Subgroups — C₁₃×#61056 #15747395

Order 3328.

2832 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3488	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3287	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3268	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3006	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×H(5,𝔽₂)	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
20	C₁₃×#576	—	2	8	no	—
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#135	—	2	8	no	—
25	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
34	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
36	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#550	C₂²	1	4	yes	complemented
40	C₁₃×#548	C₂²	1	4	yes	complemented
41	C₁₃×#546	—	2	4	no	—
42	C₁₃×#546	C₂²	1	4	yes	complemented
43	D₄²×C₁₃	—	2	4	no	—
44	D₄²×C₁₃	C₂²	1	4	yes	complemented
45	C₁₃×#537	—	2	2	no	—
46	C₁₃×#537	C₂²	1	2	yes	complemented
47	C₁₃×#535	—	2	2	no	—
48	C₁₃×#535	C₂²	1	2	yes	complemented
49	C₁₃×#525	—	2	2	no	—
50	C₁₃×#525	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#121	—	2	2	no	—
52	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
53	C₁₃×#520	C₂²	1	2	yes	complemented
54	C₁₃×#496	C₂²	1	4	yes	complemented
55	C₁₃×#495	C₂²	1	2	yes	complemented
56	C₁₃×#493	C₂²	1	2	yes	complemented
57	C₁₃×#468	C₂²	1	4	yes	complemented
58	C₁₃×#467	C₂²	1	2	yes	complemented
59	C₁₃×#466	C₂²	1	2	yes	complemented
60	C₁₃×#466	C₂²	1	2	yes	complemented
61	C₁₃×#466	C₂²	1	2	yes	complemented
62	C₁₃×#466	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×#460	C₂²	1	4	yes	complemented
67	C₁₃×#459	C₂²	1	4	yes	complemented
68	C₁₃×#452	C₂²	1	4	yes	complemented
69	C₁₃×#450	C₂²	1	4	yes	complemented
70	C₁₃×#449	C₂²	1	4	yes	complemented
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#449	C₂²	1	4	yes	complemented
73	C₁₃×#448	C₂²	1	4	yes	complemented
74	C₁₃×#447	C₂²	1	4	yes	complemented
75	C₁₃×#447	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	complemented
80	C₁₃×#435	C₂²	1	2	yes	complemented
81	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
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×#102	C₂²	1	2	yes	complemented
88	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×H(5,𝔽₂)	—	2	8	no	—
92	C₁₃×H(5,𝔽₂)	—	4	4	no	—
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	—	2	2	no	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	8	no	—
97	C₂×C₁₃×#41	—	4	4	no	—
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	4	yes	—
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	2	no	—
108	C₂²×D₄×C₁₃	—	2	4	no	—
109	C₂²×D₄×C₁₃	—	2	4	no	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
113	C₂³×C₄×C₁₃	—	2	2	no	—
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
116	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
117	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
118	C₁₃×#135	—	2	8	no	—
119	C₁₃×#135	—	2	4	no	—
120	C₁₃×#135	—	2	8	no	—
121	C₁₃×#135	—	2	8	no	—
122	C₁₃×#135	—	2	4	no	—
123	C₁₃×#135	—	2	4	no	—
124	C₁₃×#135	D₄	1	8	yes	complemented
125	C₂×C₁₃×Q₁₆	—	2	4	no	—
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×SD₁₆	—	2	8	no	—
130	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
135	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
136	C₂×C₁₃×D₈	—	2	4	no	—
137	C₂×C₁₃×D₈	—	2	8	no	—
138	C₂×C₁₃×D₈	—	2	4	no	—
139	C₂×C₁₃×D₈	C₂³	1	2	yes	—
