Subgroups — C₇₃×#20944 #32930348

Order 18688.

1702 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3428	C₂	1	1	yes	maximal, characteristic
3	C₂×#421×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#419×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#1882	C₂	1	8	yes	maximal, complemented
7	C₇₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×#137×C₇₃	—	2	4	no	—
12	C₂×#137×C₇₃	—	2	2	no	—
13	C₂×#137×C₇₃	C₄	1	8	yes	complemented
14	C₂×#137×C₇₃	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₇₃	—	2	1	no	—
16	C₂²×SD₁₆×C₇₃	—	2	1	no	—
17	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
19	#520×C₇₃	—	2	2	no	—
20	#520×C₇₃	C₂²	1	4	yes	—
21	#519×C₇₃	—	2	1	no	—
22	#518×C₇₃	—	2	1	no	—
23	#518×C₇₃	—	2	2	no	—
24	C₄×#41×C₇₃	—	2	2	no	—
25	C₄×#41×C₇₃	—	2	2	no	—
26	C₂×#117×C₇₃	—	2	2	no	—
27	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
30	#421×C₇₃	—	2	4	no	—
31	C₂×#104×C₇₃	C₂²	1	4	yes	—
32	#419×C₇₃	—	2	2	no	—
33	#419×C₇₃	C₂²	1	4	yes	complemented
34	C₂×#103×C₇₃	—	2	2	no	—
35	#391×C₇₃	—	2	2	no	—
36	#391×C₇₃	C₂²	1	4	yes	complemented
37	#381×C₇₃	—	2	2	no	—
38	#343×C₇₃	C₂²	1	4	yes	complemented
39	#339×C₇₃	C₂²	1	4	yes	complemented
40	C₂×#41×C₇₃	—	2	1	no	—
41	C₂×#41×C₇₃	—	2	1	no	—
42	C₂×#41×C₇₃	—	2	2	no	—
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂×#41×C₇₃	C₂×C₄	1	4	yes	—
45	C₂×#41×C₇₃	D₄	1	4	yes	—
46	C₂×#41×C₇₃	D₄	1	2	yes	—
47	C₂×#41×C₇₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₇₃	—	2	1	no	—
49	C₂²×Q₈×C₇₃	—	2	2	no	—
50	C₂²×Q₈×C₇₃	—	2	1	no	—
51	C₂²×Q₈×C₇₃	—	2	1	no	—
52	C₂²×Q₈×C₇₃	—	2	1	no	—
53	C₂²×Q₈×C₇₃	—	2	1	no	—
54	C₂²×Q₈×C₇₃	—	2	2	no	—
55	C₂²×Q₈×C₇₃	—	2	2	no	—
56	C₂²×Q₈×C₇₃	C₂×C₄	1	4	yes	complemented
57	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₇₃	—	2	1	no	—
60	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₃	—	2	1	no	—
62	C₂³×C₄×C₇₃	—	2	1	no	—
63	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
64	#137×C₇₃	—	2	16	no	—
65	#137×C₇₃	—	2	8	no	—
66	#137×C₇₃	C₂×C₄	1	16	yes	complemented
67	C₂×Q₁₆×C₇₃	—	2	8	no	—
68	C₂×Q₁₆×C₇₃	—	2	4	no	—
69	C₂×SD₁₆×C₇₃	—	2	8	no	—
70	C₂×SD₁₆×C₇₃	—	2	4	no	—
71	C₂×M₁₆×C₇₃	—	2	2	no	—
72	C₂×M₁₆×C₇₃	—	2	1	no	—
73	C₂×M₁₆×C₇₃	—	2	1	no	—
74	C₂×M₁₆×C₇₃	—	2	2	no	—
75	C₂×M₁₆×C₇₃	—	2	2	no	—
76	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	complemented
77	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₇₃	—	2	1	no	—
80	C₂²×C₈×C₇₃	—	2	1	no	—
81	C₄×Q₈×C₇₃	—	2	4	no	—
82	C₄×Q₈×C₇₃	—	2	4	no	—
83	C₄×D₄×C₇₃	—	2	8	no	—
84	C₄×D₄×C₇₃	—	2	4	no	—
85	C₄×D₄×C₇₃	—	2	4	no	—
86	C₄×D₄×C₇₃	—	2	8	no	—
