₁₃×#452	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#451	C₂²	semidirect
64. C₁₃×#451	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#449	C₂²	semidirect
67. C₁₃×#448	C₂²	semidirect
68. C₁₃×#428	C₂²	semidirect
69. C₁₃×#427	C₂²	semidirect
70. C₂×C₁₃×#106	C₂²	semidirect
71. C₁₃×#419	C₂²	semidirect
72. C₁₃×#417	C₂²	semidirect
73. C₁₃×#416	C₂²	semidirect
74. C₂×C₁₃×#103	C₂²	semidirect
190. #60773	C₁₃	direct (N × H)
295. #3489	C₂×C₁₃	semidirect
296. #3204	C₂×C₁₃	semidirect
297. #3202	C₂×C₁₃	semidirect
298. #3201	C₂×C₁₃	semidirect
299. #3197	C₂×C₁₃	semidirect
300. #3196	C₂×C₁₃	semidirect
301. #3195	C₂×C₁₃	semidirect
302. #3099	C₂×C₁₃	semidirect
303. #3097	C₂×C₁₃	semidirect
304. #3056	C₂×C₁₃	semidirect
305. #3054	C₂×C₁₃	semidirect
306. C₂×#470	C₂×C₁₃	semidirect
307. #3013	C₂×C₁₃	semidirect
308. #3011	C₂×C₁₃	semidirect
309. #2879	C₂×C₁₃	semidirect
374. C₂×#137	C₂²×C₁₃	semidirect
375. C₂×#135	C₂²×C₁₃	semidirect
376. C₂²×Q₁₆	C₂²×C₁₃	semidirect
394. #485	C₂²×C₁₃	semidirect
395. #485	C₂²×C₁₃	semidirect
396. #485	C₂²×C₁₃	semidirect
397. #484	C₂²×C₁₃	semidirect
398. #483	C₂²×C₁₃	semidirect
399. #483	C₂²×C₁₃	semidirect
400. #482	C₂²×C₁₃	semidirect
401. #481	C₂²×C₁₃	semidirect
406. #470	C₂²×C₁₃	semidirect
407. #470	C₂²×C₁₃	semidirect
408. #470	C₂²×C₁₃	semidirect
410. #469	C₂²×C₁₃	semidirect
413. #468	C₂²×C₁₃	semidirect
414. #467	C₂²×C₁₃	semidirect
415. #465	C₂²×C₁₃	semidirect
416. #452	C₂²×C₁₃	semidirect
417. #452	C₂²×C₁₃	semidirect
418. #452	C₂²×C₁₃	semidirect
419. #451	C₂²×C₁₃	semidirect
420. #451	C₂²×C₁₃	semidirect
421. #451	C₂²×C₁₃	semidirect
422. #449	C₂²×C₁₃	semidirect
423. #448	C₂²×C₁₃	semidirect
424. #428	C₂²×C₁₃	semidirect
425. #427	C₂²×C₁₃	semidirect
426. C₂×#106	C₂²×C₁₃	semidirect
427. #419	C₂²×C₁₃	semidirect
428. #417	C₂²×C₁₃	semidirect
429. #416	C₂²×C₁₃	semidirect
430. C₂×#103	C₂²×C₁₃	semidirect
683. C₁₃	#60773	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×#3489	2
C₁₃×#3204	2
C₁₃×#3202	2
C₁₃×#3201	2
C₁₃×#3197	2
C₁₃×#3196	2
C₁₃×#3195	2
C₁₃×#3099	2
C₁₃×#3097	2
C₁₃×#3056	2
C₁₃×#3054	2
C₂×C₁₃×#470	2
C₁₃×#3013	2
C₁₃×#3011	2
C₁₃×#2879	2
#60773	13

Subgroups — C13×#60773 #15747112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60773 #15747112