140	C₂×C₁₃×D₈	C₂³	1	4	yes	—
141	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×D₈	C₂³	1	2	yes	—
143	C₂×C₁₃×D₈	C₂³	1	2	yes	—
144	C₂×C₁₃×D₈	C₂³	1	4	yes	—
145	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
146	C₁₃×#131	—	2	4	no	—
147	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈×C₁₃	—	2	4	no	—
151	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×#127	—	2	4	no	—
159	C₁₃×#127	C₂³	1	4	yes	—
160	C₁₃×#124	—	2	4	no	—
161	C₁₃×#124	C₂³	1	4	yes	—
162	C₁₃×#123	—	2	4	no	—
163	C₁₃×#123	D₄	1	2	yes	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	4	no	—
166	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
167	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
168	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	4	no	—
171	C₁₃×#121	—	2	4	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	4	no	—
177	C₁₃×#121	—	2	4	no	—
178	C₁₃×#121	—	2	4	no	—
179	C₁₃×#121	—	2	4	no	—
180	C₁₃×#121	D₄	1	1	yes	characteristic
181	C₁₃×#121	D₄	1	1	yes	characteristic
182	C₁₃×#121	C₂³	1	4	yes	—
183	C₁₃×#121	C₂³	1	4	yes	—
184	C₁₃×#121	C₂³	1	4	yes	—
185	C₁₃×#120	—	2	4	no	—
186	C₁₃×#120	—	2	4	no	—
187	C₁₃×#120	—	2	4	no	—
188	C₁₃×#120	—	2	4	no	—
189	C₁₃×#120	D₄	1	2	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
191	C₄×D₄×C₁₃	—	2	4	no	—
192	C₄×D₄×C₁₃	—	2	4	no	—
193	C₄×D₄×C₁₃	—	2	4	no	—
194	C₄×D₄×C₁₃	C₂³	1	4	yes	—
195	C₄×D₄×C₁₃	C₂³	1	2	yes	—
196	C₄×D₄×C₁₃	C₂³	1	2	yes	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	—	2	2	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×#102	C₂³	1	4	yes	—
210	C₁₃×#102	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	#61056	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂⁴×C₁₃	—	2	2	no	—
221	C₂⁴×C₁₃	—	2	4	no	—
222	C₂⁴×C₁₃	—	2	2	no	—
223	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₁₃×#41	—	2	2	no	—
225	C₁₃×#41	—	2	4	no	—
226	C₁₃×#41	—	2	2	no	—
227	C₁₃×#41	—	2	4	no	—
228	C₁₃×#41	—	2	8	no	—
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	4	8	no	—
233	C₁₃×#41	—	4	2	no	—
234	C₁₃×#41	—	4	2	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₁₃×#41	—	4	8	no	—
237	C₁₃×#41	—	4	8	no	—
238	C₁₃×#41	C₂×D₄	1	8	yes	complemented
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	8	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
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	4	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	4	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	4	2	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	4	8	no	—
265	C₂×D₄×C₁₃	—	4	16	no	—
266	C₂×D₄×C₁₃	—	4	8	no	—
267	C₂×D₄×C₁₃	—	8	8	no	—
268	C₂×D₄×C₁₃	—	8	4	no	—
269	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
274	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	4	no	—
286	C₂²×C₄×C₁₃	—	4	8	no	—
287	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₁₃×Q₁₆	—	2	4	no	—
295	C₁₃×Q₁₆	—	2	2	no	—
296	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
297	C₁₃×SD₁₆	—	2	4	no	—
298	C₁₃×SD₁₆	—	2	8	no	—
299	C₁₃×SD₁₆	—	2	4	no	—
300	C₁₃×SD₁₆	—	2	4	no	—
301	C₁₃×SD₁₆	—	4	4	no	—
302	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
303	C₁₃×D₈	—	2	4	no	—
304	C₁₃×D₈	—	2	8	no	—
305	C₁₃×D₈	—	2	4	no	—
306	C₁₃×D₈	—	2	2	no	—
307	C₁₃×D₈	—	2	4	no	—
308	C₁₃×D₈	—	4	4	no	—
309	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
310	C₁₃×M₁₆	—	2	2	no	—
311	C₁₃×M₁₆	—	2	2	no	—
312	C₁₃×M₁₆	—	2	4	no	—
