Subgroups — C₇₃×#18792 #32928196

Order 18688.

1064 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#459×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1628	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1625	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1624	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1622	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
13	C₂²×D₈×C₇₃	—	2	1	no	—
14	#556×C₇₃	C₂²	1	1	yes	characteristic, complemented
15	#555×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	#554×C₇₃	C₂²	1	1	yes	characteristic, complemented
17	#553×C₇₃	—	2	1	no	—
18	#552×C₇₃	—	2	1	no	—
19	#552×C₇₃	—	2	1	no	—
20	#551×C₇₃	—	2	2	no	—
21	#547×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#546×C₇₃	—	2	1	no	—
23	#533×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
25	#529×C₇₃	—	2	2	no	—
26	#529×C₇₃	—	2	1	no	—
27	#525×C₇₃	—	2	1	no	—
28	C₄×#41×C₇₃	—	2	1	no	—
29	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₃	—	2	1	no	—
32	#492×C₇₃	C₂²	1	2	yes	complemented
33	#486×C₇₃	C₂²	1	2	yes	complemented
34	#460×C₇₃	—	2	2	no	—
35	#460×C₇₃	—	2	1	no	—
36	#460×C₇₃	C₂²	1	2	yes	complemented
37	#459×C₇₃	—	2	1	no	—
38	#459×C₇₃	—	2	1	no	—
39	#459×C₇₃	—	2	1	no	—
40	#459×C₇₃	C₂²	1	2	yes	—
41	#459×C₇₃	C₂²	1	2	yes	—
42	#459×C₇₃	C₂²	1	2	yes	complemented
43	#450×C₇₃	—	2	2	no	—
44	#431×C₇₃	C₂²	1	1	yes	characteristic
45	#423×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
47	#418×C₇₃	—	2	1	no	—
48	C₂×#102×C₇₃	—	2	1	no	—
49	#333×C₇₃	C₂²	1	2	yes	complemented
50	#332×C₇₃	C₂²	1	2	yes	complemented
51	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
52	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
53	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
54	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
55	C₂×#41×C₇₃	—	2	1	no	—
56	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₇₃	—	2	1	no	—
58	C₂²×D₄×C₇₃	—	2	1	no	—
59	C₂²×D₄×C₇₃	—	2	1	no	—
60	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₃	—	2	1	no	—
62	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
63	C₂×SD₁₆×C₇₃	—	2	2	no	—
64	C₂×SD₁₆×C₇₃	—	2	4	no	—
65	C₂×D₈×C₇₃	—	2	2	no	—
66	C₂×D₈×C₇₃	—	2	2	no	—
67	C₂×D₈×C₇₃	—	2	2	no	—
68	C₂×D₈×C₇₃	—	4	4	no	—
69	C₂×M₁₆×C₇₃	—	2	1	no	—
70	C₂²×C₈×C₇₃	—	2	1	no	—
71	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
73	#127×C₇₃	—	2	1	no	—
74	#127×C₇₃	—	2	1	no	—
75	#127×C₇₃	—	2	1	no	—
76	#127×C₇₃	C₂³	1	2	yes	—
77	#126×C₇₃	—	2	2	no	—
78	#126×C₇₃	—	2	2	no	—
79	#126×C₇₃	—	2	2	no	—
80	#125×C₇₃	—	2	2	no	—
81	#125×C₇₃	—	2	1	no	—
82	#125×C₇₃	—	2	1	no	—
83	#124×C₇₃	—	2	2	no	—
84	#124×C₇₃	—	2	1	no	—
85	#123×C₇₃	—	2	2	no	—
86	#123×C₇₃	—	2	2	no	—
87	#123×C₇₃	—	2	2	no	—
