Subgroups — C₁₃×#61482 #15747821

Order 3328.

1882 conjugacy classes of subgroups.

The subgroup lattice has 754 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	2	yes	maximal, complemented
2	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3330	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3314	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3175	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3124	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3110	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2951	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	2	yes	—
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#556	C₂²	1	2	yes	complemented
21	C₁₃×#554	C₂²	1	4	yes	—
22	C₁₃×#552	—	2	2	no	—
23	C₁₃×#551	—	2	4	no	—
24	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
25	C₁₃×#548	—	2	2	no	—
26	C₁₃×#547	C₂²	1	2	yes	complemented
27	C₁₃×#547	C₂²	1	2	yes	complemented
28	C₁₃×#546	C₂²	1	4	yes	—
29	C₁₃×#542	C₂²	1	4	yes	complemented
30	C₁₃×#539	—	2	4	no	—
31	C₁₃×#533	C₂²	1	2	yes	—
32	C₁₃×#529	C₂²	1	1	yes	characteristic
33	C₁₃×#525	—	2	2	no	—
34	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
35	C₁₃×#520	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#500	C₂²	1	2	yes	complemented
39	C₁₃×#495	C₂²	1	2	yes	—
40	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#489	C₂²	1	4	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#484	C₂²	1	4	yes	—
44	C₁₃×#484	C₂²	1	4	yes	complemented
45	C₁₃×#480	C₂²	1	4	yes	complemented
46	C₁₃×#477	C₂²	1	4	yes	complemented
47	C₁₃×#474	C₂²	1	4	yes	complemented
48	C₁₃×#474	C₂²	1	2	yes	complemented
49	C₁₃×#474	C₂²	1	2	yes	complemented
50	C₁₃×#468	C₂²	1	4	yes	complemented
51	C₁₃×#467	C₂²	1	2	yes	—
52	C₁₃×#467	C₂²	1	2	yes	—
53	C₁₃×#467	C₂²	1	2	yes	complemented
54	C₁₃×#466	C₂²	1	2	yes	—
55	C₁₃×#464	C₂²	1	4	yes	complemented
56	C₁₃×#463	C₂²	1	4	yes	—
57	C₁₃×#461	C₂²	1	2	yes	complemented
58	C₁₃×#461	C₂²	1	2	yes	complemented
59	C₁₃×#452	C₂²	1	4	yes	complemented
60	C₁₃×#450	C₂²	1	4	yes	—
61	C₁₃×#449	C₂²	1	4	yes	—
62	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#440	C₂²	1	4	yes	complemented
65	C₁₃×#440	C₂²	1	4	yes	complemented
66	C₁₃×#440	C₂²	1	4	yes	complemented
67	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
68	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
69	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
70	C₄×C₁₃×D₈	C₂²	1	2	yes	—
71	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×D₈	C₂²	1	2	yes	—
73	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
74	C₄×C₁₃×D₈	C₂²	1	2	yes	—
75	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
76	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
77	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#435	C₂²	1	2	yes	—
79	C₈×D₄×C₁₃	C₂²	1	2	yes	—
80	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#433	C₂²	1	2	yes	complemented
82	C₁₃×#432	C₂²	1	1	yes	characteristic
83	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
84	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
85	C₁₃×#417	C₂²	1	4	yes	complemented
86	C₂×C₁₃×#102	C₂²	1	2	yes	—
87	C₁₃×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂²×Q₈×C₁₃	—	2	2	no	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	—	2	2	no	—
