Subgroups — C₇₃×#25755 #32935159

Order 18688.

1598 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#462×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2000	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₃	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
13	#550×C₇₃	—	2	4	no	—
14	#550×C₇₃	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₇₃	—	2	1	no	—
17	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
19	C₂×#121×C₇₃	—	2	2	no	—
20	C₂×#121×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₃	—	2	1	no	—
23	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
24	#492×C₇₃	—	2	4	no	—
25	#462×C₇₃	—	2	4	no	—
26	#452×C₇₃	—	2	16	no	—
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₃	C₂²	1	2	yes	—
29	C₂×#103×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	4	yes	—
31	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	—
32	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
33	#399×C₇₃	—	2	2	no	—
34	#390×C₇₃	—	2	1	no	—
35	#384×C₇₃	—	2	1	no	—
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
37	#340×C₇₃	C₂²	1	2	yes	—
38	C₂×#41×C₇₃	—	2	4	no	—
39	C₂×#41×C₇₃	—	2	4	no	—
40	C₂×#41×C₇₃	—	2	8	no	—
41	C₂×#41×C₇₃	—	4	4	no	—
42	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
43	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	2	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₃	—	2	2	no	—
51	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
52	C₂×Q₁₆×C₇₃	—	2	8	no	—
53	C₂×Q₁₆×C₇₃	—	2	4	no	—
54	C₂×SD₁₆×C₇₃	—	2	8	no	—
55	C₂×SD₁₆×C₇₃	—	2	8	no	—
56	C₂×SD₁₆×C₇₃	—	4	4	no	—
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₇₃	—	2	2	no	—
60	C₄⋊Q₈×C₇₃	—	2	2	no	—
61	#127×C₇₃	—	2	8	no	—
62	#127×C₇₃	—	2	2	no	—
63	#127×C₇₃	D₄	1	4	yes	—
64	C₂²⋊Q₈×C₇₃	—	2	8	no	—
65	C₂²⋊Q₈×C₇₃	—	4	4	no	—
66	#121×C₇₃	—	2	16	no	—
67	#121×C₇₃	—	2	4	no	—
68	#121×C₇₃	—	2	4	no	—
69	C₄×Q₈×C₇₃	—	2	2	no	—
70	C₄×Q₈×C₇₃	D₄	1	4	yes	—
71	C₄×D₄×C₇₃	—	2	8	no	—
72	C₄×D₄×C₇₃	—	2	2	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
84	C₂×C₄²×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₇₃	—	2	2	no	—
88	#103×C₇₃	—	2	4	no	—
89	#103×C₇₃	D₄	1	8	yes	complemented
90	#102×C₇₃	—	2	8	no	—
91	C₂²⋊C₈×C₇₃	—	2	8	no	—
92	C₄×C₈×C₇₃	—	2	2	no	—
93	#95×C₇₃	—	2	1	no	—
94	C₂⁴×C₇₃	—	2	2	no	—
95	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
96	#41×C₇₃	—	4	16	no	—
97	#41×C₇₃	—	4	8	no	—
98	#41×C₇₃	—	4	8	no	—
99	C₂×Q₈×C₇₃	—	2	1	no	—
100	C₂×Q₈×C₇₃	—	2	2	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	4	no	—
103	C₂×Q₈×C₇₃	—	2	2	no	—
104	C₂×Q₈×C₇₃	—	2	4	no	—
105	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
106	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₇₃	—	2	8	no	—
108	C₂×D₄×C₇₃	—	2	8	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	4	no	—
111	C₂×D₄×C₇₃	—	2	4	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	4	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	2	4	no	—
117	C₂×D₄×C₇₃	—	4	8	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	—	4	2	no	—
120	C₂×D₄×C₇₃	—	8	2	no	—
121	C₂×D₄×C₇₃	—	8	4	no	—
122	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	8	no	—
125	C₂²×C₄×C₇₃	—	2	2	no	—
126	C₂²×C₄×C₇₃	—	2	1	no	—
127	C₂²×C₄×C₇₃	—	2	4	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	—	2	4	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	4	8	no	—
133	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₇₃	—	4	8	no	—
138	SD₁₆×C₇₃	—	4	16	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	—	2	2	no	—
141	C₂×C₈×C₇₃	—	2	4	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
144	C₄⋊C₄×C₇₃	—	2	4	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄⋊C₄×C₇₃	—	4	8	no	—
149	C₄⋊C₄×C₇₃	—	4	2	no	—
150	C₄⋊C₄×C₇₃	—	4	2	no	—
151	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₇₃	—	2	8	no	—
154	C₂²⋊C₄×C₇₃	—	2	4	no	—
155	C₂²⋊C₄×C₇₃	—	4	8	no	—
156	C₄²×C₇₃	—	2	4	no	—
157	C₄²×C₇₃	—	4	2	no	—
158	C₄²×C₇₃	C₂×D₄	1	2	yes	—
159	C₄²×C₇₃	C₂×D₄	1	2	yes	—