88	#123×C₇₃	—	2	2	no	—
89	C₂²⋊Q₈×C₇₃	—	2	1	no	—
90	C₂²⋊Q₈×C₇₃	—	2	1	no	—
91	C₂²⋊Q₈×C₇₃	—	2	2	no	—
92	C₂²⋊Q₈×C₇₃	—	2	1	no	—
93	C₂²⋊Q₈×C₇₃	—	2	1	no	—
94	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
95	#121×C₇₃	—	2	2	no	—
96	#121×C₇₃	—	2	1	no	—
97	#121×C₇₃	—	2	1	no	—
98	#121×C₇₃	—	2	1	no	—
99	#120×C₇₃	—	2	2	no	—
100	C₄×Q₈×C₇₃	—	2	1	no	—
101	C₄×Q₈×C₇₃	—	2	1	no	—
102	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
103	C₄×Q₈×C₇₃	D₄	1	2	yes	—
104	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₇₃	—	2	2	no	—
106	C₄×D₄×C₇₃	—	2	2	no	—
107	C₄×D₄×C₇₃	—	2	2	no	—
108	C₄×D₄×C₇₃	—	2	1	no	—
109	C₄×D₄×C₇₃	—	2	1	no	—
110	C₄×D₄×C₇₃	—	2	1	no	—
111	C₄×D₄×C₇₃	—	2	1	no	—
112	C₄×D₄×C₇₃	—	2	1	no	—
113	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
114	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
115	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
116	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
118	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
119	#117×C₇₃	—	2	2	no	—
120	#117×C₇₃	—	2	2	no	—
121	#117×C₇₃	—	2	2	no	—
122	#117×C₇₃	—	2	1	no	—
123	#117×C₇₃	—	2	1	no	—
124	#117×C₇₃	—	2	1	no	—
125	#117×C₇₃	—	2	1	no	—
126	#117×C₇₃	—	2	1	no	—
127	#117×C₇₃	D₄	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
133	C₂×C₄²×C₇₃	—	2	2	no	—
134	C₂×C₄²×C₇₃	—	2	1	no	—
135	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₃	—	2	1	no	—
137	C₄⋊C₈×C₇₃	—	2	1	no	—
138	C₄⋊C₈×C₇₃	—	2	1	no	—
139	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
140	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
141	#102×C₇₃	—	2	2	no	—
142	#102×C₇₃	—	2	2	no	—
143	#102×C₇₃	—	2	2	no	—
144	#102×C₇₃	—	2	2	no	—
145	#102×C₇₃	—	2	4	no	—
146	C₂²⋊C₈×C₇₃	—	2	1	no	—
147	C₄×C₈×C₇₃	C₂³	1	2	yes	—
148	C₂⁴×C₇₃	—	2	1	no	—
149	C₂⁴×C₇₃	—	4	1	no	—
150	#41×C₇₃	—	2	2	no	—
151	#41×C₇₃	—	2	2	no	—
152	#41×C₇₃	—	4	2	no	—
153	#41×C₇₃	—	4	2	no	—
154	C₂×Q₈×C₇₃	—	2	1	no	—
155	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₇₃	—	2	2	no	—
158	C₂×D₄×C₇₃	—	2	2	no	—
159	C₂×D₄×C₇₃	—	2	1	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	1	no	—
162	C₂×D₄×C₇₃	—	2	2	no	—
163	C₂×D₄×C₇₃	—	2	2	no	—
164	C₂×D₄×C₇₃	—	2	2	no	—
165	C₂×D₄×C₇₃	—	4	1	no	—
166	C₂×D₄×C₇₃	—	4	2	no	—
167	C₂×D₄×C₇₃	—	4	2	no	—
168	C₂×D₄×C₇₃	—	4	1	no	—
169	C₂×D₄×C₇₃	—	4	1	no	—
170	C₂×D₄×C₇₃	—	4	1	no	—
171	C₂×D₄×C₇₃	—	4	2	no	—
172	C₂×D₄×C₇₃	—	4	2	no	—
173	C₂×D₄×C₇₃	—	8	2	no	—
174	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	—	2	2	no	—
178	C₂²×C₄×C₇₃	—	2	1	no	—
179	C₂²×C₄×C₇₃	—	2	2	no	—
180	C₂²×C₄×C₇₃	—	2	1	no	—
181	C₂²×C₄×C₇₃	—	2	1	no	—
182	C₂²×C₄×C₇₃	—	2	1	no	—
183	C₂²×C₄×C₇₃	—	2	1	no	—
184	C₂²×C₄×C₇₃	—	2	1	no	—
185	C₂²×C₄×C₇₃	—	2	1	no	—
