Subgroups — #34315701

Order 20224.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776805	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098580	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098537	C₂	1	1	yes	maximal, characteristic
4	#23764572	C₂	1	8	yes	maximal, complemented
5	C₂×#19098335	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763110	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098320	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#421×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11929608	C₂²	1	1	yes	characteristic
10	#19099194	—	2	2	no	—
11	#19099191	—	2	2	no	—
12	#19099191	—	2	2	no	—
13	#19099189	—	2	2	no	—
14	#19099120	C₂²	1	4	yes	complemented
15	#19099116	—	2	2	no	—
16	#19099116	—	2	2	no	—
17	C₂×#14579120	C₂²	1	1	yes	characteristic
18	C₂×#14579120	C₂²	1	1	yes	characteristic
19	C₂×#14579120	C₂²	1	1	yes	characteristic
20	#19098580	—	2	2	no	—
21	#19098580	C₂²	1	4	yes	—
22	C₂×#14579088	—	2	2	no	—
23	#19098537	—	2	2	no	—
24	#19098537	C₂²	1	4	yes	—
25	C₂×#14579076	—	2	2	no	—
26	#19098335	C₂²	1	4	yes	complemented
27	#19098323	C₂²	1	4	yes	complemented
28	#19098320	C₂²	1	4	yes	complemented
29	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
32	#421×C₇₉	—	2	2	no	—
33	#421×C₇₉	—	2	2	no	—
34	C₂×#104×C₇₉	C₂²	1	4	yes	—
35	C₂×#11929608	—	2	1	no	—
36	C₂×#11929608	—	2	1	no	—
37	C₂×#11929608	—	2	1	no	—
38	C₂×#11929608	—	2	1	no	—
39	C₂×#11929608	—	2	1	no	—
40	C₂×#11929608	C₂³	1	2	yes	—
41	C₂²×C₇₉⋊C₈	—	2	1	no	—
42	#14579161	—	2	4	no	—
43	#14579160	—	2	4	no	—
44	#14579160	—	2	4	no	—
45	#14579153	—	2	4	no	—
46	#14579152	—	2	4	no	—
47	#14579152	—	2	4	no	—
48	#14579140	—	2	8	no	—
49	#14579138	—	2	8	no	—
50	#14579138	—	2	8	no	—
51	C₄×Dic₁₅₈	—	2	8	no	—
52	#14579120	—	2	1	no	—
53	#14579120	—	2	1	no	—
54	#14579120	—	2	1	no	—
55	#14579120	—	2	1	no	—
56	#14579120	—	2	1	no	—
57	#14579120	—	2	1	no	—
58	#14579120	—	2	1	no	—
59	#14579120	D₄	1	2	yes	—
60	#14579120	D₄	1	2	yes	—
61	#14579120	C₂³	1	2	yes	—
62	#14579120	C₂³	1	2	yes	—
63	#14579120	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₇₉	—	2	1	no	—
65	C₂×C₄⋊Dic₇₉	—	2	1	no	—
66	C₂×C₄⋊Dic₇₉	—	2	1	no	—
67	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
68	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
69	C₂×C₂²⋊Dic₇₉	D₄	1	2	yes	—
70	C₂×C₄×Dic₇₉	—	2	1	no	—
71	C₂×C₄×Dic₇₉	—	2	1	no	—
72	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
73	#14579088	—	2	8	no	—
74	#14579076	—	2	8	no	—
75	C₂×#41×C₇₉	—	2	1	no	—
76	C₂×#41×C₇₉	—	2	1	no	—
77	C₂×#41×C₇₉	—	2	1	no	—
78	C₂×#41×C₇₉	—	2	1	no	—
79	C₂×#41×C₇₉	—	2	1	no	—
80	C₂×#41×C₇₉	—	2	1	no	—
81	C₂×#41×C₇₉	—	2	1	no	—
82	C₂×#41×C₇₉	—	2	1	no	—
83	C₂×#41×C₇₉	—	2	1	no	—
84	C₂×#41×C₇₉	—	2	1	no	—
85	C₂×#41×C₇₉	Q₈	1	2	yes	complemented
86	C₂×#41×C₇₉	C₂³	1	2	yes	—
87	C₂²×Q₈×C₇₉	Q₈	1	1	yes	characteristic, complemented
88	C₂²×D₄×C₇₉	—	2	1	no	—
89	C₂²×D₄×C₇₉	Q₈	1	1	yes	characteristic, complemented
