Subgroups — C₇₃×#60453 #32969857

Order 18688.

2722 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3449	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3063	C₂	1	8	yes	maximal, complemented
5	C₇₃×#3062	C₂	1	8	yes	maximal, complemented
6	C₇₃×#3054	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3050	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#416×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₇₃	C₂²	1	2	yes	—
11	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
12	#575×C₇₃	—	2	8	no	—
13	C₂×#137×C₇₃	C₂²	1	4	yes	complemented
14	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	4	yes	complemented
15	C₂×#135×C₇₃	C₂²	1	4	yes	—
16	C₂×#131×C₇₃	—	2	8	no	—
17	C₂×#131×C₇₃	C₂²	1	8	yes	complemented
18	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₇₃	C₂²	1	2	yes	complemented
22	#537×C₇₃	C₂²	1	8	yes	—
23	#536×C₇₃	—	2	2	no	—
24	#536×C₇₃	C₂²	1	4	yes	complemented
25	#535×C₇₃	—	2	2	no	—
26	#535×C₇₃	C₂²	1	4	yes	complemented
27	#534×C₇₃	—	2	4	no	—
28	#532×C₇₃	—	2	4	no	—
29	#525×C₇₃	—	2	4	no	—
30	#525×C₇₃	C₂²	1	8	yes	complemented
31	C₂×#117×C₇₃	C₂²	1	2	yes	—
32	#470×C₇₃	C₂²	1	8	yes	complemented
33	#469×C₇₃	C₂²	1	8	yes	complemented
34	#468×C₇₃	C₂²	1	16	yes	complemented
35	#467×C₇₃	C₂²	1	8	yes	complemented
36	#466×C₇₃	C₂²	1	8	yes	complemented
37	#465×C₇₃	C₂²	1	16	yes	complemented
38	#428×C₇₃	C₂²	1	8	yes	complemented
39	#427×C₇₃	C₂²	1	4	yes	complemented
40	#416×C₇₃	C₂²	1	4	yes	complemented
41	#416×C₇₃	C₂²	1	4	yes	complemented
42	#416×C₇₃	C₂²	1	8	yes	complemented
43	C₂×#103×C₇₃	C₂²	1	4	yes	complemented
44	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
45	C₂×#41×C₇₃	—	2	4	no	—
46	C₂×#41×C₇₃	—	2	2	no	—
47	C₂×#41×C₇₃	—	2	2	no	—
48	C₂×#41×C₇₃	—	2	4	no	—
49	C₂×#41×C₇₃	—	2	8	no	—
50	C₂×#41×C₇₃	—	2	8	no	—
51	C₂×#41×C₇₃	D₄	1	4	yes	—
52	C₂×#41×C₇₃	C₂³	1	4	yes	—
53	C₂×#41×C₇₃	C₂³	1	4	yes	—
54	C₂×#41×C₇₃	C₂³	1	4	yes	—
55	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₇₃	—	2	2	no	—
58	C₂²×D₄×C₇₃	D₄	1	2	yes	—
59	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₇₃	—	2	2	no	—
62	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
64	#137×C₇₃	—	2	16	no	—
65	AGL(1,ℤ/8)×C₇₃	—	2	16	no	—
66	#135×C₇₃	—	2	16	no	—
67	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
68	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
69	C₂×D₈×C₇₃	C₂³	1	4	yes	—
70	#131×C₇₃	—	2	32	no	—
71	C₂×M₁₆×C₇₃	—	2	8	no	—
72	C₂×M₁₆×C₇₃	D₄	1	8	yes	complemented
73	C₂×M₁₆×C₇₃	C₂³	1	8	yes	—
74	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
75	C₂²×C₈×C₇₃	—	2	4	no	—
76	C₂²×C₈×C₇₃	—	2	8	no	—
77	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
78	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₇₃	C₂³	1	8	yes	—
81	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₇₃	—	2	4	no	—
83	#127×C₇₃	—	2	4	no	—
84	#124×C₇₃	—	2	4	no	—
85	#124×C₇₃	—	2	4	no	—
86	#123×C₇₃	—	2	8	no	—
87	#123×C₇₃	—	2	8	no	—
88	C₂²⋊Q₈×C₇₃	—	2	8	no	—
89	C₂²⋊Q₈×C₇₃	C₂³	1	16	yes	—
90	#121×C₇₃	—	2	8	no	—
91	#121×C₇₃	—	2	16	no	—
92	#121×C₇₃	C₂³	1	16	yes	—
93	#120×C₇₃	—	2	8	no	—
94	#120×C₇₃	—	2	8	no	—
