Subgroups — C₂×#23777173 #35196586

Order 20224.

12982 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×#14579207	C₂	1	2	yes	maximal, complemented
2	#23777173	C₂	1	32	yes	maximal, direct product factor
3	C₂×#19099234	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×D₃₁₆	C₂	1	4	yes	maximal, complemented
5	C₂×#19099197	C₂	1	8	yes	maximal, complemented
6	C₂×#19099131	C₂	1	4	yes	maximal, complemented
7	C₂×#19099127	C₂	1	2	yes	maximal, complemented
8	C₂×#19099114	C₂	1	2	yes	maximal, complemented
9	C₂²×#14579158	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#127×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×#11929624	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14579207	—	2	32	no	—
14	C₂×#14579207	C₂²	1	32	yes	complemented
15	C₂²×#11929625	C₂²	1	4	yes	complemented
16	C₂²×#11929624	C₂²	1	1	yes	characteristic
17	C₂²×#11929624	C₂²	1	4	yes	complemented
18	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
19	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
20	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₇₉	C₂²	1	8	yes	complemented
22	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₇₉	C₂²	1	8	yes	complemented
24	#19099234	C₂²	1	64	yes	complemented
25	D₄×D₃₁₆	C₂²	1	64	yes	complemented
26	#19099197	C₂²	1	128	yes	complemented
27	#19099131	C₂²	1	64	yes	complemented
28	#19099127	C₂²	1	32	yes	complemented
29	#19099114	C₂²	1	32	yes	complemented
30	C₂×#14579158	C₂²	1	4	yes	complemented
31	C₂×#14579158	C₂²	1	2	yes	complemented
32	C₂×#14579158	C₂²	1	2	yes	complemented
33	C₂×#14579158	C₂²	1	16	yes	complemented
34	C₂×#14579157	C₂²	1	8	yes	complemented
35	C₂×#14579157	C₂²	1	4	yes	complemented
36	#127×D₇₉	C₂²	1	32	yes	complemented
37	C₂×#14579150	C₂²	1	4	yes	complemented
38	C₂×#14579136	C₂²	1	8	yes	complemented
39	C₂×#14579135	C₂²	1	8	yes	complemented
40	C₂×#14579134	C₂²	1	16	yes	complemented
41	C₂×#14579131	C₂²	1	16	yes	complemented
42	C₂×#14579129	C₂²	1	8	yes	complemented
43	C₄×#11929624	C₂²	1	16	yes	complemented
44	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
45	C₂×C₄×D₃₁₆	C₂²	1	2	yes	complemented
46	C₂×#14579123	C₂²	1	8	yes	complemented
47	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
48	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
49	C₂×#14579118	C₂²	1	2	yes	complemented
50	C₂×C₄²×D₇₉	C₂²	1	2	yes	complemented
51	C₂²×#41×C₇₉	C₂²	1	2	yes	complemented
52	#532×C₇₉	C₂²	1	16	yes	complemented
53	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
56	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
57	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
58	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×D₇₉	C₂³	1	4	yes	—
60	C₂⁴×D₇₉	C₂³	1	8	yes	—
61	#14579207	—	2	256	no	—
62	C₂×#11929625	—	2	32	no	—
63	C₂×#11929625	C₂³	1	32	yes	complemented
64	C₂×#11929624	—	2	32	no	—
65	C₂×#11929624	D₄	1	16	yes	complemented
66	C₂×#11929624	C₂³	1	8	yes	—
67	C₂×#11929624	C₂³	1	32	yes	complemented
68	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