160	C₂³×C₇₃	—	2	2	no	—
161	C₂³×C₇₃	—	2	4	no	—
162	C₂³×C₇₃	—	2	4	no	—
163	C₂³×C₇₃	—	2	2	no	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	2	4	no	—
166	C₂³×C₇₃	—	4	4	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	4	no	—
170	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₇₃	—	2	2	no	—
172	Q₈×C₇₃	—	2	4	no	—
173	Q₈×C₇₃	—	4	2	no	—
174	Q₈×C₇₃	—	4	2	no	—
175	Q₈×C₇₃	—	4	4	no	—
176	Q₈×C₇₃	#127	1	4	yes	—
177	D₄×C₇₃	—	2	8	no	—
178	D₄×C₇₃	—	4	16	no	—
179	D₄×C₇₃	—	4	2	no	—
180	D₄×C₇₃	—	4	2	no	—
181	D₄×C₇₃	—	4	4	no	—
182	D₄×C₇₃	—	4	8	no	—
183	D₄×C₇₃	—	8	4	no	—
184	D₄×C₇₃	—	8	8	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	4	no	—
187	C₂×C₄×C₇₃	—	2	2	no	—
188	C₂×C₄×C₇₃	—	2	2	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	4	no	—
191	C₂×C₄×C₇₃	—	2	4	no	—
192	C₂×C₄×C₇₃	—	4	16	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	4	4	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	4	no	—
201	C₂×C₄×C₇₃	#120	1	2	yes	—
202	C₂×C₄×C₇₃	#120	1	2	yes	—
203	C₂×C₄×C₇₃	#135	1	2	yes	—
204	C₂×C₄×C₇₃	#137	1	2	yes	—
205	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
209	C₈×C₇₃	—	2	4	no	—
210	C₈×C₇₃	—	4	2	no	—
211	C₂²×C₇₃	—	4	4	no	—
212	C₂²×C₇₃	—	4	2	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	4	4	no	—
215	C₂²×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	4	4	no	—
217	C₂²×C₇₃	—	4	4	no	—
218	C₂²×C₇₃	—	4	4	no	—
219	C₂²×C₇₃	—	8	4	no	—
220	C₂²×C₇₃	—	8	4	no	—
221	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
222	C₂²×C₇₃	D₄²	1	2	yes	—
223	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
224	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
225	C₂²×C₇₃	#577	1	2	yes	—
226	C₄×C₇₃	—	2	4	no	—
227	C₄×C₇₃	—	2	2	no	—
228	C₄×C₇₃	—	4	2	no	—
229	C₄×C₇₃	—	4	2	no	—
230	C₄×C₇₃	—	4	4	no	—
231	C₄×C₇₃	—	8	2	no	—
232	C₄×C₇₃	#452	1	4	yes	complemented
233	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
234	C₄×C₇₃	#535	1	1	yes	characteristic
235	C₄×C₇₃	D₄²	1	2	yes	—
236	#25755	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂×C₇₃	—	8	2	no	—
238	C₂×C₇₃	—	8	4	no	—
239	C₂×C₇₃	#2433	1	1	yes	characteristic
240	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
241	C₂×C₇₃	#3009	1	1	yes	characteristic
242	C₂×C₇₃	#3278	1	2	yes	—
243	C₂×C₇₃	#3284	1	2	yes	—
244	C₂×#550	C₂×C₇₃	1	1	yes	characteristic
245	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
246	C₂×#462	C₂×C₇₃	1	1	yes	characteristic, complemented
247	C₂×#452	C₂×C₇₃	1	4	yes	complemented
248	#2542	C₂×C₇₃	1	1	yes	characteristic, complemented
249	#2000	C₂×C₇₃	1	4	yes	complemented
250	#1982	C₂×C₇₃	1	1	yes	characteristic, complemented
251	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
252	C₄×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
253	C₇₃	#25755	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×#41	C₂²×C₇₃	1	2	yes	—
255	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
256	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
257	#550	—	2	4	no	—
258	#550	—	2	4	no	—
259	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
260	C₂×#127	—	2	1	no	—
261	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
263	C₂×#121	—	2	2	no	—
264	C₂×#121	C₂²×C₇₃	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
268	#492	—	2	4	no	—
269	#462	—	2	4	no	—
270	#452	—	2	16	no	—
271	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇₃	1	2	yes	—
273	C₂×#103	C₂²×C₇₃	1	2	yes	—
274	C₂×#102	C₂²×C₇₃	1	4	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	—
276	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
277	#399	—	2	2	no	—
278	#390	—	2	1	no	—
279	#384	—	2	1	no	—
280	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
281	#340	C₂²×C₇₃	1	2	yes	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	—	2	8	no	—
285	C₂×#41	—	4	4	no	—
286	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
287	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
296	C₂×Q₁₆	—	2	8	no	—
