Subgroups — C₂×#13123850 #16727414

Order 3328.

2254 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123850	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11718685	C₂	1	2	yes	maximal, complemented
3	C₂×#11718672	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×#1055	C₂	1	2	yes	maximal, complemented
5	C₂×#11718587	C₂	1	2	yes	maximal, complemented
6	C₂×#11718587	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88043	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×#41	C₄	1	1	yes	characteristic
11	C₄×C₁₃×#41	C₄	1	8	yes	—
12	C₄×C₁₃×#41	C₂²	1	8	yes	—
13	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₄	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×#6099	C₂²	1	2	yes	—
24	C₂³×#1055	C₂²	1	4	yes	—
25	C₂×C₂²⋊#1055	C₂²	1	4	yes	—
26	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
27	#11718685	C₂²	1	16	yes	complemented
28	#11718672	C₂²	1	32	yes	complemented
29	D₄×#1055	C₂²	1	16	yes	complemented
30	#11718587	C₂²	1	16	yes	complemented
31	#11718587	C₂²	1	8	yes	complemented
32	C₂×C₄⋊#1055	C₂²	1	2	yes	—
33	C₂×C₄⋊#1055	C₂²	1	4	yes	—
34	C₄×#6099	C₂²	1	8	yes	complemented
35	C₂×#88043	C₂²	1	2	yes	—
36	C₂×#88043	C₂²	1	1	yes	characteristic
37	C₂×#88043	C₂²	1	1	yes	characteristic
38	C₂×#88043	C₂²	1	4	yes	—
39	C₂×#88043	C₂²	1	16	yes	complemented
40	C₂×C₄×#1055	C₂²	1	2	yes	—
41	C₂×C₁₃×#41	—	2	8	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
55	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	—
56	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
57	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
58	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₁₃	C₂³	1	4	yes	—
60	C₄×D₄×C₁₃	C₂³	1	8	yes	—
61	C₁₃×#117	C₂×C₄	1	8	yes	—
62	C₁₃×#117	C₂×C₄	1	16	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
75	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
81	C₂×#6099	—	2	8	no	—
82	C₂×#6099	C₂³	1	8	yes	—
83	C₂²×#1055	—	2	16	no	—
84	C₂²×#1055	C₂³	1	16	yes	—
85	C₂²×#1055	C₂³	1	4	yes	—
86	C₂²×#1055	C₂³	1	2	yes	—
87	C₂²×#1055	C₂³	1	2	yes	—
88	C₂²⋊#1055	C₂³	1	16	yes	—
89	C₂²⋊#1055	C₂³	1	8	yes	—
90	C₄⋊#1055	C₂³	1	8	yes	—
91	C₄⋊#1055	C₂³	1	16	yes	—
92	#88043	C₂³	1	16	yes	—
93	#88043	C₂³	1	4	yes	—
94	#88043	C₂³	1	8	yes	—
95	#88043	C₂³	1	4	yes	—
96	C₄×#1055	C₂³	1	8	yes	—
97	C₂×#2970	—	13	1	no	maximal, Sylow
98	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
100	C₁₃×#41	—	2	32	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂×D₄×C₁₃	—	2	8	no	—
104	C₂×D₄×C₁₃	M₁₆	1	8	yes	complemented
105	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
132	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
134	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
135	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
136	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
137	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
138	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
139	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
140	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
141	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
142	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
143	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
144	C₄²×C₁₃	C₂⁴	1	2	yes	—
145	C₄²×C₁₃	C₂⁴	1	2	yes	—
146	C₄²×C₁₃	C₂⁴	1	4	yes	—
147	#6099	—	2	16	no	—
148	C₂×#1055	—	2	8	no	—
149	C₂×#1055	—	2	4	no	—
150	C₂×#1055	—	2	32	no	—
151	C₂×#1055	#41	1	8	yes	complemented
152	C₂×#1055	C₂⁴	1	8	yes	—
153	C₂×#1055	C₂⁴	1	4	yes	—
154	C₂×#1055	C₂⁴	1	4	yes	—
155	C₂×C₄×#41	D₁₃	1	1	yes	characteristic
156	#2970	—	13	16	no	—
157	C₂×#446	—	13	2	no	—
158	C₂×#435	—	13	4	no	—
159	C₂×C₈×D₄	—	13	2	no	—
160	C₂×#432	—	13	1	no	—
161	C₂×#432	—	13	2	no	—
162	C₂×C₄×M₁₆	—	13	1	no	—
163	C₂²×#97	—	13	2	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	C₂×M₁₆	1	8	yes	—
170	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
171	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
172	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	8	no	—
174	D₄×C₁₃	—	2	16	no	—
175	D₄×C₁₃	C₂×M₁₆	1	16	yes	complemented
