Subgroups — #34307077

Order 20224.

832 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098693	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098690	C₂	1	1	yes	maximal, characteristic
3	C₄×#14579126	C₂	1	1	yes	maximal, characteristic
4	#23764122	C₂	1	2	yes	maximal
5	#23764120	C₂	1	2	yes	maximal
6	#23764119	C₂	1	1	yes	maximal, characteristic
7	#23763551	C₂	1	1	yes	maximal, characteristic
8	#23763551	C₂	1	2	yes	maximal
9	#23763252	C₂	1	2	yes	maximal
10	C₄×Dic₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
13	C₂×#14579126	C₄	1	1	yes	characteristic
14	C₂×#14579126	C₄	1	1	yes	characteristic
15	#19098693	—	2	4	no	—
16	#19098690	—	2	4	no	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
19	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
21	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
22	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
23	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
24	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×#14579071	C₂²	1	2	yes	—
26	C₂×#14579071	C₂²	1	2	yes	—
27	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
29	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
30	C₄×Dic₇₉⋊C₄	C₂²	1	2	yes	—
31	#19098414	C₄	1	2	yes	—
32	#19098414	C₄	1	2	yes	—
33	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
34	C₄²×Dic₇₉	C₂²	1	2	yes	—
35	#19098318	C₂²	1	2	yes	—
36	#19098317	C₂²	1	1	yes	characteristic
37	#19098317	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	#336×C₇₉	C₂²	1	2	yes	—
43	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₄×Dic₁₅₈	D₄	1	4	yes	—
48	C₄×Dic₁₅₈	Q₈	1	4	yes	—
49	#14579126	—	2	4	no	—
50	#14579126	—	2	4	no	—
51	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
65	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
66	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
67	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
68	Dic₇₉⋊C₈	—	2	4	no	—
69	Dic₇₉⋊C₈	—	2	4	no	—
70	Dic₇₉⋊C₈	—	2	2	no	—
71	Dic₇₉⋊C₈	—	2	4	no	—
72	Dic₇₉⋊C₈	—	4	2	no	—
73	Dic₇₉⋊C₈	Q₈	1	4	yes	complemented
74	#14579071	—	2	4	no	—
75	#14579071	—	2	4	no	—
76	C₄×C₇₉⋊C₈	—	2	2	no	—
77	C₇₉⋊#95	C₂×C₄	1	2	yes	—
78	C₇₉⋊#95	C₂×C₄	1	2	yes	—
79	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
80	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₇₉	—	2	2	no	—
87	C₄⋊C₈×C₇₉	—	4	2	no	—
88	C₄×C₈×C₇₉	—	2	2	no	—
89	#95×C₇₉	C₂×C₄	1	2	yes	—
90	C₂×Dic₁₅₈	—	2	2	no	—
91	C₂×Dic₁₅₈	—	2	2	no	—
92	C₂×Dic₁₅₈	C₄⋊C₄	1	4	yes	—
93	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	—	2	1	no	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₂×C₇₉⋊C₈	—	2	1	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	1	no	—
106	C₂×C₇₉⋊C₈	—	2	1	no	—
107	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
108	C₄⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
109	Dic₇₉⋊C₄	—	2	4	no	—
110	Dic₇₉⋊C₄	—	2	4	no	—
111	Dic₇₉⋊C₄	C₄⋊C₄	1	8	yes	—
112	C₄×Dic₇₉	—	2	4	no	—
113	C₄×Dic₇₉	—	2	4	no	—
114	C₄×Dic₇₉	—	2	2	no	—
115	C₄×Dic₇₉	—	2	4	no	—
