Subgroups — C₂×#23777805 #35196072

Order 20224.

8802 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777805	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099305	C₂	1	4	yes	maximal, complemented
3	C₂×#19099279	C₂	1	2	yes	maximal, complemented
4	C₂×#19099278	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×D₃₁₆	C₂	1	4	yes	maximal, complemented
6	C₂×#19099198	C₂	1	2	yes	maximal, complemented
7	C₂×#19099129	C₂	1	8	yes	maximal, complemented
8	C₂×#19099127	C₂	1	4	yes	maximal, complemented
9	C₂×#19099113	C₂	1	2	yes	maximal, complemented
10	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#11929624	C₂²	1	4	yes	complemented
12	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
13	C₂²×D₄×D₇₉	C₂²	1	8	yes	complemented
14	#19099305	C₂²	1	64	yes	complemented
15	#19099279	C₂²	1	32	yes	complemented
16	#19099278	C₂²	1	64	yes	complemented
17	D₄×D₃₁₆	C₂²	1	64	yes	complemented
18	#19099198	C₂²	1	32	yes	complemented
19	#19099129	C₂²	1	128	yes	complemented
20	#19099127	C₂²	1	64	yes	complemented
21	#19099113	C₂²	1	32	yes	complemented
22	C₂×#14579161	C₂²	1	2	yes	complemented
23	C₂×#14579158	C₂²	1	2	yes	—
24	C₂×#14579157	C₂²	1	8	yes	complemented
25	C₂×#14579150	C₂²	1	8	yes	complemented
26	C₂×#14579149	C₂²	1	4	yes	complemented
27	C₂×#14579147	C₂²	1	16	yes	complemented
28	C₂×#14579136	C₂²	1	8	yes	complemented
29	C₂×#14579135	C₂²	1	8	yes	complemented
30	C₂×#14579135	C₂²	1	4	yes	complemented
31	C₂×#14579135	C₂²	1	4	yes	complemented
32	C₂×#14579132	C₂²	1	8	yes	complemented
33	C₂×#14579131	C₂²	1	16	yes	complemented
34	C₂×#14579129	C₂²	1	8	yes	complemented
35	C₂×#14579129	C₂²	1	8	yes	complemented
36	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
37	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
38	C₂×#14579120	C₂²	1	4	yes	complemented
39	C₂×#14579119	C₂²	1	8	yes	complemented
40	C₂²×#41×C₇₉	C₂²	1	2	yes	complemented
41	#532×C₇₉	C₂²	1	16	yes	complemented
42	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
45	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
46	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
47	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	C₂⁴×D₇₉	C₂³	1	8	yes	—
49	C₂×#11929624	—	4	16	no	—
50	C₂×#11929624	C₂³	1	32	yes	complemented
51	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
52	C₂²×D₃₁₆	—	4	16	no	—
53	C₂²×D₃₁₆	C₂³	1	4	yes	—
54	C₂²×D₃₁₆	C₂³	1	4	yes	—
55	C₂²×D₃₁₆	C₂³	1	4	yes	—
56	C₂²×D₃₁₆	C₂³	1	8	yes	—
57	C₂²×D₃₁₆	C₂³	1	32	yes	complemented
58	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
59	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
60	C₂×D₄×D₇₉	—	4	32	no	—
61	C₂×D₄×D₇₉	C₂³	1	64	yes	complemented
62	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
63	#14579161	C₂³	1	16	yes	complemented
64	#14579158	C₂³	1	16	yes	—
65	#14579157	C₂³	1	64	yes	complemented
66	#14579150	C₂³	1	64	yes	complemented
67	#14579149	C₂³	1	32	yes	complemented
68	#14579147	C₂³	1	128	yes	complemented
69	#14579136	C₂³	1	64	yes	complemented
70	#14579135	C₂³	1	64	yes	complemented
71	#14579135	C₂³	1	32	yes	complemented
