Subgroups — C₂×#13128639 #16770823

Order 3328.

7738 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128639	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719244	C₂	1	8	yes	maximal, complemented
3	C₂×#11719248	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×Dic₂₆	C₂	1	4	yes	maximal, complemented
5	C₂×#11719205	C₂	1	2	yes	maximal, complemented
6	C₂×#11719188	C₂	1	4	yes	maximal, complemented
7	C₂×#11719175	C₂	1	2	yes	maximal, complemented
8	C₂²×#88178	C₂	1	4	yes	maximal, complemented
9	C₂×#11719503	C₂	1	2	yes	maximal
10	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂³×Dic₂₆	C₂²	1	4	yes	complemented
14	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊Dic₁₃	C₂²	1	8	yes	—
21	#11719503	C₂²	1	32	yes	—
22	C₂×D₄×Dic₁₃	C₂²	1	8	yes	—
23	C₂×D₄×Dic₁₃	C₂²	1	8	yes	—
24	C₂×#88180	C₂²	1	4	yes	—
25	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	complemented
26	C₂×#88178	C₂²	1	4	yes	—
27	C₂×#88178	C₂²	1	8	yes	—
28	C₂×#88178	C₂²	1	4	yes	—
29	C₂×#88178	C₂²	1	8	yes	complemented
30	C₂×#88178	C₂²	1	8	yes	complemented
31	C₂×#88178	C₂²	1	64	yes	complemented
32	C₂²×#6101	C₂²	1	8	yes	complemented
33	#11719248	C₂²	1	64	yes	complemented
34	#11719244	C₂²	1	128	yes	complemented
35	D₄×Dic₂₆	C₂²	1	64	yes	complemented
36	#11719205	C₂²	1	32	yes	complemented
37	C₂×#88144	C₂²	1	8	yes	complemented
38	C₂×#88142	C₂²	1	8	yes	complemented
39	#11719188	C₂²	1	64	yes	complemented
40	C₂×#88132	C₂²	1	16	yes	complemented
41	C₂×#88132	C₂²	1	16	yes	complemented
42	#11719175	C₂²	1	32	yes	complemented
43	C₂×#88124	C₂²	1	4	yes	complemented
44	C₂×#88123	C₂²	1	2	yes	complemented
45	C₂×#88123	C₂²	1	2	yes	complemented
46	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
47	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
48	C₂⁵×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	Q₈	1	16	yes	complemented
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
52	C₂³×C₄×C₁₃	—	4	8	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×Dic₁₃	C₂³	1	8	yes	—
61	C₂³×Dic₁₃	C₂³	1	8	yes	—
62	C₂²×Dic₂₆	—	4	16	no	—
63	C₂²×Dic₂₆	C₂³	1	4	yes	—
64	C₂²×Dic₂₆	C₂³	1	4	yes	—
65	C₂²×Dic₂₆	C₂³	1	8	yes	—
66	C₂²×Dic₂₆	C₂³	1	32	yes	complemented
67	C₄×D₄×C₁₃	C₂³	1	32	yes	—
68	C₄×D₄×C₁₃	C₂³	1	32	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
76	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
77	C₂×C₂²⋊Dic₁₃	C₂³	1	64	yes	—
78	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
79	D₄×Dic₁₃	C₂³	1	64	yes	—
80	D₄×Dic₁₃	C₂³	1	64	yes	—
81	#88180	C₂³	1	32	yes	—
82	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
83	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
84	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
85	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
86	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
87	C₂×C₄⋊Dic₁₃	C₂³	1	32	yes	complemented
88	#88178	C₂³	1	32	yes	—
89	#88178	C₂³	1	32	yes	—
90	#88178	C₂³	1	64	yes	—
91	#88178	C₂³	1	64	yes	complemented
92	#88178	C₂³	1	64	yes	complemented
93	C₂×#6101	C₂³	1	8	yes	—
94	C₂×#6101	C₂³	1	8	yes	—
95	C₂×#6101	C₂³	1	16	yes	—
96	C₂×#6101	C₂³	1	64	yes	complemented
97	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
98	#88144	C₂³	1	64	yes	complemented
99	#88142	C₂³	1	64	yes	complemented
100	#88132	C₂³	1	128	yes	complemented
101	#88132	C₂³	1	128	yes	complemented