90	C₂³×C₄×C₇₉	—	2	1	no	—
91	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₇₉	—	2	1	no	—
93	C₂×M₁₆×C₇₉	—	2	1	no	—
94	C₂×M₁₆×C₇₉	—	2	1	no	—
95	C₂×M₁₆×C₇₉	—	2	1	no	—
96	C₂×M₁₆×C₇₉	—	2	1	no	—
97	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
98	C₂²×C₈×C₇₉	—	2	1	no	—
99	#117×C₇₉	—	2	1	no	—
100	#117×C₇₉	—	2	1	no	—
101	#117×C₇₉	D₄	1	2	yes	—
102	#117×C₇₉	D₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
105	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
106	#104×C₇₉	—	2	8	no	—
107	C₂×Dic₁₅₈	—	2	8	no	—
108	C₂²×Dic₇₉	—	2	2	no	—
109	C₂²×Dic₇₉	—	2	2	no	—
110	C₂²×Dic₇₉	—	4	1	no	—
111	#11929608	—	2	2	no	—
112	#11929608	—	2	2	no	—
113	#11929608	—	4	1	no	—
114	#11929608	—	4	1	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₂×C₇₉⋊C₈	—	4	1	no	—
117	C₂×C₇₉⋊C₈	—	4	1	no	—
118	C₄⋊Dic₇₉	—	2	8	no	—
119	C₄⋊Dic₇₉	—	2	2	no	—
120	C₄⋊Dic₇₉	—	2	2	no	—
121	C₄⋊Dic₇₉	—	2	2	no	—
122	C₄⋊Dic₇₉	—	2	2	no	—
123	C₄⋊Dic₇₉	—	2	2	no	—
124	C₄⋊Dic₇₉	—	4	1	no	—
125	Dic₇₉⋊C₄	—	2	8	no	—
126	Dic₇₉⋊C₄	—	2	8	no	—
127	C₂²⋊Dic₇₉	—	2	2	no	—
128	C₂²⋊Dic₇₉	—	2	2	no	—
129	C₂²⋊Dic₇₉	—	2	2	no	—
130	C₂²⋊Dic₇₉	—	2	2	no	—
131	C₂²⋊Dic₇₉	—	4	1	no	—
132	C₂²⋊Dic₇₉	C₂×D₄	1	4	yes	—
133	C₄×Dic₇₉	—	2	2	no	—
134	C₄×Dic₇₉	—	2	2	no	—
135	C₄×Dic₇₉	—	2	2	no	—
136	C₄×Dic₇₉	—	2	2	no	—
137	C₄×Dic₇₉	—	4	1	no	—
138	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
139	C₂⁴×C₇₉	—	2	1	no	—
140	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
141	#41×C₇₉	—	2	2	no	—
142	#41×C₇₉	—	2	2	no	—
143	#41×C₇₉	—	2	2	no	—
144	#41×C₇₉	—	2	2	no	—
145	#41×C₇₉	—	2	2	no	—
146	#41×C₇₉	—	2	2	no	—
147	#41×C₇₉	—	2	2	no	—
148	#41×C₇₉	—	2	2	no	—
149	#41×C₇₉	—	4	1	no	—
150	#41×C₇₉	—	4	1	no	—
151	#41×C₇₉	—	4	1	no	—
152	#41×C₇₉	—	4	1	no	—
153	#41×C₇₉	—	4	1	no	—
154	#41×C₇₉	—	4	1	no	—
155	#41×C₇₉	—	4	1	no	—
156	#41×C₇₉	—	4	1	no	—
157	C₂×Q₈×C₇₉	—	2	1	no	—
158	C₂×Q₈×C₇₉	—	2	1	no	—
159	C₂×Q₈×C₇₉	—	2	1	no	—
160	C₂×Q₈×C₇₉	—	2	1	no	—
161	C₂×Q₈×C₇₉	—	2	1	no	—
162	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	—
163	C₂×D₄×C₇₉	—	2	2	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
165	C₂×D₄×C₇₉	—	2	1	no	—
166	C₂×D₄×C₇₉	—	2	1	no	—
167	C₂×D₄×C₇₉	—	2	1	no	—
168	C₂×D₄×C₇₉	—	2	1	no	—
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	—	4	1	no	—
171	C₂×D₄×C₇₉	—	4	1	no	—
172	C₂×D₄×C₇₉	—	4	1	no	—
173	C₂×D₄×C₇₉	—	4	1	no	—
174	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	2	no	—
177	C₂²×C₄×C₇₉	—	2	2	no	—
178	C₂²×C₄×C₇₉	—	2	2	no	—
179	C₂²×C₄×C₇₉	—	4	1	no	—
180	C₂²×C₄×C₇₉	—	4	1	no	—
181	C₂²×C₄×C₇₉	—	4	1	no	—
182	C₂²×C₄×C₇₉	—	4	1	no	—
183	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
191	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
192	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
193	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
194	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
195	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