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	16	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	4	8	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
192	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
195	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
202	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
203	#1055	—	2	8	no	—
204	#1055	—	2	4	no	—
205	#1055	C₂×#41	1	8	yes	complemented
206	C₂²×#41	Dic₁₃	1	1	yes	characteristic
207	C₂²×M₁₆	—	13	2	no	—
208	C₂³×C₈	—	13	4	no	—
209	C₄×#41	Dic₁₃	1	8	yes	—
210	C₄×#41	C₂×D₁₃	1	8	yes	—
211	C₂×C₄×Q₈	Dic₁₃	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
213	C₂×C₄×D₄	Dic₁₃	1	2	yes	—
214	C₂×C₄×D₄	Dic₁₃	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
217	C₂×#117	Dic₁₃	1	1	yes	characteristic
218	C₂×#117	Dic₁₃	1	2	yes	—
219	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
220	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
221	#446	—	13	16	no	—
222	#435	—	13	32	no	—
223	C₈×D₄	—	13	16	no	—
224	#432	—	13	8	no	—
225	#432	—	13	16	no	—
226	C₂×C₄⋊C₈	—	13	2	no	—
227	C₂×C₄⋊C₈	—	13	4	no	—
228	C₂×C₂²⋊C₈	—	13	4	no	—
229	C₂×C₂²⋊C₈	—	13	2	no	—
230	C₄×M₁₆	—	13	8	no	—
231	C₂×#97	—	13	1	no	—
232	C₂×#97	—	13	2	no	—
233	C₂×#97	—	13	4	no	—
234	C₂×#97	—	13	16	no	—
235	C₂×#97	—	13	1	no	—
236	C₂×C₄×C₈	—	13	2	no	—
237	C₂²×C₁₃	—	2	4	no	—
238	C₂²×C₁₃	—	2	16	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	C₄×#41	1	2	yes	—
245	C₂²×C₁₃	C₂²×M₁₆	1	8	yes	—
246	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
247	C₂²×C₁₃	#568	1	2	yes	—
248	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	4	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	C₄×#41	1	2	yes	—
257	C₄×C₁₃	C₂²×M₁₆	1	4	yes	—
258	C₄×C₁₃	C₂²×#41	1	2	yes	—
259	C₂×#41	—	2	8	no	—
260	C₂×#41	C₂×Dic₁₃	1	8	yes	—
261	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
262	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
263	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
264	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
265	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
266	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
267	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
268	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
269	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
270	C₂×M₁₆	—	13	8	no	—
271	C₂×M₁₆	—	26	8	no	—
272	C₂²×C₈	—	13	2	no	—
273	C₂²×C₈	—	13	16	no	—
274	C₂²×C₈	—	13	4	no	—
275	C₂²×C₈	—	13	2	no	—
276	C₂²×C₈	—	26	16	no	—
277	C₄×Q₈	C₂×Dic₁₃	1	8	yes	—
278	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
279	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
280	C₄×D₄	C₂×Dic₁₃	1	16	yes	—
281	C₄×D₄	C₂×Dic₁₃	1	8	yes	—
282	C₄×D₄	C₂×Dic₁₃	1	8	yes	—
283	C₄×D₄	C₂×Dic₁₃	1	4	yes	—
284	C₄×D₄	C₂²×D₁₃	1	4	yes	—
285	C₄×D₄	C₂²×D₁₃	1	8	yes	—
286	#117	C₂×Dic₁₃	1	8	yes	—
287	#117	C₂×Dic₁₃	1	16	yes	—
288	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
295	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
296	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
297	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
298	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂×Dic₁₃	1	8	yes	—
300	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
301	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
302	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
303	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
305	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
306	C₄⋊C₈	—	13	8	no	—
307	C₄⋊C₈	—	13	16	no	—
308	C₂²⋊C₈	—	13	16	no	—
309	C₂²⋊C₈	—	13	8	no	—
310	#97	—	13	4	no	—
311	#97	—	13	8	no	—
312	#97	—	13	16	no	—
313	#97	—	13	4	no	—
314	C₄×C₈	—	13	8	no	—
315	C₂×C₁₃	—	2	8	no	—
316	C₂×C₁₃	—	4	2	no	—
317	C₂×C₁₃	#2970	1	4	yes	complemented
318	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
319	C₂×C₁₃	C₂³×M₁₆	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
321	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
322	C₂⁴	C₂²×Dic₁₃	1	2	yes	—
323	#41	—	2	32	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	#6099	1	8	yes	complemented
328	C₂×D₄	C₂²×Dic₁₃	1	8	yes	—
329	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
339	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