102	#88124	C₂³	1	32	yes	complemented
103	#88123	C₂³	1	16	yes	complemented
104	#88123	C₂³	1	16	yes	complemented
105	C₄×Dic₂₆	C₂³	1	32	yes	complemented
106	C₄×Dic₂₆	C₂³	1	32	yes	complemented
107	C₂×#3501	—	13	1	no	maximal, Sylow
108	C₂⁴×C₁₃	—	4	4	no	—
109	C₂⁴×C₁₃	—	4	4	no	—
110	C₂⁴×C₁₃	C₂×Q₈	1	16	yes	complemented
111	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
114	C₂×D₄×C₁₃	C₂×Q₈	1	32	yes	complemented
115	C₂×D₄×C₁₃	C₂×Q₈	1	64	yes	complemented
116	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
117	C₂²×C₄×C₁₃	—	2	16	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	4	32	no	—
120	C₂²×C₄×C₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₃	—	4	8	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	complemented
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²×Dic₁₃	—	4	16	no	—
136	C₂²×Dic₁₃	—	4	16	no	—
137	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
138	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
139	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
140	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
141	C₂×Dic₂₆	—	2	16	no	—
142	C₂×Dic₂₆	—	4	64	no	—
143	C₂×Dic₂₆	—	4	16	no	—
144	C₂×Dic₂₆	—	4	8	no	—
145	C₂×Dic₂₆	C₂⁴	1	16	yes	—
146	C₂×Dic₂₆	C₂⁴	1	16	yes	—
147	C₂×Dic₂₆	C₂⁴	1	32	yes	—
148	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
149	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
150	C₄²×C₁₃	C₂⁴	1	8	yes	—
151	C₄²×C₁₃	C₂⁴	1	8	yes	—
152	C₂²⋊Dic₁₃	C₂⁴	1	64	yes	—
153	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
154	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
155	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
156	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
157	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
158	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
159	#6101	C₂⁴	1	32	yes	—
160	#6101	C₂⁴	1	32	yes	—
161	#6101	C₂⁴	1	64	yes	—
162	C₄×Dic₁₃	C₂⁴	1	32	yes	—
163	#3501	—	13	32	no	—
164	C₂×#554	—	13	4	no	—
165	C₂×#554	—	13	8	no	—
166	C₂×D₄×Q₈	—	13	4	no	—
167	C₂×#544	—	13	2	no	—
168	C₂×#543	—	13	4	no	—
169	C₂×#533	—	13	2	no	—
170	C₂²×C₂²⋊Q₈	—	13	4	no	—
171	C₂×#518	—	13	2	no	—
172	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic
173	C₂³×C₁₃	—	2	8	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	8	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	4	8	no	—
178	C₂³×C₁₃	—	4	32	no	—
179	C₂³×C₁₃	—	4	8	no	—
180	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
181	C₂³×C₁₃	C₂²×Q₈	1	16	yes	—
182	C₂³×C₁₃	C₂²×Q₈	1	32	yes	complemented
183	C₂³×C₁₃	C₂⁵	1	2	yes	—
184	C₂³×C₁₃	C₂⁵	1	8	yes	—
185	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
186	D₄×C₁₃	C₂²×Q₈	1	64	yes	complemented
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	32	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	4	8	no	—
193	C₂×C₄×C₁₃	—	4	16	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
196	C₂×C₄×C₁₃	C₂²×Q₈	1	16	yes	complemented
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
198	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
200	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
201	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
202	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
203	C₂×Dic₁₃	—	2	16	no	—
204	C₂×Dic₁₃	—	2	16	no	—
205	C₂×Dic₁₃	—	4	32	no	—
206	C₂×Dic₁₃	—	4	32	no	—
207	C₂×Dic₁₃	C₂⁵	1	16	yes	—