196	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
197	M₁₆×C₇₉	—	2	2	no	—
198	M₁₆×C₇₉	—	2	2	no	—
199	M₁₆×C₇₉	—	4	1	no	—
200	M₁₆×C₇₉	—	4	1	no	—
201	C₂×C₈×C₇₉	—	2	2	no	—
202	C₂×C₈×C₇₉	—	4	1	no	—
203	C₂×C₈×C₇₉	—	4	1	no	—
204	C₄⋊C₄×C₇₉	—	2	2	no	—
205	C₄⋊C₄×C₇₉	—	2	2	no	—
206	C₂²⋊C₄×C₇₉	—	2	2	no	—
207	C₂²⋊C₄×C₇₉	—	2	2	no	—
208	C₄²×C₇₉	—	2	2	no	—
209	C₄²×C₇₉	C₂×D₄	1	4	yes	—
210	C₂³×C₇₉	—	2	2	no	—
211	C₂³×C₇₉	—	4	1	no	—
212	C₂³×C₇₉	—	4	1	no	—
213	C₂³×C₇₉	—	8	1	no	—
214	C₂³×C₇₉	—	8	2	no	—
215	C₂³×C₇₉	#120	1	1	yes	characteristic
216	C₂³×C₇₉	#120	1	1	yes	characteristic
217	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂³×C₇₉	#124	1	1	yes	characteristic
220	C₂³×C₇₉	#124	1	1	yes	characteristic
221	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
222	Q₈×C₇₉	—	2	2	no	—
223	Q₈×C₇₉	—	2	2	no	—
224	Q₈×C₇₉	—	4	1	no	—
225	Q₈×C₇₉	—	4	1	no	—
226	D₄×C₇₉	—	2	2	no	—
227	D₄×C₇₉	—	2	2	no	—
228	D₄×C₇₉	—	4	2	no	—
229	D₄×C₇₉	—	4	2	no	—
230	D₄×C₇₉	—	4	2	no	—
231	D₄×C₇₉	—	4	2	no	—
232	D₄×C₇₉	—	4	1	no	—
233	D₄×C₇₉	—	4	1	no	—
234	C₂×C₄×C₇₉	—	2	4	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	4	1	no	—
237	C₂×C₄×C₇₉	—	4	1	no	—
238	C₂×C₄×C₇₉	—	4	2	no	—
239	C₂×C₄×C₇₉	—	4	2	no	—
240	C₂×C₄×C₇₉	—	4	2	no	—
241	C₂×C₄×C₇₉	—	4	2	no	—
242	C₂×C₄×C₇₉	—	8	2	no	—
243	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
256	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
257	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
258	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
259	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
260	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
261	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
262	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
263	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
264	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
265	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
268	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
271	C₂×Dic₇₉	—	2	4	no	—
272	C₂×Dic₇₉	—	2	4	no	—
273	C₂×Dic₇₉	—	4	2	no	—
274	C₂×Dic₇₉	—	8	2	no	—
275	C₂×Dic₇₉	—	8	2	no	—
276	C₂×Dic₇₉	—	8	2	no	—
277	Dic₁₅₈	—	8	8	no	—
278	C₈×C₇₉	—	4	2	no	—
279	C₇₉⋊C₈	—	4	2	no	—
280	C₂²×C₇₉	—	4	1	no	—
281	C₂²×C₇₉	—	4	1	no	—
282	C₂²×C₇₉	—	4	1	no	—
283	C₂²×C₇₉	—	4	1	no	—
284	C₂²×C₇₉	—	4	1	no	—
285	C₂²×C₇₉	—	4	1	no	—
286	C₂²×C₇₉	—	4	1	no	—
287	C₂²×C₇₉	—	4	2	no	—
288	C₂²×C₇₉	—	8	2	no	—
289	C₂²×C₇₉	—	8	2	no	—
290	C₂²×C₇₉	—	8	2	no	—
291	C₂²×C₇₉	#393	1	1	yes	characteristic
292	C₂²×C₇₉	#393	1	1	yes	characteristic
293	C₂²×C₇₉	#393	1	1	yes	characteristic
294	C₂²×C₇₉	#393	1	1	yes	characteristic
295	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
296	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
297	C₂²×C₇₉	C₂×#124	1	1	yes	characteristic
298	C₄×C₇₉	—	4	4	no	—
299	C₄×C₇₉	—	4	2	no	—
300	C₄×C₇₉	#393	1	1	yes	characteristic
301	C₄×C₇₉	#393	1	1	yes	characteristic