95	C₄×D₄×C₇₃	—	2	16	no	—
96	#117×C₇₃	—	2	2	no	—
97	#117×C₇₃	—	2	2	no	—
98	#117×C₇₃	C₂³	1	4	yes	—
99	#117×C₇₃	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
102	C₂×C₄²×C₇₃	—	2	2	no	—
103	#107×C₇₃	C₂³	1	8	yes	—
104	#106×C₇₃	C₂³	1	8	yes	—
105	#103×C₇₃	C₂³	1	8	yes	—
106	#103×C₇₃	C₂³	1	8	yes	—
107	#102×C₇₃	C₂³	1	8	yes	—
108	#102×C₇₃	C₂³	1	8	yes	—
109	C₂⁴×C₇₃	—	2	2	no	—
110	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
111	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
112	#41×C₇₃	—	2	16	no	—
113	#41×C₇₃	—	2	8	no	—
114	#41×C₇₃	—	2	8	no	—
115	#41×C₇₃	—	2	8	no	—
116	#41×C₇₃	—	2	8	no	—
117	#41×C₇₃	—	2	8	no	—
118	#41×C₇₃	—	2	8	no	—
119	#41×C₇₃	—	4	8	no	—
120	#41×C₇₃	—	4	8	no	—
121	C₂×Q₈×C₇₃	—	2	4	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	4	no	—
124	C₂×Q₈×C₇₃	—	2	4	no	—
125	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
127	C₂×D₄×C₇₃	—	2	8	no	—
128	C₂×D₄×C₇₃	—	2	4	no	—
129	C₂×D₄×C₇₃	—	2	4	no	—
130	C₂×D₄×C₇₃	—	2	16	no	—
131	C₂×D₄×C₇₃	—	2	4	no	—
132	C₂×D₄×C₇₃	—	2	4	no	—
133	C₂×D₄×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	4	no	—
135	C₂×D₄×C₇₃	—	4	8	no	—
136	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
137	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₇₃	—	2	4	no	—
140	C₂²×C₄×C₇₃	—	2	4	no	—
141	C₂²×C₄×C₇₃	—	2	2	no	—
142	C₂²×C₄×C₇₃	—	2	4	no	—
143	C₂²×C₄×C₇₃	—	2	4	no	—
144	C₂²×C₄×C₇₃	—	2	4	no	—
145	C₂²×C₄×C₇₃	—	4	8	no	—
146	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₇₃	#41	1	4	yes	—
152	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₇₃	—	2	8	no	—
156	SD₁₆×C₇₃	—	2	16	no	—
157	D₈×C₇₃	—	2	8	no	—
158	M₁₆×C₇₃	—	2	16	no	—
159	M₁₆×C₇₃	C₂×D₄	1	16	yes	—
160	C₂×C₈×C₇₃	—	2	2	no	—
161	C₂×C₈×C₇₃	—	2	2	no	—
162	C₂×C₈×C₇₃	—	2	8	no	—
163	C₂×C₈×C₇₃	—	2	16	no	—
164	C₂×C₈×C₇₃	C₂×D₄	1	8	yes	—
165	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
166	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
167	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₇₃	—	2	4	no	—
169	C₄⋊C₄×C₇₃	—	2	16	no	—
170	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
171	C₂²⋊C₄×C₇₃	—	2	4	no	—
172	C₂²⋊C₄×C₇₃	—	2	4	no	—
173	C₂²⋊C₄×C₇₃	—	2	16	no	—
174	C₂²⋊C₄×C₇₃	—	2	16	no	—
175	C₄²×C₇₃	—	2	4	no	—
176	C₄²×C₇₃	—	2	4	no	—
177	C₂³×C₇₃	—	2	4	no	—
178	C₂³×C₇₃	—	2	4	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	—	4	4	no	—
181	C₂³×C₇₃	—	4	4	no	—
182	C₂³×C₇₃	—	8	4	no	—
183	C₂³×C₇₃	#121	1	4	yes	—
184	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
185	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
186	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
187	Q₈×C₇₃	—	2	8	no	—
188	Q₈×C₇₃	—	2	4	no	—
189	Q₈×C₇₃	—	2	4	no	—
190	Q₈×C₇₃	—	4	4	no	—
191	D₄×C₇₃	—	2	16	no	—
192	D₄×C₇₃	—	2	8	no	—
193	D₄×C₇₃	—	2	4	no	—
194	D₄×C₇₃	—	2	4	no	—
195	D₄×C₇₃	—	4	8	no	—
196	D₄×C₇₃	—	4	8	no	—
197	D₄×C₇₃	—	4	4	no	—
198	D₄×C₇₃	—	8	16	no	—
199	C₂×C₄×C₇₃	—	2	4	no	—
200	C₂×C₄×C₇₃	—	2	8	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	8	no	—
204	C₂×C₄×C₇₃	—	2	4	no	—
205	C₂×C₄×C₇₃	—	4	4	no	—
206	C₂×C₄×C₇₃	—	4	8	no	—
207	C₂×C₄×C₇₃	—	4	8	no	—