208	C₂×Dic₁₃	C₂⁵	1	16	yes	—
209	Dic₂₆	—	2	32	no	—
210	Dic₂₆	—	4	32	no	—
211	Dic₂₆	—	4	16	no	—
212	C₂³×Q₈	—	13	4	no	—
213	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
214	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
215	#554	—	13	128	no	—
216	#554	—	13	64	no	—
217	D₄×Q₈	—	13	64	no	—
218	#544	—	13	32	no	—
219	#543	—	13	64	no	—
220	#533	—	13	32	no	—
221	C₂×C₄⋊Q₈	—	13	8	no	—
222	C₂×C₄⋊Q₈	—	13	2	no	—
223	C₂×C₄⋊Q₈	—	13	2	no	—
224	C₂×#125	—	13	8	no	—
225	C₂×#125	—	13	4	no	—
226	C₂×C₂²⋊Q₈	—	13	4	no	—
227	C₂×C₂²⋊Q₈	—	13	8	no	—
228	C₂×C₂²⋊Q₈	—	13	4	no	—
229	C₂×C₂²⋊Q₈	—	13	8	no	—
230	C₂×C₂²⋊Q₈	—	13	8	no	—
231	C₂×C₂²⋊Q₈	—	13	64	no	—
232	C₂×C₂²⋊Q₈	—	13	16	no	—
233	C₂×C₂²⋊Q₈	—	13	16	no	—
234	#518	—	13	32	no	—
235	C₂×C₄×Q₈	—	13	4	no	—
236	C₂×C₄×Q₈	—	13	4	no	—
237	C₂×C₄×D₄	—	13	8	no	—
238	C₂×C₄×D₄	—	13	8	no	—
239	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	—
240	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	—
241	C₂×C₄×D₄	C₂×D₁₃	1	16	yes	—
242	C₂×#117	—	13	4	no	—
243	C₂²×C₄⋊C₄	—	13	8	no	—
244	C₂²×C₄⋊C₄	—	13	4	no	—
245	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	—	13	8	no	—
247	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
248	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
249	C₂²×C₁₃	—	2	8	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	8	no	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	8	no	—
254	C₂²×C₁₃	—	2	32	no	—
255	C₂²×C₁₃	—	4	32	no	—
256	C₂²×C₁₃	C₂³×Q₈	1	4	yes	—
257	C₂²×C₁₃	C₂³×Q₈	1	16	yes	—
258	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
259	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
260	C₂²×C₁₃	#585	1	2	yes	—
261	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
262	C₄×C₁₃	—	2	8	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	C₂³×Q₈	1	8	yes	—
266	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
267	Dic₁₃	—	2	16	no	—
268	Dic₁₃	—	2	16	no	—
269	C₂⁵	C₂²×D₁₃	1	2	yes	—
270	C₂²×Q₈	—	13	4	no	—
271	C₂²×Q₈	—	13	4	no	—
272	C₂²×Q₈	—	13	8	no	—
273	C₂²×Q₈	—	13	32	no	—
274	C₂²×Q₈	—	52	16	no	—
275	C₂²×D₄	Dic₂₆	1	16	yes	complemented
276	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
277	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
278	C₂³×C₄	—	4	8	no	—
279	C₂³×C₄	—	13	8	no	—
280	C₂³×C₄	—	13	8	no	—
281	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
282	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
285	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
286	C₂³×C₄	C₂²×D₁₃	1	16	yes	—
287	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
288	C₄⋊Q₈	—	13	64	no	—
289	C₄⋊Q₈	—	13	16	no	—
290	C₄⋊Q₈	—	13	16	no	—
291	#125	—	13	64	no	—
292	#125	—	13	32	no	—
293	C₂²⋊Q₈	—	13	32	no	—
294	C₂²⋊Q₈	—	13	64	no	—
295	C₂²⋊Q₈	—	13	64	no	—
296	C₂²⋊Q₈	—	13	64	no	—
297	C₂²⋊Q₈	—	13	32	no	—
298	C₂²⋊Q₈	—	13	128	no	—
299	C₂²⋊Q₈	—	13	128	no	—
300	C₄×Q₈	—	13	32	no	—
301	C₄×Q₈	—	13	32	no	—
302	C₄×D₄	—	13	64	no	—
303	C₄×D₄	—	13	64	no	—
304	C₄×D₄	C₂²×D₁₃	1	32	yes	—
305	C₄×D₄	C₂²×D₁₃	1	32	yes	—
306	#117	—	13	32	no	—
307	C₂×C₄⋊C₄	—	13	8	no	—
308	C₂×C₄⋊C₄	—	13	4	no	—
309	C₂×C₄⋊C₄	—	13	8	no	—
310	C₂×C₄⋊C₄	—	13	16	no	—
311	C₂×C₄⋊C₄	—	13	64	no	—
312	C₂×C₄⋊C₄	—	13	32	no	—
313	C₂×C₄⋊C₄	—	13	4	no	—
314	C₂×C₄⋊C₄	—	13	4	no	—
315	C₂×C₄⋊C₄	—	13	8	no	—
316	C₂×C₄⋊C₄	—	13	4	no	—
317	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