302	C₄×C₇₉	#393	1	1	yes	characteristic
303	C₄×C₇₉	#393	1	1	yes	characteristic
304	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
306	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
307	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
308	Dic₇₉	—	4	4	no	—
309	Dic₇₉	—	4	4	no	—
310	Dic₇₉	—	8	2	no	—
311	#23472	—	79	1	no	maximal, Sylow
312	C₂×C₇₉	—	2	1	no	—
313	C₂×C₇₉	—	2	1	no	—
314	C₂×C₇₉	—	2	1	no	—
315	C₂×C₇₉	—	2	1	no	—
316	C₂×C₇₉	—	2	1	no	—
317	C₂×C₇₉	—	2	1	no	—
318	C₂×C₇₉	—	2	1	no	—
319	C₂×C₇₉	—	8	2	no	—
320	C₂×C₇₉	C₂×#393	1	1	yes	characteristic
321	#3458	—	79	1	no	—
322	C₂×#421	—	79	1	no	—
323	C₂×#421	D₇₉	1	1	yes	characteristic
324	C₂×#410	—	79	1	no	—
325	#2031	—	79	8	no	—
326	C₂×#344	—	79	1	no	—
327	#1733	—	79	1	no	—
328	C₂×H(3,ℤ/4)	—	79	1	no	—
329	C₇₉	#23472	1	1	yes	characteristic, complemented, Sylow
330	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
331	C₂²×M₁₆	—	79	1	no	—
332	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
333	#544	—	158	2	no	—
334	#544	—	158	2	no	—
335	#544	—	158	2	no	—
336	#543	—	158	2	no	—
337	#533	—	79	4	no	—
338	#533	—	158	2	no	—
339	#533	—	158	2	no	—
340	C₂×#117	—	79	1	no	—
341	C₂×#117	—	79	1	no	—
342	C₂×#117	—	79	1	no	—
343	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
344	#421	—	2	2	no	—
345	#421	—	2	2	no	—
346	#421	—	79	4	no	—
347	#421	—	158	2	no	—
348	C₂×#104	—	158	2	no	—
349	C₂×#104	C₂×D₇₉	1	4	yes	—
350	#410	—	79	4	no	—
351	#410	—	158	2	no	—
352	C₂×#99	—	158	2	no	—
353	#344	—	79	4	no	—
354	#339	—	79	4	no	—
355	H(3,ℤ/4)	—	79	4	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	Dic₁₅₈	1	2	yes	complemented
367	C₂×#41	C₂²×D₇₉	1	2	yes	—
368	C₂²×Q₈	Dic₁₅₈	1	1	yes	characteristic, complemented
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	Dic₁₅₈	1	1	yes	characteristic, complemented
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	79	2	no	—
379	C₂×M₁₆	—	158	1	no	—
380	C₂×M₁₆	—	158	1	no	—
381	C₂×M₁₆	—	158	1	no	—
382	C₂×M₁₆	—	158	1	no	—
383	C₂×M₁₆	—	158	1	no	—
384	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	158	1	no	—
387	C₄⋊Q₈	—	158	4	no	—
388	C₄⋊Q₈	—	158	4	no	—
389	C₄⋊Q₈	—	158	4	no	—
390	#125	—	158	4	no	—
391	#125	—	158	4	no	—
392	#125	—	158	4	no	—
393	C₂²⋊Q₈	—	158	8	no	—
394	C₂²⋊Q₈	—	158	8	no	—
395	C₂²⋊Q₈	—	158	8	no	—
396	C₄×Q₈	—	158	8	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	79	2	no	—
400	#117	—	79	2	no	—
401	#117	—	79	2	no	—
402	#117	—	79	2	no	—
403	#117	—	79	2	no	—
404	#117	—	158	1	no	—
405	#117	—	158	1	no	—
406	#117	—	158	1	no	—
407	#117	—	158	1	no	—
408	#117	—	158	1	no	—
409	#117	—	158	1	no	—
410	#117	—	158	1	no	—
411	#117	C₂²⋊D₇₉	1	2	yes	—
412	#117	C₂²⋊D₇₉	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	158	1	no	—
415	C₂×C₄⋊C₄	—	158	1	no	—
416	C₂×C₄⋊C₄	—	158	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	79	2	no	—
419	C₂×C₂²⋊C₄	—	158	1	no	—
420	C₂×C₂²⋊C₄	—	158	1	no	—
421	C₂×C₄²	—	79	2	no	—