208	C₂×C₄×C₇₃	—	8	4	no	—
209	C₂×C₄×C₇₃	#121	1	8	yes	—
210	C₂×C₄×C₇₃	#121	1	4	yes	—
211	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
217	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
218	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
219	C₈×C₇₃	—	2	2	no	—
220	C₈×C₇₃	—	2	2	no	—
221	C₈×C₇₃	C₂²×D₄	1	8	yes	—
222	C₂²×C₇₃	—	2	4	no	—
223	C₂²×C₇₃	—	2	2	no	—
224	C₂²×C₇₃	—	2	8	no	—
225	C₂²×C₇₃	—	2	4	no	—
226	C₂²×C₇₃	—	4	4	no	—
227	C₂²×C₇₃	—	4	8	no	—
228	C₂²×C₇₃	—	4	8	no	—
229	C₂²×C₇₃	—	4	4	no	—
230	C₂²×C₇₃	—	8	8	no	—
231	C₂²×C₇₃	C₂×#121	1	2	yes	—
232	C₂²×C₇₃	C₂×#121	1	4	yes	—
233	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
234	C₄×C₇₃	—	2	4	no	—
235	C₄×C₇₃	—	4	8	no	—
236	C₄×C₇₃	—	4	4	no	—
237	C₄×C₇₃	C₂×#121	1	2	yes	—
238	C₄×C₇₃	C₂×#121	1	4	yes	—
239	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
241	#60453	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₇₃	—	2	2	no	—
243	C₂×C₇₃	—	2	4	no	—
244	C₂×C₇₃	—	4	4	no	—
245	C₂×C₇₃	—	8	4	no	—
246	C₂×C₇₃	C₂²×#121	1	1	yes	characteristic
247	C₂×C₇₃	#3584	1	2	yes	—
248	C₂×#575	C₂×C₇₃	1	1	yes	characteristic, complemented
249	C₂²×#131	C₂×C₇₃	1	1	yes	characteristic, complemented
250	#3449	C₂×C₇₃	1	2	yes	complemented
251	#3063	C₂×C₇₃	1	8	yes	complemented
252	#3062	C₂×C₇₃	1	8	yes	complemented
253	#3054	C₂×C₇₃	1	4	yes	complemented
254	#3050	C₂×C₇₃	1	4	yes	complemented
255	#2911	C₂×C₇₃	1	1	yes	characteristic, complemented
256	C₂×#416	C₂×C₇₃	1	2	yes	complemented
257	C₇₃	#60453	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×#41	C₂²×C₇₃	1	2	yes	—
259	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
260	#575	—	2	8	no	—
261	C₂×#137	C₂²×C₇₃	1	4	yes	complemented
262	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	4	yes	complemented
263	C₂×#135	C₂²×C₇₃	1	4	yes	—
264	C₂×#131	—	2	8	no	—
265	C₂×#131	C₂²×C₇₃	1	8	yes	complemented
266	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	complemented
268	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₇₃	1	2	yes	complemented
270	#537	C₂²×C₇₃	1	8	yes	—
271	#536	—	2	2	no	—
272	#536	C₂²×C₇₃	1	4	yes	complemented
273	#535	—	2	2	no	—
274	#535	C₂²×C₇₃	1	4	yes	complemented
275	#534	—	2	4	no	—
276	#532	—	2	4	no	—
277	#525	—	2	4	no	—
278	#525	C₂²×C₇₃	1	8	yes	complemented
279	C₂×#117	C₂²×C₇₃	1	2	yes	—
280	#470	C₂²×C₇₃	1	8	yes	complemented
281	#469	C₂²×C₇₃	1	8	yes	complemented
282	#468	C₂²×C₇₃	1	16	yes	complemented
283	#467	C₂²×C₇₃	1	8	yes	complemented
284	#466	C₂²×C₇₃	1	8	yes	complemented
285	#465	C₂²×C₇₃	1	16	yes	complemented
286	#428	C₂²×C₇₃	1	8	yes	complemented
287	#427	C₂²×C₇₃	1	4	yes	complemented
288	#416	C₂²×C₇₃	1	4	yes	complemented
289	#416	C₂²×C₇₃	1	4	yes	complemented
290	#416	C₂²×C₇₃	1	8	yes	complemented
291	C₂×#103	C₂²×C₇₃	1	4	yes	complemented
292	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	8	no	—
298	C₂×#41	—	2	8	no	—
299	C₂×#41	D₄×C₇₃	1	4	yes	—
300	C₂×#41	C₂³×C₇₃	1	4	yes	—
301	C₂×#41	C₂³×C₇₃	1	4	yes	—
302	C₂×#41	C₂³×C₇₃	1	4	yes	—
303	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
