Subgroups — C₂×#13128629 #16771391

Order 3328.

11534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88257	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#88256	C₂	1	1	yes	maximal, characteristic, complemented
3	#13128629	C₂	1	32	yes	maximal, direct product factor
4	C₂×#11719281	C₂	1	4	yes	maximal, complemented
5	C₂×#11719259	C₂	1	12	yes	maximal, complemented
6	C₂×#11719231	C₂	1	3	yes	maximal, complemented
7	C₂×#11719230	C₂	1	3	yes	maximal, complemented
8	C₂×#11719182	C₂	1	3	yes	maximal, complemented
9	C₂²×#88129	C₂	1	3	yes	maximal, complemented
10	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂×#88257	—	2	16	no	—
13	C₂×#88257	C₂²	1	16	yes	complemented
14	C₂×#88256	—	2	16	no	—
15	C₂×#88256	C₂²	1	16	yes	complemented
16	C₂²×#6131	C₂²	1	2	yes	—
17	C₂²×Q₈×D₁₃	C₂²	1	2	yes	complemented
18	C₂²×#6129	C₂²	1	6	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	6	yes	—
20	C₂²×#6127	C₂²	1	3	yes	—
21	C₂²×#6127	C₂²	1	3	yes	complemented
22	C₂³×D₅₂	C₂²	1	3	yes	—
23	C₂³×Dic₂₆	C₂²	1	3	yes	complemented
24	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
27	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
28	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
29	C₂×#88184	C₂²	1	12	yes	complemented
30	C₂²×#6103	C₂²	1	12	yes	complemented
31	#11719281	C₂²	1	64	yes	complemented
32	#11719259	C₂²	1	192	yes	complemented
33	#11719231	C₂²	1	48	yes	complemented
34	#11719230	C₂²	1	48	yes	complemented
35	C₂×#88151	C₂²	1	12	yes	complemented
36	C₂×#88149	C₂²	1	12	yes	complemented
37	C₂×#88140	C₂²	1	12	yes	complemented
38	C₂×#88136	C₂²	1	12	yes	complemented
39	#11719182	C₂²	1	48	yes	complemented
40	C₂×#88129	C₂²	1	12	yes	complemented
41	C₂×#88129	C₂²	1	3	yes	complemented
42	C₂×#88129	C₂²	1	6	yes	complemented
43	C₂×#88129	C₂²	1	1	yes	characteristic, complemented
44	C₂×#88129	C₂²	1	48	yes	complemented
45	C₂×#88128	C₂²	1	3	yes	complemented
46	C₂×C₄×D₅₂	C₂²	1	12	yes	complemented
47	C₂×#88123	C₂²	1	3	yes	complemented
48	C₂⁴×D₁₃	C₂³	1	6	yes	—
49	C₂×C₁₃×#41	D₄	1	16	yes	complemented
50	C₂×C₁₃×#41	C₂³	1	8	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
55	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
56	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
57	C₂³×Dic₁₃	C₂³	1	6	yes	—
58	#88257	—	2	128	no	—
59	#88256	—	2	128	no	—
60	C₂×#6131	—	2	16	no	—
61	C₂×#6131	C₂³	1	16	yes	—
62	C₂×Q₈×D₁₃	—	2	16	no	—
63	C₂×Q₈×D₁₃	C₂³	1	16	yes	complemented
64	C₂×#6129	—	2	48	no	—
65	C₂×#6129	C₂³	1	48	yes	complemented
66	C₂×D₄×D₁₃	—	2	48	no	—
67	C₂×D₄×D₁₃	C₂³	1	48	yes	—
68	C₂×#6127	—	2	24	no	—
69	C₂×#6127	—	2	24	no	—
70	C₂×#6127	C₂³	1	24	yes	—
71	C₂×#6127	C₂³	1	24	yes	complemented
72	C₂²×D₅₂	—	2	24	no	—
73	C₂²×D₅₂	C₂³	1	1	yes	characteristic
74	C₂²×D₅₂	C₂³	1	3	yes	—
75	C₂²×D₅₂	C₂³	1	6	yes	—
76	C₂²×D₅₂	C₂³	1	24	yes	—
77	C₂²×D₅₂	C₂³	1	12	yes	—
78	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
