Subgroups — C₂×C₇₉×#1514 #34129245

Order 20224.

1302 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#383×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1514	C₂	1	8	yes	maximal, direct product factor
5	C₂×#327×C₇₉	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₇₉	—	2	1	no	—
7	#532×C₇₉	—	2	2	no	—
8	#532×C₇₉	—	2	2	no	—
9	#532×C₇₉	C₄	1	4	yes	complemented
10	#532×C₇₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₇₉	C₄	1	1	yes	characteristic, complemented
12	C₂×#127×C₇₉	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₇₉	—	2	1	no	—
14	C₂×#121×C₇₉	—	2	1	no	—
15	C₂×#121×C₇₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₇₉	—	2	1	no	—
17	C₂×C₄×D₄×C₇₉	C₄	1	2	yes	complemented
18	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
19	#432×C₇₉	—	2	2	no	—
20	#432×C₇₉	C₂²	1	4	yes	complemented
21	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
22	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
23	C₂×#97×C₇₉	—	2	1	no	—
24	#383×C₇₉	—	2	2	no	—
25	#383×C₇₉	C₂²	1	4	yes	complemented
26	C₂×#95×C₇₉	—	2	1	no	—
27	C₂×#95×C₇₉	—	2	1	no	—
28	C₂×#95×C₇₉	C₂²	1	2	yes	—
29	#327×C₇₉	C₂²	1	16	yes	complemented
30	C₂×#41×C₇₉	—	2	4	no	—
31	C₂×#41×C₇₉	—	2	4	no	—
32	C₂×#41×C₇₉	—	4	8	no	—
33	C₂²×Q₈×C₇₉	—	2	1	no	—
34	C₂²×D₄×C₇₉	—	2	2	no	—
35	C₂²×D₄×C₇₉	—	2	1	no	—
36	C₂²×D₄×C₇₉	—	2	1	no	—
37	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₇₉	—	2	2	no	—
39	C₂³×C₄×C₇₉	—	2	2	no	—
40	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₇₉	—	2	2	no	—
44	C₄⋊Q₈×C₇₉	—	2	2	no	—
45	C₄⋊Q₈×C₇₉	C₂×C₄	1	4	yes	complemented
46	#127×C₇₉	—	2	2	no	—
47	#127×C₇₉	C₂×C₄	1	4	yes	complemented
48	#124×C₇₉	—	2	4	no	—
49	#124×C₇₉	—	2	4	no	—
50	#121×C₇₉	—	2	4	no	—
51	#121×C₇₉	—	2	4	no	—
52	#121×C₇₉	—	2	2	no	—
53	#121×C₇₉	—	2	2	no	—
54	#121×C₇₉	C₂×C₄	1	4	yes	—
55	#121×C₇₉	C₂³	1	4	yes	—
56	C₄×D₄×C₇₉	—	2	4	no	—
57	C₄×D₄×C₇₉	—	2	4	no	—
58	C₄×D₄×C₇₉	—	2	4	no	—
59	C₄×D₄×C₇₉	C₂×C₄	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₇₉	D₄	1	2	yes	—
68	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₉	D₄	1	2	yes	—
70	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
72	C₄⋊C₈×C₇₉	—	2	4	no	—
73	C₂²⋊C₈×C₇₉	—	2	2	no	—
74	C₂²⋊C₈×C₇₉	C₂³	1	4	yes	—
75	#97×C₇₉	—	2	4	no	—
76	#95×C₇₉	—	2	4	no	—
77	#95×C₇₉	—	2	4	no	—
78	#95×C₇₉	—	2	2	no	—
79	#95×C₇₉	C₂³	1	4	yes	—
80	C₂⁴×C₇₉	—	2	2	no	—
81	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
82	#41×C₇₉	—	4	16	no	—
83	#41×C₇₉	—	4	16	no	—
84	C₂×Q₈×C₇₉	—	2	4	no	—
85	C₂×Q₈×C₇₉	—	4	4	no	—
86	C₂×D₄×C₇₉	—	2	4	no	—
87	C₂×D₄×C₇₉	—	2	4	no	—
88	C₂×D₄×C₇₉	—	2	2	no	—
89	C₂×D₄×C₇₉	—	2	4	no	—
90	C₂×D₄×C₇₉	—	2	4	no	—
91	C₂×D₄×C₇₉	—	4	4	no	—
92	C₂×D₄×C₇₉	—	4	4	no	—
93	C₂×D₄×C₇₉	—	4	4	no	—
94	C₂×D₄×C₇₉	—	4	8	no	—
95	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₇₉	—	2	4	no	—
97	C₂²×C₄×C₇₉	—	2	2	no	—
98	C₂²×C₄×C₇₉	—	2	8	no	—
99	C₂²×C₄×C₇₉	—	2	4	no	—
100	C₂²×C₄×C₇₉	—	4	2	no	—
101	C₂²×C₄×C₇₉	—	4	2	no	—
102	C₂²×C₄×C₇₉	—	4	8	no	—
103	C₂²×C₄×C₇₉	—	4	4	no	—
104	C₂²×C₄×C₇₉	—	4	4	no	—
105	C₂²×C₄×C₇₉	—	4	4	no	—
106	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₇₉	—	2	4	no	—
121	C₂×C₈×C₇₉	—	4	4	no	—
122	C₄⋊C₄×C₇₉	—	2	4	no	—
123	C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
125	C₂²⋊C₄×C₇₉	—	2	4	no	—
126	C₂²⋊C₄×C₇₉	—	2	8	no	—
127	C₂²⋊C₄×C₇₉	—	2	4	no	—
128	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
133	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
134	C₄²×C₇₉	C₂×D₄	1	2	yes	—
135	C₄²×C₇₉	C₂×D₄	1	2	yes	—
136	C₂³×C₇₉	—	2	2	no	—
137	C₂³×C₇₉	—	2	2	no	—
138	C₂³×C₇₉	—	2	4	no	—