87	#117×C₇₃	—	2	4	no	—
88	#117×C₇₃	—	2	4	no	—
89	#117×C₇₃	—	2	1	no	—
90	#117×C₇₃	—	2	1	no	—
91	#117×C₇₃	—	2	1	no	—
92	#117×C₇₃	—	2	1	no	—
93	#117×C₇₃	—	2	1	no	—
94	#117×C₇₃	—	2	1	no	—
95	#117×C₇₃	—	2	4	no	—
96	#117×C₇₃	—	2	2	no	—
97	#117×C₇₃	—	2	2	no	—
98	#117×C₇₃	D₄	1	2	yes	—
99	#117×C₇₃	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
101	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
108	C₂×C₄²×C₇₃	—	2	4	no	—
109	C₂×C₄²×C₇₃	—	2	1	no	—
110	C₂×C₄²×C₇₃	D₄	1	2	yes	—
111	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
112	#104×C₇₃	—	2	8	no	—
113	#103×C₇₃	—	2	8	no	—
114	#95×C₇₃	—	2	8	no	—
115	C₂⁴×C₇₃	—	2	1	no	—
116	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
117	#41×C₇₃	—	2	4	no	—
118	#41×C₇₃	—	2	4	no	—
119	#41×C₇₃	—	2	4	no	—
120	#41×C₇₃	—	2	4	no	—
121	#41×C₇₃	—	2	4	no	—
122	#41×C₇₃	—	2	2	no	—
123	#41×C₇₃	—	2	2	no	—
124	#41×C₇₃	C₂²⋊C₄	1	8	yes	—
125	#41×C₇₃	C₂²×C₄	1	4	yes	—
126	#41×C₇₃	C₂×D₄	1	4	yes	—
127	C₂×Q₈×C₇₃	—	2	4	no	—
128	C₂×Q₈×C₇₃	—	2	1	no	—
129	C₂×Q₈×C₇₃	—	2	2	no	—
130	C₂×Q₈×C₇₃	—	2	2	no	—
131	C₂×Q₈×C₇₃	—	2	4	no	—
132	C₂×Q₈×C₇₃	—	2	4	no	—
133	C₂×Q₈×C₇₃	—	2	4	no	—
134	C₂×Q₈×C₇₃	—	2	4	no	—
135	C₂×Q₈×C₇₃	—	2	2	no	—
136	C₂×Q₈×C₇₃	—	2	2	no	—
137	C₂×Q₈×C₇₃	—	2	2	no	—
138	C₂×Q₈×C₇₃	—	2	2	no	—
139	C₂×Q₈×C₇₃	—	4	1	no	—
140	C₂×Q₈×C₇₃	—	4	1	no	—
141	C₂×Q₈×C₇₃	—	4	2	no	—
142	C₂×Q₈×C₇₃	—	4	2	no	—
143	C₂×Q₈×C₇₃	—	4	2	no	—
144	C₂×Q₈×C₇₃	—	4	2	no	—
145	C₂×Q₈×C₇₃	—	4	2	no	—
146	C₂×Q₈×C₇₃	C₂²⋊C₄	1	4	yes	—
147	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
148	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₇₃	—	2	4	no	—
150	C₂×D₄×C₇₃	—	2	2	no	—
151	C₂×D₄×C₇₃	—	2	4	no	—
152	C₂×D₄×C₇₃	—	2	2	no	—
153	C₂×D₄×C₇₃	—	2	1	no	—
154	C₂×D₄×C₇₃	—	2	2	no	—
155	C₂×D₄×C₇₃	C₂²⋊C₄	1	4	yes	—
156	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₇₃	—	2	1	no	—
158	C₂²×C₄×C₇₃	—	2	4	no	—
159	C₂²×C₄×C₇₃	—	2	2	no	—
160	C₂²×C₄×C₇₃	—	2	4	no	—
161	C₂²×C₄×C₇₃	—	2	2	no	—
162	C₂²×C₄×C₇₃	—	2	4	no	—
163	C₂²×C₄×C₇₃	—	2	2	no	—
164	C₂²×C₄×C₇₃	—	2	8	no	—
165	C₂²×C₄×C₇₃	—	2	2	no	—
166	C₂²×C₄×C₇₃	—	2	2	no	—
167	C₂²×C₄×C₇₃	—	4	1	no	—
168	C₂²×C₄×C₇₃	—	4	1	no	—
169	C₂²×C₄×C₇₃	—	4	2	no	—
170	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₃	#41	1	2	yes	—
179	C₂²×C₄×C₇₃	#41	1	2	yes	—
180	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
181	Q₁₆×C₇₃	—	2	16	no	—
182	SD₁₆×C₇₃	—	2	16	no	—
183	M₁₆×C₇₃	—	2	4	no	—
184	M₁₆×C₇₃	—	2	2	no	—
185	M₁₆×C₇₃	—	2	2	no	—
186	M₁₆×C₇₃	—	2	2	no	—
187	M₁₆×C₇₃	—	4	2	no	—
188	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
189	C₂×C₈×C₇₃	—	2	4	no	—