186	C₂²×C₄×C₇₃	—	2	1	no	—
187	C₂²×C₄×C₇₃	—	4	2	no	—
188	C₂²×C₄×C₇₃	—	4	2	no	—
189	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
192	SD₁₆×C₇₃	—	4	4	no	—
193	SD₁₆×C₇₃	—	8	4	no	—
194	D₈×C₇₃	—	4	4	no	—
195	D₈×C₇₃	—	4	4	no	—
196	D₈×C₇₃	—	4	4	no	—
197	M₁₆×C₇₃	—	4	2	no	—
198	C₂×C₈×C₇₃	—	2	2	no	—
199	C₂×C₈×C₇₃	—	2	2	no	—
200	C₂×C₈×C₇₃	—	2	2	no	—
201	C₂×C₈×C₇₃	—	4	2	no	—
202	C₄⋊C₄×C₇₃	—	2	2	no	—
203	C₄⋊C₄×C₇₃	—	2	2	no	—
204	C₄⋊C₄×C₇₃	—	2	2	no	—
205	C₄⋊C₄×C₇₃	—	2	2	no	—
206	C₄⋊C₄×C₇₃	—	2	1	no	—
207	C₄⋊C₄×C₇₃	—	2	2	no	—
208	C₄⋊C₄×C₇₃	—	2	1	no	—
209	C₄⋊C₄×C₇₃	—	2	2	no	—
210	C₄⋊C₄×C₇₃	—	2	1	no	—
211	C₄⋊C₄×C₇₃	—	2	1	no	—
212	C₄⋊C₄×C₇₃	—	2	1	no	—
213	C₄⋊C₄×C₇₃	—	2	1	no	—
214	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
215	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
218	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
219	C₂²⋊C₄×C₇₃	—	2	2	no	—
220	C₂²⋊C₄×C₇₃	—	2	2	no	—
221	C₂²⋊C₄×C₇₃	—	2	2	no	—
222	C₂²⋊C₄×C₇₃	—	2	2	no	—
223	C₂²⋊C₄×C₇₃	—	2	2	no	—
224	C₂²⋊C₄×C₇₃	—	2	2	no	—
225	C₂²⋊C₄×C₇₃	—	2	1	no	—
226	C₂²⋊C₄×C₇₃	—	2	2	no	—
227	C₂²⋊C₄×C₇₃	—	2	1	no	—
228	C₂²⋊C₄×C₇₃	—	2	1	no	—
229	C₂²⋊C₄×C₇₃	—	2	1	no	—
230	C₂²⋊C₄×C₇₃	—	2	1	no	—
231	C₂²⋊C₄×C₇₃	—	2	1	no	—
232	C₂²⋊C₄×C₇₃	—	2	1	no	—
233	C₄²×C₇₃	—	2	2	no	—
234	C₄²×C₇₃	—	2	2	no	—
235	C₄²×C₇₃	—	2	1	no	—
236	C₄²×C₇₃	—	2	2	no	—
237	C₄²×C₇₃	—	2	1	no	—
238	C₄²×C₇₃	—	2	1	no	—
239	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
242	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂³×C₇₃	—	2	1	no	—
244	C₂³×C₇₃	—	2	1	no	—
245	C₂³×C₇₃	—	2	1	no	—
246	C₂³×C₇₃	—	4	2	no	—
247	C₂³×C₇₃	—	4	2	no	—
248	C₂³×C₇₃	—	4	2	no	—
249	C₂³×C₇₃	—	8	1	no	—
250	C₂³×C₇₃	—	8	2	no	—
251	C₂³×C₇₃	—	8	2	no	—
252	C₂³×C₇₃	—	8	2	no	—
253	C₂³×C₇₃	#120	1	1	yes	characteristic
254	Q₈×C₇₃	—	2	1	no	—
255	Q₈×C₇₃	—	2	1	no	—
256	Q₈×C₇₃	—	4	2	no	—
257	Q₈×C₇₃	—	4	1	no	—
258	Q₈×C₇₃	—	4	1	no	—
259	D₄×C₇₃	—	2	1	no	—
260	D₄×C₇₃	—	2	1	no	—
261	D₄×C₇₃	—	2	1	no	—
262	D₄×C₇₃	—	2	1	no	—
263	D₄×C₇₃	—	2	1	no	—
264	D₄×C₇₃	—	4	2	no	—
265	D₄×C₇₃	—	4	4	no	—
266	D₄×C₇₃	—	4	4	no	—
267	D₄×C₇₃	—	4	2	no	—
268	D₄×C₇₃	—	4	2	no	—
269	D₄×C₇₃	—	4	2	no	—
270	D₄×C₇₃	—	4	2	no	—
271	D₄×C₇₃	—	4	2	no	—
272	D₄×C₇₃	—	8	2	no	—
273	D₄×C₇₃	—	8	2	no	—
274	D₄×C₇₃	—	8	2	no	—
275	D₄×C₇₃	—	8	2	no	—
276	D₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
277	C₂×C₄×C₇₃	—	2	1	no	—
278	C₂×C₄×C₇₃	—	2	1	no	—
279	C₂×C₄×C₇₃	—	2	1	no	—
280	C₂×C₄×C₇₃	—	2	1	no	—
281	C₂×C₄×C₇₃	—	2	1	no	—
282	C₂×C₄×C₇₃	—	2	1	no	—
283	C₂×C₄×C₇₃	—	2	2	no	—
284	C₂×C₄×C₇₃	—	2	2	no	—
285	C₂×C₄×C₇₃	—	2	1	no	—
286	C₂×C₄×C₇₃	—	4	1	no	—
287	C₂×C₄×C₇₃	—	4	4	no	—
288	C₂×C₄×C₇₃	—	4	2	no	—
289	C₂×C₄×C₇₃	—	4	1	no	—
290	C₂×C₄×C₇₃	—	4	1	no	—
291	C₂×C₄×C₇₃	—	4	1	no	—
