Subgroups — C₂×C₁₃×#3278 #15747376

Order 3328.

2794 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3278	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#137	—	2	16	no	—
16	C₂×C₁₃×#137	C₂²	1	16	yes	complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
23	C₁₃×#550	—	2	4	no	—
24	C₁₃×#550	C₂²	1	8	yes	—
25	D₄×Q₈×C₁₃	—	2	4	no	—
26	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
27	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#127	—	2	1	no	—
30	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₁₃×#121	—	2	2	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	—	2	1	no	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#492	C₂²	1	8	yes	complemented
41	C₁₃×#468	C₂²	1	16	yes	complemented
42	C₁₃×#462	C₂²	1	8	yes	complemented
43	C₁₃×#460	C₂²	1	8	yes	complemented
44	C₁₃×#452	C₂²	1	16	yes	complemented
45	C₁₃×#448	C₂²	1	16	yes	complemented
46	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
47	C₁₃×#436	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
55	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	—	2	8	no	—
58	C₂×C₁₃×#41	—	4	4	no	—
59	C₂×C₁₃×#41	C₂³	1	8	yes	—
60	C₂²×Q₈×C₁₃	—	2	2	no	—
61	C₂²×Q₈×C₁₃	—	2	4	no	—
62	C₂²×Q₈×C₁₃	—	2	8	no	—
63	C₂²×Q₈×C₁₃	—	4	4	no	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	—	2	2	no	—
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	—	2	2	no	—
75	C₂³×C₄×C₁₃	—	2	2	no	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#137	—	2	64	no	—
78	C₂×C₁₃×Q₁₆	—	2	8	no	—
79	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
80	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
82	C₂×C₁₃×SD₁₆	—	2	8	no	—
83	C₂×C₁₃×SD₁₆	—	2	8	no	—
84	C₂×C₁₃×SD₁₆	—	4	4	no	—
85	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
86	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
88	C₂×C₁₃×M₁₆	—	2	8	no	—
89	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	—	2	8	no	—
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
96	C₁₃×#127	—	2	8	no	—
97	C₁₃×#127	—	2	2	no	—
98	C₁₃×#127	C₂³	1	4	yes	—
99	C₁₃×C₂²⋊Q₈	—	2	4	no	—
100	C₁₃×C₂²⋊Q₈	—	2	16	no	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
102	C₁₃×#121	—	2	4	no	—
103	C₁₃×#121	—	2	16	no	—
104	C₁₃×#121	C₂³	1	8	yes	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	—	2	2	no	—
107	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
108	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
109	C₄×D₄×C₁₃	—	2	8	no	—
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	D₄	1	4	yes	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
124	C₂×C₄²×C₁₃	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×#107	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
129	C₁₃×#103	C₂³	1	4	yes	—
130	C₁₃×#103	C₂³	1	4	yes	—
131	C₁₃×#103	C₂³	1	8	yes	—
132	C₁₃×#102	C₂³	1	8	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
134	C₄×C₈×C₁₃	C₂³	1	4	yes	—
135	C₂×#3278	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁴×C₁₃	—	2	2	no	—
137	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
138	C₁₃×#41	—	2	16	no	—
139	C₁₃×#41	—	4	8	no	—
140	C₁₃×#41	—	4	16	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	8	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	16	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	4	8	no	—
151	C₂×Q₈×C₁₃	—	4	8	no	—
152	C₂×Q₈×C₁₃	—	4	16	no	—
153	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
154	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
155	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
156	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
157	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×D₄×C₁₃	—	2	8	no	—
159	C₂×D₄×C₁₃	—	2	8	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	4	no	—
166	C₂×D₄×C₁₃	—	4	8	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	8	2	no	—
169	C₂×D₄×C₁₃	—	8	4	no	—
170	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	8	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	8	no	—
181	C₂²×C₄×C₁₃	—	4	8	no	—
182	C₂²×C₄×C₁₃	—	4	8	no	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₁₃×Q₁₆	—	2	16	no	—