79	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
80	C₂²×Dic₂₆	—	2	24	no	—
81	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
82	C₂²×Dic₂₆	C₂³	1	3	yes	—
83	C₂²×Dic₂₆	C₂³	1	6	yes	—
84	C₂²×Dic₂₆	C₂³	1	24	yes	complemented
85	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
86	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
87	C₁₃×#117	C₂³	1	24	yes	complemented
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
94	#88184	C₂³	1	96	yes	complemented
95	C₂×#6103	C₂³	1	4	yes	—
96	C₂×#6103	C₂³	1	12	yes	—
97	C₂×#6103	C₂³	1	24	yes	—
98	C₂×#6103	C₂³	1	96	yes	complemented
99	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
100	#88151	C₂³	1	96	yes	complemented
101	#88149	C₂³	1	96	yes	complemented
102	#88140	C₂³	1	96	yes	complemented
103	#88136	C₂³	1	96	yes	complemented
104	#88129	C₂³	1	24	yes	complemented
105	#88129	C₂³	1	48	yes	complemented
106	#88129	C₂³	1	96	yes	complemented
107	#88129	C₂³	1	8	yes	complemented
108	#88128	C₂³	1	24	yes	complemented
109	C₄×D₅₂	C₂³	1	96	yes	complemented
110	#88123	C₂³	1	24	yes	complemented
111	C₂×#3500	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
113	C₂³×D₁₃	—	2	24	no	—
114	C₂³×D₁₃	—	4	24	no	—
115	C₂³×D₁₃	C₂⁴	1	6	yes	—
116	C₂³×D₁₃	C₂⁴	1	2	yes	—
117	C₂³×D₁₃	C₂⁴	1	24	yes	—
118	C₁₃×#41	C₂×D₄	1	64	yes	complemented
119	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	—
122	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
123	C₂²×C₄×C₁₃	—	4	12	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
131	C₂×C₂²⋊D₁₃	—	2	24	no	—
132	C₂×C₂²⋊D₁₃	—	2	24	no	—
133	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
134	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
135	C₂²×Dic₁₃	—	2	24	no	—
136	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
137	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
138	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
139	#6131	—	2	64	no	—
140	Q₈×D₁₃	—	2	64	no	—
141	#6129	—	2	192	no	—
142	D₄×D₁₃	—	2	192	no	—
143	#6127	—	2	96	no	—
144	#6127	—	2	96	no	—
145	C₂×D₅₂	—	2	12	no	—
146	C₂×D₅₂	—	2	24	no	—
147	C₂×D₅₂	—	2	96	no	—
148	C₂×D₅₂	—	2	4	no	—
149	C₂×D₅₂	—	4	24	no	—
150	C₂×D₅₂	C₂⁴	1	4	yes	—
151	C₂×D₅₂	C₂⁴	1	12	yes	—
152	C₂×D₅₂	C₂⁴	1	24	yes	—
153	C₂×D₅₂	C₂⁴	1	48	yes	—
154	C₂×C₄×D₁₃	—	2	24	no	—
155	C₂×C₄×D₁₃	—	2	24	no	—
156	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
157	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
158	C₂×Dic₂₆	—	2	12	no	—
159	C₂×Dic₂₆	—	2	24	no	—
160	C₂×Dic₂₆	—	2	96	no	—
161	C₂×Dic₂₆	—	2	4	no	—
162	C₂×Dic₂₆	C₂⁴	1	4	yes	—
163	C₂×Dic₂₆	C₂⁴	1	12	yes	—
164	C₂×Dic₂₆	C₂⁴	1	24	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
166	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
167	C₄²×C₁₃	C₂⁴	1	12	yes	—
168	C₄²×C₁₃	C₂⁴	1	24	yes	—
169	C₄²×C₁₃	C₂⁴	1	4	yes	—
170	#6103	C₂⁴	1	16	yes	—
171	#6103	C₂⁴	1	48	yes	—