72	#14579135	C₂³	1	32	yes	complemented
73	#14579132	C₂³	1	64	yes	complemented
74	#14579131	C₂³	1	128	yes	complemented
75	#14579129	C₂³	1	64	yes	complemented
76	#14579129	C₂³	1	64	yes	complemented
77	C₄×D₃₁₆	C₂³	1	32	yes	complemented
78	C₄×D₃₁₆	C₂³	1	32	yes	complemented
79	#14579120	C₂³	1	32	yes	complemented
80	#14579119	C₂³	1	64	yes	complemented
81	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
82	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
83	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
84	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
85	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
86	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
87	C₂×C₄×Dic₇₉	C₂³	1	8	yes	—
88	C₂×#41×C₇₉	—	4	8	no	—
89	C₂×#41×C₇₉	C₂³	1	16	yes	complemented
90	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
98	#127×C₇₉	C₂³	1	8	yes	—
99	#124×C₇₉	C₂³	1	16	yes	complemented
100	#121×C₇₉	C₂³	1	32	yes	complemented
101	C₄×D₄×C₇₉	C₂³	1	32	yes	complemented
102	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
104	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	C₂³	1	8	yes	complemented
108	C₂³×D₇₉	—	4	32	no	—
109	C₂³×D₇₉	—	4	16	no	—
110	C₂³×D₇₉	C₂⁴	1	8	yes	—
111	C₂³×D₇₉	C₂⁴	1	32	yes	—
112	#11929624	—	4	64	no	—
113	C₂×Dic₁₅₈	—	4	8	no	—
114	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
115	C₂×D₃₁₆	—	2	16	no	—
116	C₂×D₃₁₆	—	2	16	no	—
117	C₂×D₃₁₆	—	4	8	no	—
118	C₂×D₃₁₆	—	4	16	no	—
119	C₂×D₃₁₆	—	4	64	no	—
120	C₂×D₃₁₆	C₂⁴	1	16	yes	—
121	C₂×D₃₁₆	C₂⁴	1	16	yes	—
122	C₂×D₃₁₆	C₂⁴	1	16	yes	—
123	C₂×D₃₁₆	C₂⁴	1	32	yes	—
124	C₂×C₂²⋊D₇₉	—	4	16	no	—
125	C₂×C₂²⋊D₇₉	—	4	32	no	—
126	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
127	C₂×C₂²⋊D₇₉	C₂⁴	1	64	yes	—
128	D₄×D₇₉	—	4	128	no	—
129	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
130	C₂×C₄×D₇₉	—	2	32	no	—
131	C₂×C₄×D₇₉	C₂⁴	1	32	yes	—
132	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
133	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
134	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
135	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	—
136	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
137	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
138	C₄×Dic₇₉	C₂⁴	1	32	yes	—
139	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
140	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
141	#41×C₇₉	—	4	32	no	—
142	C₂×Q₈×C₇₉	—	4	4	no	—
143	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
144	C₂×D₄×C₇₉	—	2	16	no	—
145	C₂×D₄×C₇₉	—	4	8	no	—
146	C₂×D₄×C₇₉	—	4	4	no	—
147	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
148	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
149	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
150	C₂²×C₄×C₇₉	—	2	8	no	—
151	C₂²×C₄×C₇₉	—	2	4	no	—
152	C₂²×C₄×C₇₉	—	2	16	no	—
153	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
159	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
162	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
163	C₄²×C₇₉	C₂⁴	1	8	yes	—
164	C₄²×C₇₉	C₂⁴	1	4	yes	—