190	C₂×C₈×C₇₃	—	2	2	no	—
191	C₂×C₈×C₇₃	—	2	2	no	—
192	C₂×C₈×C₇₃	—	4	2	no	—
193	C₄⋊C₄×C₇₃	—	2	8	no	—
194	C₄⋊C₄×C₇₃	—	2	2	no	—
195	C₄⋊C₄×C₇₃	—	2	2	no	—
196	C₄⋊C₄×C₇₃	—	2	2	no	—
197	C₄⋊C₄×C₇₃	—	4	2	no	—
198	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
199	C₂²⋊C₄×C₇₃	—	2	8	no	—
200	C₂²⋊C₄×C₇₃	—	2	2	no	—
201	C₂²⋊C₄×C₇₃	—	2	2	no	—
202	C₂²⋊C₄×C₇₃	—	2	2	no	—
203	C₂²⋊C₄×C₇₃	—	2	2	no	—
204	C₂²⋊C₄×C₇₃	—	4	2	no	—
205	C₄²×C₇₃	—	2	8	no	—
206	C₄²×C₇₃	—	2	2	no	—
207	C₄²×C₇₃	—	2	2	no	—
208	C₄²×C₇₃	—	2	2	no	—
209	C₄²×C₇₃	—	2	2	no	—
210	C₄²×C₇₃	—	2	2	no	—
211	C₄²×C₇₃	—	2	2	no	—
212	C₂³×C₇₃	—	2	2	no	—
213	C₂³×C₇₃	—	2	4	no	—
214	C₂³×C₇₃	—	4	2	no	—
215	C₂³×C₇₃	—	8	2	no	—
216	C₂³×C₇₃	C₄×D₄	1	2	yes	—
217	C₂³×C₇₃	#120	1	1	yes	characteristic
218	C₂³×C₇₃	#120	1	1	yes	characteristic
219	C₂³×C₇₃	#121	1	2	yes	—
220	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₇₃	—	2	2	no	—
222	Q₈×C₇₃	—	2	4	no	—
223	Q₈×C₇₃	—	2	4	no	—
224	Q₈×C₇₃	—	2	4	no	—
225	Q₈×C₇₃	—	4	2	no	—
226	Q₈×C₇₃	—	4	2	no	—
227	Q₈×C₇₃	—	4	4	no	—
228	Q₈×C₇₃	—	4	4	no	—
229	Q₈×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
230	D₄×C₇₃	—	2	4	no	—
231	D₄×C₇₃	—	2	4	no	—
232	D₄×C₇₃	—	2	8	no	—
233	D₄×C₇₃	—	2	2	no	—
234	D₄×C₇₃	—	2	4	no	—
235	D₄×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₇₃	—	2	2	no	—
237	C₂×C₄×C₇₃	—	2	4	no	—
238	C₂×C₄×C₇₃	—	2	4	no	—
239	C₂×C₄×C₇₃	—	2	4	no	—
240	C₂×C₄×C₇₃	—	2	8	no	—
241	C₂×C₄×C₇₃	—	2	4	no	—
242	C₂×C₄×C₇₃	—	2	4	no	—
243	C₂×C₄×C₇₃	—	2	4	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	2	no	—
246	C₂×C₄×C₇₃	—	4	4	no	—
247	C₂×C₄×C₇₃	—	4	4	no	—
248	C₂×C₄×C₇₃	—	4	4	no	—
249	C₂×C₄×C₇₃	—	4	4	no	—
250	C₂×C₄×C₇₃	—	4	2	no	—
251	C₂×C₄×C₇₃	—	8	2	no	—
252	C₂×C₄×C₇₃	—	8	8	no	—
253	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
259	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
260	C₂×C₄×C₇₃	#121	1	2	yes	—
261	C₂×C₄×C₇₃	#121	1	2	yes	—
262	C₂×C₄×C₇₃	#121	1	2	yes	—
263	C₂×C₄×C₇₃	#123	1	2	yes	—
264	C₂×C₄×C₇₃	#123	1	2	yes	—
265	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
271	C₈×C₇₃	—	2	4	no	—
272	C₈×C₇₃	—	4	2	no	—
273	C₂²×C₇₃	—	2	2	no	—
274	C₂²×C₇₃	—	2	2	no	—
275	C₂²×C₇₃	—	2	2	no	—
276	C₂²×C₇₃	—	2	4	no	—
277	C₂²×C₇₃	—	4	2	no	—
278	C₂²×C₇₃	—	4	2	no	—
279	C₂²×C₇₃	—	4	4	no	—
280	C₂²×C₇₃	—	8	4	no	—
281	C₂²×C₇₃	#386	1	2	yes	—
282	C₂²×C₇₃	#386	1	2	yes	—
283	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
285	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
286	C₄×C₇₃	—	2	4	no	—
287	C₄×C₇₃	—	4	4	no	—
288	C₄×C₇₃	—	4	4	no	—
289	C₄×C₇₃	—	4	4	no	—
290	C₄×C₇₃	—	8	2	no	—