172	#6103	C₂⁴	1	96	yes	—
173	C₄⋊Dic₁₃	C₂⁴	1	48	yes	—
174	C₂²×2₋¹⁺⁴	—	13	1	no	—
175	C₂²×H(5,𝔽₂)	—	13	1	no	—
176	#3500	—	13	32	no	—
177	C₂×#548	—	13	4	no	—
178	C₂×#546	—	13	12	no	—
179	C₂×#536	—	13	3	no	—
180	C₂×#535	—	13	3	no	—
181	C₂×#532	—	13	3	no	—
182	C₂²×#124	—	13	3	no	—
183	C₂×C₄×#41	D₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	12	no	—
185	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
186	C₂³×C₁₃	C₂⁵	1	6	yes	—
187	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
188	C₂²×D₁₃	—	2	4	no	—
189	C₂²×D₁₃	—	2	12	no	—
190	C₂²×D₁₃	—	2	8	no	—
191	C₂²×D₁₃	—	2	24	no	—
192	C₂²×D₁₃	—	2	48	no	—
193	C₂²×D₁₃	—	4	48	no	—
194	C₂²×D₁₃	—	8	48	no	—
195	C₂²×D₁₃	C₂⁵	1	12	yes	—
196	C₂²×D₁₃	C₂⁵	1	4	yes	—
197	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
198	D₄×C₁₃	C₂²×D₄	1	48	yes	—
199	C₂×C₄×C₁₃	—	2	12	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	4	24	no	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	—
205	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
206	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
207	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
208	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
209	C₂²⋊D₁₃	—	2	48	no	—
210	C₂²⋊D₁₃	—	2	48	no	—
211	C₂×Dic₁₃	—	2	12	no	—
212	C₂×Dic₁₃	—	2	48	no	—
213	C₂×Dic₁₃	—	2	4	no	—
214	C₂×Dic₁₃	C₂⁵	1	4	yes	—
215	C₂×Dic₁₃	C₂⁵	1	12	yes	—
216	D₅₂	—	2	24	no	—
217	D₅₂	—	2	48	no	—
218	D₅₂	—	2	8	no	—
219	D₅₂	—	4	48	no	—
220	C₄×D₁₃	—	2	48	no	—
221	C₄×D₁₃	—	2	48	no	—
222	Dic₂₆	—	2	24	no	—
223	Dic₂₆	—	2	48	no	—
224	Dic₂₆	—	2	8	no	—
225	C₂×2₋¹⁺⁴	—	13	16	no	—
226	C₂×2₋¹⁺⁴	—	26	16	no	—
227	C₂×H(5,𝔽₂)	—	13	16	no	—
228	C₂×H(5,𝔽₂)	—	26	16	no	—
229	C₂²×#41	—	13	2	no	—
230	C₂²×#41	—	13	6	no	—
231	C₂²×#41	—	13	3	no	—
232	C₂²×#41	—	13	3	no	—
233	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
234	C₂³×Q₈	—	13	2	no	—
235	C₂³×Q₈	—	13	3	no	—
236	C₂³×D₄	—	13	6	no	—
237	C₂³×D₄	—	13	3	no	—
238	#548	—	13	64	no	—
239	#546	—	13	192	no	—
240	#536	—	13	48	no	—
241	#535	—	13	48	no	—
242	#532	—	13	48	no	—
243	C₂×C₄⋊Q₈	—	13	3	no	—
244	C₂×#127	—	13	3	no	—
245	C₂×#124	—	13	3	no	—
246	C₂×#124	—	13	6	no	—
247	C₂×#124	—	13	12	no	—
248	C₂×#124	—	13	1	no	—
249	C₂×#124	—	13	48	no	—
250	C₂×#123	—	13	12	no	—
251	C₂×C₂²⋊Q₈	—	13	12	no	—
252	C₂×#121	—	13	12	no	—
253	C₂×#121	—	13	12	no	—
254	C₂×#120	—	13	12	no	—
255	C₄×#41	C₂×D₁₃	1	16	yes	complemented
256	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
257	C₂×C₄×D₄	—	13	12	no	—
258	C₂×C₄×D₄	C₂×D₁₃	1	6	yes	complemented
259	C₂×#117	C₂×D₁₃	1	3	yes	complemented
260	C₂²×C₂²⋊C₄	—	13	12	no	—
261	C₂²×C₄²	C₂×D₁₃	1	3	yes	complemented
262	C₂²×C₁₃	—	2	12	no	—
263	C₂²×C₁₃	—	2	24	no	—
264	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
265	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
266	C₂²×C₁₃	#585	1	4	yes	—
267	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