313	C₂×C₈×C₁₃	—	2	2	no	—
314	C₂×C₈×C₁₃	—	2	2	no	—
315	C₂×C₈×C₁₃	—	2	2	no	—
316	C₂×C₈×C₁₃	—	2	2	no	—
317	C₂×C₈×C₁₃	—	2	2	no	—
318	C₂×C₈×C₁₃	—	2	4	no	—
319	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
320	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	4	no	—
328	C₁₃×C₄⋊C₄	—	2	4	no	—
329	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
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	—	2	4	no	—
340	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
346	C₄²×C₁₃	—	2	4	no	—
347	C₄²×C₁₃	C₂⁴	1	2	yes	—
348	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3488	C₂×C₁₃	1	2	yes	complemented
351	#3287	C₂×C₁₃	1	2	yes	complemented
352	#3285	C₂×C₁₃	1	2	yes	complemented
353	#3280	C₂×C₁₃	1	2	yes	complemented
354	D₄×D₈	C₂×C₁₃	1	2	yes	complemented
355	#3268	C₂×C₁₃	1	4	yes	complemented
356	#3265	C₂×C₁₃	1	4	yes	complemented
357	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3045	C₂×C₁₃	1	2	yes	complemented
361	#3012	C₂×C₁₃	1	2	yes	complemented
362	#3006	C₂×C₁₃	1	2	yes	complemented
363	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	4	1	no	—
371	C₂³×C₁₃	—	4	4	no	—
372	C₂³×C₁₃	—	4	8	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	4	4	no	—
375	C₂³×C₁₃	—	8	2	no	—
376	C₂³×C₁₃	—	8	2	no	—
377	C₂³×C₁₃	—	8	4	no	—
378	C₂³×C₁₃	—	8	2	no	—
379	C₂³×C₁₃	—	8	4	no	—
380	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
381	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₁₃	—	2	2	no	—
385	Q₈×C₁₃	—	2	2	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	2	2	no	—
388	Q₈×C₁₃	—	4	4	no	—
389	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
390	D₄×C₁₃	—	2	8	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	4	no	—
393	D₄×C₁₃	—	2	2	no	—
394	D₄×C₁₃	—	2	4	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	2	2	no	—
397	D₄×C₁₃	—	2	2	no	—
398	D₄×C₁₃	—	2	4	no	—
399	D₄×C₁₃	—	4	2	no	—
400	D₄×C₁₃	—	4	8	no	—
401	D₄×C₁₃	—	4	4	no	—
402	D₄×C₁₃	—	4	8	no	—
403	D₄×C₁₃	—	4	4	no	—
404	D₄×C₁₃	—	4	4	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	8	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	8	4	no	—
409	D₄×C₁₃	—	8	4	no	—
410	D₄×C₁₃	—	8	4	no	—
411	D₄×C₁₃	—	8	4	no	—
412	D₄×C₁₃	C₂²×D₄	1	4	yes	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	8	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	4	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	4	4	no	—
427	C₂×C₄×C₁₃	—	4	8	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	4	no	—
430	C₂×C₄×C₁₃	—	4	4	no	—
431	C₂×C₄×C₁₃	—	8	4	no	—
432	C₂×C₄×C₁₃	—	8	2	no	—
433	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
442	C₈×C₁₃	—	2	1	no	—
443	C₈×C₁₃	—	2	1	no	—
444	C₈×C₁₃	—	2	2	no	—
445	C₈×C₁₃	—	2	2	no	—
446	C₈×C₁₃	C₂²×D₄	1	2	yes	—
447	C₈×C₁₃	C₂²×D₄	1	2	yes	—
448	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
449	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
450	#576	—	2	8	no	—
451	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
452	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
453	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
454	C₂×#135	—	2	8	no	—
455	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
458	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
459	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
461	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
464	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