341	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
342	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
344	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
345	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
346	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
347	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
348	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
349	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
351	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
352	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
353	M₁₆	—	26	16	no	—
354	C₂×C₈	—	13	8	no	—
355	C₂×C₈	—	13	4	no	—
356	C₂×C₈	—	13	4	no	—
357	C₂×C₈	—	13	8	no	—
358	C₂×C₈	—	26	32	no	—
359	C₂×C₈	—	26	8	no	—
360	C₂×C₈	—	26	4	no	—
361	C₄⋊C₄	C₂²×Dic₁₃	1	8	yes	—
362	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
363	C₄⋊C₄	C₂²×Dic₁₃	1	8	yes	—
364	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
365	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
366	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
367	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
368	C₄²	C₂²×Dic₁₃	1	2	yes	—
369	C₄²	C₂²×Dic₁₃	1	8	yes	—
370	C₄²	C₂²×Dic₁₃	1	4	yes	—
371	C₄²	C₂²×Dic₁₃	1	8	yes	—
372	C₄²	C₂²×Dic₁₃	1	4	yes	—
373	C₄²	C₂²×Dic₁₃	1	4	yes	—
374	C₄²	C₂²×Dic₁₃	1	2	yes	—
375	C₄²	C₂³×D₁₃	1	2	yes	—
376	C₄²	C₂³×D₁₃	1	2	yes	—
377	C₄²	C₂³×D₁₃	1	4	yes	—
378	C₁₃	C₂×#2970	1	1	yes	characteristic, complemented, Sylow
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	C₂×#6099	1	8	yes	—
385	C₂³	C₂³×Dic₁₃	1	2	yes	—
386	C₂³	C₂³×Dic₁₃	1	4	yes	—
387	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	D₄	—	2	16	no	—
390	D₄	C₂×#6099	1	16	yes	complemented
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₂×#6099	1	4	yes	—
407	C₂×C₄	#41×D₁₃	1	4	yes	—
408	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
409	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
410	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
411	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
412	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
413	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
414	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
415	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
416	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
418	C₈	—	13	8	no	—
419	C₈	—	26	8	no	—
420	C₈	—	26	4	no	—
421	C₂²	—	2	16	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₂²×#6099	1	8	yes	—
429	C₂²	C₂²×#6099	1	2	yes	—
430	C₂²	#11719524	1	2	yes	—
431	C₂²	#41×Dic₁₃	1	2	yes	—
432	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	C₂²×#6099	1	4	yes	—
441	C₄	#41×Dic₁₃	1	2	yes	—
442	C₄	C₂×#41×D₁₃	1	2	yes	—
443	C₂	—	2	8	no	—
444	C₂	—	4	2	no	—
445	C₂	#13123850	1	4	yes	direct product factor
446	C₂	C₂×#41×Dic₁₃	1	1	yes	characteristic
447	C₂	C₂³×#6099	1	1	yes	characteristic
448	C₂	C₂×#11719524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×C₁₃×#41	C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	C₂×#2970
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #13123850	C₂	direct (N × H)
2. C₂×#11718685	C₂	semidirect
3. C₂×#11718672	C₂	semidirect
4. C₂×D₄×#1055	C₂	semidirect
5. C₂×#11718587	C₂	semidirect
6. C₂×#11718587	C₂	semidirect
7. C₂×C₄×#6099	C₂	semidirect
8. C₂²×#88043	C₂	semidirect
27. #11718685	C₂²	semidirect
28. #11718672	C₂²	semidirect
29. D₄×#1055	C₂²	semidirect
30. #11718587	C₂²	semidirect
31. #11718587	C₂²	semidirect
34. C₄×#6099	C₂²	semidirect
39. C₂×#88043	C₂²	semidirect
104. C₂×D₄×C₁₃	M₁₆	semidirect
151. C₂×#1055	#41	semidirect
175. D₄×C₁₃	C₂×M₁₆	semidirect
205. #1055	C₂×#41	semidirect
317. C₂×C₁₃	#2970	semidirect
327. C₂×D₄	#6099	semidirect
378. C₁₃	C₂×#2970	semidirect
390. D₄	C₂×#6099	semidirect
445. C₂	#13123850	direct (N × H)

Maximal subgroups

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

subgroup	index
#13123850	2
C₂×#11718685	2
C₂×#11718672	2
C₂×D₄×#1055	2
C₂×#11718587	2
C₂×C₄×#6099	2
C₂²×#88043	2
C₂×C₄×C₁₃×#41	2
C₂×#2970	13

Subgroups — C2×#13123850 #16727414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123850 #16727414