Subgroups — C₂×#22624164 #33993217

Order 18688.

8890 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624164	C₂	1	32	yes	maximal, direct product factor
2	C₂×#17989326	C₂	1	2	yes	maximal, complemented
3	C₂×#17989324	C₂	1	2	yes	maximal, complemented
4	C₂×#17989284	C₂	1	2	yes	maximal, complemented
5	C₂×#17989281	C₂	1	2	yes	maximal, complemented
6	C₂×#17989222	C₂	1	2	yes	maximal, complemented
7	C₂×#17989221	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×C₂²⋊D₇₃	C₂	1	2	yes	maximal, complemented
9	C₂×#17989219	C₂	1	2	yes	maximal, complemented
10	C₂×#17989190	C₂	1	2	yes	maximal, complemented
11	C₂×#17989171	C₂	1	4	yes	maximal, complemented
12	C₂×#17989151	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17989147	C₂	1	4	yes	maximal, complemented
14	C₂×#17989094	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×D₇₃	C₂	1	2	yes	maximal, complemented
16	C₂×#535×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₂²⋊D₇₃	C₂²	1	4	yes	complemented
19	C₂²×D₄×D₇₃	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₇₃	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₇₃	C₂²	1	2	yes	complemented
22	C₂³×C₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
23	#17989326	C₂²	1	32	yes	complemented
24	#17989324	C₂²	1	32	yes	complemented
25	#17989284	C₂²	1	32	yes	complemented
26	#17989281	C₂²	1	32	yes	complemented
27	#17989222	C₂²	1	32	yes	complemented
28	#17989221	C₂²	1	32	yes	complemented
29	D₄×C₂²⋊D₇₃	C₂²	1	32	yes	complemented
30	#17989219	C₂²	1	32	yes	complemented
31	#17989190	C₂²	1	32	yes	complemented
32	#17989171	C₂²	1	64	yes	complemented
33	#17989151	C₂²	1	16	yes	complemented
34	#17989147	C₂²	1	64	yes	complemented
35	C₂×#14556587	C₂²	1	2	yes	complemented
36	C₂×#14556587	C₂²	1	2	yes	complemented
37	C₂×#14556585	C₂²	1	4	yes	complemented
38	C₂×#14556584	C₂²	1	4	yes	complemented
39	C₂×#14556582	C₂²	1	2	yes	complemented
40	C₂×#14556580	C₂²	1	2	yes	complemented
41	#17989094	C₂²	1	16	yes	complemented
42	C₂×#14556575	C₂²	1	4	yes	complemented
43	C₂×#14556573	C₂²	1	4	yes	complemented
44	C₂×#14556573	C₂²	1	4	yes	complemented
45	C₂×#14556572	C₂²	1	4	yes	complemented
46	C₂×#14556572	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14556572	C₂²	1	1	yes	characteristic, complemented
48	C₂×#14556567	C₂²	1	2	yes	complemented
49	C₂×#14556566	C₂²	1	2	yes	complemented
50	C₂×#14556565	C₂²	1	2	yes	complemented
51	C₂×#14556565	C₂²	1	2	yes	complemented
52	C₂×#14556564	C₂²	1	4	yes	complemented
53	C₂×#14556564	C₂²	1	4	yes	complemented
54	C₂×#14556564	C₂²	1	4	yes	complemented
55	C₂×#14556563	C₂²	1	4	yes	complemented
56	C₂×#14556563	C₂²	1	4	yes	complemented
57	C₂×#14556563	C₂²	1	4	yes	complemented
58	C₂×#14556562	C₂²	1	2	yes	complemented
59	C₂×#14556562	C₂²	1	4	yes	complemented
60	C₂×#14556562	C₂²	1	4	yes	complemented
61	C₂×#14556562	C₂²	1	2	yes	complemented
62	#121×D₇₃	C₂²	1	32	yes	complemented
63	C₂×#14556561	C₂²	1	4	yes	complemented
64	C₂×#14556560	C₂²	1	4	yes	complemented
65	C₂×#14556559	C₂²	1	2	yes	complemented
66	C₂×#14556559	C₂²	1	4	yes	complemented
67	C₂×#14556559	C₂²	1	2	yes	complemented
68	C₂×#14556559	C₂²	1	4	yes	complemented
69	C₂×#14556559	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14556559	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×D₂₉₂	C₂²	1	4	yes	complemented
72	C₂×D₄×Dic₇₃	C₂²	1	2	yes	complemented
73	C₂×#14556553	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
75	C₂×C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
76	C₂×#14556551	C₂²	1	4	yes	complemented
77	C₂×#14556550	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14556550	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊C₄×D₇₃	C₂²	1	4	yes	complemented
81	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
82	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
83	#535×C₇₃	C₂²	1	16	yes	complemented
84	C₂×#127×C₇₃	C₂²	1	2	yes	complemented
85	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
86	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
87	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
88	C₂×#120×C₇₃	C₂²	1	2	yes	complemented
89	C₂×#120×C₇₃	C₂²	1	2	yes	complemented
90	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₇₃	C₂³	1	1	yes	characteristic
92	C₂⁴×D₇₃	C₂³	1	4	yes	—
93	C₂⁴×D₇₃	C₂³	1	2	yes	—
94	C₂²×D₂₉₂	—	4	4	no	—
95	C₂²×D₂₉₂	C₂³	1	2	yes	—