467	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#550	C₂²×C₁₃	1	4	yes	complemented
470	#548	C₂²×C₁₃	1	4	yes	complemented
471	#546	—	2	4	no	—
472	#546	C₂²×C₁₃	1	4	yes	complemented
473	D₄²	—	2	4	no	—
474	D₄²	C₂²×C₁₃	1	4	yes	complemented
475	#537	—	2	2	no	—
476	#537	C₂²×C₁₃	1	2	yes	complemented
477	#535	—	2	2	no	—
478	#535	C₂²×C₁₃	1	2	yes	complemented
479	#525	—	2	2	no	—
480	#525	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#121	—	2	2	no	—
482	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
483	#520	C₂²×C₁₃	1	2	yes	complemented
484	#496	C₂²×C₁₃	1	4	yes	complemented
485	#495	C₂²×C₁₃	1	2	yes	complemented
486	#493	C₂²×C₁₃	1	2	yes	complemented
487	#468	C₂²×C₁₃	1	4	yes	complemented
488	#467	C₂²×C₁₃	1	2	yes	complemented
489	#466	C₂²×C₁₃	1	2	yes	complemented
490	#466	C₂²×C₁₃	1	2	yes	complemented
491	#466	C₂²×C₁₃	1	2	yes	complemented
492	#466	C₂²×C₁₃	1	2	yes	complemented
493	#466	C₂²×C₁₃	1	2	yes	complemented
494	#464	C₂²×C₁₃	1	4	yes	complemented
495	#463	C₂²×C₁₃	1	4	yes	complemented
496	#460	C₂²×C₁₃	1	4	yes	complemented
497	#459	C₂²×C₁₃	1	4	yes	complemented
498	#452	C₂²×C₁₃	1	4	yes	complemented
499	#450	C₂²×C₁₃	1	4	yes	complemented
500	#449	C₂²×C₁₃	1	4	yes	complemented
501	#449	C₂²×C₁₃	1	4	yes	complemented
502	#449	C₂²×C₁₃	1	4	yes	complemented
503	#448	C₂²×C₁₃	1	4	yes	complemented
504	#447	C₂²×C₁₃	1	4	yes	complemented
505	#447	C₂²×C₁₃	1	4	yes	complemented
506	#440	C₂²×C₁₃	1	4	yes	complemented
507	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
508	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
509	#435	C₂²×C₁₃	1	2	yes	complemented
510	#435	C₂²×C₁₃	1	2	yes	complemented
511	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
512	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
513	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
514	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	#417	C₂²×C₁₃	1	2	yes	complemented
516	#417	C₂²×C₁₃	1	2	yes	complemented
517	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
518	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
519	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	C₂²×C₁₃	—	2	1	no	—
522	C₂²×C₁₃	—	2	1	no	—
523	C₂²×C₁₃	—	2	1	no	—
524	C₂²×C₁₃	—	2	1	no	—
525	C₂²×C₁₃	—	2	1	no	—
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	1	no	—
528	C₂²×C₁₃	—	2	4	no	—
529	C₂²×C₁₃	—	2	2	no	—
530	C₂²×C₁₃	—	2	2	no	—
531	C₂²×C₁₃	—	2	1	no	—
532	C₂²×C₁₃	—	4	4	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	4	2	no	—
536	C₂²×C₁₃	—	4	4	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	4	4	no	—
539	C₂²×C₁₃	—	4	4	no	—
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	8	8	no	—
542	C₂²×C₁₃	—	16	4	no	—
543	C₂²×C₁₃	—	16	8	no	—
544	C₂²×C₁₃	D₄²	1	2	yes	—
545	C₂²×C₁₃	#576	1	2	yes	complemented
546	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
547	C₄×C₁₃	—	2	2	no	—
548	C₄×C₁₃	—	2	1	no	—
549	C₄×C₁₃	—	2	1	no	—
550	C₄×C₁₃	—	2	4	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₄×C₁₃	—	4	4	no	—
555	C₄×C₁₃	D₄²	1	2	yes	—
556	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
558	H(5,𝔽₂)	—	2	8	no	—
559	H(5,𝔽₂)	—	4	4	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	2	2	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	—	2	8	no	—
564	C₂×#41	—	4	4	no	—
565	C₂×#41	C₂³×C₁₃	1	2	yes	—
566	C₂×#41	C₂³×C₁₃	1	2	yes	—
567	C₂×#41	C₂³×C₁₃	1	4	yes	—
