Subgroups — C₇₃×#25613 #32935017

Order 18688.

1116 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#497×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#487×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2001	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2000	C₂	1	2	yes	maximal
7	C₇₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1878	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
14	#542×C₇₃	—	2	4	no	—
15	#542×C₇₃	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#126×C₇₃	—	2	1	no	—
19	C₂×#124×C₇₃	—	2	1	no	—
20	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#123×C₇₃	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
25	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
29	#497×C₇₃	—	2	4	no	—
30	#487×C₇₃	—	2	4	no	—
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#103×C₇₃	C₂²	1	2	yes	—
33	C₂×#103×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
36	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
38	#398×C₇₃	—	2	1	no	—
39	#398×C₇₃	—	2	1	no	—
40	#397×C₇₃	—	2	1	no	—
41	#397×C₇₃	—	2	1	no	—
42	#391×C₇₃	C₂²	1	2	yes	—
43	#382×C₇₃	C₂²	1	1	yes	characteristic
44	#340×C₇₃	C₂²	1	2	yes	—
45	#340×C₇₃	C₂²	1	2	yes	—
46	#336×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	—	2	1	no	—
48	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	—	2	1	no	—
53	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₇₃	—	2	4	no	—
55	C₂×Q₁₆×C₇₃	—	2	4	no	—
56	C₂×Q₁₆×C₇₃	—	4	2	no	—
57	C₂×SD₁₆×C₇₃	—	2	4	no	—
58	C₂×SD₁₆×C₇₃	—	2	4	no	—
59	C₂×SD₁₆×C₇₃	—	4	2	no	—
60	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
62	C₄⋊Q₈×C₇₃	—	2	2	no	—
63	C₄⋊Q₈×C₇₃	—	2	2	no	—
64	C₄⋊Q₈×C₇₃	—	2	2	no	—
65	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
66	#126×C₇₃	—	2	8	no	—
67	#124×C₇₃	—	2	8	no	—
68	#124×C₇₃	—	2	2	no	—
69	#124×C₇₃	D₄	1	4	yes	—
70	#123×C₇₃	—	2	8	no	—
71	C₂²⋊Q₈×C₇₃	—	2	8	no	—
72	C₂²⋊Q₈×C₇₃	—	2	2	no	—
73	C₂²⋊Q₈×C₇₃	—	2	2	no	—
74	C₂²⋊Q₈×C₇₃	—	4	2	no	—
75	C₂²⋊Q₈×C₇₃	—	4	2	no	—
76	#121×C₇₃	—	2	2	no	—
77	#121×C₇₃	—	2	2	no	—
78	C₄×Q₈×C₇₃	—	2	2	no	—
79	C₄×Q₈×C₇₃	—	2	2	no	—
80	C₄×D₄×C₇₃	—	2	2	no	—
81	C₄×D₄×C₇₃	—	2	2	no	—
82	#117×C₇₃	—	2	2	no	—
83	#117×C₇₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
90	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₇₃	—	2	1	no	—
104	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
106	#103×C₇₃	—	2	4	no	—
107	#103×C₇₃	—	2	4	no	—
108	#103×C₇₃	—	4	2	no	—
109	#102×C₇₃	—	4	2	no	—
110	C₂²⋊C₈×C₇₃	—	2	4	no	—
111	#97×C₇₃	—	2	2	no	—
112	C₄×C₈×C₇₃	—	2	2	no	—
113	#95×C₇₃	—	2	1	no	—
114	#95×C₇₃	—	2	1	no	—
115	#95×C₇₃	—	2	2	no	—
116	#95×C₇₃	—	2	2	no	—
117	C₂⁴×C₇₃	—	2	1	no	—
118	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₇₃	—	2	4	no	—
120	C₂×Q₈×C₇₃	—	2	1	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	2	no	—
124	C₂×Q₈×C₇₃	—	2	2	no	—
125	C₂×Q₈×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	2	2	no	—