292	C₂×C₄×C₇₃	—	4	1	no	—
293	C₂×C₄×C₇₃	—	4	1	no	—
294	C₂×C₄×C₇₃	—	4	1	no	—
295	C₂×C₄×C₇₃	—	4	2	no	—
296	C₂×C₄×C₇₃	—	4	2	no	—
297	C₂×C₄×C₇₃	—	4	2	no	—
298	C₂×C₄×C₇₃	—	8	1	no	—
299	C₂×C₄×C₇₃	—	8	2	no	—
300	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
301	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
302	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
303	C₂×C₄×C₇₃	#135	1	2	yes	—
304	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
305	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
308	C₈×C₇₃	—	4	2	no	—
309	C₈×C₇₃	—	4	2	no	—
310	C₈×C₇₃	—	4	2	no	—
311	C₂²×C₇₃	—	2	1	no	—
312	C₂²×C₇₃	—	2	1	no	—
313	C₂²×C₇₃	—	2	2	no	—
314	C₂²×C₇₃	—	4	1	no	—
315	C₂²×C₇₃	—	4	1	no	—
316	C₂²×C₇₃	—	4	1	no	—
317	C₂²×C₇₃	—	4	1	no	—
318	C₂²×C₇₃	—	4	1	no	—
319	C₂²×C₇₃	—	4	1	no	—
320	C₂²×C₇₃	—	4	1	no	—
321	C₂²×C₇₃	—	4	1	no	—
322	C₂²×C₇₃	—	8	4	no	—
323	C₂²×C₇₃	—	8	2	no	—
324	C₂²×C₇₃	—	8	2	no	—
325	C₂²×C₇₃	—	8	2	no	—
326	C₂²×C₇₃	—	16	4	no	—
327	C₂²×C₇₃	#449	1	2	yes	—
328	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
329	C₄×C₇₃	—	2	1	no	—
330	C₄×C₇₃	—	2	1	no	—
331	C₄×C₇₃	—	2	1	no	—
332	C₄×C₇₃	—	4	1	no	—
333	C₄×C₇₃	—	4	1	no	—
334	C₄×C₇₃	—	4	1	no	—
335	C₄×C₇₃	—	4	1	no	—
336	C₄×C₇₃	—	4	2	no	—
337	C₄×C₇₃	—	4	1	no	—
338	C₄×C₇₃	—	4	2	no	—
339	C₄×C₇₃	#449	1	2	yes	—
340	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
341	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₄×C₇₃	#575	1	1	yes	characteristic
344	#18792	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₇₃	—	2	2	no	—
346	C₂×C₇₃	—	4	2	no	—
347	C₂×C₇₃	—	8	1	no	—
348	C₂×C₇₃	—	8	1	no	—
349	C₂×C₇₃	—	16	2	no	—
350	C₂×C₇₃	C₂×#449	1	1	yes	characteristic
351	C₂×C₇₃	#3006	1	1	yes	characteristic
352	C₂×C₇₃	#3021	1	1	yes	characteristic
353	#3475	C₂×C₇₃	1	1	yes	characteristic, complemented
354	#3208	C₂×C₇₃	1	1	yes	characteristic, complemented
355	#3038	C₂×C₇₃	1	1	yes	characteristic, complemented
356	C₂×#459	C₂×C₇₃	1	1	yes	characteristic, complemented
357	#1628	C₂×C₇₃	1	2	yes	complemented
358	#1625	C₂×C₇₃	1	2	yes	complemented
359	#1624	C₂×C₇₃	1	2	yes	complemented
360	#1622	C₂×C₇₃	1	2	yes	complemented
361	#1550	C₂×C₇₃	1	1	yes	characteristic, complemented
362	#1486	C₂×C₇₃	1	1	yes	characteristic, complemented
363	#1477	C₂×C₇₃	1	1	yes	characteristic, complemented
364	C₇₃	#18792	1	1	yes	characteristic, direct product factor, Sylow
365	C₂×AGL(1,ℤ/8)	—	2	1	no	—
366	C₂²×D₈	—	2	1	no	—
367	#556	C₂²×C₇₃	1	1	yes	characteristic, complemented
368	#555	C₂²×C₇₃	1	1	yes	characteristic, complemented
369	#554	C₂²×C₇₃	1	1	yes	characteristic, complemented
370	#553	—	2	1	no	—
371	#552	—	2	1	no	—
372	#552	—	2	1	no	—
373	#551	—	2	2	no	—