139	C₂³×C₇₉	—	4	4	no	—
140	C₂³×C₇₉	—	4	4	no	—
141	C₂³×C₇₉	—	4	4	no	—
142	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
145	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₇₉	—	4	8	no	—
147	D₄×C₇₉	—	4	4	no	—
148	D₄×C₇₉	—	4	4	no	—
149	D₄×C₇₉	—	4	8	no	—
150	D₄×C₇₉	—	4	8	no	—
151	D₄×C₇₉	—	4	8	no	—
152	D₄×C₇₉	—	4	8	no	—
153	C₂×C₄×C₇₉	—	2	4	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	2	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	2	4	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	4	no	—
162	C₂×C₄×C₇₉	—	4	2	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	2	no	—
167	C₂×C₄×C₇₉	—	4	1	no	—
168	C₂×C₄×C₇₉	—	4	16	no	—
169	C₂×C₄×C₇₉	—	4	4	no	—
170	C₂×C₄×C₇₉	—	4	4	no	—
171	C₂×C₄×C₇₉	—	4	4	no	—
172	C₂×C₄×C₇₉	—	4	4	no	—
173	C₂×C₄×C₇₉	—	8	8	no	—
174	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₇₉	—	4	4	no	—
183	C₂²×C₇₉	—	2	1	no	—
184	C₂²×C₇₉	—	2	1	no	—
185	C₂²×C₇₉	—	2	1	no	—
186	C₂²×C₇₉	—	2	1	no	—
187	C₂²×C₇₉	—	2	8	no	—
188	C₂²×C₇₉	—	4	4	no	—
189	C₂²×C₇₉	—	4	4	no	—
190	C₂²×C₇₉	—	4	4	no	—
191	C₂²×C₇₉	—	8	8	no	—
192	C₂²×C₇₉	#410	1	2	yes	—
193	C₂²×C₇₉	#418	1	2	yes	—
194	C₂²×C₇₉	#418	1	2	yes	—
195	C₂²×C₇₉	#421	1	2	yes	—
196	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
198	C₄×C₇₉	—	2	1	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	2	2	no	—
203	C₄×C₇₉	—	2	2	no	—
204	C₄×C₇₉	—	2	2	no	—
205	C₄×C₇₉	—	2	2	no	—
206	C₄×C₇₉	—	4	4	no	—
207	C₄×C₇₉	—	8	4	no	—
208	C₂×#1514	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂×C₇₉	—	2	2	no	—
210	C₂×C₇₉	—	2	2	no	—
211	C₂×C₇₉	—	8	4	no	—
212	C₂×C₇₉	#1514	1	4	yes	direct product factor
213	C₂×C₇₉	C₂×#410	1	1	yes	characteristic
214	C₂×C₇₉	C₂×#418	1	1	yes	characteristic
215	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
216	C₂×#532	C₂×C₇₉	1	1	yes	characteristic
217	C₂×#432	C₂×C₇₉	1	1	yes	characteristic, complemented
218	C₂×#383	C₂×C₇₉	1	1	yes	characteristic, complemented
219	#1514	C₂×C₇₉	1	8	yes	direct product factor
220	C₂×#327	C₂×C₇₉	1	4	yes	complemented
221	C₇₉	C₂×#1514	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×#41	—	2	1	no	—
223	#532	—	2	2	no	—
224	#532	—	2	2	no	—
225	#532	C₄×C₇₉	1	4	yes	complemented
226	#532	C₂²×C₇₉	1	4	yes	—
227	C₂×C₄⋊Q₈	C₄×C₇₉	1	1	yes	characteristic, complemented
228	C₂×#127	C₄×C₇₉	1	1	yes	characteristic, complemented
229	C₂×#124	—	2	1	no	—
230	C₂×#121	—	2	1	no	—
231	C₂×#121	C₂²×C₇₉	1	2	yes	—
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	C₄×C₇₉	1	2	yes	complemented
234	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
235	#432	—	2	2	no	—
236	#432	C₂²×C₇₉	1	4	yes	complemented
237	C₂×C₄⋊C₈	—	2	1	no	—
238	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
239	C₂×#97	—	2	1	no	—
240	#383	—	2	2	no	—
241	#383	C₂²×C₇₉	1	4	yes	complemented
242	C₂×#95	—	2	1	no	—
243	C₂×#95	—	2	1	no	—
244	C₂×#95	C₂²×C₇₉	1	2	yes	—
245	#327	C₂²×C₇₉	1	16	yes	complemented
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	4	8	no	—
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂×C₄×C₇₉	1	2	yes	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
259	C₂²×C₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	C₂×C₄×C₇₉	1	4	yes	complemented
262	#127	—	2	2	no	—
263	#127	C₂×C₄×C₇₉	1	4	yes	complemented
264	#124	—	2	4	no	—
265	#124	—	2	4	no	—
266	#121	—	2	4	no	—
267	#121	—	2	4	no	—
268	#121	—	2	2	no	—
269	#121	—	2	2	no	—
270	#121	C₂×C₄×C₇₉	1	4	yes	—
271	#121	C₂³×C₇₉	1	4	yes	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	C₂×C₄×C₇₉	1	8	yes	complemented
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