116	C₄×Dic₇₉	—	2	2	no	—
117	C₄×Dic₇₉	—	2	1	no	—
118	C₄×Dic₇₉	—	2	1	no	—
119	C₄×Dic₇₉	—	4	1	no	—
120	C₄×Dic₇₉	—	4	2	no	—
121	C₄×Dic₇₉	M₁₆	1	4	yes	—
122	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
123	C₄×Dic₇₉	C₂×Q₈	1	4	yes	—
124	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
125	C₄×Dic₇₉	#41	1	2	yes	—
126	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₇₉	—	2	1	no	—
132	C₂×C₈×C₇₉	—	2	1	no	—
133	C₂×C₈×C₇₉	—	2	2	no	—
134	C₂×C₈×C₇₉	—	2	2	no	—
135	C₂×C₈×C₇₉	—	2	1	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	M₁₆	1	4	yes	—
142	C₄²×C₇₉	—	2	2	no	—
143	C₄²×C₇₉	—	2	2	no	—
144	C₄²×C₇₉	C₂×D₄	1	2	yes	—
145	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
146	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	1	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	2	2	no	—
153	C₂×C₄×C₇₉	—	2	2	no	—
154	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
157	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
158	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×Dic₇₉	—	2	1	no	—
166	C₂×Dic₇₉	—	2	1	no	—
167	C₂×Dic₇₉	—	2	2	no	—
168	C₂×Dic₇₉	—	2	2	no	—
169	C₂×Dic₇₉	—	2	2	no	—
170	C₂×Dic₇₉	—	2	1	no	—
171	C₂×Dic₇₉	—	2	2	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	—	2	1	no	—
175	C₂×Dic₇₉	—	2	1	no	—
176	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
177	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
179	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
180	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
181	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
182	C₂×Dic₇₉	#131	1	2	yes	—
183	Dic₁₅₈	—	2	8	no	—
184	C₈×C₇₉	—	2	2	no	—
185	C₈×C₇₉	—	4	1	no	—
186	C₈×C₇₉	—	4	2	no	—
187	C₇₉⋊C₈	—	2	2	no	—
188	C₇₉⋊C₈	—	4	1	no	—
189	C₇₉⋊C₈	—	4	2	no	—
190	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
192	C₂²×C₇₉	#520	1	1	yes	characteristic
193	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
194	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
195	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
196	C₂²×C₇₉	#568	1	1	yes	characteristic
197	C₄×C₇₉	—	2	2	no	—
198	C₄×C₇₉	—	2	4	no	—
199	C₄×C₇₉	—	4	2	no	—
200	C₄×C₇₉	#423	1	4	yes	—
201	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
202	C₄×C₇₉	#550	1	1	yes	characteristic
203	C₄×C₇₉	#557	1	1	yes	characteristic
204	C₄×C₇₉	Q₈²	1	1	yes	characteristic
205	Dic₇₉	—	2	4	no	—
206	Dic₇₉	—	2	4	no	—
207	Dic₇₉	—	2	2	no	—
208	Dic₇₉	—	2	2	no	—
209	Dic₇₉	—	4	1	no	—
210	Dic₇₉	#446	1	4	yes	complemented
211	#22722	—	79	1	no	maximal, Sylow
212	C₂×C₇₉	Q₈×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₇₉	C₂×#423	1	1	yes	characteristic
214	C₂×C₇₉	#2906	1	1	yes	characteristic
215	C₂×C₇₉	C₂×#446	1	1	yes	characteristic
216	C₂×C₇₉	Q₈×M₁₆	1	1	yes	characteristic
217	C₂×C₇₉	#2989	1	1	yes	characteristic
218	C₂×C₇₉	#2990	1	1	yes	characteristic
219	C₂×#446	—	79	1	no	—
220	C₂×#446	—	79	1	no	—
221	C₄²×Q₈	—	79	1	no	—
222	#1940	—	79	2	no	—
223	#1940	—	79	2	no	—
224	#1939	—	79	1	no	—