69	C₂²×D₃₁₆	—	2	16	no	—
70	C₂²×D₃₁₆	—	2	32	no	—
71	C₂²×D₃₁₆	—	4	16	no	—
72	C₂²×D₃₁₆	C₂³	1	8	yes	—
73	C₂²×D₃₁₆	C₂³	1	8	yes	—
74	C₂²×D₃₁₆	C₂³	1	4	yes	—
75	C₂²×D₃₁₆	C₂³	1	4	yes	—
76	C₂²×D₃₁₆	C₂³	1	8	yes	—
77	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
78	C₂²×D₃₁₆	C₂³	1	32	yes	complemented
79	C₂²×D₃₁₆	C₂³	1	16	yes	complemented
80	C₂²×D₃₁₆	C₂³	1	32	yes	complemented
81	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
82	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
83	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
84	C₂×D₄×D₇₉	—	2	64	no	—
85	C₂×D₄×D₇₉	—	2	32	no	—
86	C₂×D₄×D₇₉	—	4	32	no	—
87	C₂×D₄×D₇₉	C₂³	1	64	yes	complemented
88	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
89	C₂×D₄×D₇₉	C₂³	1	64	yes	complemented
90	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
91	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
92	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
93	#14579158	C₂³	1	32	yes	complemented
94	#14579158	C₂³	1	16	yes	complemented
95	#14579158	C₂³	1	16	yes	complemented
96	#14579157	C₂³	1	64	yes	complemented
97	#14579157	C₂³	1	32	yes	complemented
98	#14579150	C₂³	1	32	yes	complemented
99	#14579136	C₂³	1	64	yes	complemented
100	#14579135	C₂³	1	64	yes	complemented
101	#14579134	C₂³	1	128	yes	complemented
102	#14579131	C₂³	1	128	yes	complemented
103	#14579129	C₂³	1	64	yes	complemented
104	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
105	C₄×D₃₁₆	C₂³	1	16	yes	complemented
106	#14579123	C₂³	1	64	yes	complemented
107	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
108	#14579120	C₂³	1	8	yes	complemented
109	#14579118	C₂³	1	16	yes	complemented
110	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
111	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
112	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
113	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
114	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
115	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
116	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
117	C₄²×D₇₉	C₂³	1	16	yes	complemented
118	C₂×#41×C₇₉	—	2	16	no	—
119	C₂×#41×C₇₉	C₂³	1	16	yes	complemented
120	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
121	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
122	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
123	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
126	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
128	#127×C₇₉	C₂³	1	8	yes	complemented
129	#124×C₇₉	C₂³	1	16	yes	complemented
130	#121×C₇₉	C₂³	1	32	yes	complemented
131	C₄×D₄×C₇₉	C₂³	1	32	yes	complemented
132	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
134	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₇₉	C₂³	1	8	yes	complemented
138	C₂³×D₇₉	—	2	16	no	—
139	C₂³×D₇₉	—	2	32	no	—
140	C₂³×D₇₉	—	4	32	no	—
141	C₂³×D₇₉	—	4	16	no	—
142	C₂³×D₇₉	C₂⁴	1	8	yes	—
143	C₂³×D₇₉	C₂⁴	1	2	yes	—
144	C₂³×D₇₉	C₂⁴	1	16	yes	—
145	C₂³×D₇₉	C₂⁴	1	32	yes	—
146	#11929625	—	2	128	no	—