129	C₂×Q₈×C₇₃	—	8	2	no	—
130	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₇₃	—	2	4	no	—
132	C₂×D₄×C₇₃	—	2	1	no	—
133	C₂×D₄×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	2	no	—
135	C₂×D₄×C₇₃	—	8	2	no	—
136	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	1	no	—
139	C₂²×C₄×C₇₃	—	2	1	no	—
140	C₂²×C₄×C₇₃	—	2	4	no	—
141	C₂²×C₄×C₇₃	—	2	1	no	—
142	C₂²×C₄×C₇₃	—	2	1	no	—
143	C₂²×C₄×C₇₃	—	2	2	no	—
144	C₂²×C₄×C₇₃	—	2	2	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	8	2	no	—
148	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₇₃	—	4	8	no	—
155	SD₁₆×C₇₃	—	4	8	no	—
156	C₂×C₈×C₇₃	—	2	2	no	—
157	C₂×C₈×C₇₃	—	2	2	no	—
158	C₂×C₈×C₇₃	—	2	2	no	—
159	C₂×C₈×C₇₃	—	2	2	no	—
160	C₂×C₈×C₇₃	—	2	2	no	—
161	C₂×C₈×C₇₃	#41	1	4	yes	—
162	C₄⋊C₄×C₇₃	—	2	4	no	—
163	C₄⋊C₄×C₇₃	—	2	4	no	—
164	C₄⋊C₄×C₇₃	—	2	4	no	—
165	C₄⋊C₄×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	—	2	2	no	—
167	C₄⋊C₄×C₇₃	—	2	1	no	—
168	C₄⋊C₄×C₇₃	—	2	1	no	—
169	C₄⋊C₄×C₇₃	—	2	2	no	—
170	C₄⋊C₄×C₇₃	—	2	2	no	—
171	C₄⋊C₄×C₇₃	—	4	4	no	—
172	C₄⋊C₄×C₇₃	—	4	2	no	—
173	C₄⋊C₄×C₇₃	—	4	2	no	—
174	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
176	C₂²⋊C₄×C₇₃	—	2	4	no	—
177	C₂²⋊C₄×C₇₃	—	2	4	no	—
178	C₂²⋊C₄×C₇₃	—	2	4	no	—
179	C₂²⋊C₄×C₇₃	—	2	4	no	—
180	C₂²⋊C₄×C₇₃	—	2	4	no	—
181	C₂²⋊C₄×C₇₃	—	2	2	no	—
182	C₂²⋊C₄×C₇₃	—	2	2	no	—
183	C₂²⋊C₄×C₇₃	—	4	4	no	—
184	C₄²×C₇₃	—	2	4	no	—
185	C₄²×C₇₃	—	2	1	no	—
186	C₄²×C₇₃	—	2	1	no	—
187	C₄²×C₇₃	C₂×D₄	1	2	yes	—
188	C₄²×C₇₃	C₂×D₄	1	2	yes	—
189	C₂³×C₇₃	—	2	1	no	—
190	C₂³×C₇₃	—	2	2	no	—
191	C₂³×C₇₃	—	2	1	no	—
192	C₂³×C₇₃	—	2	1	no	—
193	C₂³×C₇₃	—	2	2	no	—
194	C₂³×C₇₃	—	2	2	no	—
195	C₂³×C₇₃	—	4	1	no	—
196	C₂³×C₇₃	—	4	1	no	—
197	C₂³×C₇₃	—	4	2	no	—
198	C₂³×C₇₃	—	4	2	no	—
199	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₇₃	—	2	4	no	—
201	Q₈×C₇₃	—	4	2	no	—
202	Q₈×C₇₃	—	4	2	no	—
203	Q₈×C₇₃	—	4	2	no	—
204	Q₈×C₇₃	—	4	2	no	—
205	Q₈×C₇₃	—	4	2	no	—
206	Q₈×C₇₃	—	8	4	no	—
207	D₄×C₇₃	—	2	4	no	—
208	D₄×C₇₃	—	4	2	no	—
209	D₄×C₇₃	—	8	4	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	1	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	1	no	—
217	C₂×C₄×C₇₃	—	2	2	no	—
218	C₂×C₄×C₇₃	—	2	1	no	—
219	C₂×C₄×C₇₃	—	2	1	no	—
220	C₂×C₄×C₇₃	—	2	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	4	1	no	—
223	C₂×C₄×C₇₃	—	4	1	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	—	4	2	no	—
228	C₂×C₄×C₇₃	—	4	2	no	—
229	C₂×C₄×C₇₃	—	4	2	no	—
230	C₂×C₄×C₇₃	—	4	2	no	—
231	C₂×C₄×C₇₃	—	4	2	no	—
232	C₂×C₄×C₇₃	—	4	2	no	—
233	C₂×C₄×C₇₃	—	4	2	no	—
234	C₂×C₄×C₇₃	—	8	4	no	—
235	C₂×C₄×C₇₃	#120	1	2	yes	—
236	C₂×C₄×C₇₃	#120	1	2	yes	—
237	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
240	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₇₃	—	2	4	no	—
242	C₈×C₇₃	—	4	2	no	—
243	C₂²×C₇₃	—	4	2	no	—
244	C₂²×C₇₃	—	4	1	no	—
245	C₂²×C₇₃	—	4	2	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	4	1	no	—
249	C₂²×C₇₃	—	4	1	no	—