225	#1939	D₇₉	1	1	yes	characteristic
226	#1842	—	79	1	no	—
227	#1842	—	79	2	no	—
228	#1767	—	79	2	no	—
229	C₄×C₄⋊C₈	—	79	1	no	—
230	C₇₉	#22722	1	1	yes	characteristic, complemented, Sylow
231	C₂×C₄×Q₈	—	79	1	no	—
232	C₂×C₄×Q₈	—	79	1	no	—
233	C₂×C₄×Q₈	—	79	1	no	—
234	#446	—	158	4	no	—
235	#446	—	158	4	no	—
236	C₂×C₄⋊C₈	—	79	2	no	—
237	C₂×C₄⋊C₈	—	79	2	no	—
238	C₂×C₄⋊C₈	—	79	1	no	—
239	C₂×C₄⋊C₈	—	79	1	no	—
240	C₂×C₄⋊C₈	—	79	2	no	—
241	C₂×C₄⋊C₈	—	79	2	no	—
242	C₂×C₄⋊C₈	—	79	2	no	—
243	C₂×C₄⋊C₈	—	79	1	no	—
244	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
246	C₂×#97	—	79	2	no	—
247	C₂×#97	—	79	2	no	—
248	C₂×C₄×C₈	—	79	1	no	—
249	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
250	C₄×C₄⋊C₄	—	79	1	no	—
251	C₄×C₄⋊C₄	—	79	1	no	—
252	C₄×C₄⋊C₄	—	79	2	no	—
253	C₄×C₄⋊C₄	—	79	2	no	—
254	C₄×C₄⋊C₄	—	79	2	no	—
255	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
256	C₄³	—	79	1	no	—
257	C₄³	—	79	2	no	—
258	#336	—	79	1	no	—
259	#336	—	79	1	no	—
260	#336	—	79	2	no	—
261	#336	C₂×D₇₉	1	2	yes	—
262	C₂²×Q₈	—	79	1	no	—
263	C₂²×C₈	—	79	1	no	—
264	C₂²×C₈	—	79	1	no	—
265	C₂²×C₈	—	79	2	no	—
266	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
268	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
269	C₄×Q₈	—	79	4	no	—
270	C₄×Q₈	—	79	4	no	—
271	C₄×Q₈	—	158	4	no	—
272	C₄×Q₈	—	158	4	no	—
273	C₂×C₄⋊C₄	—	79	2	no	—
274	C₂×C₄⋊C₄	—	79	1	no	—
275	C₂×C₄⋊C₄	—	79	2	no	—
276	C₂×C₄⋊C₄	—	79	2	no	—
277	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
279	C₂×C₄²	—	79	2	no	—
280	C₂×C₄²	—	79	1	no	—
281	C₂×C₄²	—	79	1	no	—
282	C₂×C₄²	—	79	2	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	2	no	—
285	C₂×C₄²	—	79	2	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	—	79	2	no	—
288	C₂×C₄²	—	79	1	no	—
289	C₂×C₄²	—	79	1	no	—
290	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
291	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	4	2	no	—
294	C₄⋊C₈	—	316	2	no	—
295	C₄⋊C₈	—	316	2	no	—
296	C₄⋊C₈	—	79	4	no	—
297	C₄⋊C₈	—	158	2	no	—
298	C₄⋊C₈	—	158	4	no	—
299	C₄⋊C₈	—	158	4	no	—
300	C₄⋊C₈	—	158	4	no	—
301	C₄⋊C₈	—	158	2	no	—
302	#97	—	158	4	no	—
303	#97	—	158	4	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	158	2	no	—
306	#95	—	79	2	no	—
307	#95	—	79	2	no	—
308	#95	C₄×D₇₉	1	2	yes	—
309	C₂×Q₈	—	79	4	no	—
310	C₂×Q₈	—	158	2	no	—
311	C₂×Q₈	—	158	2	no	—
312	C₂²×C₄	—	79	1	no	—
313	C₂²×C₄	—	79	2	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	2	no	—
317	C₂²×C₄	—	79	1	no	—
318	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
319	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
321	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
322	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	79	2	no	—
332	C₂×C₈	—	158	1	no	—
333	C₂×C₈	—	158	2	no	—
334	C₂×C₈	—	158	2	no	—
335	C₂×C₈	—	158	1	no	—
336	C₂×C₈	—	158	1	no	—
337	C₂×C₈	—	158	2	no	—
338	C₂×C₈	—	158	1	no	—
339	C₂×C₈	—	158	1	no	—
340	C₂×C₈	Q₈×D₇₉	1	2	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	79	8	no	—
343	C₄⋊C₄	—	79	4	no	—