147	#11929624	—	2	128	no	—
148	#11929624	C₂×D₄	1	64	yes	complemented
149	C₂×Dic₁₅₈	C₂×D₄	1	8	yes	complemented
150	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
151	C₂×D₃₁₆	—	2	128	no	—
152	C₂×D₃₁₆	—	2	32	no	—
153	C₂×D₃₁₆	—	2	16	no	—
154	C₂×D₃₁₆	—	2	16	no	—
155	C₂×D₃₁₆	—	2	64	no	—
156	C₂×D₃₁₆	—	2	32	no	—
157	C₂×D₃₁₆	—	4	16	no	—
158	C₂×D₃₁₆	—	4	64	no	—
159	C₂×D₃₁₆	C₂×D₄	1	8	yes	complemented
160	C₂×D₃₁₆	C₂⁴	1	16	yes	—
161	C₂×D₃₁₆	C₂⁴	1	32	yes	—
162	C₂×D₃₁₆	C₂⁴	1	16	yes	—
163	C₂×D₃₁₆	C₂⁴	1	32	yes	—
164	C₂×D₃₁₆	C₂⁴	1	32	yes	—
165	C₂×D₃₁₆	C₂⁴	1	4	yes	—
166	C₂×C₂²⋊D₇₉	—	2	32	no	—
167	C₂×C₂²⋊D₇₉	—	4	32	no	—
168	C₂×C₂²⋊D₇₉	C₂×D₄	1	16	yes	complemented
169	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
170	C₂×C₂²⋊D₇₉	C₂⁴	1	64	yes	—
171	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
172	D₄×D₇₉	—	2	128	no	—
173	D₄×D₇₉	—	2	256	no	—
174	D₄×D₇₉	—	4	128	no	—
175	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
176	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
177	C₂×C₄×D₇₉	—	2	32	no	—
178	C₂×C₄×D₇₉	—	2	16	no	—
179	C₂×C₄×D₇₉	C₂×D₄	1	16	yes	complemented
180	C₂×C₄×D₇₉	C₂⁴	1	32	yes	—
181	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
182	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
183	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
184	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
185	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
186	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
187	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	—
188	C₄×Dic₇₉	C₂⁴	1	8	yes	—
189	C₄×Dic₇₉	C₂⁴	1	16	yes	—
190	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
191	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
192	#41×C₇₉	—	2	64	no	—
193	C₂×Q₈×C₇₉	—	2	8	no	—
194	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
195	C₂×D₄×C₇₉	—	2	16	no	—
196	C₂×D₄×C₇₉	—	2	8	no	—
197	C₂×D₄×C₇₉	—	2	16	no	—
198	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
199	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
200	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
201	C₂²×C₄×C₇₉	—	2	16	no	—
202	C₂²×C₄×C₇₉	—	2	8	no	—
203	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	complemented
204	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
205	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
207	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
212	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
213	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
214	C₄²×C₇₉	C₂⁴	1	8	yes	—
215	C₄²×C₇₉	C₂⁴	1	4	yes	—
216	C₄²×C₇₉	C₂⁴	1	4	yes	—
217	C₂³×C₇₉	—	2	4	no	—
218	C₂³×C₇₉	—	2	8	no	—
219	C₂³×C₇₉	—	2	16	no	—
220	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
221	C₂³×C₇₉	C₂⁵	1	8	yes	—
222	C₂³×C₇₉	C₂⁵	1	2	yes	—
223	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
224	C₂²×D₇₉	—	2	8	no	—
225	C₂²×D₇₉	—	2	16	no	—
226	C₂²×D₇₉	—	2	32	no	—
227	C₂²×D₇₉	—	2	32	no	—
228	C₂²×D₇₉	—	2	64	no	—
229	C₂²×D₇₉	—	4	64	no	—
230	C₂²×D₇₉	—	4	32	no	—
231	C₂²×D₇₉	—	8	64	no	—