374	#547	C₂²×C₇₃	1	1	yes	characteristic, complemented
375	#546	—	2	1	no	—
376	#533	C₂²×C₇₃	1	1	yes	characteristic
377	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
378	#529	—	2	2	no	—
379	#529	—	2	1	no	—
380	#525	—	2	1	no	—
381	C₄×#41	—	2	1	no	—
382	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
384	C₂×#117	—	2	1	no	—
385	#492	C₂²×C₇₃	1	2	yes	complemented
386	#486	C₂²×C₇₃	1	2	yes	complemented
387	#460	—	2	2	no	—
388	#460	—	2	1	no	—
389	#460	C₂²×C₇₃	1	2	yes	complemented
390	#459	—	2	1	no	—
391	#459	—	2	1	no	—
392	#459	—	2	1	no	—
393	#459	C₂²×C₇₃	1	2	yes	—
394	#459	C₂²×C₇₃	1	2	yes	—
395	#459	C₂²×C₇₃	1	2	yes	complemented
396	#450	—	2	2	no	—
397	#431	C₂²×C₇₃	1	1	yes	characteristic
398	#423	C₂²×C₇₃	1	1	yes	characteristic
399	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
400	#418	—	2	1	no	—
401	C₂×#102	—	2	1	no	—
402	#333	C₂²×C₇₃	1	2	yes	complemented
403	#332	C₂²×C₇₃	1	2	yes	complemented
404	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
405	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
406	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
407	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
408	C₂×#41	—	2	1	no	—
409	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
410	C₂²×D₄	—	2	1	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	AGL(1,ℤ/8)	—	4	4	no	—
416	C₂×SD₁₆	—	2	2	no	—
417	C₂×SD₁₆	—	2	4	no	—
418	C₂×D₈	—	2	2	no	—
419	C₂×D₈	—	2	2	no	—
420	C₂×D₈	—	2	2	no	—
421	C₂×D₈	—	4	4	no	—
422	C₂×M₁₆	—	2	1	no	—
423	C₂²×C₈	—	2	1	no	—
424	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
425	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
426	#127	—	2	1	no	—
427	#127	—	2	1	no	—
428	#127	—	2	1	no	—
429	#127	C₂³×C₇₃	1	2	yes	—
430	#126	—	2	2	no	—
431	#126	—	2	2	no	—
432	#126	—	2	2	no	—
433	#125	—	2	2	no	—
434	#125	—	2	1	no	—
435	#125	—	2	1	no	—
436	#124	—	2	2	no	—
437	#124	—	2	1	no	—
438	#123	—	2	2	no	—
439	#123	—	2	2	no	—
440	#123	—	2	2	no	—
441	#123	—	2	2	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	1	no	—
446	C₂²⋊Q₈	—	2	1	no	—
447	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
448	#121	—	2	2	no	—
449	#121	—	2	1	no	—
450	#121	—	2	1	no	—
451	#121	—	2	1	no	—
452	#120	—	2	2	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
456	C₄×Q₈	D₄×C₇₃	1	2	yes	—
457	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
467	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
468	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
469	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
470	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
471	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
472	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	#117	—	2	2	no	—