304	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	D₄×C₇₃	1	2	yes	—
307	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
311	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
312	#137	—	2	16	no	—
313	AGL(1,ℤ/8)	—	2	16	no	—
314	#135	—	2	16	no	—
315	C₂×Q₁₆	C₂³×C₇₃	1	4	yes	—
316	C₂×SD₁₆	C₂³×C₇₃	1	8	yes	—
317	C₂×D₈	C₂³×C₇₃	1	4	yes	—
318	#131	—	2	32	no	—
319	C₂×M₁₆	—	2	8	no	—
320	C₂×M₁₆	D₄×C₇₃	1	8	yes	complemented
321	C₂×M₁₆	C₂³×C₇₃	1	8	yes	—
322	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	—	2	8	no	—
325	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
328	C₂²×C₈	C₂³×C₇₃	1	8	yes	—
329	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
330	C₄⋊Q₈	—	2	4	no	—
331	#127	—	2	4	no	—
332	#124	—	2	4	no	—
333	#124	—	2	4	no	—
334	#123	—	2	8	no	—
335	#123	—	2	8	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	C₂³×C₇₃	1	16	yes	—
338	#121	—	2	8	no	—
339	#121	—	2	16	no	—
340	#121	C₂³×C₇₃	1	16	yes	—
341	#120	—	2	8	no	—
342	#120	—	2	8	no	—
343	C₄×D₄	—	2	16	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	C₂³×C₇₃	1	4	yes	—
347	#117	C₂³×C₇₃	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	#107	C₂³×C₇₃	1	8	yes	—
352	#106	C₂³×C₇₃	1	8	yes	—
353	#103	C₂³×C₇₃	1	8	yes	—
354	#103	C₂³×C₇₃	1	8	yes	—
355	#102	C₂³×C₇₃	1	8	yes	—
356	#102	C₂³×C₇₃	1	8	yes	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
359	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
360	#41	—	2	16	no	—
361	#41	—	2	8	no	—
362	#41	—	2	8	no	—
363	#41	—	2	8	no	—
364	#41	—	2	8	no	—
365	#41	—	2	8	no	—
366	#41	—	2	8	no	—
367	#41	—	4	8	no	—
368	#41	—	4	8	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
374	C₂×Q₈	C₂⁴×C₇₃	1	4	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
385	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
386	C₂×D₄	C₂⁴×C₇₃	1	4	yes	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
399	C₂²×C₄	#41×C₇₃	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	D₈	—	2	8	no	—
406	M₁₆	—	2	16	no	—
407	M₁₆	C₂×D₄×C₇₃	1	16	yes	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	8	no	—
411	C₂×C₈	—	2	16	no	—
412	C₂×C₈	C₂×D₄×C₇₃	1	8	yes	—
413	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
414	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
415	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	16	no	—
418	C₄⋊C₄	C₂⁴×C₇₃	1	8	yes	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	16	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	4	no	—
431	C₂³	#121×C₇₃	1	4	yes	—
432	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
433	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
434	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
435	Q₈	—	2	8	no	—
436	Q₈	—	2	4	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	4	4	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	4	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	8	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	16	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	#121×C₇₃	1	8	yes	—
458	C₂×C₄	#121×C₇₃	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
460	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