94	C₁₃×#135	—	2	8	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×D₈	—	2	4	no	—
100	C₂×C₁₃×D₈	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#126	D₄	1	2	yes	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	D₄	1	1	yes	characteristic
116	C₁₃×#124	—	2	4	no	—
117	C₁₃×#124	D₄	1	1	yes	characteristic
118	C₁₃×#124	C₂³	1	4	yes	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	D₄	1	2	yes	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	D₄	1	1	yes	characteristic
138	C₁₃×#121	C₂³	1	4	yes	—
139	C₁₃×#120	—	2	4	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
142	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
143	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	C₂³	1	2	yes	—
150	C₄×D₄×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	C₂³	1	4	yes	—
154	C₄×D₄×C₁₃	C₂³	1	2	yes	—
155	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#117	—	2	2	no	—
157	C₁₃×#117	—	2	4	no	—
158	C₁₃×#117	—	2	2	no	—
159	C₁₃×#117	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
164	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#107	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	2	yes	—
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	4	yes	—
172	C₁₃×#107	C₂³	1	2	yes	—
173	C₁₃×#107	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#103	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#102	C₂³	1	2	yes	—
183	C₁₃×#102	C₂³	1	2	yes	—
184	C₁₃×#102	C₂³	1	2	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₁₃×#97	C₂³	1	2	yes	—
192	C₁₃×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₃	C₂³	1	2	yes	—
198	#61482	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂⁴×C₁₃	—	2	2	no	—
200	C₁₃×#41	—	2	8	no	—
201	C₁₃×#41	—	4	4	no	—
202	C₁₃×#41	—	8	4	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	4	no	—
205	C₂×Q₈×C₁₃	—	8	4	no	—
206	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	8	4	no	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₁₃×Q₁₆	—	2	4	no	—
231	C₁₃×Q₁₆	—	4	2	no	—
232	C₁₃×SD₁₆	—	2	8	no	—
233	C₁₃×SD₁₆	—	4	4	no	—
234	C₁₃×D₈	—	2	4	no	—
235	C₁₃×D₈	—	2	2	no	—
236	C₁₃×D₈	#41	1	4	yes	complemented
237	C₁₃×M₁₆	—	4	2	no	—
238	C₂×C₈×C₁₃	—	2	2	no	—
239	C₂×C₈×C₁₃	—	2	4	no	—
240	C₂×C₈×C₁₃	—	4	1	no	—
241	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₄²×C₁₃	C₂⁴	1	2	yes	—
288	#3520	C₂×C₁₃	1	2	yes	complemented
289	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
290	Q₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3367	C₂×C₁₃	1	2	yes	complemented
292	#3338	C₂×C₁₃	1	2	yes	complemented
293	#3334	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#3330	C₂×C₁₃	1	2	yes	complemented
295	#3314	C₂×C₁₃	1	4	yes	complemented
296	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#3280	C₂×C₁₃	1	2	yes	complemented
298	#3175	C₂×C₁₃	1	2	yes	complemented
299	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3124	C₂×C₁₃	1	4	yes	complemented
301	#3110	C₂×C₁₃	1	2	yes	complemented
302	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2951	C₂×C₁₃	1	2	yes	complemented
304	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	4	4	no	—
308	C₂³×C₁₃	—	4	4	no	—
309	C₂³×C₁₃	—	8	2	no	—
310	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