568	C₂×#41	C₂³×C₁₃	1	2	yes	—
569	C₂×#41	C₂³×C₁₃	1	2	yes	—
570	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	4	no	—
576	C₂²×D₄	—	2	4	no	—
577	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
578	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
579	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
580	C₂³×C₄	—	2	2	no	—
581	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
582	AGL(1,ℤ/8)	—	2	8	no	—
583	AGL(1,ℤ/8)	—	2	16	no	—
584	AGL(1,ℤ/8)	—	4	4	no	—
585	#135	—	2	8	no	—
586	#135	—	2	4	no	—
587	#135	—	2	8	no	—
588	#135	—	2	8	no	—
589	#135	—	2	4	no	—
590	#135	—	2	4	no	—
591	#135	D₄×C₁₃	1	8	yes	complemented
592	C₂×Q₁₆	—	2	4	no	—
593	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
594	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×SD₁₆	—	2	8	no	—
597	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
598	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
601	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
603	C₂×D₈	—	2	4	no	—
604	C₂×D₈	—	2	8	no	—
605	C₂×D₈	—	2	4	no	—
606	C₂×D₈	C₂³×C₁₃	1	2	yes	—
607	C₂×D₈	C₂³×C₁₃	1	2	yes	—
608	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×D₈	C₂³×C₁₃	1	4	yes	—
610	C₂×D₈	C₂³×C₁₃	1	2	yes	—
611	C₂×D₈	C₂³×C₁₃	1	4	yes	—
612	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
613	#131	—	2	4	no	—
614	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
616	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
617	C₂²×C₈	—	2	4	no	—
618	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
620	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
624	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
625	#127	—	2	4	no	—
626	#127	C₂³×C₁₃	1	4	yes	—
627	#124	—	2	4	no	—
628	#124	C₂³×C₁₃	1	4	yes	—
629	#123	—	2	4	no	—
630	#123	D₄×C₁₃	1	2	yes	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	4	no	—
633	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
634	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
635	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
636	#121	—	2	2	no	—
637	#121	—	2	4	no	—
638	#121	—	2	4	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	4	no	—
644	#121	—	2	4	no	—
645	#121	—	2	4	no	—
646	#121	—	2	4	no	—
647	#121	D₄×C₁₃	1	1	yes	characteristic
648	#121	D₄×C₁₃	1	1	yes	characteristic
649	#121	C₂³×C₁₃	1	4	yes	—
650	#121	C₂³×C₁₃	1	4	yes	—
651	#121	C₂³×C₁₃	1	4	yes	—
652	#120	—	2	4	no	—
653	#120	—	2	4	no	—
654	#120	—	2	4	no	—
655	#120	—	2	4	no	—
656	#120	D₄×C₁₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
658	C₄×D₄	—	2	4	no	—
659	C₄×D₄	—	2	4	no	—
660	C₄×D₄	—	2	4	no	—
661	C₄×D₄	C₂³×C₁₃	1	4	yes	—
662	C₄×D₄	C₂³×C₁₃	1	2	yes	—
663	C₄×D₄	C₂³×C₁₃	1	2	yes	—
664	#117	—	2	2	no	—
665	#117	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	—	2	2	no	—
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	—	2	2	no	—
669	C₂×C₂²⋊C₄	—	2	4	no	—
670	#107	C₂³×C₁₃	1	2	yes	—
671	#107	C₂³×C₁₃	1	2	yes	—
672	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
673	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
674	#103	C₂³×C₁₃	1	4	yes	—
675	#103	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	4	yes	—
677	#102	C₂³×C₁₃	1	4	yes	—
678	#102	C₂³×C₁₃	1	4	yes	—
679	#102	C₂³×C₁₃	1	4	yes	—
680	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
684	#97	C₂³×C₁₃	1	2	yes	—
685	C₄×C₈	C₂³×C₁₃	1	2	yes	—
686	C₂×C₁₃	—	2	2	no	—
687	C₂×C₁₃	—	2	2	no	—
688	C₂×C₁₃	—	4	1	no	—