165	C₄²×C₇₉	C₂⁴	1	4	yes	—
166	C₂³×C₇₉	—	2	4	no	—
167	C₂³×C₇₉	—	2	16	no	—
168	C₂³×C₇₉	—	2	8	no	—
169	C₂³×C₇₉	—	2	2	no	—
170	C₂³×C₇₉	C₂⁵	1	8	yes	—
171	C₂³×C₇₉	C₂⁵	1	2	yes	—
172	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
173	C₂²×D₇₉	—	2	16	no	—
174	C₂²×D₇₉	—	2	16	no	—
175	C₂²×D₇₉	—	2	16	no	—
176	C₂²×D₇₉	—	4	64	no	—
177	C₂²×D₇₉	—	4	32	no	—
178	C₂²×D₇₉	—	8	64	no	—
179	C₂²×D₇₉	C₂⁵	1	16	yes	—
180	Q₈×C₇₉	—	4	8	no	—
181	D₄×C₇₉	—	2	32	no	—
182	D₄×C₇₉	—	4	8	no	—
183	D₄×C₇₉	—	4	16	no	—
184	C₂×C₄×C₇₉	—	2	4	no	—
185	C₂×C₄×C₇₉	—	2	8	no	—
186	C₂×C₄×C₇₉	—	2	2	no	—
187	C₂×C₄×C₇₉	—	2	32	no	—
188	C₂×C₄×C₇₉	—	2	16	no	—
189	C₂×C₄×C₇₉	—	2	8	no	—
190	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
191	C₂×C₄×C₇₉	H(5,𝔽₂)	1	8	yes	—
192	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
193	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
194	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
195	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
196	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
197	C₂²⋊D₇₉	—	4	64	no	—
198	C₂²⋊D₇₉	—	4	32	no	—
199	C₂×Dic₇₉	—	2	16	no	—
200	C₂×Dic₇₉	C₂⁵	1	16	yes	—
201	D₃₁₆	—	2	32	no	—
202	D₃₁₆	—	2	32	no	—
203	D₃₁₆	—	4	32	no	—
204	D₃₁₆	—	4	16	no	—
205	C₄×D₇₉	—	2	64	no	—
206	Dic₁₅₈	—	4	16	no	—
207	C₂²×C₇₉	—	2	4	no	—
208	C₂²×C₇₉	—	2	16	no	—
209	C₂²×C₇₉	—	2	2	no	—
210	C₂²×C₇₉	—	2	8	no	—
211	C₂²×C₇₉	—	4	16	no	—
212	C₂²×C₇₉	—	4	4	no	—
213	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
215	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
216	C₂×D₇₉	—	2	16	no	—
217	C₂×D₇₉	—	2	16	no	—
218	C₂×D₇₉	—	2	16	no	—
219	C₂×D₇₉	—	4	32	no	—
220	C₂×D₇₉	—	8	64	no	—
221	C₄×C₇₉	—	2	2	no	—
222	C₄×C₇₉	—	2	8	no	—
223	C₄×C₇₉	—	2	4	no	—
224	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
225	C₄×C₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
226	Dic₇₉	—	2	16	no	—
227	C₂×#3549	—	79	1	no	maximal, Sylow
228	C₂×C₇₉	—	4	8	no	—
229	C₂×C₇₉	—	4	2	no	—
230	C₂×C₇₉	#3549	1	4	yes	complemented
231	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
233	D₇₉	—	4	16	no	—
234	#3549	—	79	32	no	—
235	C₂×H(3,𝔽₄)	—	79	4	no	—
236	C₂×#555	—	79	2	no	—
237	C₂×#555	—	79	4	no	—
238	C₂×D₄²	—	79	2	no	—
239	C₂×D₄²	—	79	4	no	—
240	C₂×#535	—	79	4	no	—
241	C₂×#535	—	79	8	no	—
242	C₂×#532	—	79	2	no	—
243	C₂×#532	D₇₉	1	1	yes	characteristic, complemented
244	C₇₉	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
245	C₂²×#41	—	79	4	no	—
246	C₂²×#41	C₂×D₇₉	1	2	yes	complemented
247	C₂³×D₄	—	79	8	no	—
248	C₂³×D₄	—	79	4	no	—
249	H(3,𝔽₄)	—	79	64	no	—
250	#555	—	79	32	no	—
251	#555	—	79	64	no	—
252	D₄²	—	79	32	no	—
253	D₄²	—	79	64	no	—
254	#535	—	79	64	no	—
255	#535	—	79	128	no	—
256	#532	—	79	32	no	—
257	#532	C₂×D₇₉	1	16	yes	complemented
258	C₂×C₄⋊Q₈	—	79	2	no	—
259	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
260	C₂×#127	—	79	8	no	—
261	C₂×#127	—	79	2	no	—
262	C₂×#127	C₂×D₇₉	1	1	yes	characteristic
263	C₂×#124	—	79	8	no	—
264	C₂×#124	—	79	16	no	—
265	C₂×#124	—	79	4	no	—
266	C₂×#124	C₂×D₇₉	1	2	yes	complemented
267	C₂×#121	—	79	8	no	—