190	C₁₃×Q₁₆	C₂×D₄	1	16	yes	complemented
191	C₁₃×SD₁₆	—	2	16	no	—
192	C₁₃×SD₁₆	—	2	16	no	—
193	C₁₃×SD₁₆	—	4	8	no	—
194	C₁₃×M₁₆	—	2	16	no	—
195	C₂×C₈×C₁₃	—	2	4	no	—
196	C₂×C₈×C₁₃	—	2	2	no	—
197	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
198	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
199	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
200	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	8	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₁₃×C₂²⋊C₄	—	2	8	no	—
212	C₁₃×C₂²⋊C₄	—	2	8	no	—
213	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	—	2	4	no	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×#137	C₂×C₁₃	1	2	yes	complemented
219	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
220	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3278	C₂×C₁₃	1	16	yes	direct product factor
222	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#468	C₂×C₁₃	1	2	yes	complemented
224	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂×#452	C₂×C₁₃	1	2	yes	complemented
227	C₂×#448	C₂×C₁₃	1	2	yes	complemented
228	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	4	4	no	—
236	C₂³×C₁₃	—	4	4	no	—
237	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
238	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	2	4	no	—
240	Q₈×C₁₃	—	2	4	no	—
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	2	2	no	—
243	Q₈×C₁₃	—	2	4	no	—
244	Q₈×C₁₃	—	2	4	no	—
245	Q₈×C₁₃	—	4	16	no	—
246	Q₈×C₁₃	—	4	4	no	—
247	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
248	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
249	D₄×C₁₃	—	2	8	no	—
250	D₄×C₁₃	—	2	4	no	—
251	D₄×C₁₃	—	2	4	no	—
252	D₄×C₁₃	—	4	16	no	—
253	D₄×C₁₃	—	4	4	no	—
254	D₄×C₁₃	—	4	8	no	—
255	D₄×C₁₃	—	8	4	no	—
256	D₄×C₁₃	—	8	8	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	4	16	no	—
270	C₂×C₄×C₁₃	—	4	16	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	#137	1	4	yes	complemented
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
282	C₈×C₁₃	—	2	4	no	—
283	C₈×C₁₃	—	2	2	no	—
284	C₈×C₁₃	C₂²×D₄	1	4	yes	—
285	C₂²×#41	C₂²×C₁₃	1	2	yes	—
286	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
287	C₂×#137	—	2	16	no	—
288	C₂×#137	C₂²×C₁₃	1	16	yes	complemented
289	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
290	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
292	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
293	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
294	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
295	#550	—	2	4	no	—
296	#550	C₂²×C₁₃	1	8	yes	—
297	D₄×Q₈	—	2	4	no	—
298	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
299	C₂×C₄⋊Q₈	—	2	1	no	—
300	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#127	—	2	1	no	—
302	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊Q₈	—	2	2	no	—
304	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
305	C₂×#121	—	2	2	no	—
306	C₂×#121	C₂²×C₁₃	1	2	yes	—
307	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×D₄	—	2	1	no	—
310	C₂×C₄×D₄	—	2	1	no	—
311	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
312	#492	C₂²×C₁₃	1	8	yes	complemented
313	#468	C₂²×C₁₃	1	16	yes	complemented
314	#462	C₂²×C₁₃	1	8	yes	complemented
315	#460	C₂²×C₁₃	1	8	yes	complemented
316	#452	C₂²×C₁₃	1	16	yes	complemented
317	#448	C₂²×C₁₃	1	16	yes	complemented
318	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
319	#436	C₂²×C₁₃	1	8	yes	complemented
320	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#103	C₂²×C₁₃	1	2	yes	—
325	C₂×#102	C₂²×C₁₃	1	2	yes	—
326	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
327	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂²×C₁₃	—	2	4	no	—
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	4	8	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	8	8	no	—
336	C₂²×C₁₃	D₄²	1	2	yes	—
337	C₂²×C₁₃	C₂×#137	1	2	yes	—
338	C₂²×C₁₃	#577	1	2	yes	—
339	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
340	C₄×C₁₃	—	2	4	no	—
341	C₄×C₁₃	—	2	4	no	—