689	C₂×C₁₃	—	4	2	no	—
690	C₂×C₁₃	—	4	4	no	—
691	C₂×C₁₃	—	8	2	no	—
692	C₂×C₁₃	—	8	4	no	—
693	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
694	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
695	C₂×C₁₃	#3584	1	1	yes	characteristic
696	C₂⁴	—	2	2	no	—
697	C₂⁴	—	2	4	no	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
700	#41	—	2	2	no	—
701	#41	—	2	4	no	—
702	#41	—	2	2	no	—
703	#41	—	2	4	no	—
704	#41	—	2	8	no	—
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	4	8	no	—
709	#41	—	4	2	no	—
710	#41	—	4	2	no	—
711	#41	—	4	4	no	—
712	#41	—	4	8	no	—
713	#41	—	4	8	no	—
714	#41	C₂×D₄×C₁₃	1	8	yes	complemented
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	4	no	—
717	C₂×Q₈	—	4	2	no	—
718	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
720	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	8	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	16	no	—
742	C₂×D₄	—	4	8	no	—
743	C₂×D₄	—	8	8	no	—
744	C₂×D₄	—	8	4	no	—
745	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
749	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
750	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	4	8	no	—
763	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	Q₁₆	—	2	4	no	—
771	Q₁₆	—	2	2	no	—
772	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
773	SD₁₆	—	2	4	no	—
774	SD₁₆	—	2	8	no	—
775	SD₁₆	—	2	4	no	—
776	SD₁₆	—	2	4	no	—
777	SD₁₆	—	4	4	no	—
778	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
779	D₈	—	2	4	no	—
780	D₈	—	2	8	no	—
781	D₈	—	2	4	no	—
782	D₈	—	2	2	no	—
783	D₈	—	2	4	no	—
784	D₈	—	4	4	no	—
785	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
786	M₁₆	—	2	2	no	—
787	M₁₆	—	2	2	no	—
788	M₁₆	—	2	4	no	—
789	C₂×C₈	—	2	2	no	—
790	C₂×C₈	—	2	2	no	—
791	C₂×C₈	—	2	2	no	—
792	C₂×C₈	—	2	2	no	—
793	C₂×C₈	—	2	2	no	—
794	C₂×C₈	—	2	4	no	—
795	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
796	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
797	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
798	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
800	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
806	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
808	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
818	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
821	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
822	C₄²	—	2	4	no	—
823	C₄²	C₂⁴×C₁₃	1	2	yes	—
824	C₁₃	#61056	1	1	yes	characteristic, direct product factor, Sylow
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	8	no	—
833	C₂³	—	4	4	no	—
834	C₂³	—	4	4	no	—
835	C₂³	—	8	2	no	—
836	C₂³	—	8	2	no	—
837	C₂³	—	8	4	no	—
838	C₂³	—	8	2	no	—
839	C₂³	—	8	4	no	—
840	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
841	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
842	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	Q₈	—	2	2	no	—
845	Q₈	—	2	2	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	4	no	—
849	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
850	D₄	—	2	8	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	8	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	8	no	—
867	D₄	—	4	4	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	4	no	—
870	D₄	—	8	4	no	—
871	D₄	—	8	4	no	—
872	D₄	C₂²×D₄×C₁₃	1	4	yes	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	8	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	4	4	no	—