464	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
465	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
466	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	C₂²×D₄×C₇₃	1	8	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	8	8	no	—
479	C₂²	C₂×#121×C₇₃	1	2	yes	—
480	C₂²	C₂×#121×C₇₃	1	4	yes	—
481	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	4	8	no	—
484	C₄	—	4	4	no	—
485	C₄	C₂×#121×C₇₃	1	2	yes	—
486	C₄	C₂×#121×C₇₃	1	4	yes	—
487	C₄	C₂³×D₄×C₇₃	1	1	yes	characteristic
488	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	4	no	—
491	C₂	—	4	4	no	—
492	C₂	—	8	4	no	—
493	C₂	C₂²×#121×C₇₃	1	1	yes	characteristic
494	C₂	C₇₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
socle	C₂²×C₇₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ C₂²×#41×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₇₃	C₂	semidirect
2. C₂²×#131×C₇₃	C₂	semidirect
3. C₇₃×#3449	C₂	semidirect
4. C₇₃×#3063	C₂	semidirect
5. C₇₃×#3062	C₂	semidirect
6. C₇₃×#3054	C₂	semidirect
7. C₇₃×#3050	C₂	semidirect
8. C₇₃×#2911	C₂	semidirect
9. C₂×#416×C₇₃	C₂	semidirect
13. C₂×#137×C₇₃	C₂²	semidirect
14. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
17. C₂×#131×C₇₃	C₂²	semidirect
19. C₂²×M₁₆×C₇₃	C₂²	semidirect
21. C₂³×C₈×C₇₃	C₂²	semidirect
24. #536×C₇₃	C₂²	semidirect
26. #535×C₇₃	C₂²	semidirect
30. #525×C₇₃	C₂²	semidirect
32. #470×C₇₃	C₂²	semidirect
33. #469×C₇₃	C₂²	semidirect
34. #468×C₇₃	C₂²	semidirect
35. #467×C₇₃	C₂²	semidirect
36. #466×C₇₃	C₂²	semidirect
37. #465×C₇₃	C₂²	semidirect
38. #428×C₇₃	C₂²	semidirect
39. #427×C₇₃	C₂²	semidirect
40. #416×C₇₃	C₂²	semidirect
41. #416×C₇₃	C₂²	semidirect
42. #416×C₇₃	C₂²	semidirect
43. C₂×#103×C₇₃	C₂²	semidirect
44. C₂×#102×C₇₃	C₂²	semidirect
72. C₂×M₁₆×C₇₃	D₄	semidirect
241. #60453	C₇₃	direct (N × H)
248. C₂×#575	C₂×C₇₃	semidirect
249. C₂²×#131	C₂×C₇₃	semidirect
250. #3449	C₂×C₇₃	semidirect
251. #3063	C₂×C₇₃	semidirect
252. #3062	C₂×C₇₃	semidirect
253. #3054	C₂×C₇₃	semidirect
254. #3050	C₂×C₇₃	semidirect
255. #2911	C₂×C₇₃	semidirect
256. C₂×#416	C₂×C₇₃	semidirect
257. C₇₃	#60453	direct (N × H)
261. C₂×#137	C₂²×C₇₃	semidirect
262. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
265. C₂×#131	C₂²×C₇₃	semidirect
267. C₂²×M₁₆	C₂²×C₇₃	semidirect
269. C₂³×C₈	C₂²×C₇₃	semidirect
272. #536	C₂²×C₇₃	semidirect
274. #535	C₂²×C₇₃	semidirect
278. #525	C₂²×C₇₃	semidirect
280. #470	C₂²×C₇₃	semidirect
281. #469	C₂²×C₇₃	semidirect
282. #468	C₂²×C₇₃	semidirect
283. #467	C₂²×C₇₃	semidirect
284. #466	C₂²×C₇₃	semidirect
285. #465	C₂²×C₇₃	semidirect
286. #428	C₂²×C₇₃	semidirect
287. #427	C₂²×C₇₃	semidirect
288. #416	C₂²×C₇₃	semidirect
289. #416	C₂²×C₇₃	semidirect
290. #416	C₂²×C₇₃	semidirect
291. C₂×#103	C₂²×C₇₃	semidirect
292. C₂×#102	C₂²×C₇₃	semidirect
320. C₂×M₁₆	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₇₃	2
C₂²×#131×C₇₃	2
C₇₃×#3449	2
C₇₃×#3063	2
C₇₃×#3062	2
C₇₃×#3054	2
C₇₃×#3050	2
C₇₃×#2911	2
C₂×#416×C₇₃	2
#60453	73

Subgroups — C73×#60453 #32969857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#60453 #32969857