311	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₁₃	—	2	2	no	—
313	Q₈×C₁₃	—	2	4	no	—
314	Q₈×C₁₃	—	2	4	no	—
315	Q₈×C₁₃	—	4	4	no	—
316	Q₈×C₁₃	—	8	4	no	—
317	D₄×C₁₃	—	2	4	no	—
318	D₄×C₁₃	—	2	2	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	2	2	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	4	4	no	—
323	D₄×C₁₃	—	4	8	no	—
324	D₄×C₁₃	—	8	4	no	—
325	D₄×C₁₃	C₂×#41	1	4	yes	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	4	8	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	8	2	no	—
340	C₂×C₄×C₁₃	—	8	2	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	—	8	2	no	—
343	C₂×C₄×C₁₃	—	8	4	no	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
353	C₈×C₁₃	—	2	1	no	—
354	C₈×C₁₃	—	2	2	no	—
355	C₈×C₁₃	—	2	1	no	—
356	C₈×C₁₃	—	2	1	no	—
357	C₈×C₁₃	—	2	2	no	—
358	C₈×C₁₃	C₂×#41	1	2	yes	—
359	C₂×#135	C₂²×C₁₃	1	2	yes	—
360	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
361	#556	C₂²×C₁₃	1	2	yes	complemented
362	#554	C₂²×C₁₃	1	4	yes	—
363	#552	—	2	2	no	—
364	#551	—	2	4	no	—
365	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
366	#548	—	2	2	no	—
367	#547	C₂²×C₁₃	1	2	yes	complemented
368	#547	C₂²×C₁₃	1	2	yes	complemented
369	#546	C₂²×C₁₃	1	4	yes	—
370	#542	C₂²×C₁₃	1	4	yes	complemented
371	#539	—	2	4	no	—
372	#533	C₂²×C₁₃	1	2	yes	—
373	#529	C₂²×C₁₃	1	1	yes	characteristic
374	#525	—	2	2	no	—
375	C₂×C₂²⋊Q₈	—	2	2	no	—
376	#520	C₂²×C₁₃	1	4	yes	complemented
377	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
378	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	#500	C₂²×C₁₃	1	2	yes	complemented
380	#495	C₂²×C₁₃	1	2	yes	—
381	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	#489	C₂²×C₁₃	1	4	yes	complemented
383	#487	C₂²×C₁₃	1	2	yes	complemented
384	#484	C₂²×C₁₃	1	4	yes	—
385	#484	C₂²×C₁₃	1	4	yes	complemented
386	#480	C₂²×C₁₃	1	4	yes	complemented
387	#477	C₂²×C₁₃	1	4	yes	complemented
388	#474	C₂²×C₁₃	1	2	yes	complemented
389	#474	C₂²×C₁₃	1	2	yes	complemented
390	#474	C₂²×C₁₃	1	4	yes	complemented
391	#468	C₂²×C₁₃	1	4	yes	complemented
392	#467	C₂²×C₁₃	1	2	yes	—
393	#467	C₂²×C₁₃	1	2	yes	—
394	#467	C₂²×C₁₃	1	2	yes	complemented
395	#466	C₂²×C₁₃	1	2	yes	—
396	#464	C₂²×C₁₃	1	4	yes	complemented
397	#463	C₂²×C₁₃	1	4	yes	—
398	#461	C₂²×C₁₃	1	2	yes	complemented
399	#461	C₂²×C₁₃	1	2	yes	complemented
400	#452	C₂²×C₁₃	1	4	yes	complemented
401	#450	C₂²×C₁₃	1	4	yes	—
402	#449	C₂²×C₁₃	1	4	yes	—
403	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#440	C₂²×C₁₃	1	4	yes	complemented
406	#440	C₂²×C₁₃	1	4	yes	complemented
407	#440	C₂²×C₁₃	1	4	yes	complemented
408	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
409	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
410	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
411	C₄×D₈	C₂²×C₁₃	1	2	yes	—
412	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
413	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
414	C₄×D₈	C₂²×C₁₃	1	2	yes	—
415	C₄×D₈	C₂²×C₁₃	1	2	yes	—
416	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
418	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#435	C₂²×C₁₃	1	2	yes	—
420	C₈×D₄	C₂²×C₁₃	1	2	yes	—
421	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#433	C₂²×C₁₃	1	2	yes	complemented
423	#432	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