250	C₂²×C₇₃	—	4	2	no	—
251	C₂²×C₇₃	—	8	2	no	—
252	C₂²×C₇₃	—	8	2	no	—
253	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₇₃	#532	1	1	yes	characteristic
255	C₂²×C₇₃	#535	1	1	yes	characteristic
256	C₂²×C₇₃	#577	1	2	yes	—
257	C₂²×C₇₃	#578	1	2	yes	—
258	C₄×C₇₃	—	2	2	no	—
259	C₄×C₇₃	—	2	2	no	—
260	C₄×C₇₃	—	4	1	no	—
261	C₄×C₇₃	—	4	2	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	—	4	2	no	—
264	C₄×C₇₃	—	4	2	no	—
265	C₄×C₇₃	—	4	1	no	—
266	C₄×C₇₃	—	8	2	no	—
267	C₄×C₇₃	—	8	2	no	—
268	C₄×C₇₃	#546	1	2	yes	—
269	C₄×C₇₃	#550	1	2	yes	—
270	#25613	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂×C₇₃	—	8	1	no	—
272	C₂×C₇₃	—	8	2	no	—
273	C₂×C₇₃	#2431	1	1	yes	characteristic
274	C₂×C₇₃	#3009	1	1	yes	characteristic
275	C₂×C₇₃	#3011	1	1	yes	characteristic
276	C₂×C₇₃	#3178	1	2	yes	—
277	C₂×C₇₃	#3225	1	2	yes	—
278	C₂×#542	C₂×C₇₃	1	1	yes	characteristic
279	C₂×#497	C₂×C₇₃	1	1	yes	characteristic, complemented
280	C₂×#487	C₂×C₇₃	1	1	yes	characteristic, complemented
281	#2621	C₂×C₇₃	1	1	yes	characteristic, complemented
282	#2001	C₂×C₇₃	1	2	yes	complemented
283	#2000	C₂×C₇₃	1	2	yes	—
284	#1993	C₂×C₇₃	1	1	yes	characteristic, complemented
285	#1958	C₂×C₇₃	1	1	yes	characteristic, complemented
286	#1878	C₂×C₇₃	1	2	yes	complemented
287	#1877	C₂×C₇₃	1	2	yes	complemented
288	#1750	C₂×C₇₃	1	1	yes	characteristic, complemented
289	C₇₃	#25613	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
291	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
292	#542	—	2	4	no	—
293	#542	—	2	4	no	—
294	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
296	C₂×#126	—	2	1	no	—
297	C₂×#124	—	2	1	no	—
298	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
299	C₂×#123	—	2	1	no	—
300	C₂×C₂²⋊Q₈	—	2	1	no	—
301	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
303	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
306	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
307	#497	—	2	4	no	—
308	#487	—	2	4	no	—
309	C₂×#103	C₂²×C₇₃	1	2	yes	—
310	C₂×#103	C₂²×C₇₃	1	2	yes	—
311	C₂×#103	C₂²×C₇₃	1	2	yes	—
312	C₂×#102	C₂²×C₇₃	1	2	yes	—
313	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
314	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
316	#398	—	2	1	no	—
317	#398	—	2	1	no	—
318	#397	—	2	1	no	—
319	#397	—	2	1	no	—
320	#391	C₂²×C₇₃	1	2	yes	—
321	#382	C₂²×C₇₃	1	1	yes	characteristic
322	#340	C₂²×C₇₃	1	2	yes	—
323	#340	C₂²×C₇₃	1	2	yes	—
324	#336	C₂²×C₇₃	1	2	yes	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
327	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
332	C₂×Q₁₆	—	2	4	no	—
333	C₂×Q₁₆	—	2	4	no	—
334	C₂×Q₁₆	—	4	2	no	—
335	C₂×SD₁₆	—	2	4	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	4	2	no	—
338	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
339	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
344	#126	—	2	8	no	—
345	#124	—	2	8	no	—
346	#124	—	2	2	no	—
347	#124	D₄×C₇₃	1	4	yes	—