281	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
282	C₂×C₄²	C₂×C₄×C₇₉	1	2	yes	—
283	C₂×C₄²	D₄×C₇₉	1	2	yes	—
284	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₇₉	1	2	yes	—
287	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
288	C₄⋊C₈	—	2	4	no	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₂²⋊C₈	C₂³×C₇₉	1	4	yes	—
291	#97	—	2	4	no	—
292	#95	—	2	4	no	—
293	#95	—	2	4	no	—
294	#95	—	2	2	no	—
295	#95	C₂³×C₇₉	1	4	yes	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
298	#41	—	4	16	no	—
299	#41	—	4	16	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	C₂²×C₄×C₇₉	1	4	yes	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	8	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
323	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
324	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
327	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	4	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	C₂²×C₄×C₇₉	1	4	yes	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
345	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
346	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
347	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
348	C₄²	C₂²×C₄×C₇₉	1	2	yes	—
349	C₄²	C₂²×C₄×C₇₉	1	2	yes	—
350	C₄²	C₂×D₄×C₇₉	1	2	yes	—
351	C₄²	C₂×D₄×C₇₉	1	2	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
359	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
360	C₂³	AGL(1,ℤ/8)×C₇₉	1	4	yes	—
361	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
362	Q₈	—	4	8	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	8	8	no	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
398	C₈	—	4	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	8	no	—
408	C₂²	#410×C₇₉	1	2	yes	—
409	C₂²	#418×C₇₉	1	2	yes	—
410	C₂²	#418×C₇₉	1	2	yes	—
411	C₂²	#421×C₇₉	1	2	yes	—
412	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
413	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	8	4	no	—
424	C₂	—	2	2	no	—
425	C₂	—	2	2	no	—
426	C₂	—	8	4	no	—
427	C₂	C₇₉×#1514	1	4	yes	direct product factor
428	C₂	C₂×#410×C₇₉	1	1	yes	characteristic
429	C₂	C₂×#418×C₇₉	1	1	yes	characteristic
430	C₂	C₂×#421×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#532×C₇₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₇₉	C₂	semidirect
3. C₂×#383×C₇₉	C₂	semidirect
4. C₇₉×#1514	C₂	direct (N × H)
5. C₂×#327×C₇₉	C₂	semidirect
9. #532×C₇₉	C₄	semidirect
11. C₂×C₄⋊Q₈×C₇₉	C₄	semidirect
12. C₂×#127×C₇₉	C₄	semidirect
17. C₂×C₄×D₄×C₇₉	C₄	semidirect
20. #432×C₇₉	C₂²	semidirect
25. #383×C₇₉	C₂²	semidirect
29. #327×C₇₉	C₂²	semidirect
45. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
47. #127×C₇₉	C₂×C₄	semidirect
59. C₄×D₄×C₇₉	C₂×C₄	semidirect
208. C₂×#1514	C₇₉	direct (N × H)
212. C₂×C₇₉	#1514	direct (N × H)
217. C₂×#432	C₂×C₇₉	semidirect
218. C₂×#383	C₂×C₇₉	semidirect
219. #1514	C₂×C₇₉	direct (N × H)
220. C₂×#327	C₂×C₇₉	semidirect
221. C₇₉	C₂×#1514	direct (N × H)
225. #532	C₄×C₇₉	semidirect
227. C₂×C₄⋊Q₈	C₄×C₇₉	semidirect
228. C₂×#127	C₄×C₇₉	semidirect
233. C₂×C₄×D₄	C₄×C₇₉	semidirect
236. #432	C₂²×C₇₉	semidirect
241. #383	C₂²×C₇₉	semidirect
245. #327	C₂²×C₇₉	semidirect
261. C₄⋊Q₈	C₂×C₄×C₇₉	semidirect
263. #127	C₂×C₄×C₇₉	semidirect
275. C₄×D₄	C₂×C₄×C₇₉	semidirect
427. C₂	C₇₉×#1514	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#532×C₇₉	2
C₂×#432×C₇₉	2
C₂×#383×C₇₉	2
C₇₉×#1514	2
C₂×#327×C₇₉	2
C₂×#1514	79

Subgroups — C2×C79×#1514 #34129245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#1514 #34129245