426	#417	C₂²×C₁₃	1	4	yes	complemented
427	C₂×#102	C₂²×C₁₃	1	2	yes	—
428	#405	C₂²×C₁₃	1	2	yes	complemented
429	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂²×C₁₃	—	2	1	no	—
431	C₂²×C₁₃	—	2	1	no	—
432	C₂²×C₁₃	—	2	2	no	—
433	C₂²×C₁₃	—	2	4	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	2	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	8	8	no	—
442	C₂²×C₁₃	#578	1	2	yes	—
443	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
444	C₄×C₁₃	—	2	2	no	—
445	C₄×C₁₃	—	2	1	no	—
446	C₄×C₁₃	—	2	1	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	1	no	—
449	C₄×C₁₃	—	2	1	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	4	4	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	4	no	—
455	C₄×C₁₃	#576	1	2	yes	—
456	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
457	C₄×C₁₃	#585	1	1	yes	characteristic
458	C₂×#41	—	2	2	no	—
459	C₂×#41	C₂³×C₁₃	1	4	yes	—
460	C₂²×Q₈	—	2	2	no	—
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂³×C₄	—	2	2	no	—
463	#135	—	2	8	no	—
464	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
465	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
466	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
467	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
468	C₂×D₈	—	2	4	no	—
469	C₂×D₈	C₂³×C₁₃	1	2	yes	—
470	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
473	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
475	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
477	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
478	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
479	#126	—	2	4	no	—
480	#126	—	2	4	no	—
481	#126	D₄×C₁₃	1	2	yes	—
482	#125	—	2	4	no	—
483	#125	—	2	2	no	—
484	#125	D₄×C₁₃	1	1	yes	characteristic
485	#124	—	2	4	no	—
486	#124	D₄×C₁₃	1	1	yes	characteristic
487	#124	C₂³×C₁₃	1	4	yes	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	D₄×C₁₃	1	2	yes	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
502	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
503	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
504	#121	—	2	2	no	—
505	#121	—	2	4	no	—
506	#121	D₄×C₁₃	1	1	yes	characteristic
507	#121	C₂³×C₁₃	1	4	yes	—
508	#120	—	2	4	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
511	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
512	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	C₂³×C₁₃	1	2	yes	—
519	C₄×D₄	C₂³×C₁₃	1	2	yes	—
520	C₄×D₄	C₂³×C₁₃	1	2	yes	—
521	C₄×D₄	C₂³×C₁₃	1	2	yes	—
522	C₄×D₄	C₂³×C₁₃	1	4	yes	—
523	C₄×D₄	C₂³×C₁₃	1	2	yes	—
524	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
525	#117	—	2	2	no	—
526	#117	—	2	4	no	—
527	#117	—	2	2	no	—
528	#117	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄⋊C₄	—	2	4	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₂²⋊C₄	—	2	4	no	—
535	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
536	#107	C₂³×C₁₃	1	1	yes	characteristic
537	#107	C₂³×C₁₃	1	1	yes	characteristic
538	#107	C₂³×C₁₃	1	2	yes	—
539	#107	C₂³×C₁₃	1	2	yes	—
540	#107	C₂³×C₁₃	1	4	yes	—
541	#107	C₂³×C₁₃	1	2	yes	—
542	#107	C₂³×C₁₃	1	4	yes	—
543	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
546	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
547	#103	C₂³×C₁₃	1	4	yes	—
548	#103	C₂³×C₁₃	1	4	yes	—