422	C₂×C₄²	—	158	1	no	—
423	C₂×C₄²	—	158	1	no	—
424	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
425	#104	—	2	8	no	—
426	#104	—	158	8	no	—
427	#99	—	158	8	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	D₄×D₇₉	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	#41	—	4	1	no	—
441	#41	—	4	1	no	—
442	#41	—	4	1	no	—
443	#41	—	4	1	no	—
444	#41	—	4	1	no	—
445	#41	—	4	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	158	8	no	—
452	C₂×Q₈	C₂×Dic₁₅₈	1	2	yes	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	C₂×Dic₁₅₈	1	2	yes	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	316	1	no	—
474	C₂²×C₄	—	158	2	no	—
475	C₂²×C₄	—	158	2	no	—
476	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
478	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
482	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
483	C₂²×C₄	#11929623	1	1	yes	characteristic
484	C₂²×C₄	#11929623	1	1	yes	characteristic
485	C₂²×C₄	#11929623	1	1	yes	characteristic
486	C₂²×C₄	#11929623	1	1	yes	characteristic
487	C₂²×C₄	#11929624	1	1	yes	characteristic
488	C₂²×C₄	#11929624	1	1	yes	characteristic
489	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	4	1	no	—
493	M₁₆	—	4	1	no	—
494	M₁₆	—	316	1	no	—
495	M₁₆	—	316	1	no	—
496	M₁₆	—	158	2	no	—
497	M₁₆	—	158	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	4	1	no	—
500	C₂×C₈	—	4	1	no	—
501	C₂×C₈	—	316	1	no	—
502	C₂×C₈	—	316	1	no	—
503	C₂×C₈	—	158	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	316	1	no	—
507	C₄⋊C₄	—	158	8	no	—
508	C₄⋊C₄	—	158	8	no	—
509	C₄⋊C₄	—	158	8	no	—
510	C₄⋊C₄	—	158	2	no	—
511	C₄⋊C₄	—	158	2	no	—
512	C₄⋊C₄	—	158	2	no	—
513	C₄⋊C₄	—	158	2	no	—
514	C₄⋊C₄	—	158	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	316	1	no	—
518	C₂²⋊C₄	—	79	4	no	—
519	C₂²⋊C₄	—	158	2	no	—
520	C₂²⋊C₄	—	158	2	no	—
521	C₂²⋊C₄	—	158	2	no	—
522	C₂²⋊C₄	—	158	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	316	1	no	—
525	C₄²	—	79	4	no	—
526	C₄²	—	158	2	no	—
527	C₄²	—	158	2	no	—
528	C₄²	—	158	2	no	—
529	C₄²	—	158	2	no	—
530	C₄²	C₂×C₂²⋊D₇₉	1	4	yes	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	8	1	no	—
535	C₂³	—	8	2	no	—
536	C₂³	#14579129	1	1	yes	characteristic
537	C₂³	#14579129	1	1	yes	characteristic
538	C₂³	#14579138	1	1	yes	characteristic
539	C₂³	#14579138	1	1	yes	characteristic
540	C₂³	#14579147	1	1	yes	characteristic
541	C₂³	#14579147	1	1	yes	characteristic
542	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	632	8	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	316	2	no	—
566	C₂×C₄	—	632	2	no	—
567	C₂×C₄	—	632	2	no	—
568	C₂×C₄	—	632	2	no	—
569	C₂×C₄	—	158	4	no	—
570	C₂×C₄	—	158	4	no	—
571	C₂×C₄	#14579129	1	1	yes	characteristic
572	C₂×C₄	#14579129	1	1	yes	characteristic
573	C₂×C₄	#14579138	1	1	yes	characteristic
574	C₂×C₄	#14579138	1	1	yes	characteristic
575	C₂×C₄	#14579138	1	1	yes	characteristic
576	C₂×C₄	#14579138	1	1	yes	characteristic