268	C₂×D₁₃	—	2	4	no	—
269	C₂×D₁₃	—	2	12	no	—
270	C₂×D₁₃	—	2	8	no	—
271	C₂×D₁₃	—	2	24	no	—
272	C₂×D₁₃	—	4	8	no	—
273	C₂×D₁₃	—	4	24	no	—
274	C₂×D₁₃	—	8	48	no	—
275	C₄×C₁₃	—	2	12	no	—
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	C₂³×D₄	1	4	yes	—
278	C₄×C₁₃	C₂³×D₄	1	12	yes	—
279	Dic₁₃	—	2	12	no	—
280	Dic₁₃	—	2	4	no	—
281	C₂⁵	—	13	6	no	—
282	2₋¹⁺⁴	—	26	128	no	—
283	H(5,𝔽₂)	—	26	128	no	—
284	C₂×#41	—	13	16	no	—
285	C₂×#41	—	13	48	no	—
286	C₂×#41	—	13	24	no	—
287	C₂×#41	—	13	24	no	—
288	C₂×#41	—	26	16	no	—
289	C₂×#41	—	26	48	no	—
290	C₂×#41	—	26	24	no	—
291	C₂×#41	—	26	24	no	—
292	C₂×#41	D₅₂	1	16	yes	complemented
293	C₂×#41	C₂²×D₁₃	1	8	yes	—
294	C₂²×Q₈	—	13	16	no	—
295	C₂²×Q₈	—	13	6	no	—
296	C₂²×Q₈	—	13	3	no	—
297	C₂²×Q₈	—	13	24	no	—
298	C₂²×Q₈	—	13	1	no	—
299	C₂²×Q₈	—	26	16	no	—
300	C₂²×Q₈	—	26	24	no	—
301	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
302	C₂²×D₄	—	13	6	no	—
303	C₂²×D₄	—	13	6	no	—
304	C₂²×D₄	—	13	48	no	—
305	C₂²×D₄	—	13	6	no	—
306	C₂²×D₄	—	13	3	no	—
307	C₂²×D₄	—	13	24	no	—
308	C₂²×D₄	—	13	1	no	—
309	C₂²×D₄	—	13	12	no	—
310	C₂²×D₄	—	26	48	no	—
311	C₂²×D₄	—	26	24	no	—
312	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
313	C₂³×C₄	—	13	6	no	—
314	C₂³×C₄	—	13	6	no	—
315	C₂³×C₄	—	13	6	no	—
316	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
317	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
318	C₄⋊Q₈	—	13	24	no	—
319	#127	—	13	24	no	—
320	#124	—	13	24	no	—
321	#124	—	13	48	no	—
322	#124	—	13	96	no	—
323	#124	—	13	8	no	—
324	#123	—	13	96	no	—
325	C₂²⋊Q₈	—	13	96	no	—
326	#121	—	13	96	no	—
327	#121	—	13	96	no	—
328	#120	—	13	96	no	—
329	C₄×Q₈	C₂²×D₁₃	1	16	yes	complemented
330	C₄×D₄	—	13	96	no	—
331	C₄×D₄	C₂²×D₁₃	1	48	yes	complemented
332	#117	C₂²×D₁₃	1	24	yes	complemented
333	C₂×C₄⋊C₄	—	13	12	no	—
334	C₂×C₄⋊C₄	C₂²×D₁₃	1	6	yes	—
335	C₂×C₂²⋊C₄	—	13	12	no	—
336	C₂×C₂²⋊C₄	—	13	24	no	—
337	C₂×C₂²⋊C₄	—	13	96	no	—
338	C₂×C₂²⋊C₄	—	13	4	no	—
339	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
340	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
341	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
342	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
343	C₂×C₄²	C₂²×D₁₃	1	24	yes	complemented
344	C₂×C₁₃	—	2	12	no	—
345	C₂×C₁₃	#3500	1	4	yes	complemented
346	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#585	1	2	yes	—
348	D₁₃	—	4	4	no	—
349	D₁₃	—	4	12	no	—
350	C₂⁴	—	13	6	no	—
351	C₂⁴	—	13	2	no	—
352	C₂⁴	—	13	24	no	—
353	C₂⁴	—	26	24	no	—
354	C₂⁴	—	52	24	no	—
355	C₂⁴	C₂³×D₁₃	1	3	yes	—
356	#41	—	26	64	no	—
357	#41	—	26	192	no	—
358	#41	—	26	96	no	—
359	#41	—	26	96	no	—
360	#41	C₂×D₅₂	1	64	yes	complemented
361	C₂×Q₈	—	13	24	no	—
362	C₂×Q₈	—	13	12	no	—
363	C₂×Q₈	—	13	4	no	—
364	C₂×Q₈	—	26	64	no	—
365	C₂×Q₈	—	26	24	no	—
366	C₂×Q₈	—	26	12	no	—
367	C₂×Q₈	—	26	96	no	—
368	C₂×Q₈	—	26	4	no	—