549	#103	C₂³×C₁₃	1	4	yes	—
550	#103	C₂³×C₁₃	1	4	yes	—
551	#102	C₂³×C₁₃	1	2	yes	—
552	#102	C₂³×C₁₃	1	2	yes	—
553	#102	C₂³×C₁₃	1	2	yes	—
554	#102	C₂³×C₁₃	1	2	yes	—
555	#102	C₂³×C₁₃	1	4	yes	—
556	#102	C₂³×C₁₃	1	4	yes	—
557	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
560	#97	C₂³×C₁₃	1	2	yes	—
561	#97	C₂³×C₁₃	1	2	yes	—
562	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
564	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₁₃	1	2	yes	—
567	C₂×C₁₃	—	2	2	no	—
568	C₂×C₁₃	—	4	2	no	—
569	C₂×C₁₃	—	4	4	no	—
570	C₂×C₁₃	—	8	2	no	—
571	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
572	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
573	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
574	C₂⁴	—	2	2	no	—
575	#41	—	2	8	no	—
576	#41	—	4	4	no	—
577	#41	—	8	4	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	8	4	no	—
581	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
582	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
589	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
591	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	8	4	no	—
601	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	Q₁₆	—	2	4	no	—
606	Q₁₆	—	4	2	no	—
607	SD₁₆	—	2	8	no	—
608	SD₁₆	—	4	4	no	—
609	D₈	—	2	4	no	—
610	D₈	—	2	2	no	—
611	D₈	C₁₃×#41	1	4	yes	complemented
612	M₁₆	—	4	2	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	4	no	—
615	C₂×C₈	—	4	1	no	—
616	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
620	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
621	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
655	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
661	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
662	C₄²	C₂⁴×C₁₃	1	2	yes	—
663	C₁₃	#61482	1	1	yes	characteristic, direct product factor, Sylow
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	4	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	8	2	no	—
669	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
670	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	4	4	no	—
675	Q₈	—	8	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	8	no	—
683	D₄	—	8	4	no	—
684	D₄	C₂×C₁₃×#41	1	4	yes	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	2	no	—
717	C₈	C₂×C₁₃×#41	1	2	yes	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	8	8	no	—
730	C₂²	C₁₃×#578	1	2	yes	—
731	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	1	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	C₁₃×#576	1	2	yes	—
744	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
745	C₄	C₁₃×#585	1	1	yes	characteristic
746	C₂	—	2	2	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
751	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
752	C₂	C₂×C₁₃×#578	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3520	C₂	semidirect
2. C₁₃×#3393	C₂	semidirect
3. Q₈×C₁₃×D₈	C₂	semidirect
4. C₁₃×#3367	C₂	semidirect
5. C₁₃×#3338	C₂	semidirect
6. C₁₃×#3334	C₂	semidirect
7. C₁₃×#3330	C₂	semidirect
8. C₁₃×#3314	C₂	semidirect
9. C₁₃×#3283	C₂	semidirect
10. C₁₃×#3280	C₂	semidirect
11. C₁₃×#3175	C₂	semidirect
12. C₁₃×#3170	C₂	semidirect
13. C₁₃×#3124	C₂	semidirect
14. C₁₃×#3110	C₂	semidirect
15. C₁₃×#2966	C₂	semidirect
16. C₁₃×#2951	C₂	semidirect