887	C₂×C₄	—	4	8	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	8	4	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
895	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
900	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
901	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
902	C₈	—	2	1	no	—
903	C₈	—	2	1	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₈	C₂²×D₄×C₁₃	1	2	yes	—
907	C₈	C₂²×D₄×C₁₃	1	2	yes	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	4	4	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	4	no	—
928	C₂²	—	8	8	no	—
929	C₂²	—	16	4	no	—
930	C₂²	—	16	8	no	—
931	C₂²	D₄²×C₁₃	1	2	yes	—
932	C₂²	C₁₃×#576	1	2	yes	complemented
933	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	4	no	—
941	C₄	—	4	2	no	—
942	C₄	D₄²×C₁₃	1	2	yes	—
943	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
944	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂	—	2	2	no	—
946	C₂	—	2	2	no	—
947	C₂	—	4	1	no	—
948	C₂	—	4	2	no	—
949	C₂	—	4	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	4	no	—
952	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
953	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
954	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×#576	C₂	semidirect
2. C₂²×C₁₃×#135	C₂	semidirect
3. C₁₃×#3488	C₂	semidirect
4. C₁₃×#3287	C₂	semidirect
5. C₁₃×#3285	C₂	semidirect
6. C₁₃×#3280	C₂	semidirect
7. D₄×C₁₃×D₈	C₂	semidirect
8. C₁₃×#3268	C₂	semidirect
9. C₁₃×#3265	C₂	semidirect
10. C₁₃×#3155	C₂	semidirect
11. C₁₃×#3061	C₂	semidirect
12. C₂×C₁₃×#466	C₂	semidirect
13. C₁₃×#3045	C₂	semidirect
14. C₁₃×#3012	C₂	semidirect
15. C₁₃×#3006	C₂	semidirect
16. C₁₃×#2951	C₂	semidirect
17. C₁₃×#2929	C₂	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₁₃×#135	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
28. C₂×C₁₃×#135	C₂²	semidirect
29. C₂×C₁₃×#135	C₂²	semidirect
30. C₂×C₁₃×#135	C₂²	semidirect
31. C₂×C₁₃×#135	C₂²	semidirect
32. C₂²×C₁₃×Q₁₆	C₂²	semidirect
33. C₂²×C₁₃×SD₁₆	C₂²	semidirect
34. C₂²×C₁₃×D₈	C₂²	semidirect
35. C₂²×C₁₃×D₈	C₂²	semidirect
36. C₂²×C₁₃×D₈	C₂²	semidirect
37. C₂×C₁₃×#131	C₂²	semidirect
38. C₂³×C₈×C₁₃	C₂²	semidirect
39. C₁₃×#550	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
44. D₄²×C₁₃	C₂²	semidirect
46. C₁₃×#537	C₂²	semidirect
48. C₁₃×#535	C₂²	semidirect
52. C₂×C₁₃×#121	C₂²	semidirect
53. C₁₃×#520	C₂²	semidirect
54. C₁₃×#496	C₂²	semidirect
55. C₁₃×#495	C₂²	semidirect
56. C₁₃×#493	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
58. C₁₃×#467	C₂²	semidirect
59. C₁₃×#466	C₂²	semidirect
60. C₁₃×#466	C₂²	semidirect
61. C₁₃×#466	C₂²	semidirect
62. C₁₃×#466	C₂²	semidirect
63. C₁₃×#466	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#459	C₂²	semidirect
68. C₁₃×#452	C₂²	semidirect
69. C₁₃×#450	C₂²	semidirect
70. C₁₃×#449	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#449	C₂²	semidirect
73. C₁₃×#448	C₂²	semidirect
74. C₁₃×#447	C₂²	semidirect
75. C₁₃×#447	C₂²	semidirect
76. C₁₃×#440	C₂²	semidirect
77. C₄×C₁₃×Q₁₆	C₂²	semidirect
78. C₄×C₁₃×D₈	C₂²	semidirect
79. C₁₃×#435	C₂²	semidirect
80. C₁₃×#435	C₂²	semidirect
81. C₈×D₄×C₁₃	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×#102	C₂²	semidirect
88. C₁₃×#408	C₂²	semidirect
89. C₁₃×#407	C₂²	semidirect
90. C₁₃×#405	C₂²	semidirect
124. C₁₃×#135	D₄	semidirect
219. #61056	C₁₃	direct (N × H)