291	C₄×C₇₃	#386	1	2	yes	—
292	C₄×C₇₃	#386	1	2	yes	—
293	C₄×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
296	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
297	#20944	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂×C₇₃	—	2	1	no	—
299	C₂×C₇₃	—	2	2	no	—
300	C₂×C₇₃	—	2	1	no	—
301	C₂×C₇₃	—	2	2	no	—
302	C₂×C₇₃	—	4	4	no	—
303	C₂×C₇₃	C₂×#386	1	1	yes	characteristic
304	C₂×C₇₃	#3022	1	2	yes	—
305	C₂²×#137	C₂×C₇₃	1	1	yes	characteristic
306	#3428	C₂×C₇₃	1	1	yes	characteristic
307	C₂×#421	C₂×C₇₃	1	1	yes	characteristic
308	C₂×#419	C₂×C₇₃	1	1	yes	characteristic, complemented
309	#2310	C₂×C₇₃	1	1	yes	characteristic, complemented
310	#1882	C₂×C₇₃	1	8	yes	complemented
311	#1742	C₂×C₇₃	1	1	yes	characteristic, complemented
312	#1733	C₂×C₇₃	1	1	yes	characteristic, complemented
313	C₇₃	#20944	1	1	yes	characteristic, direct product factor, Sylow
314	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
315	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
316	C₂×#137	—	2	4	no	—
317	C₂×#137	—	2	2	no	—
318	C₂×#137	C₄×C₇₃	1	8	yes	complemented
319	C₂×#137	C₂²×C₇₃	1	4	yes	—
320	C₂²×Q₁₆	—	2	1	no	—
321	C₂²×SD₁₆	—	2	1	no	—
322	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
323	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
324	#520	—	2	2	no	—
325	#520	C₂²×C₇₃	1	4	yes	—
326	#519	—	2	1	no	—
327	#518	—	2	1	no	—
328	#518	—	2	2	no	—
329	C₄×#41	—	2	2	no	—
330	C₄×#41	—	2	2	no	—
331	C₂×#117	—	2	2	no	—
332	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
333	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
334	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
335	#421	—	2	4	no	—
336	C₂×#104	C₂²×C₇₃	1	4	yes	—
337	#419	—	2	2	no	—
338	#419	C₂²×C₇₃	1	4	yes	complemented
339	C₂×#103	—	2	2	no	—
340	#391	—	2	2	no	—
341	#391	C₂²×C₇₃	1	4	yes	complemented
342	#381	—	2	2	no	—
343	#343	C₂²×C₇₃	1	4	yes	complemented
344	#339	C₂²×C₇₃	1	4	yes	complemented
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	C₂×C₄×C₇₃	1	4	yes	—
350	C₂×#41	D₄×C₇₃	1	4	yes	—
351	C₂×#41	D₄×C₇₃	1	2	yes	—
352	C₂×#41	C₂³×C₇₃	1	2	yes	—
353	C₂²×Q₈	—	2	1	no	—
354	C₂²×Q₈	—	2	2	no	—
355	C₂²×Q₈	—	2	1	no	—
356	C₂²×Q₈	—	2	1	no	—
357	C₂²×Q₈	—	2	2	no	—
358	C₂²×Q₈	—	2	1	no	—
359	C₂²×Q₈	—	2	1	no	—
360	C₂²×Q₈	—	2	2	no	—
361	C₂²×Q₈	C₂×C₄×C₇₃	1	4	yes	complemented
362	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
363	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
369	#137	—	2	16	no	—
370	#137	—	2	8	no	—
371	#137	C₂×C₄×C₇₃	1	16	yes	complemented
372	C₂×Q₁₆	—	2	8	no	—
373	C₂×Q₁₆	—	2	4	no	—