232	C₂²×D₇₉	—	8	32	no	—
233	C₂²×D₇₉	C₂²×D₄	1	8	yes	—
234	C₂²×D₇₉	C₂⁵	1	16	yes	—
235	C₂²×D₇₉	C₂⁵	1	4	yes	—
236	Q₈×C₇₉	—	2	16	no	—
237	D₄×C₇₉	—	2	32	no	—
238	D₄×C₇₉	—	2	16	no	—
239	D₄×C₇₉	—	2	32	no	—
240	C₂×C₄×C₇₉	—	2	8	no	—
241	C₂×C₄×C₇₉	—	2	4	no	—
242	C₂×C₄×C₇₉	—	2	32	no	—
243	C₂×C₄×C₇₉	—	2	16	no	—
244	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₇₉	C₂²×D₄	1	16	yes	complemented
247	C₂×C₄×C₇₉	H(5,𝔽₂)	1	8	yes	complemented
248	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
249	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
250	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
251	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
252	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
253	C₂²⋊D₇₉	—	2	64	no	—
254	C₂²⋊D₇₉	—	4	64	no	—
255	C₂²⋊D₇₉	C₂²×D₄	1	32	yes	complemented
256	C₂×Dic₇₉	—	2	8	no	—
257	C₂×Dic₇₉	C₂²×D₄	1	8	yes	—
258	C₂×Dic₇₉	C₂⁵	1	8	yes	—
259	C₂×Dic₇₉	C₂⁵	1	4	yes	—
260	D₃₁₆	—	2	64	no	—
261	D₃₁₆	—	2	32	no	—
262	D₃₁₆	—	2	32	no	—
263	D₃₁₆	—	2	64	no	—
264	D₃₁₆	—	4	32	no	—
265	D₃₁₆	C₂²×D₄	1	16	yes	complemented
266	C₄×D₇₉	—	2	32	no	—
267	C₄×D₇₉	—	2	64	no	—
268	C₄×D₇₉	C₂²×D₄	1	32	yes	complemented
269	Dic₁₅₈	C₂²×D₄	1	16	yes	complemented
270	C₂²×C₇₉	—	2	4	no	—
271	C₂²×C₇₉	—	2	8	no	—
272	C₂²×C₇₉	—	2	8	no	—
273	C₂²×C₇₉	—	2	16	no	—
274	C₂²×C₇₉	—	4	16	no	—
275	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
276	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
277	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
278	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
279	C₂×D₇₉	—	2	8	no	—
280	C₂×D₇₉	—	2	16	no	—
281	C₂×D₇₉	—	2	16	no	—
282	C₂×D₇₉	—	2	32	no	—
283	C₂×D₇₉	—	4	32	no	—
284	C₂×D₇₉	—	8	64	no	—
285	C₂×D₇₉	—	8	32	no	—
286	C₂×D₇₉	C₂³×D₄	1	8	yes	—
287	C₄×C₇₉	—	2	8	no	—
288	C₄×C₇₉	—	2	4	no	—
289	C₄×C₇₉	C₂³×D₄	1	4	yes	—
290	C₄×C₇₉	C₂³×D₄	1	4	yes	—
291	C₄×C₇₉	C₂×H(5,𝔽₂)	1	8	yes	complemented
292	Dic₇₉	—	2	8	no	—
293	Dic₇₉	C₂³×D₄	1	8	yes	—
294	C₂×#3498	—	79	1	no	maximal, Sylow
295	C₂×C₇₉	—	2	4	no	—
296	C₂×C₇₉	—	4	8	no	—
297	C₂×C₇₉	#3498	1	4	yes	complemented
298	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
299	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
300	D₇₉	—	2	8	no	—
301	D₇₉	—	4	16	no	—
302	C₂²×H(5,𝔽₂)	—	79	2	no	—
303	#3498	—	79	32	no	—
304	C₂×#550	—	79	4	no	—
305	C₂×D₄²	—	79	8	no	—
306	C₂×D₄²	—	79	4	no	—
307	C₂×#535	—	79	2	no	—
308	C₂×#535	—	79	4	no	—
309	C₂×#532	—	79	2	no	—
310	C₂×#532	D₇₉	1	1	yes	characteristic, complemented
311	C₂²×#127	—	79	1	no	—
312	C₂²×#127	—	79	2	no	—
313	C₂×C₄×#41	—	79	1	no	—
314	C₇₉	C₂×#3498	1	1	yes	characteristic, complemented, Sylow
315	C₂×H(5,𝔽₂)	—	79	32	no	—
316	C₂×H(5,𝔽₂)	—	158	32	no	—
317	C₂²×#41	—	79	4	no	—
318	C₂²×#41	—	79	1	no	—
319	C₂²×#41	—	79	4	no	—
320	C₂²×#41	C₂×D₇₉	1	2	yes	complemented
321	C₂³×D₄	—	79	8	no	—
322	C₂³×D₄	—	79	4	no	—
323	C₂³×D₄	—	79	8	no	—
324	C₂³×D₄	—	79	4	no	—
325	C₂³×D₄	—	79	2	no	—
326	C₂³×D₄	—	79	4	no	—
327	#550	—	79	64	no	—
328	D₄²	—	79	128	no	—
329	D₄²	—	79	64	no	—
330	#535	—	79	32	no	—