238. C₁₃×#41	C₂×D₄	semidirect
296. C₁₃×Q₁₆	C₂×D₄	semidirect
302. C₁₃×SD₁₆	C₂×D₄	semidirect
309. C₁₃×D₈	C₂×D₄	semidirect
319. C₂×C₈×C₁₃	C₂×D₄	semidirect
348. C₂×#576	C₂×C₁₃	semidirect
349. C₂²×#135	C₂×C₁₃	semidirect
350. #3488	C₂×C₁₃	semidirect
351. #3287	C₂×C₁₃	semidirect
352. #3285	C₂×C₁₃	semidirect
353. #3280	C₂×C₁₃	semidirect
354. D₄×D₈	C₂×C₁₃	semidirect
355. #3268	C₂×C₁₃	semidirect
356. #3265	C₂×C₁₃	semidirect
357. #3155	C₂×C₁₃	semidirect
358. #3061	C₂×C₁₃	semidirect
359. C₂×#466	C₂×C₁₃	semidirect
360. #3045	C₂×C₁₃	semidirect
361. #3012	C₂×C₁₃	semidirect
362. #3006	C₂×C₁₃	semidirect
363. #2951	C₂×C₁₃	semidirect
364. #2929	C₂×C₁₃	semidirect
448. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
449. C₂²×#41	C₂²×C₁₃	semidirect
451. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
452. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
453. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
456. C₂×#135	C₂²×C₁₃	semidirect
457. C₂×#135	C₂²×C₁₃	semidirect
458. C₂×#135	C₂²×C₁₃	semidirect
459. C₂×#135	C₂²×C₁₃	semidirect
460. C₂×#135	C₂²×C₁₃	semidirect
461. C₂×#135	C₂²×C₁₃	semidirect
462. C₂²×Q₁₆	C₂²×C₁₃	semidirect
463. C₂²×SD₁₆	C₂²×C₁₃	semidirect
464. C₂²×D₈	C₂²×C₁₃	semidirect
465. C₂²×D₈	C₂²×C₁₃	semidirect
466. C₂²×D₈	C₂²×C₁₃	semidirect
467. C₂×#131	C₂²×C₁₃	semidirect
468. C₂³×C₈	C₂²×C₁₃	semidirect
469. #550	C₂²×C₁₃	semidirect
470. #548	C₂²×C₁₃	semidirect
472. #546	C₂²×C₁₃	semidirect
474. D₄²	C₂²×C₁₃	semidirect
476. #537	C₂²×C₁₃	semidirect
478. #535	C₂²×C₁₃	semidirect
482. C₂×#121	C₂²×C₁₃	semidirect
483. #520	C₂²×C₁₃	semidirect
484. #496	C₂²×C₁₃	semidirect
485. #495	C₂²×C₁₃	semidirect
486. #493	C₂²×C₁₃	semidirect
487. #468	C₂²×C₁₃	semidirect
488. #467	C₂²×C₁₃	semidirect
489. #466	C₂²×C₁₃	semidirect
490. #466	C₂²×C₁₃	semidirect
491. #466	C₂²×C₁₃	semidirect
492. #466	C₂²×C₁₃	semidirect
493. #466	C₂²×C₁₃	semidirect
494. #464	C₂²×C₁₃	semidirect
495. #463	C₂²×C₁₃	semidirect
496. #460	C₂²×C₁₃	semidirect
497. #459	C₂²×C₁₃	semidirect
498. #452	C₂²×C₁₃	semidirect
499. #450	C₂²×C₁₃	semidirect
500. #449	C₂²×C₁₃	semidirect
501. #449	C₂²×C₁₃	semidirect
502. #449	C₂²×C₁₃	semidirect
503. #448	C₂²×C₁₃	semidirect
504. #447	C₂²×C₁₃	semidirect
505. #447	C₂²×C₁₃	semidirect
506. #440	C₂²×C₁₃	semidirect
507. C₄×Q₁₆	C₂²×C₁₃	semidirect
508. C₄×D₈	C₂²×C₁₃	semidirect
509. #435	C₂²×C₁₃	semidirect
510. #435	C₂²×C₁₃	semidirect
511. C₈×D₄	C₂²×C₁₃	semidirect
512. C₈×D₄	C₂²×C₁₃	semidirect
513. C₂×#107	C₂²×C₁₃	semidirect
514. #424	C₂²×C₁₃	semidirect
515. #417	C₂²×C₁₃	semidirect
516. #417	C₂²×C₁₃	semidirect
517. C₂×#102	C₂²×C₁₃	semidirect
518. #408	C₂²×C₁₃	semidirect
519. #407	C₂²×C₁₃	semidirect
520. #405	C₂²×C₁₃	semidirect
545. C₂²×C₁₃	#576	semidirect
591. #135	D₄×C₁₃	semidirect
714. #41	C₂×D₄×C₁₃	semidirect
772. Q₁₆	C₂×D₄×C₁₃	semidirect
778. SD₁₆	C₂×D₄×C₁₃	semidirect
785. D₈	C₂×D₄×C₁₃	semidirect
795. C₂×C₈	C₂×D₄×C₁₃	semidirect
824. C₁₃	#61056	direct (N × H)
932. C₂²	C₁₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#576	2
C₂²×C₁₃×#135	2
C₁₃×#3488	2
C₁₃×#3287	2
C₁₃×#3285	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#3268	2
C₁₃×#3265	2
C₁₃×#3155	2
C₁₃×#3061	2
C₂×C₁₃×#466	2
C₁₃×#3045	2
C₁₃×#3012	2
C₁₃×#3006	2
C₁₃×#2951	2
C₁₃×#2929	2
#61056	13

Subgroups — C13×#61056 #15747395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61056 #15747395