374	C₂×SD₁₆	—	2	8	no	—
375	C₂×SD₁₆	—	2	4	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	C₂×C₄×C₇₃	1	4	yes	complemented
382	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
383	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₄×Q₈	—	2	4	no	—
387	C₄×Q₈	—	2	4	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	8	no	—
392	#117	—	2	4	no	—
393	#117	—	2	4	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	4	no	—
401	#117	—	2	2	no	—
402	#117	—	2	2	no	—
403	#117	D₄×C₇₃	1	2	yes	—
404	#117	C₂³×C₇₃	1	2	yes	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
413	C₂×C₄²	—	2	4	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	D₄×C₇₃	1	2	yes	—
416	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
417	#104	—	2	8	no	—
418	#103	—	2	8	no	—
419	#95	—	2	8	no	—
420	C₂⁴	—	2	1	no	—
421	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	C₂²⋊C₄×C₇₃	1	8	yes	—
430	#41	C₂²×C₄×C₇₃	1	4	yes	—
431	#41	C₂×D₄×C₇₃	1	4	yes	—
432	C₂×Q₈	—	2	4	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	—	4	1	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	—	4	2	no	—
448	C₂×Q₈	—	4	2	no	—
449	C₂×Q₈	—	4	2	no	—
450	C₂×Q₈	—	4	2	no	—
451	C₂×Q₈	C₂²⋊C₄×C₇₃	1	4	yes	—
452	C₂×Q₈	C₂²×C₄×C₇₃	1	4	yes	—
453	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	C₂²⋊C₄×C₇₃	1	4	yes	—
461	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
476	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
477	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
480	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
483	C₂²×C₄	#41×C₇₃	1	2	yes	—
484	C₂²×C₄	#41×C₇₃	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
486	Q₁₆	—	2	16	no	—
487	SD₁₆	—	2	16	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	4	2	no	—
493	M₁₆	C₂²×C₄×C₇₃	1	4	yes	—
494	C₂×C₈	—	2	4	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	4	2	no	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₄²	—	2	8	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	8	2	no	—
521	C₂³	C₄×D₄×C₇₃	1	2	yes	—
522	C₂³	#120×C₇₃	1	1	yes	characteristic
523	C₂³	#120×C₇₃	1	1	yes	characteristic
524	C₂³	#121×C₇₃	1	2	yes	—
525	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
526	Q₈	—	2	4	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	4	4	no	—
531	Q₈	—	4	4	no	—
532	Q₈	—	4	2	no	—
533	Q₈	—	4	2	no	—
534	Q₈	C₂×C₂²⋊C₄×C₇₃	1	4	yes	—
535	D₄	—	2	8	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	2	2	no	—
540	D₄	C₂×C₂²⋊C₄×C₇₃	1	4	yes	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	8	no	—
558	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