331	#535	—	79	64	no	—
332	#532	—	79	32	no	—
333	#532	C₂×D₇₉	1	16	yes	complemented
334	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
335	C₂×#127	—	79	4	no	—
336	C₂×#127	—	79	8	no	—
337	C₂×#127	—	79	32	no	—
338	C₂×#127	—	79	2	no	—
339	C₂×#127	—	79	2	no	—
340	C₂×#127	—	79	4	no	—
341	C₂×#127	—	79	16	no	—
342	C₂×#127	C₂×D₇₉	1	1	yes	characteristic, complemented
343	C₂×#124	—	79	4	no	—
344	C₂×#124	C₂×D₇₉	1	2	yes	complemented
345	C₂×#121	—	79	8	no	—
346	C₂×#121	—	79	8	no	—
347	C₂×#121	—	79	16	no	—
348	C₂×#121	C₂×D₇₉	1	4	yes	complemented
349	C₂×#120	—	79	8	no	—
350	C₂×#120	—	79	16	no	—
351	C₄×#41	—	79	16	no	—
352	C₂×C₄×Q₈	—	79	2	no	—
353	C₂×C₄×D₄	—	79	4	no	—
354	C₂×C₄×D₄	—	79	8	no	—
355	C₂×C₄×D₄	—	79	2	no	—
356	C₂×C₄×D₄	C₂×D₇₉	1	4	yes	complemented
357	C₂×#117	—	79	1	no	—
358	C₂×#117	—	79	2	no	—
359	C₂²×C₄²	—	79	2	no	—
360	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
361	C₂⁵	—	79	8	no	—
362	C₂⁵	—	79	4	no	—
363	H(5,𝔽₂)	—	158	256	no	—
364	C₂×#41	—	2	16	no	—
365	C₂×#41	—	79	32	no	—
366	C₂×#41	—	79	16	no	—
367	C₂×#41	—	79	8	no	—
368	C₂×#41	—	79	32	no	—
369	C₂×#41	—	158	32	no	—
370	C₂×#41	—	158	32	no	—
371	C₂×#41	C₂²×D₇₉	1	16	yes	complemented
372	C₂²×Q₈	—	79	1	no	—
373	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
374	C₂²×D₄	—	316	16	no	—
375	C₂²×D₄	—	316	32	no	—
376	C₂²×D₄	—	79	16	no	—
377	C₂²×D₄	—	79	64	no	—
378	C₂²×D₄	—	79	2	no	—
379	C₂²×D₄	—	79	8	no	—
380	C₂²×D₄	—	79	32	no	—
381	C₂²×D₄	—	79	64	no	—
382	C₂²×D₄	—	79	8	no	—
383	C₂²×D₄	—	79	32	no	—
384	C₂²×D₄	—	79	1	no	—
385	C₂²×D₄	—	79	8	no	—
386	C₂²×D₄	—	79	8	no	—
387	C₂²×D₄	—	79	4	no	—
388	C₂²×D₄	—	79	4	no	—
389	C₂²×D₄	—	79	16	no	—
390	C₂²×D₄	—	79	32	no	—
391	C₂²×D₄	—	158	32	no	—
392	C₂²×D₄	—	158	32	no	—
393	C₂²×D₄	—	158	64	no	—
394	C₂²×D₄	—	158	16	no	—
395	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
396	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
397	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
398	C₂³×C₄	—	79	2	no	—
399	C₂³×C₄	—	79	4	no	—
400	C₂³×C₄	—	79	8	no	—
401	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
402	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
403	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
404	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
405	#127	—	79	32	no	—
406	#127	—	79	64	no	—
407	#127	—	79	16	no	—
408	#127	—	79	16	no	—
409	#127	—	79	32	no	—
410	#127	C₂²×D₇₉	1	8	yes	complemented
411	#124	—	79	32	no	—
412	#124	C₂²×D₇₉	1	16	yes	complemented
413	#121	—	79	64	no	—
414	#121	—	79	64	no	—
415	#121	—	79	128	no	—
416	#121	C₂²×D₇₉	1	32	yes	complemented
417	#120	—	79	64	no	—
418	#120	—	79	128	no	—
419	C₄×Q₈	—	79	16	no	—
420	C₄×D₄	—	79	32	no	—
421	C₄×D₄	—	79	64	no	—
422	C₄×D₄	—	79	16	no	—
423	C₄×D₄	C₂²×D₇₉	1	32	yes	complemented
424	#117	—	79	8	no	—
425	#117	—	79	16	no	—
426	C₂×C₄⋊C₄	—	79	4	no	—
427	C₂×C₄⋊C₄	—	79	2	no	—
428	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
429	C₂×C₂²⋊C₄	—	79	2	no	—
430	C₂×C₂²⋊C₄	—	79	4	no	—
431	C₂×C₂²⋊C₄	—	79	16	no	—