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	2	8	no	—
299	C₂×SD₁₆	—	2	8	no	—
300	C₂×SD₁₆	—	4	4	no	—
301	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
302	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	#127	—	2	8	no	—
306	#127	—	2	2	no	—
307	#127	D₄×C₇₃	1	4	yes	—
308	C₂²⋊Q₈	—	2	8	no	—
309	C₂²⋊Q₈	—	4	4	no	—
310	#121	—	2	16	no	—
311	#121	—	2	4	no	—
312	#121	—	2	4	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	D₄×C₇₃	1	4	yes	—
315	C₄×D₄	—	2	8	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
331	C₄⋊C₈	—	2	2	no	—
332	#103	—	2	4	no	—
333	#103	D₄×C₇₃	1	8	yes	complemented
334	#102	—	2	8	no	—
335	C₂²⋊C₈	—	2	8	no	—
336	C₄×C₈	—	2	2	no	—
337	#95	—	2	1	no	—
338	C₂⁴	—	2	2	no	—
339	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
340	#41	—	4	16	no	—
341	#41	—	4	8	no	—
342	#41	—	4	8	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
350	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	4	8	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	—	8	4	no	—
366	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	8	no	—
377	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
381	Q₁₆	—	4	8	no	—
382	SD₁₆	—	4	16	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	8	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
396	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	4	8	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	4	2	no	—
402	C₄²	C₂×D₄×C₇₃	1	2	yes	—
403	C₄²	C₂×D₄×C₇₃	1	2	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	4	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	4	no	—
414	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	2	4	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	4	no	—
420	Q₈	#127×C₇₃	1	4	yes	—
421	D₄	—	2	8	no	—
422	D₄	—	4	16	no	—
423	D₄	—	4	4	no	—
424	D₄	—	4	8	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	8	4	no	—
428	D₄	—	8	8	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	16	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	#120×C₇₃	1	2	yes	—
446	C₂×C₄	#120×C₇₃	1	2	yes	—
447	C₂×C₄	#135×C₇₃	1	2	yes	—
448	C₂×C₄	#137×C₇₃	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
452	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	8	4	no	—
464	C₂²	—	8	4	no	—
465	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
466	C₂²	D₄²×C₇₃	1	2	yes	—
467	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
468	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
469	C₂²	#577×C₇₃	1	2	yes	—
470	C₄	—	2	2	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	#452×C₇₃	1	4	yes	complemented
477	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
478	C₄	#535×C₇₃	1	1	yes	characteristic
479	C₄	D₄²×C₇₃	1	2	yes	—
480	C₂	—	8	2	no	—
481	C₂	—	8	4	no	—
482	C₂	C₇₃×#2433	1	1	yes	characteristic
483	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
484	C₂	C₇₃×#3009	1	1	yes	characteristic
485	C₂	C₇₃×#3278	1	2	yes	—
486	C₂	C₇₃×#3284	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#550×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#492×C₇₃	C₂	semidirect
3. C₂×#462×C₇₃	C₂	semidirect
4. C₂×#452×C₇₃	C₂	semidirect
5. C₇₃×#2542	C₂	semidirect
6. C₇₃×#2000	C₂	semidirect
7. C₇₃×#1982	C₂	semidirect
8. C₇₃×#1954	C₂	semidirect
9. C₄×#103×C₇₃	C₂	semidirect
89. #103×C₇₃	D₄	semidirect
232. C₄×C₇₃	#452	semidirect
236. #25755	C₇₃	direct (N × H)
245. C₂×#492	C₂×C₇₃	semidirect
246. C₂×#462	C₂×C₇₃	semidirect
247. C₂×#452	C₂×C₇₃	semidirect
248. #2542	C₂×C₇₃	semidirect
249. #2000	C₂×C₇₃	semidirect
250. #1982	C₂×C₇₃	semidirect
251. #1954	C₂×C₇₃	semidirect
252. C₄×#103	C₂×C₇₃	semidirect
253. C₇₃	#25755	direct (N × H)
333. #103	D₄×C₇₃	semidirect
476. C₄	#452×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₇₃	2
C₂×#492×C₇₃	2
C₂×#462×C₇₃	2
C₂×#452×C₇₃	2
C₇₃×#2542	2
C₇₃×#2000	2
C₇₃×#1982	2
C₇₃×#1954	2
C₄×#103×C₇₃	2
#25755	73

Subgroups — C73×#25755 #32935159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25755 #32935159