577	C₂×C₄	#14579138	1	1	yes	characteristic
578	C₂×C₄	#14579138	1	1	yes	characteristic
579	C₂×C₄	#14579140	1	1	yes	characteristic
580	C₂×C₄	#14579140	1	1	yes	characteristic
581	C₂×C₄	#14579140	1	1	yes	characteristic
582	C₂×C₄	#14579140	1	1	yes	characteristic
583	C₂×C₄	#14579147	1	1	yes	characteristic
584	C₂×C₄	#14579147	1	1	yes	characteristic
585	C₂×C₄	#14579147	1	1	yes	characteristic
586	C₂×C₄	#14579147	1	1	yes	characteristic
587	C₂×C₄	#14579147	1	1	yes	characteristic
588	C₂×C₄	#14579147	1	1	yes	characteristic
589	C₂×C₄	#14579148	1	1	yes	characteristic
590	C₂×C₄	#14579148	1	1	yes	characteristic
591	C₂×C₄	#14579148	1	1	yes	characteristic
592	C₂×C₄	#14579148	1	1	yes	characteristic
593	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
594	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
595	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
596	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
597	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
598	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
599	C₈	—	4	2	no	—
600	C₈	—	316	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	#19098475	1	1	yes	characteristic
613	C₂²	#19098475	1	1	yes	characteristic
614	C₂²	#19098475	1	1	yes	characteristic
615	C₂²	#19098475	1	1	yes	characteristic
616	C₂²	C₂×#14579129	1	1	yes	characteristic
617	C₂²	C₂×#14579138	1	1	yes	characteristic
618	C₂²	C₂×#14579147	1	1	yes	characteristic
619	C₄	—	4	4	no	—
620	C₄	—	4	2	no	—
621	C₄	—	316	4	no	—
622	C₄	—	316	4	no	—
623	C₄	—	632	2	no	—
624	C₄	#19098475	1	1	yes	characteristic
625	C₄	#19098475	1	1	yes	characteristic
626	C₄	#19098475	1	1	yes	characteristic
627	C₄	#19098475	1	1	yes	characteristic
628	C₄	C₂×#14579138	1	1	yes	characteristic
629	C₄	C₂×#14579140	1	1	yes	characteristic
630	C₄	C₂×#14579147	1	1	yes	characteristic
631	C₄	C₂×#14579148	1	1	yes	characteristic
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	8	2	no	—
640	C₂	C₂×#19098475	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14579147
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#421×C₇₉	C₂
socle	C₂×C₇₉	C₂×#393
prime radical	C₂²×#41×C₇₉	C₂²
hypercenter	C₂×#421	D₇₉
hypocenter	C₇₉	#23472
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
1. #23776805	C₂	semidirect
4. #23764572	C₂	semidirect
5. C₂×#19098335	C₂	semidirect
6. #23763110	C₂	semidirect
7. C₂×#19098320	C₂	semidirect
14. #19099120	C₂²	semidirect
26. #19098335	C₂²	semidirect
27. #19098323	C₂²	semidirect
28. #19098320	C₂²	semidirect
85. C₂×#41×C₇₉	Q₈	semidirect
87. C₂²×Q₈×C₇₉	Q₈	semidirect
89. C₂²×D₄×C₇₉	Q₈	semidirect
329. C₇₉	#23472	semidirect
366. C₂×#41	Dic₁₅₈	semidirect
368. C₂²×Q₈	Dic₁₅₈	semidirect
370. C₂²×D₄	Dic₁₅₈	semidirect

Maximal subgroups

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

subgroup	index
#23776805	2
C₂×#19098580	2
C₂×#19098537	2
#23764572	2
C₂×#19098335	2
#23763110	2
C₂×#19098320	2
C₂×#421×C₇₉	2
#23472	79