348	#123	—	2	8	no	—
349	C₂²⋊Q₈	—	2	8	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	C₂²⋊Q₈	—	4	2	no	—
353	C₂²⋊Q₈	—	4	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
384	#103	—	2	4	no	—
385	#103	—	2	4	no	—
386	#103	—	4	2	no	—
387	#102	—	4	2	no	—
388	C₂²⋊C₈	—	2	4	no	—
389	#97	—	2	2	no	—
390	C₄×C₈	—	2	2	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	2	no	—
394	#95	—	2	2	no	—
395	C₂⁴	—	2	1	no	—
396	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	8	2	no	—
408	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	8	2	no	—
414	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	8	2	no	—
426	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
432	Q₁₆	—	4	8	no	—
433	SD₁₆	—	4	8	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	#41×C₇₃	1	4	yes	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
453	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	4	4	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	C₂×D₄×C₇₃	1	2	yes	—
466	C₄²	C₂×D₄×C₇₃	1	2	yes	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
478	Q₈	—	2	4	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	8	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	4	2	no	—
487	D₄	—	8	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	#120×C₇₃	1	2	yes	—
514	C₂×C₄	#120×C₇₃	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
518	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
519	C₈	—	2	4	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
532	C₂²	#532×C₇₃	1	1	yes	characteristic
533	C₂²	#535×C₇₃	1	1	yes	characteristic
534	C₂²	#577×C₇₃	1	2	yes	—
535	C₂²	#578×C₇₃	1	2	yes	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	8	2	no	—
545	C₄	—	8	2	no	—
546	C₄	#546×C₇₃	1	2	yes	—
547	C₄	#550×C₇₃	1	2	yes	—
548	C₂	—	8	1	no	—
549	C₂	—	8	2	no	—
550	C₂	C₇₃×#2431	1	1	yes	characteristic
551	C₂	C₇₃×#3009	1	1	yes	characteristic
552	C₂	C₇₃×#3011	1	1	yes	characteristic
553	C₂	C₇₃×#3178	1	2	yes	—
554	C₂	C₇₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#497×C₇₃	C₂	semidirect
3. C₂×#487×C₇₃	C₂	semidirect
4. C₇₃×#2621	C₂	semidirect
5. C₇₃×#2001	C₂	semidirect
7. C₇₃×#1993	C₂	semidirect
8. C₇₃×#1958	C₂	semidirect
9. C₇₃×#1878	C₂	semidirect
10. C₇₃×#1877	C₂	semidirect
11. C₇₃×#1750	C₂	semidirect
270. #25613	C₇₃	direct (N × H)
279. C₂×#497	C₂×C₇₃	semidirect
280. C₂×#487	C₂×C₇₃	semidirect
281. #2621	C₂×C₇₃	semidirect
282. #2001	C₂×C₇₃	semidirect
284. #1993	C₂×C₇₃	semidirect
285. #1958	C₂×C₇₃	semidirect
286. #1878	C₂×C₇₃	semidirect
287. #1877	C₂×C₇₃	semidirect
288. #1750	C₂×C₇₃	semidirect
289. C₇₃	#25613	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×#542×C₇₃	2
C₂×#497×C₇₃	2
C₂×#487×C₇₃	2
C₇₃×#2621	2
C₇₃×#2001	2
C₇₃×#2000	2
C₇₃×#1993	2
C₇₃×#1958	2
C₇₃×#1878	2
C₇₃×#1877	2
C₇₃×#1750	2
#25613	73

Subgroups — C73×#25613 #32935017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25613 #32935017