559	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
560	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
561	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
562	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
563	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
564	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
565	C₂×C₄	#121×C₇₃	1	2	yes	—
566	C₂×C₄	#121×C₇₃	1	2	yes	—
567	C₂×C₄	#121×C₇₃	1	2	yes	—
568	C₂×C₄	#123×C₇₃	1	2	yes	—
569	C₂×C₄	#123×C₇₃	1	2	yes	—
570	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
574	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
576	C₈	—	2	4	no	—
577	C₈	—	4	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	8	4	no	—
586	C₂²	#386×C₇₃	1	2	yes	—
587	C₂²	#386×C₇₃	1	2	yes	—
588	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
589	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
590	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
591	C₄	—	2	4	no	—
592	C₄	—	4	4	no	—
593	C₄	—	4	4	no	—
594	C₄	—	4	4	no	—
595	C₄	—	8	2	no	—
596	C₄	#386×C₇₃	1	2	yes	—
597	C₄	#386×C₇₃	1	2	yes	—
598	C₄	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
599	C₄	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
600	C₄	C₂×#121×C₇₃	1	1	yes	characteristic
601	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	2	1	no	—
606	C₂	—	4	4	no	—
607	C₂	C₂×#386×C₇₃	1	1	yes	characteristic
608	C₂	C₇₃×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#419×C₇₃	C₂	semidirect
5. C₇₃×#2310	C₂	semidirect
6. C₇₃×#1882	C₂	semidirect
7. C₇₃×#1742	C₂	semidirect
8. C₇₃×#1733	C₂	semidirect
13. C₂×#137×C₇₃	C₄	semidirect
33. #419×C₇₃	C₂²	semidirect
36. #391×C₇₃	C₂²	semidirect
38. #343×C₇₃	C₂²	semidirect
39. #339×C₇₃	C₂²	semidirect
56. C₂²×Q₈×C₇₃	C₂×C₄	semidirect
66. #137×C₇₃	C₂×C₄	semidirect
76. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
297. #20944	C₇₃	direct (N × H)
308. C₂×#419	C₂×C₇₃	semidirect
309. #2310	C₂×C₇₃	semidirect
310. #1882	C₂×C₇₃	semidirect
311. #1742	C₂×C₇₃	semidirect
312. #1733	C₂×C₇₃	semidirect
313. C₇₃	#20944	direct (N × H)
318. C₂×#137	C₄×C₇₃	semidirect
338. #419	C₂²×C₇₃	semidirect
341. #391	C₂²×C₇₃	semidirect
343. #343	C₂²×C₇₃	semidirect
344. #339	C₂²×C₇₃	semidirect
361. C₂²×Q₈	C₂×C₄×C₇₃	semidirect
371. #137	C₂×C₄×C₇₃	semidirect
381. C₂×M₁₆	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₇₃	2
C₇₃×#3428	2
C₂×#421×C₇₃	2
C₂×#419×C₇₃	2
C₇₃×#2310	2
C₇₃×#1882	2
C₇₃×#1742	2
C₇₃×#1733	2
#20944	73

Subgroups — C73×#20944 #32930348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#20944 #32930348