17. C₂×C₄×C₁₃×D₈	C₂	semidirect
20. C₁₃×#556	C₂²	semidirect
24. D₄×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#547	C₂²	semidirect
27. C₁₃×#547	C₂²	semidirect
29. C₁₃×#542	C₂²	semidirect
35. C₁₃×#520	C₂²	semidirect
37. C₁₃×#500	C₂²	semidirect
38. C₁₃×#500	C₂²	semidirect
40. C₁₃×#494	C₂²	semidirect
41. C₁₃×#489	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
44. C₁₃×#484	C₂²	semidirect
45. C₁₃×#480	C₂²	semidirect
46. C₁₃×#477	C₂²	semidirect
47. C₁₃×#474	C₂²	semidirect
48. C₁₃×#474	C₂²	semidirect
49. C₁₃×#474	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
53. C₁₃×#467	C₂²	semidirect
55. C₁₃×#464	C₂²	semidirect
57. C₁₃×#461	C₂²	semidirect
58. C₁₃×#461	C₂²	semidirect
59. C₁₃×#452	C₂²	semidirect
62. C₁₃×#446	C₂²	semidirect
63. C₈×Q₈×C₁₃	C₂²	semidirect
64. C₁₃×#440	C₂²	semidirect
65. C₁₃×#440	C₂²	semidirect
66. C₁₃×#440	C₂²	semidirect
67. C₄×C₁₃×Q₁₆	C₂²	semidirect
68. C₄×C₁₃×Q₁₆	C₂²	semidirect
69. C₄×C₁₃×Q₁₆	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
80. C₈×D₄×C₁₃	C₂²	semidirect
81. C₁₃×#433	C₂²	semidirect
84. C₂×C₁₃×#107	C₂²	semidirect
85. C₁₃×#417	C₂²	semidirect
87. C₁₃×#405	C₂²	semidirect
198. #61482	C₁₃	direct (N × H)
236. C₁₃×D₈	#41	semidirect
288. #3520	C₂×C₁₃	semidirect
289. #3393	C₂×C₁₃	semidirect
290. Q₈×D₈	C₂×C₁₃	semidirect
291. #3367	C₂×C₁₃	semidirect
292. #3338	C₂×C₁₃	semidirect
293. #3334	C₂×C₁₃	semidirect
294. #3330	C₂×C₁₃	semidirect
295. #3314	C₂×C₁₃	semidirect
296. #3283	C₂×C₁₃	semidirect
297. #3280	C₂×C₁₃	semidirect
298. #3175	C₂×C₁₃	semidirect
299. #3170	C₂×C₁₃	semidirect
300. #3124	C₂×C₁₃	semidirect
301. #3110	C₂×C₁₃	semidirect
302. #2966	C₂×C₁₃	semidirect
303. #2951	C₂×C₁₃	semidirect
304. C₂×C₄×D₈	C₂×C₁₃	semidirect
361. #556	C₂²×C₁₃	semidirect
365. D₄×Q₈	C₂²×C₁₃	semidirect
367. #547	C₂²×C₁₃	semidirect
368. #547	C₂²×C₁₃	semidirect
370. #542	C₂²×C₁₃	semidirect
376. #520	C₂²×C₁₃	semidirect
378. #500	C₂²×C₁₃	semidirect
379. #500	C₂²×C₁₃	semidirect
381. #494	C₂²×C₁₃	semidirect
382. #489	C₂²×C₁₃	semidirect
383. #487	C₂²×C₁₃	semidirect
385. #484	C₂²×C₁₃	semidirect
386. #480	C₂²×C₁₃	semidirect
387. #477	C₂²×C₁₃	semidirect
388. #474	C₂²×C₁₃	semidirect
389. #474	C₂²×C₁₃	semidirect
390. #474	C₂²×C₁₃	semidirect
391. #468	C₂²×C₁₃	semidirect
394. #467	C₂²×C₁₃	semidirect
396. #464	C₂²×C₁₃	semidirect
398. #461	C₂²×C₁₃	semidirect
399. #461	C₂²×C₁₃	semidirect
400. #452	C₂²×C₁₃	semidirect
403. #446	C₂²×C₁₃	semidirect
404. C₈×Q₈	C₂²×C₁₃	semidirect
405. #440	C₂²×C₁₃	semidirect
406. #440	C₂²×C₁₃	semidirect
407. #440	C₂²×C₁₃	semidirect
408. C₄×Q₁₆	C₂²×C₁₃	semidirect
409. C₄×Q₁₆	C₂²×C₁₃	semidirect
410. C₄×Q₁₆	C₂²×C₁₃	semidirect
418. #436	C₂²×C₁₃	semidirect
421. C₈×D₄	C₂²×C₁₃	semidirect
422. #433	C₂²×C₁₃	semidirect
425. C₂×#107	C₂²×C₁₃	semidirect
426. #417	C₂²×C₁₃	semidirect
428. #405	C₂²×C₁₃	semidirect
611. D₈	C₁₃×#41	semidirect
663. C₁₃	#61482	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
C₁₃×#3393	2
Q₈×C₁₃×D₈	2
C₁₃×#3367	2
C₁₃×#3338	2
C₁₃×#3334	2
C₁₃×#3330	2
C₁₃×#3314	2
C₁₃×#3283	2
C₁₃×#3280	2
C₁₃×#3175	2
C₁₃×#3170	2
C₁₃×#3124	2
C₁₃×#3110	2
C₁₃×#2966	2
C₁₃×#2951	2
C₂×C₄×C₁₃×D₈	2
#61482	13

Subgroups — C13×#61482 #15747821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61482 #15747821