268	C₂×#121	—	79	4	no	—
269	C₂×#121	—	79	4	no	—
270	C₂×#121	—	79	8	no	—
271	C₂×#121	—	79	8	no	—
272	C₂×#121	C₂×D₇₉	1	4	yes	complemented
273	C₂×#120	—	79	8	no	—
274	C₂×#120	—	79	8	no	—
275	C₂×#120	—	79	16	no	—
276	C₂×C₄×D₄	—	79	4	no	—
277	C₂×C₄×D₄	—	79	4	no	—
278	C₂×C₄×D₄	C₂×D₇₉	1	4	yes	complemented
279	C₂×#117	—	79	4	no	—
280	C₂×#117	—	79	8	no	—
281	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
282	C₂⁵	—	79	8	no	—
283	C₂×#41	—	4	8	no	—
284	C₂×#41	—	316	16	no	—
285	C₂×#41	—	79	32	no	—
286	C₂×#41	C₂²×D₇₉	1	16	yes	complemented
287	C₂²×Q₈	—	79	4	no	—
288	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
289	C₂²×D₄	—	316	16	no	—
290	C₂²×D₄	—	316	32	no	—
291	C₂²×D₄	—	79	16	no	—
292	C₂²×D₄	—	79	8	no	—
293	C₂²×D₄	—	79	64	no	—
294	C₂²×D₄	—	79	4	no	—
295	C₂²×D₄	—	79	8	no	—
296	C₂²×D₄	—	79	32	no	—
297	C₂²×D₄	—	79	4	no	—
298	C₂²×D₄	—	79	4	no	—
299	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
300	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
301	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
302	C₂³×C₄	—	79	8	no	—
303	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
304	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
305	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
306	C₄⋊Q₈	—	79	16	no	—
307	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
308	#127	—	79	64	no	—
309	#127	—	79	16	no	—
310	#127	C₂²×D₇₉	1	8	yes	—
311	#124	—	79	64	no	—
312	#124	—	79	128	no	—
313	#124	—	79	32	no	—
314	#124	C₂²×D₇₉	1	16	yes	complemented
315	#121	—	79	64	no	—
316	#121	—	79	32	no	—
317	#121	—	79	32	no	—
318	#121	—	79	64	no	—
319	#121	—	79	64	no	—
320	#121	C₂²×D₇₉	1	32	yes	complemented
321	#120	—	79	64	no	—
322	#120	—	79	64	no	—
323	#120	—	79	128	no	—
324	C₄×D₄	—	79	32	no	—
325	C₄×D₄	—	79	32	no	—
326	C₄×D₄	C₂²×D₇₉	1	32	yes	complemented
327	#117	—	79	32	no	—
328	#117	—	79	64	no	—
329	C₂×C₄⋊C₄	—	79	4	no	—
330	C₂×C₄⋊C₄	—	79	4	no	—
331	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
332	C₂×C₂²⋊C₄	—	79	8	no	—
333	C₂×C₂²⋊C₄	—	79	16	no	—
334	C₂×C₂²⋊C₄	—	79	8	no	—
335	C₂×C₂²⋊C₄	—	79	8	no	—
336	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
337	C₂×C₄²	—	79	8	no	—
338	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
339	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
340	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₇₉	1	8	yes	complemented
342	C₂⁴	—	316	16	no	—
343	C₂⁴	—	316	32	no	—
344	C₂⁴	—	79	32	no	—
345	C₂⁴	—	79	8	no	—
346	C₂⁴	C₂³×D₇₉	1	4	yes	—
347	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
348	#41	—	4	32	no	—
349	#41	—	316	64	no	—
350	C₂×Q₈	—	4	4	no	—
351	C₂×Q₈	—	316	8	no	—
352	C₂×Q₈	—	79	16	no	—
353	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
354	C₂×D₄	—	2	16	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂×D₄	—	316	16	no	—
358	C₂×D₄	—	316	8	no	—
359	C₂×D₄	—	316	64	no	—
360	C₂×D₄	—	316	128	no	—
361	C₂×D₄	—	316	32	no	—
362	C₂×D₄	—	316	16	no	—
363	C₂×D₄	—	79	64	no	—
364	C₂×D₄	—	79	32	no	—
365	C₂×D₄	—	79	16	no	—
366	C₂×D₄	—	79	32	no	—
367	C₂×D₄	—	79	16	no	—