432	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
433	C₂×C₄²	—	79	2	no	—
434	C₂×C₄²	—	79	4	no	—
435	C₂×C₄²	—	79	16	no	—
436	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
438	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
439	C₂×C₄²	C₂²×D₇₉	1	8	yes	complemented
440	C₂⁴	—	316	16	no	—
441	C₂⁴	—	316	32	no	—
442	C₂⁴	—	79	32	no	—
443	C₂⁴	—	79	16	no	—
444	C₂⁴	—	79	2	no	—
445	C₂⁴	—	79	8	no	—
446	C₂⁴	—	158	32	no	—
447	C₂⁴	—	158	16	no	—
448	C₂⁴	C₂³×D₇₉	1	4	yes	—
449	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
450	#41	—	2	64	no	—
451	#41	—	79	64	no	—
452	#41	—	158	128	no	—
453	#41	—	158	128	no	—
454	C₂×Q₈	—	2	8	no	—
455	C₂×Q₈	—	79	4	no	—
456	C₂×Q₈	—	79	8	no	—
457	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	316	16	no	—
462	C₂×D₄	—	316	64	no	—
463	C₂×D₄	—	316	128	no	—
464	C₂×D₄	—	316	32	no	—
465	C₂×D₄	—	79	64	no	—
466	C₂×D₄	—	79	8	no	—
467	C₂×D₄	—	79	16	no	—
468	C₂×D₄	—	79	32	no	—
469	C₂×D₄	—	79	32	no	—
470	C₂×D₄	—	79	4	no	—
471	C₂×D₄	—	79	32	no	—
472	C₂×D₄	—	79	32	no	—
473	C₂×D₄	—	79	16	no	—
474	C₂×D₄	—	79	16	no	—
475	C₂×D₄	—	79	8	no	—
476	C₂×D₄	—	158	128	no	—
477	C₂×D₄	—	158	32	no	—
478	C₂×D₄	—	158	128	no	—
479	C₂×D₄	—	158	32	no	—
480	C₂×D₄	—	158	256	no	—
481	C₂×D₄	—	158	32	no	—
482	C₂×D₄	—	158	16	no	—
483	C₂×D₄	—	158	16	no	—
484	C₂×D₄	—	158	64	no	—
485	C₂×D₄	C₂³×D₇₉	1	16	yes	—
486	C₂×D₄	C₂³×D₇₉	1	16	yes	—
487	C₂×D₄	C₂³×D₇₉	1	8	yes	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	2	16	no	—
490	C₂²×C₄	—	79	2	no	—
491	C₂²×C₄	—	79	8	no	—
492	C₂²×C₄	—	79	16	no	—
493	C₂²×C₄	—	79	4	no	—
494	C₂²×C₄	—	79	16	no	—
495	C₂²×C₄	—	79	32	no	—
496	C₂²×C₄	—	158	32	no	—
497	C₂²×C₄	—	158	16	no	—
498	C₂²×C₄	D₄×D₇₉	1	8	yes	complemented
499	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
500	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
501	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
502	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
503	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
504	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
505	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
507	C₄⋊C₄	—	79	16	no	—
508	C₄⋊C₄	—	79	8	no	—
509	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
510	C₂²⋊C₄	—	79	8	no	—
511	C₂²⋊C₄	—	79	16	no	—
512	C₂²⋊C₄	—	79	64	no	—
513	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
514	C₄²	—	79	8	no	—
515	C₄²	—	79	16	no	—
516	C₄²	C₂³×D₇₉	1	4	yes	—
517	C₄²	C₂³×D₇₉	1	4	yes	—
518	C₄²	C₂³×D₇₉	1	8	yes	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	16	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	316	32	no	—
523	C₂³	—	316	64	no	—
524	C₂³	—	79	4	no	—
525	C₂³	—	79	8	no	—
526	C₂³	—	79	16	no	—
527	C₂³	—	632	32	no	—
528	C₂³	—	632	64	no	—
529	C₂³	—	158	64	no	—
530	C₂³	—	158	32	no	—
531	C₂³	—	158	16	no	—
532	C₂³	—	158	32	no	—
533	C₂³	—	158	8	no	—
534	C₂³	C₂×D₄×D₇₉	1	4	yes	—
535	C₂³	C₂⁴×D₇₉	1	8	yes	—
536	C₂³	C₂⁴×D₇₉	1	2	yes	—
537	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
538	Q₈	—	2	16	no	—
539	Q₈	—	79	16	no	—