344	C₄⋊C₄	—	158	4	no	—
345	C₄⋊C₄	—	158	4	no	—
346	C₄⋊C₄	#11929607	1	4	yes	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	316	1	no	—
350	C₄²	—	316	2	no	—
351	C₄²	—	79	2	no	—
352	C₄²	—	79	4	no	—
353	C₄²	—	79	2	no	—
354	C₄²	—	79	4	no	—
355	C₄²	—	79	4	no	—
356	C₄²	—	158	2	no	—
357	C₄²	—	158	4	no	—
358	C₄²	—	158	4	no	—
359	C₄²	—	158	1	no	—
360	C₄²	—	158	1	no	—
361	C₄²	—	158	2	no	—
362	C₄²	—	158	4	no	—
363	C₄²	D₄×D₇₉	1	2	yes	—
364	C₄²	Q₈×D₇₉	1	2	yes	—
365	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
366	Q₈	—	158	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	79	2	no	—
375	C₂×C₄	—	79	2	no	—
376	C₂×C₄	—	79	2	no	—
377	C₂×C₄	—	79	4	no	—
378	C₂×C₄	—	79	4	no	—
379	C₂×C₄	—	79	2	no	—
380	C₂×C₄	—	79	2	no	—
381	C₂×C₄	—	158	1	no	—
382	C₂×C₄	—	158	1	no	—
383	C₂×C₄	—	158	1	no	—
384	C₂×C₄	—	158	1	no	—
385	C₂×C₄	—	158	2	no	—
386	C₂×C₄	—	158	1	no	—
387	C₂×C₄	—	158	2	no	—
388	C₂×C₄	—	158	2	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	2	no	—
391	C₂×C₄	—	158	1	no	—
392	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
393	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
394	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
395	C₂×C₄	C₂×#11929607	1	4	yes	—
396	C₂×C₄	C₂×#11929607	1	2	yes	—
397	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
398	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
400	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
401	C₂×C₄	#14579206	1	1	yes	characteristic
402	C₂×C₄	#14579208	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	316	1	no	—
407	C₈	—	316	2	no	—
408	C₈	—	158	2	no	—
409	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
410	C₂²	C₄×Q₈×D₇₉	1	1	yes	characteristic
411	C₂²	#19099042	1	1	yes	characteristic
412	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
413	C₂²	C₂²×#11929607	1	1	yes	characteristic
414	C₂²	#131×D₇₉	1	1	yes	characteristic
415	C₂²	#19099328	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	316	1	no	—
420	C₄	—	79	4	no	—
421	C₄	—	158	4	no	—
422	C₄	—	158	4	no	—
423	C₄	—	158	2	no	—
424	C₄	—	158	2	no	—
425	C₄	#19098585	1	4	yes	—
426	C₄	#19099226	1	1	yes	characteristic
427	C₄	#19099231	1	1	yes	characteristic
428	C₄	#19099290	1	1	yes	characteristic
429	C₄	#19099293	1	1	yes	characteristic
430	C₂	#23766314	1	1	yes	characteristic
431	C₂	C₂×#19098585	1	1	yes	characteristic
432	C₂	#23771967	1	1	yes	characteristic
433	C₂	#446×D₇₉	1	1	yes	characteristic
434	C₂	Q₈×#11929607	1	1	yes	characteristic
435	C₂	#23772515	1	1	yes	characteristic
436	C₂	#23772523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1939	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1939	D₇₉
hypocenter	C₇₉	#22722
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
73. Dic₇₉⋊C₈	Q₈	semidirect
210. Dic₇₉	#446	semidirect
230. C₇₉	#22722	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098693	2
C₂×#19098690	2
C₄×#14579126	2
#23764122	2
#23764120	2
#23764119	2
#23763551	2
#23763252	2
C₄×Dic₇₉⋊C₈	2
C₇₉×#1939	2
#22722	79