368	C₂×D₄	—	79	16	no	—
369	C₂×D₄	—	158	16	no	—
370	C₂×D₄	—	158	16	no	—
371	C₂×D₄	C₂³×D₇₉	1	16	yes	—
372	C₂×D₄	C₂³×D₇₉	1	8	yes	—
373	C₂×D₄	C₂³×D₇₉	1	16	yes	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	79	8	no	—
378	C₂²×C₄	—	79	32	no	—
379	C₂²×C₄	—	158	32	no	—
380	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
381	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
382	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
383	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
384	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
385	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
386	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
387	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
388	C₄⋊C₄	—	79	16	no	—
389	C₄⋊C₄	—	79	16	no	—
390	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
391	C₂²⋊C₄	—	79	32	no	—
392	C₂²⋊C₄	—	79	64	no	—
393	C₂²⋊C₄	—	79	32	no	—
394	C₂²⋊C₄	—	79	32	no	—
395	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
396	C₄²	—	79	32	no	—
397	C₄²	C₂³×D₇₉	1	4	yes	—
398	C₄²	C₂³×D₇₉	1	8	yes	—
399	C₄²	C₂³×D₇₉	1	4	yes	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	8	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	16	no	—
404	C₂³	—	316	32	no	—
405	C₂³	—	316	64	no	—
406	C₂³	—	79	16	no	—
407	C₂³	—	632	64	no	—
408	C₂³	—	158	16	no	—
409	C₂³	—	158	16	no	—
410	C₂³	—	158	16	no	—
411	C₂³	C₂⁴×D₇₉	1	8	yes	—
412	C₂³	C₂⁴×D₇₉	1	2	yes	—
413	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
414	Q₈	—	4	8	no	—
415	Q₈	—	316	16	no	—
416	D₄	—	2	32	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	16	no	—
419	D₄	—	316	32	no	—
420	D₄	—	316	16	no	—
421	D₄	—	316	64	no	—
422	D₄	—	316	32	no	—
423	D₄	—	158	32	no	—
424	D₄	—	158	32	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	32	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	16	no	—
431	C₂×C₄	—	79	16	no	—
432	C₂×C₄	—	158	16	no	—
433	C₂×C₄	—	158	64	no	—
434	C₂×C₄	#14579206	1	4	yes	—
435	C₂×C₄	#14579207	1	8	yes	—
436	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
437	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
438	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
439	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
440	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	16	no	—
445	C₂²	—	4	16	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	316	32	no	—
448	C₂²	—	632	64	no	—
449	C₂²	—	158	16	no	—
450	C₂²	—	158	16	no	—
451	C₂²	—	158	16	no	—
452	C₂²	C₂×#14579206	1	2	yes	—
453	C₂²	C₂×#14579207	1	4	yes	—
454	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	8	no	—
457	C₄	—	2	4	no	—
458	C₄	—	158	16	no	—
459	C₄	C₂×#14579206	1	4	yes	—
460	C₄	C₂×#14579207	1	8	yes	—
461	C₂	—	4	8	no	—
462	C₂	—	4	2	no	—
463	C₂	—	316	16	no	—
464	C₂	#23777805	1	4	yes	direct product factor
465	C₂	C₂²×#14579206	1	1	yes	characteristic
466	C₂	C₂²×#14579207	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#532×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#532	D₇₉
hypocenter	C₇₉	C₂×#3549
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #23777805	C₂	direct (N × H)