540	D₄	—	2	32	no	—
541	D₄	—	2	32	no	—
542	D₄	—	2	16	no	—
543	D₄	—	316	32	no	—
544	D₄	—	316	64	no	—
545	D₄	—	79	32	no	—
546	D₄	—	79	16	no	—
547	D₄	—	158	64	no	—
548	D₄	—	158	64	no	—
549	D₄	—	158	64	no	—
550	D₄	—	158	32	no	—
551	D₄	—	158	32	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	32	no	—
556	C₂×C₄	—	79	4	no	—
557	C₂×C₄	—	79	8	no	—
558	C₂×C₄	—	79	32	no	—
559	C₂×C₄	—	79	8	no	—
560	C₂×C₄	—	158	64	no	—
561	C₂×C₄	—	158	8	no	—
562	C₂×C₄	—	158	32	no	—
563	C₂×C₄	C₂×D₄×D₇₉	1	4	yes	—
564	C₂×C₄	C₂×D₄×D₇₉	1	4	yes	—
565	C₂×C₄	C₂×D₄×D₇₉	1	16	yes	complemented
566	C₂×C₄	#14579207	1	8	yes	complemented
567	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
568	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
569	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
570	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
571	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	4	16	no	—
577	C₂²	—	316	32	no	—
578	C₂²	—	79	8	no	—
579	C₂²	—	632	32	no	—
580	C₂²	—	632	64	no	—
581	C₂²	—	158	16	no	—
582	C₂²	—	158	32	no	—
583	C₂²	—	158	16	no	—
584	C₂²	—	158	8	no	—
585	C₂²	C₂²×D₄×D₇₉	1	4	yes	—
586	C₂²	C₂²×D₄×D₇₉	1	2	yes	—
587	C₂²	C₂×#14579207	1	4	yes	—
588	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
589	C₄	—	2	8	no	—
590	C₄	—	2	4	no	—
591	C₄	—	79	8	no	—
592	C₄	—	158	8	no	—
593	C₄	C₂²×D₄×D₇₉	1	4	yes	—
594	C₄	C₂²×D₄×D₇₉	1	4	yes	—
595	C₄	C₂×#14579207	1	8	yes	complemented
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	316	16	no	—
599	C₂	—	158	8	no	—
600	C₂	#23777173	1	4	yes	direct product factor
601	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
602	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×#3498
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. C₂²×#14579207	C₂	semidirect
2. #23777173	C₂	direct (N × H)
3. C₂×#19099234	C₂	semidirect
4. C₂×D₄×D₃₁₆	C₂	semidirect
5. C₂×#19099197	C₂	semidirect
6. C₂×#19099131	C₂	semidirect
7. C₂×#19099127	C₂	semidirect
8. C₂×#19099114	C₂	semidirect
9. C₂²×#14579158	C₂	semidirect
10. C₂×#127×D₇₉	C₂	semidirect
11. C₂×C₄×#11929624	C₂	semidirect
12. C₂×#532×C₇₉	C₂	semidirect
14. C₂×#14579207	C₂²	semidirect
15. C₂²×#11929625	C₂²	semidirect
17. C₂²×#11929624	C₂²	semidirect
18. C₂³×D₃₁₆	C₂²	semidirect
19. C₂³×D₃₁₆	C₂²	semidirect
20. C₂³×D₃₁₆	C₂²	semidirect
21. C₂²×D₄×D₇₉	C₂²	semidirect
22. C₂²×D₄×D₇₉	C₂²	semidirect
23. C₂²×D₄×D₇₉	C₂²	semidirect
24. #19099234	C₂²	semidirect
25. D₄×D₃₁₆	C₂²	semidirect
26. #19099197	C₂²	semidirect
27. #19099131	C₂²	semidirect
28. #19099127	C₂²	semidirect
29. #19099114	C₂²	semidirect
30. C₂×#14579158	C₂²	semidirect
31. C₂×#14579158	C₂²	semidirect
32. C₂×#14579158	C₂²	semidirect
33. C₂×#14579158	C₂²	semidirect
34. C₂×#14579157	C₂²	semidirect
35. C₂×#14579157	C₂²	semidirect
36. #127×D₇₉	C₂²	semidirect
37. C₂×#14579150	C₂²	semidirect
38. C₂×#14579136	C₂²	semidirect
39. C₂×#14579135	C₂²	semidirect
40. C₂×#14579134	C₂²	semidirect
41. C₂×#14579131	C₂²	semidirect
42. C₂×#14579129	C₂²	semidirect
43. C₄×#11929624	C₂²	semidirect