342	C₄×C₁₃	—	2	4	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	4	4	no	—
345	C₄×C₁₃	—	4	2	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	D₄²	1	2	yes	—
348	C₄×C₁₃	C₂×#137	1	4	yes	complemented
349	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
350	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×#41	—	2	4	no	—
352	C₂×#41	—	2	8	no	—
353	C₂×#41	—	4	4	no	—
354	C₂×#41	C₂³×C₁₃	1	8	yes	—
355	C₂²×Q₈	—	2	2	no	—
356	C₂²×Q₈	—	2	4	no	—
357	C₂²×Q₈	—	2	8	no	—
358	C₂²×Q₈	—	4	4	no	—
359	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
360	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
361	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
369	C₂³×C₄	—	2	2	no	—
370	C₂³×C₄	—	2	2	no	—
371	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
372	#137	—	2	64	no	—
373	C₂×Q₁₆	—	2	8	no	—
374	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
375	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
376	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
377	C₂×SD₁₆	—	2	8	no	—
378	C₂×SD₁₆	—	2	8	no	—
379	C₂×SD₁₆	—	4	4	no	—
380	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
381	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
382	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
383	C₂×M₁₆	—	2	8	no	—
384	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
385	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
386	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄⋊Q₈	—	2	8	no	—
389	C₄⋊Q₈	—	2	2	no	—
390	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
391	#127	—	2	8	no	—
392	#127	—	2	2	no	—
393	#127	C₂³×C₁₃	1	4	yes	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	16	no	—
396	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
397	#121	—	2	4	no	—
398	#121	—	2	16	no	—
399	#121	C₂³×C₁₃	1	8	yes	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
403	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
404	C₄×D₄	—	2	8	no	—
405	C₄×D₄	—	2	8	no	—
406	C₄×D₄	D₄×C₁₃	1	4	yes	—
407	C₄×D₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
422	#107	C₂³×C₁₃	1	4	yes	—
423	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
424	#103	C₂³×C₁₃	1	4	yes	—
425	#103	C₂³×C₁₃	1	4	yes	—
426	#103	C₂³×C₁₃	1	8	yes	—
427	#102	C₂³×C₁₃	1	8	yes	—
428	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
429	C₄×C₈	C₂³×C₁₃	1	4	yes	—
430	C₂×C₁₃	—	4	4	no	—
431	C₂×C₁₃	—	8	4	no	—
432	C₂×C₁₃	#3278	1	4	yes	direct product factor
433	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
434	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
435	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
436	C₂⁴	—	2	2	no	—
437	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
438	#41	—	2	16	no	—
439	#41	—	4	8	no	—
440	#41	—	4	16	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	8	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	16	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	4	8	no	—
451	C₂×Q₈	—	4	8	no	—
452	C₂×Q₈	—	4	16	no	—
453	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
454	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
455	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
456	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
457	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
458	C₂×D₄	—	2	8	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	8	2	no	—
469	C₂×D₄	—	8	4	no	—
470	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
471	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	4	8	no	—
482	C₂²×C₄	—	4	8	no	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
489	Q₁₆	—	2	16	no	—
490	Q₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
491	SD₁₆	—	2	16	no	—
492	SD₁₆	—	2	16	no	—
493	SD₁₆	—	4	8	no	—
494	M₁₆	—	2	16	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
498	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
499	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
500	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
509	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