2. C₂×#19099305	C₂	semidirect
3. C₂×#19099279	C₂	semidirect
4. C₂×#19099278	C₂	semidirect
5. C₂×D₄×D₃₁₆	C₂	semidirect
6. C₂×#19099198	C₂	semidirect
7. C₂×#19099129	C₂	semidirect
8. C₂×#19099127	C₂	semidirect
9. C₂×#19099113	C₂	semidirect
10. C₂×#532×C₇₉	C₂	semidirect
11. C₂²×#11929624	C₂²	semidirect
12. C₂³×D₃₁₆	C₂²	semidirect
13. C₂²×D₄×D₇₉	C₂²	semidirect
14. #19099305	C₂²	semidirect
15. #19099279	C₂²	semidirect
16. #19099278	C₂²	semidirect
17. D₄×D₃₁₆	C₂²	semidirect
18. #19099198	C₂²	semidirect
19. #19099129	C₂²	semidirect
20. #19099127	C₂²	semidirect
21. #19099113	C₂²	semidirect
22. C₂×#14579161	C₂²	semidirect
24. C₂×#14579157	C₂²	semidirect
25. C₂×#14579150	C₂²	semidirect
26. C₂×#14579149	C₂²	semidirect
27. C₂×#14579147	C₂²	semidirect
28. C₂×#14579136	C₂²	semidirect
29. C₂×#14579135	C₂²	semidirect
30. C₂×#14579135	C₂²	semidirect
31. C₂×#14579135	C₂²	semidirect
32. C₂×#14579132	C₂²	semidirect
33. C₂×#14579131	C₂²	semidirect
34. C₂×#14579129	C₂²	semidirect
35. C₂×#14579129	C₂²	semidirect
36. C₂×C₄×D₃₁₆	C₂²	semidirect
37. C₂×C₄×D₃₁₆	C₂²	semidirect
38. C₂×#14579120	C₂²	semidirect
39. C₂×#14579119	C₂²	semidirect
40. C₂²×#41×C₇₉	C₂²	semidirect
41. #532×C₇₉	C₂²	semidirect
42. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
44. C₂×#124×C₇₉	C₂²	semidirect
45. C₂×#121×C₇₉	C₂²	semidirect
46. C₂×C₄×D₄×C₇₉	C₂²	semidirect
47. C₂²×C₄²×C₇₉	C₂²	semidirect
50. C₂×#11929624	C₂³	semidirect
57. C₂²×D₃₁₆	C₂³	semidirect
61. C₂×D₄×D₇₉	C₂³	semidirect
63. #14579161	C₂³	semidirect
65. #14579157	C₂³	semidirect
66. #14579150	C₂³	semidirect
67. #14579149	C₂³	semidirect
68. #14579147	C₂³	semidirect
69. #14579136	C₂³	semidirect
70. #14579135	C₂³	semidirect
71. #14579135	C₂³	semidirect
72. #14579135	C₂³	semidirect
73. #14579132	C₂³	semidirect
74. #14579131	C₂³	semidirect
75. #14579129	C₂³	semidirect
76. #14579129	C₂³	semidirect
77. C₄×D₃₁₆	C₂³	semidirect
78. C₄×D₃₁₆	C₂³	semidirect
79. #14579120	C₂³	semidirect
80. #14579119	C₂³	semidirect
89. C₂×#41×C₇₉	C₂³	semidirect
97. C₄⋊Q₈×C₇₉	C₂³	semidirect
99. #124×C₇₉	C₂³	semidirect
100. #121×C₇₉	C₂³	semidirect
101. C₄×D₄×C₇₉	C₂³	semidirect
107. C₂×C₄²×C₇₉	C₂³	semidirect
230. C₂×C₇₉	#3549	semidirect
243. C₂×#532	D₇₉	semidirect
244. C₇₉	C₂×#3549	semidirect
246. C₂²×#41	C₂×D₇₉	semidirect
257. #532	C₂×D₇₉	semidirect
259. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
266. C₂×#124	C₂×D₇₉	semidirect
272. C₂×#121	C₂×D₇₉	semidirect
278. C₂×C₄×D₄	C₂×D₇₉	semidirect
281. C₂²×C₄²	C₂×D₇₉	semidirect
286. C₂×#41	C₂²×D₇₉	semidirect
307. C₄⋊Q₈	C₂²×D₇₉	semidirect
314. #124	C₂²×D₇₉	semidirect
320. #121	C₂²×D₇₉	semidirect
326. C₄×D₄	C₂²×D₇₉	semidirect
341. C₂×C₄²	C₂²×D₇₉	semidirect
464. C₂	#23777805	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777805	2
C₂×#19099305	2
C₂×#19099279	2
C₂×#19099278	2
C₂×D₄×D₃₁₆	2
C₂×#19099198	2
C₂×#19099129	2
C₂×#19099127	2
C₂×#19099113	2
C₂×#532×C₇₉	2
C₂×#3549	79

Subgroups — C2×#23777805 #35196072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777805 #35196072