44. C₂×C₄×Dic₁₅₈	C₂²	semidirect
45. C₂×C₄×D₃₁₆	C₂²	semidirect
46. C₂×#14579123	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
48. C₂×#14579120	C₂²	semidirect
49. C₂×#14579118	C₂²	semidirect
50. C₂×C₄²×D₇₉	C₂²	semidirect
51. C₂²×#41×C₇₉	C₂²	semidirect
52. #532×C₇₉	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
54. C₂×#127×C₇₉	C₂²	semidirect
55. C₂×#124×C₇₉	C₂²	semidirect
56. C₂×#121×C₇₉	C₂²	semidirect
57. C₂×C₄×D₄×C₇₉	C₂²	semidirect
58. C₂²×C₄²×C₇₉	C₂²	semidirect
63. C₂×#11929625	C₂³	semidirect
65. C₂×#11929624	D₄	semidirect
67. C₂×#11929624	C₂³	semidirect
78. C₂²×D₃₁₆	C₂³	semidirect
79. C₂²×D₃₁₆	C₂³	semidirect
80. C₂²×D₃₁₆	C₂³	semidirect
87. C₂×D₄×D₇₉	C₂³	semidirect
88. C₂×D₄×D₇₉	C₂³	semidirect
89. C₂×D₄×D₇₉	C₂³	semidirect
93. #14579158	C₂³	semidirect
94. #14579158	C₂³	semidirect
95. #14579158	C₂³	semidirect
96. #14579157	C₂³	semidirect
97. #14579157	C₂³	semidirect
98. #14579150	C₂³	semidirect
99. #14579136	C₂³	semidirect
100. #14579135	C₂³	semidirect
101. #14579134	C₂³	semidirect
102. #14579131	C₂³	semidirect
103. #14579129	C₂³	semidirect
104. C₄×Dic₁₅₈	C₂³	semidirect
105. C₄×D₃₁₆	C₂³	semidirect
106. #14579123	C₂³	semidirect
107. C₄×C₂²⋊D₇₉	C₂³	semidirect
108. #14579120	C₂³	semidirect
109. #14579118	C₂³	semidirect
117. C₄²×D₇₉	C₂³	semidirect
119. C₂×#41×C₇₉	C₂³	semidirect
127. C₄⋊Q₈×C₇₉	C₂³	semidirect
128. #127×C₇₉	C₂³	semidirect
129. #124×C₇₉	C₂³	semidirect
130. #121×C₇₉	C₂³	semidirect
131. C₄×D₄×C₇₉	C₂³	semidirect
137. C₂×C₄²×C₇₉	C₂³	semidirect
148. #11929624	C₂×D₄	semidirect
149. C₂×Dic₁₅₈	C₂×D₄	semidirect
159. C₂×D₃₁₆	C₂×D₄	semidirect
168. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
179. C₂×C₄×D₇₉	C₂×D₄	semidirect
203. C₂²×C₄×C₇₉	C₂×D₄	semidirect
246. C₂×C₄×C₇₉	C₂²×D₄	semidirect
247. C₂×C₄×C₇₉	H(5,𝔽₂)	semidirect
255. C₂²⋊D₇₉	C₂²×D₄	semidirect
265. D₃₁₆	C₂²×D₄	semidirect
268. C₄×D₇₉	C₂²×D₄	semidirect
269. Dic₁₅₈	C₂²×D₄	semidirect
291. C₄×C₇₉	C₂×H(5,𝔽₂)	semidirect
297. C₂×C₇₉	#3498	semidirect
310. C₂×#532	D₇₉	semidirect
314. C₇₉	C₂×#3498	semidirect
320. C₂²×#41	C₂×D₇₉	semidirect
333. #532	C₂×D₇₉	semidirect
334. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
342. C₂×#127	C₂×D₇₉	semidirect
344. C₂×#124	C₂×D₇₉	semidirect
348. C₂×#121	C₂×D₇₉	semidirect
356. C₂×C₄×D₄	C₂×D₇₉	semidirect
360. C₂²×C₄²	C₂×D₇₉	semidirect
371. C₂×#41	C₂²×D₇₉	semidirect
404. C₄⋊Q₈	C₂²×D₇₉	semidirect
410. #127	C₂²×D₇₉	semidirect
412. #124	C₂²×D₇₉	semidirect
416. #121	C₂²×D₇₉	semidirect
423. C₄×D₄	C₂²×D₇₉	semidirect
439. C₂×C₄²	C₂²×D₇₉	semidirect
498. C₂²×C₄	D₄×D₇₉	semidirect
565. C₂×C₄	C₂×D₄×D₇₉	semidirect
566. C₂×C₄	#14579207	semidirect
595. C₄	C₂×#14579207	semidirect
600. C₂	#23777173	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×#14579207	2
#23777173	2
C₂×#19099234	2
C₂×D₄×D₃₁₆	2
C₂×#19099197	2
C₂×#19099131	2
C₂×#19099127	2
C₂×#19099114	2
C₂²×#14579158	2
C₂×#127×D₇₉	2
C₂×C₄×#11929624	2
C₂×#532×C₇₉	2
C₂×#3498	79

Subgroups — C2×#23777173 #35196586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777173 #35196586