475	#117	—	2	1	no	—
476	#117	—	2	1	no	—
477	#117	—	2	1	no	—
478	#117	—	2	1	no	—
479	#117	—	2	1	no	—
480	#117	D₄×C₇₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	—	2	2	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₄²	—	2	2	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
489	C₄⋊C₈	—	2	1	no	—
490	C₄⋊C₈	—	2	1	no	—
491	C₄⋊C₈	—	2	1	no	—
492	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
493	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
494	#102	—	2	2	no	—
495	#102	—	2	2	no	—
496	#102	—	2	2	no	—
497	#102	—	2	2	no	—
498	#102	—	2	4	no	—
499	C₂²⋊C₈	—	2	1	no	—
500	C₄×C₈	C₂³×C₇₃	1	2	yes	—
501	C₂⁴	—	2	1	no	—
502	C₂⁴	—	4	1	no	—
503	#41	—	2	2	no	—
504	#41	—	2	2	no	—
505	#41	—	4	2	no	—
506	#41	—	4	2	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
509	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	1	no	—
522	C₂×D₄	—	4	1	no	—
523	C₂×D₄	—	4	1	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	—	8	2	no	—
527	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
528	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
529	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
545	SD₁₆	—	4	4	no	—
546	SD₁₆	—	8	4	no	—
547	D₈	—	4	4	no	—
548	D₈	—	4	4	no	—
549	D₈	—	4	4	no	—
550	M₁₆	—	4	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	2	2	no	—
553	C₂×C₈	—	2	2	no	—
554	C₂×C₈	—	4	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
568	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
569	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
570	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
571	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
593	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
594	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
595	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	2	no	—
602	C₂³	—	8	1	no	—
603	C₂³	—	8	2	no	—
604	C₂³	—	8	2	no	—
605	C₂³	—	8	2	no	—
606	C₂³	#120×C₇₃	1	1	yes	characteristic
607	Q₈	—	2	1	no	—
608	Q₈	—	2	1	no	—
609	Q₈	—	4	2	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	4	1	no	—
612	D₄	—	2	1	no	—
613	D₄	—	2	1	no	—
614	D₄	—	2	1	no	—
615	D₄	—	2	1	no	—
616	D₄	—	2	1	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	4	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	2	no	—
625	D₄	—	8	2	no	—
626	D₄	—	8	2	no	—
627	D₄	—	8	2	no	—
628	D₄	—	8	2	no	—
629	D₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	complemented
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	8	1	no	—
652	C₂×C₄	—	8	2	no	—
653	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
654	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
655	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