318	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	—
319	C₂×C₂²⋊C₄	—	13	8	no	—
320	C₂×C₂²⋊C₄	—	13	16	no	—
321	C₂×C₂²⋊C₄	—	13	64	no	—
322	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
323	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	—
324	C₂×C₄²	—	13	8	no	—
325	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
326	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
327	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
328	C₂×C₁₃	—	2	4	no	—
329	C₂×C₁₃	—	2	16	no	—
330	C₂×C₁₃	#3501	1	4	yes	complemented
331	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
332	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
334	C₂⁴	—	4	4	no	—
335	C₂⁴	—	4	4	no	—
336	C₂⁴	C₂×Dic₂₆	1	16	yes	complemented
337	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
338	C₂⁴	C₂³×D₁₃	1	4	yes	—
339	C₂⁴	C₂³×D₁₃	1	8	yes	—
340	C₂×Q₈	—	13	16	no	—
341	C₂×Q₈	—	13	16	no	—
342	C₂×Q₈	—	13	32	no	—
343	C₂×Q₈	—	26	16	no	—
344	C₂×Q₈	—	52	16	no	—
345	C₂×Q₈	—	52	8	no	—
346	C₂×Q₈	—	52	64	no	—
347	C₂×D₄	C₂×Dic₂₆	1	32	yes	complemented
348	C₂×D₄	C₂×Dic₂₆	1	64	yes	complemented
349	C₂×D₄	C₂³×D₁₃	1	16	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	16	no	—
352	C₂²×C₄	—	4	32	no	—
353	C₂²×C₄	—	4	8	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	13	8	no	—
357	C₂²×C₄	—	13	8	no	—
358	C₂²×C₄	—	13	32	no	—
359	C₂²×C₄	—	13	32	no	—
360	C₂²×C₄	—	52	16	no	—
361	C₂²×C₄	—	52	16	no	—
362	C₂²×C₄	C₂×Dic₂₆	1	8	yes	complemented
363	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
364	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
365	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
366	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
368	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
369	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
370	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
371	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
372	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
373	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
374	C₄⋊C₄	—	13	32	no	—
375	C₄⋊C₄	—	13	16	no	—
376	C₄⋊C₄	—	13	32	no	—
377	C₄⋊C₄	—	13	64	no	—
378	C₄⋊C₄	—	13	16	no	—
379	C₄⋊C₄	—	13	16	no	—
380	C₄⋊C₄	—	13	32	no	—
381	C₄⋊C₄	—	13	16	no	—
382	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
383	C₂²⋊C₄	—	13	32	no	—
384	C₂²⋊C₄	—	13	64	no	—
385	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
386	C₄²	—	13	32	no	—
387	C₄²	C₂³×D₁₃	1	8	yes	—
388	C₄²	C₂³×D₁₃	1	8	yes	—
389	C₁₃	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
390	C₂³	—	2	2	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	32	no	—
396	C₂³	—	4	8	no	—
397	C₂³	C₂²×Dic₂₆	1	4	yes	—
398	C₂³	C₂²×Dic₂₆	1	16	yes	—
399	C₂³	C₂²×Dic₂₆	1	32	yes	complemented
400	C₂³	C₂⁴×D₁₃	1	2	yes	—
401	C₂³	C₂⁴×D₁₃	1	8	yes	—
402	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
403	Q₈	—	26	32	no	—
404	Q₈	—	52	16	no	—
405	Q₈	—	52	32	no	—
406	D₄	C₂²×Dic₂₆	1	64	yes	complemented
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	32	no	—
412	C₂×C₄	—	4	16	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	13	16	no	—
416	C₂×C₄	—	13	16	no	—
417	C₂×C₄	—	26	16	no	—
418	C₂×C₄	—	26	16	no	—
419	C₂×C₄	—	52	32	no	—
420	C₂×C₄	—	52	32	no	—
421	C₂×C₄	C₂²×Dic₂₆	1	8	yes	—
422	C₂×C₄	C₂²×Dic₂₆	1	16	yes	complemented
423	C₂×C₄	#88251	1	4	yes	—