369	C₂×Q₈	C₂×D₅₂	1	8	yes	—
370	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
371	C₂×D₄	—	13	24	no	—
372	C₂×D₄	—	13	24	no	—
373	C₂×D₄	—	13	24	no	—
374	C₂×D₄	—	13	12	no	—
375	C₂×D₄	—	13	4	no	—
376	C₂×D₄	—	13	48	no	—
377	C₂×D₄	—	26	24	no	—
378	C₂×D₄	—	26	24	no	—
379	C₂×D₄	—	26	192	no	—
380	C₂×D₄	—	26	24	no	—
381	C₂×D₄	—	26	12	no	—
382	C₂×D₄	—	26	96	no	—
383	C₂×D₄	—	26	4	no	—
384	C₂×D₄	—	52	24	no	—
385	C₂×D₄	C₂×D₅₂	1	24	yes	—
386	C₂×D₄	C₂³×D₁₃	1	12	yes	—
387	C₂²×C₄	—	4	12	no	—
388	C₂²×C₄	—	13	24	no	—
389	C₂²×C₄	—	13	6	no	—
390	C₂²×C₄	—	13	2	no	—
391	C₂²×C₄	—	13	24	no	—
392	C₂²×C₄	—	13	24	no	—
393	C₂²×C₄	—	26	24	no	—
394	C₂²×C₄	—	26	24	no	—
395	C₂²×C₄	—	26	24	no	—
396	C₂²×C₄	C₂×D₅₂	1	24	yes	—
397	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
398	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
399	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
400	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
401	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
403	C₄⋊C₄	—	13	48	no	—
404	C₄⋊C₄	C₂³×D₁₃	1	24	yes	—
405	C₂²⋊C₄	—	13	48	no	—
406	C₂²⋊C₄	—	13	96	no	—
407	C₂²⋊C₄	—	13	16	no	—
408	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
409	C₄²	C₂³×D₁₃	1	4	yes	—
410	C₄²	C₂³×D₁₃	1	12	yes	—
411	C₄²	C₂³×D₁₃	1	24	yes	—
412	C₁₃	C₂×#3500	1	1	yes	characteristic, complemented, Sylow
413	C₂³	—	2	12	no	—
414	C₂³	—	13	12	no	—
415	C₂³	—	13	4	no	—
416	C₂³	—	26	4	no	—
417	C₂³	—	26	12	no	—
418	C₂³	—	26	8	no	—
419	C₂³	—	26	24	no	—
420	C₂³	—	26	48	no	—
421	C₂³	—	52	48	no	—
422	C₂³	—	104	48	no	—
423	C₂³	C₂²×D₅₂	1	12	yes	—
424	C₂³	C₂⁴×D₁₃	1	6	yes	—
425	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
426	Q₈	—	26	48	no	—
427	Q₈	—	26	24	no	—
428	Q₈	—	26	8	no	—
429	Q₈	C₂²×D₅₂	1	16	yes	—
430	D₄	—	26	48	no	—
431	D₄	—	26	48	no	—
432	D₄	—	26	48	no	—
433	D₄	—	26	24	no	—
434	D₄	—	26	8	no	—
435	D₄	—	52	48	no	—
436	D₄	C₂²×D₅₂	1	48	yes	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	12	no	—
439	C₂×C₄	—	4	24	no	—
440	C₂×C₄	—	13	12	no	—
441	C₂×C₄	—	13	4	no	—
442	C₂×C₄	—	26	4	no	—
443	C₂×C₄	—	26	12	no	—
444	C₂×C₄	—	26	48	no	—
445	C₂×C₄	—	26	48	no	—
446	C₂×C₄	—	26	48	no	—
447	C₂×C₄	C₂²×D₅₂	1	12	yes	—
448	C₂×C₄	C₂²×D₅₂	1	4	yes	—
449	C₂×C₄	C₂²×D₅₂	1	48	yes	—
450	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
451	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
452	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
453	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	24	no	—
456	C₂²	—	26	4	no	—
457	C₂²	—	26	12	no	—
458	C₂²	—	26	8	no	—
459	C₂²	—	26	24	no	—
460	C₂²	—	52	8	no	—
461	C₂²	—	52	24	no	—
462	C₂²	—	104	48	no	—
463	C₂²	C₂³×D₅₂	1	12	yes	—
464	C₂²	C₂³×D₅₂	1	2	yes	—
465	C₂²	#11719648	1	4	yes	—
466	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	12	no	—
469	C₄	—	26	4	no	—
470	C₄	—	26	12	no	—
471	C₄	C₂³×D₅₂	1	12	yes	—
472	C₄	C₂³×D₅₂	1	4	yes	—