656	C₂×C₄	#135×C₇₃	1	2	yes	—
657	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
661	C₈	—	4	2	no	—
662	C₈	—	4	2	no	—
663	C₈	—	4	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	8	4	no	—
676	C₂²	—	8	2	no	—
677	C₂²	—	8	2	no	—
678	C₂²	—	8	2	no	—
679	C₂²	—	16	4	no	—
680	C₂²	#449×C₇₃	1	2	yes	—
681	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	#449×C₇₃	1	2	yes	—
693	C₄	C₂×#135×C₇₃	1	1	yes	characteristic
694	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
695	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
696	C₄	#575×C₇₃	1	1	yes	characteristic
697	C₂	—	2	2	no	—
698	C₂	—	4	2	no	—
699	C₂	—	8	1	no	—
700	C₂	—	8	1	no	—
701	C₂	—	16	2	no	—
702	C₂	C₂×#449×C₇₃	1	1	yes	characteristic
703	C₂	C₇₃×#3006	1	1	yes	characteristic
704	C₂	C₇₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3475	C₂	semidirect
2. C₇₃×#3208	C₂	semidirect
3. C₇₃×#3038	C₂	semidirect
4. C₂×#459×C₇₃	C₂	semidirect
5. C₇₃×#1628	C₂	semidirect
6. C₇₃×#1625	C₂	semidirect
7. C₇₃×#1624	C₂	semidirect
8. C₇₃×#1622	C₂	semidirect
9. C₇₃×#1550	C₂	semidirect
10. C₇₃×#1486	C₂	semidirect
11. C₇₃×#1477	C₂	semidirect
14. #556×C₇₃	C₂²	semidirect
15. #555×C₇₃	C₂²	semidirect
16. #554×C₇₃	C₂²	semidirect
21. #547×C₇₃	C₂²	semidirect
32. #492×C₇₃	C₂²	semidirect
33. #486×C₇₃	C₂²	semidirect
36. #460×C₇₃	C₂²	semidirect
42. #459×C₇₃	C₂²	semidirect
49. #333×C₇₃	C₂²	semidirect
50. #332×C₇₃	C₂²	semidirect
51. Q₈⋊C₈×C₇₃	C₂²	semidirect
52. D₄⋊C₈×C₇₃	C₂²	semidirect
53. D₄⋊C₈×C₇₃	C₂²	semidirect
54. D₄⋊C₈×C₇₃	C₂²	semidirect
276. D₄×C₇₃	AGL(1,ℤ/8)	semidirect
344. #18792	C₇₃	direct (N × H)
353. #3475	C₂×C₇₃	semidirect
354. #3208	C₂×C₇₃	semidirect
355. #3038	C₂×C₇₃	semidirect
356. C₂×#459	C₂×C₇₃	semidirect
357. #1628	C₂×C₇₃	semidirect
358. #1625	C₂×C₇₃	semidirect
359. #1624	C₂×C₇₃	semidirect
360. #1622	C₂×C₇₃	semidirect
361. #1550	C₂×C₇₃	semidirect
362. #1486	C₂×C₇₃	semidirect
363. #1477	C₂×C₇₃	semidirect
364. C₇₃	#18792	direct (N × H)
367. #556	C₂²×C₇₃	semidirect
368. #555	C₂²×C₇₃	semidirect
369. #554	C₂²×C₇₃	semidirect
374. #547	C₂²×C₇₃	semidirect
385. #492	C₂²×C₇₃	semidirect
386. #486	C₂²×C₇₃	semidirect
389. #460	C₂²×C₇₃	semidirect
395. #459	C₂²×C₇₃	semidirect
402. #333	C₂²×C₇₃	semidirect
403. #332	C₂²×C₇₃	semidirect
404. Q₈⋊C₈	C₂²×C₇₃	semidirect
405. D₄⋊C₈	C₂²×C₇₃	semidirect
406. D₄⋊C₈	C₂²×C₇₃	semidirect
407. D₄⋊C₈	C₂²×C₇₃	semidirect
629. D₄	AGL(1,ℤ/8)×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3475	2
C₇₃×#3208	2
C₇₃×#3038	2
C₂×#459×C₇₃	2
C₇₃×#1628	2
C₇₃×#1625	2
C₇₃×#1624	2
C₇₃×#1622	2
C₇₃×#1550	2
C₇₃×#1486	2
C₇₃×#1477	2
#18792	73

Subgroups — C73×#18792 #32928196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18792 #32928196