424	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
425	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
426	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
427	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
428	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	8	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	8	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	32	no	—
435	C₂²	—	4	32	no	—
436	C₂²	C₂³×Dic₂₆	1	4	yes	—
437	C₂²	C₂³×Dic₂₆	1	16	yes	—
438	C₂²	C₂³×Dic₂₆	1	2	yes	—
439	C₂²	C₂×#88251	1	2	yes	—
440	C₂²	#11719648	1	2	yes	—
441	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	8	no	—
444	C₄	—	2	4	no	—
445	C₄	—	26	16	no	—
446	C₄	—	26	16	no	—
447	C₄	C₂³×Dic₂₆	1	8	yes	—
448	C₄	C₂×#88251	1	4	yes	—
449	C₂	—	2	4	no	—
450	C₂	—	2	16	no	—
451	C₂	#13128639	1	4	yes	direct product factor
452	C₂	C₂⁴×Dic₂₆	1	1	yes	characteristic
453	C₂	C₂²×#88251	1	1	yes	characteristic
454	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂³×D₄×C₁₃	C₂²
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂×#3501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #13128639	C₂	direct (N × H)
2. C₂×#11719244	C₂	semidirect
3. C₂×#11719248	C₂	semidirect
4. C₂×D₄×Dic₂₆	C₂	semidirect
5. C₂×#11719205	C₂	semidirect
6. C₂×#11719188	C₂	semidirect
7. C₂×#11719175	C₂	semidirect
8. C₂²×#88178	C₂	semidirect
13. C₂³×Dic₂₆	C₂²	semidirect
25. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
29. C₂×#88178	C₂²	semidirect
30. C₂×#88178	C₂²	semidirect
31. C₂×#88178	C₂²	semidirect
32. C₂²×#6101	C₂²	semidirect
33. #11719248	C₂²	semidirect
34. #11719244	C₂²	semidirect
35. D₄×Dic₂₆	C₂²	semidirect
36. #11719205	C₂²	semidirect
37. C₂×#88144	C₂²	semidirect
38. C₂×#88142	C₂²	semidirect
39. #11719188	C₂²	semidirect
40. C₂×#88132	C₂²	semidirect
41. C₂×#88132	C₂²	semidirect
42. #11719175	C₂²	semidirect
43. C₂×#88124	C₂²	semidirect
44. C₂×#88123	C₂²	semidirect
45. C₂×#88123	C₂²	semidirect
46. C₂×C₄×Dic₂₆	C₂²	semidirect
47. C₂×C₄×Dic₂₆	C₂²	semidirect
49. C₂²×D₄×C₁₃	Q₈	semidirect
66. C₂²×Dic₂₆	C₂³	semidirect
87. C₂×C₄⋊Dic₁₃	C₂³	semidirect
91. #88178	C₂³	semidirect
92. #88178	C₂³	semidirect
96. C₂×#6101	C₂³	semidirect
98. #88144	C₂³	semidirect
99. #88142	C₂³	semidirect
100. #88132	C₂³	semidirect
101. #88132	C₂³	semidirect
102. #88124	C₂³	semidirect
103. #88123	C₂³	semidirect
104. #88123	C₂³	semidirect
105. C₄×Dic₂₆	C₂³	semidirect
106. C₄×Dic₂₆	C₂³	semidirect
110. C₂⁴×C₁₃	C₂×Q₈	semidirect
114. C₂×D₄×C₁₃	C₂×Q₈	semidirect
115. C₂×D₄×C₁₃	C₂×Q₈	semidirect
123. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
182. C₂³×C₁₃	C₂²×Q₈	semidirect
186. D₄×C₁₃	C₂²×Q₈	semidirect
196. C₂×C₄×C₁₃	C₂²×Q₈	semidirect
275. C₂²×D₄	Dic₂₆	semidirect
330. C₂×C₁₃	#3501	semidirect
336. C₂⁴	C₂×Dic₂₆	semidirect
347. C₂×D₄	C₂×Dic₂₆	semidirect
348. C₂×D₄	C₂×Dic₂₆	semidirect
362. C₂²×C₄	C₂×Dic₂₆	semidirect
389. C₁₃	C₂×#3501	semidirect
399. C₂³	C₂²×Dic₂₆	semidirect
406. D₄	C₂²×Dic₂₆	semidirect
422. C₂×C₄	C₂²×Dic₂₆	semidirect
451. C₂	#13128639	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128639	2
C₂×#11719244	2
C₂×#11719248	2
C₂×D₄×Dic₂₆	2
C₂×#11719205	2
C₂×#11719188	2
C₂×#11719175	2
C₂²×#88178	2
C₂×#11719503	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3501	13

Subgroups — C2×#13128639 #16770823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128639 #16770823