473	C₂	—	2	12	no	—
474	C₂	—	52	12	no	—
475	C₂	—	52	4	no	—
476	C₂	#13128629	1	4	yes	direct product factor
477	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
478	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	C₂×#3500
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#88257	C₂	semidirect
2. C₂²×#88256	C₂	semidirect
3. #13128629	C₂	direct (N × H)
4. C₂×#11719281	C₂	semidirect
5. C₂×#11719259	C₂	semidirect
6. C₂×#11719231	C₂	semidirect
7. C₂×#11719230	C₂	semidirect
8. C₂×#11719182	C₂	semidirect
9. C₂²×#88129	C₂	semidirect
10. C₂×C₄×C₁₃×#41	C₂	semidirect
13. C₂×#88257	C₂²	semidirect
15. C₂×#88256	C₂²	semidirect
17. C₂²×Q₈×D₁₃	C₂²	semidirect
18. C₂²×#6129	C₂²	semidirect
21. C₂²×#6127	C₂²	semidirect
23. C₂³×Dic₂₆	C₂²	semidirect
24. C₄×C₁₃×#41	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
27. C₂×C₁₃×#117	C₂²	semidirect
28. C₂²×C₄²×C₁₃	C₂²	semidirect
29. C₂×#88184	C₂²	semidirect
30. C₂²×#6103	C₂²	semidirect
31. #11719281	C₂²	semidirect
32. #11719259	C₂²	semidirect
33. #11719231	C₂²	semidirect
34. #11719230	C₂²	semidirect
35. C₂×#88151	C₂²	semidirect
36. C₂×#88149	C₂²	semidirect
37. C₂×#88140	C₂²	semidirect
38. C₂×#88136	C₂²	semidirect
39. #11719182	C₂²	semidirect
40. C₂×#88129	C₂²	semidirect
41. C₂×#88129	C₂²	semidirect
42. C₂×#88129	C₂²	semidirect
43. C₂×#88129	C₂²	semidirect
44. C₂×#88129	C₂²	semidirect
45. C₂×#88128	C₂²	semidirect
46. C₂×C₄×D₅₂	C₂²	semidirect
47. C₂×#88123	C₂²	semidirect
49. C₂×C₁₃×#41	D₄	semidirect
63. C₂×Q₈×D₁₃	C₂³	semidirect
65. C₂×#6129	C₂³	semidirect
71. C₂×#6127	C₂³	semidirect
84. C₂²×Dic₂₆	C₂³	semidirect
85. C₄×Q₈×C₁₃	C₂³	semidirect
86. C₄×D₄×C₁₃	C₂³	semidirect
87. C₁₃×#117	C₂³	semidirect
93. C₂×C₄²×C₁₃	C₂³	semidirect
94. #88184	C₂³	semidirect
98. C₂×#6103	C₂³	semidirect
100. #88151	C₂³	semidirect
101. #88149	C₂³	semidirect
102. #88140	C₂³	semidirect
103. #88136	C₂³	semidirect
104. #88129	C₂³	semidirect
105. #88129	C₂³	semidirect
106. #88129	C₂³	semidirect
107. #88129	C₂³	semidirect
108. #88128	C₂³	semidirect
109. C₄×D₅₂	C₂³	semidirect
110. #88123	C₂³	semidirect
118. C₁₃×#41	C₂×D₄	semidirect
183. C₂×C₄×#41	D₁₃	semidirect
255. C₄×#41	C₂×D₁₃	semidirect
256. C₂×C₄×Q₈	C₂×D₁₃	semidirect
258. C₂×C₄×D₄	C₂×D₁₃	semidirect
259. C₂×#117	C₂×D₁₃	semidirect
261. C₂²×C₄²	C₂×D₁₃	semidirect
292. C₂×#41	D₅₂	semidirect
329. C₄×Q₈	C₂²×D₁₃	semidirect
331. C₄×D₄	C₂²×D₁₃	semidirect
332. #117	C₂²×D₁₃	semidirect
343. C₂×C₄²	C₂²×D₁₃	semidirect
345. C₂×C₁₃	#3500	semidirect
360. #41	C₂×D₅₂	semidirect
412. C₁₃	C₂×#3500	semidirect
476. C₂	#13128629	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×#88257	2
C₂²×#88256	2
#13128629	2
C₂×#11719281	2
C₂×#11719259	2
C₂×#11719231	2
C₂×#11719230	2
C₂×#11719182	2
C₂²×#88129	2
C₂×C₄×C₁₃×#41	2
C₂×#3500	13

Subgroups — C2×#13128629 #16771391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128629 #16771391