510	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	8	no	—
513	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	4	no	—
516	C₄²	C₂×D₄×C₁₃	1	2	yes	—
517	C₄²	C₂⁴×C₁₃	1	2	yes	—
518	C₁₃	C₂×#3278	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³	—	2	4	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	4	4	no	—
525	C₂³	—	4	4	no	—
526	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
527	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	4	no	—
533	Q₈	—	2	4	no	—
534	Q₈	—	4	16	no	—
535	Q₈	—	4	4	no	—
536	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
537	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
538	D₄	—	2	8	no	—
539	D₄	—	2	4	no	—
540	D₄	—	2	4	no	—
541	D₄	—	4	16	no	—
542	D₄	—	4	4	no	—
543	D₄	—	4	8	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	8	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	4	16	no	—
559	C₂×C₄	—	4	16	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	C₁₃×#137	1	4	yes	complemented
564	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
570	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
571	C₈	—	2	4	no	—
572	C₈	—	2	2	no	—
573	C₈	C₂²×D₄×C₁₃	1	4	yes	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	4	8	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	8	8	no	—
582	C₂²	D₄²×C₁₃	1	2	yes	—
583	C₂²	C₂×C₁₃×#137	1	2	yes	—
584	C₂²	C₁₃×#577	1	2	yes	—
585	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	4	no	—
588	C₄	—	2	4	no	—
589	C₄	—	2	4	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	4	no	—
593	C₄	D₄²×C₁₃	1	2	yes	—
594	C₄	C₂×C₁₃×#137	1	4	yes	complemented
595	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
596	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂	—	4	4	no	—
598	C₂	—	8	4	no	—
599	C₂	C₁₃×#3278	1	4	yes	direct product factor
600	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
601	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
602	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
3. C₂×D₄×Q₈×C₁₃	C₂	semidirect
4. C₁₃×#3278	C₂	direct (N × H)
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#468	C₂	semidirect
7. C₂×C₁₃×#462	C₂	semidirect
8. C₂×C₁₃×#460	C₂	semidirect
9. C₂×C₁₃×#452	C₂	semidirect
10. C₂×C₁₃×#448	C₂	semidirect
11. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
12. C₂×C₁₃×#436	C₂	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
26. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#468	C₂²	semidirect
42. C₁₃×#462	C₂²	semidirect
43. C₁₃×#460	C₂²	semidirect
44. C₁₃×#452	C₂²	semidirect
45. C₁₃×#448	C₂²	semidirect
46. C₄×C₁₃×Q₁₆	C₂²	semidirect
47. C₁₃×#436	C₂²	semidirect
79. C₂×C₁₃×Q₁₆	D₄	semidirect
135. C₂×#3278	C₁₃	direct (N × H)
190. C₁₃×Q₁₆	C₂×D₄	semidirect
218. C₂²×#137	C₂×C₁₃	semidirect
220. C₂×D₄×Q₈	C₂×C₁₃	semidirect
221. #3278	C₂×C₁₃	direct (N × H)
222. C₂×#492	C₂×C₁₃	semidirect
223. C₂×#468	C₂×C₁₃	semidirect
224. C₂×#462	C₂×C₁₃	semidirect
225. C₂×#460	C₂×C₁₃	semidirect
226. C₂×#452	C₂×C₁₃	semidirect
227. C₂×#448	C₂×C₁₃	semidirect
228. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
229. C₂×#436	C₂×C₁₃	semidirect
274. C₂×C₄×C₁₃	#137	semidirect
288. C₂×#137	C₂²×C₁₃	semidirect
298. D₄×Q₈	C₂²×C₁₃	semidirect
312. #492	C₂²×C₁₃	semidirect
313. #468	C₂²×C₁₃	semidirect
314. #462	C₂²×C₁₃	semidirect
315. #460	C₂²×C₁₃	semidirect
316. #452	C₂²×C₁₃	semidirect
317. #448	C₂²×C₁₃	semidirect
318. C₄×Q₁₆	C₂²×C₁₃	semidirect
319. #436	C₂²×C₁₃	semidirect
348. C₄×C₁₃	C₂×#137	semidirect
374. C₂×Q₁₆	D₄×C₁₃	semidirect
432. C₂×C₁₃	#3278	direct (N × H)
490. Q₁₆	C₂×D₄×C₁₃	semidirect
518. C₁₃	C₂×#3278	direct (N × H)
563. C₂×C₄	C₁₃×#137	semidirect
594. C₄	C₂×C₁₃×#137	semidirect
599. C₂	C₁₃×#3278	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#137	2
C₂×C₁₃×#550	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3278	2
C₂×C₁₃×#492	2
C₂×C₁₃×#468	2
C₂×C₁₃×#462	2
C₂×C₁₃×#460	2
C₂×C₁₃×#452	2
C₂×C₁₃×#448	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₁₃×#436	2
C₂×#3278	13

Subgroups — C2×C13×#3278 #15747376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3278 #15747376