96	C₂²×D₂₉₂	C₂³	1	4	yes	—
97	C₂²×D₂₉₂	C₂³	1	2	yes	—
98	C₂²×D₂₉₂	C₂³	1	8	yes	complemented
99	C₂²×C₂²⋊D₇₃	—	4	16	no	—
100	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
101	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
102	C₂²×C₂²⋊D₇₃	C₂³	1	2	yes	—
103	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
106	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₇₃	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₇₃	C₂³	1	32	yes	complemented
109	C₂×D₄×D₇₃	—	4	8	no	—
110	C₂×D₄×D₇₃	—	4	16	no	—
111	C₂×D₄×D₇₃	—	4	16	no	—
112	C₂×D₄×D₇₃	C₂³	1	32	yes	complemented
113	C₂×D₄×D₇₃	C₂³	1	32	yes	complemented
114	C₂×D₄×D₇₃	C₂³	1	16	yes	complemented
115	C₂³×Dic₇₃	C₂³	1	1	yes	characteristic
116	C₂³×Dic₇₃	C₂³	1	4	yes	—
117	C₂²×C₄×D₇₃	—	4	4	no	—
118	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
119	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
120	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
121	C₂²×C₄×D₇₃	C₂³	1	4	yes	—
122	C₂²×C₄×D₇₃	C₂³	1	8	yes	complemented
123	#14556587	C₂³	1	16	yes	complemented
124	#14556587	C₂³	1	16	yes	complemented
125	#14556585	C₂³	1	32	yes	complemented
126	#14556584	C₂³	1	32	yes	complemented
127	#14556582	C₂³	1	16	yes	complemented
128	#14556580	C₂³	1	16	yes	complemented
129	#14556575	C₂³	1	32	yes	complemented
130	#14556573	C₂³	1	32	yes	complemented
131	#14556573	C₂³	1	32	yes	complemented
132	#14556572	C₂³	1	32	yes	complemented
133	#14556572	C₂³	1	8	yes	complemented
134	#14556572	C₂³	1	8	yes	complemented
135	#14556567	C₂³	1	16	yes	complemented
136	#14556566	C₂³	1	16	yes	complemented
137	#14556565	C₂³	1	16	yes	complemented
138	#14556565	C₂³	1	16	yes	complemented
139	#14556564	C₂³	1	32	yes	complemented
140	#14556564	C₂³	1	32	yes	complemented
141	#14556564	C₂³	1	32	yes	complemented
142	#14556563	C₂³	1	32	yes	complemented
143	#14556563	C₂³	1	32	yes	complemented
144	#14556563	C₂³	1	32	yes	complemented
145	#14556562	C₂³	1	16	yes	complemented
146	#14556562	C₂³	1	32	yes	complemented
147	#14556562	C₂³	1	32	yes	complemented
148	#14556562	C₂³	1	16	yes	complemented
149	#14556561	C₂³	1	32	yes	complemented
150	#14556560	C₂³	1	32	yes	complemented
151	#14556559	C₂³	1	16	yes	complemented
152	#14556559	C₂³	1	32	yes	complemented
153	#14556559	C₂³	1	16	yes	complemented
154	#14556559	C₂³	1	32	yes	complemented
155	#14556559	C₂³	1	8	yes	complemented
156	#14556559	C₂³	1	8	yes	complemented
157	C₄×D₂₉₂	C₂³	1	32	yes	complemented
158	D₄×Dic₇₃	C₂³	1	16	yes	complemented
159	#14556553	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	complemented
161	C₄×C₂²⋊D₇₃	C₂³	1	16	yes	complemented
162	#14556551	C₂³	1	32	yes	complemented
163	#14556550	C₂³	1	8	yes	complemented
164	#14556550	C₂³	1	8	yes	complemented
165	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
168	C₂×#11924007	C₂³	1	4	yes	—
169	C₂×#11924007	C₂³	1	4	yes	—
170	C₂×#11924007	C₂³	1	2	yes	—
171	C₂×#11924007	C₂³	1	2	yes	—
172	C₄⋊C₄×D₇₃	C₂³	1	16	yes	complemented
173	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
174	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊Dic₇₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊Dic₇₃	C₂³	1	4	yes	—
180	C₂×#11924005	C₂³	1	4	yes	—
181	C₂×#11924005	C₂³	1	4	yes	—
182	C₂×#11924005	C₂³	1	2	yes	—
183	C₂×#11924005	C₂³	1	2	yes	—
184	C₂×#11924005	C₂³	1	4	yes	—
185	C₂×#11924005	C₂³	1	4	yes	—
186	C₂²⋊C₄×D₇₃	C₂³	1	32	yes	complemented
187	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
188	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
189	C₂⁵×C₇₃	C₂³	1	2	yes	—
190	C₂×#41×C₇₃	—	4	4	no	—
191	C₂×#41×C₇₃	C₂³	1	8	yes	complemented
192	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₇₃	—	4	4	no	—
194	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
195	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
197	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
198	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
200	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₇₃	C₂³	1	8	yes	complemented
202	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
205	#127×C₇₃	C₂³	1	16	yes	complemented
206	#124×C₇₃	C₂³	1	16	yes	complemented
207	#121×C₇₃	C₂³	1	16	yes	complemented
208	#121×C₇₃	C₂³	1	16	yes	complemented
209	#120×C₇₃	C₂³	1	16	yes	complemented
210	#120×C₇₃	C₂³	1	16	yes	complemented
211	#117×C₇₃	C₂³	1	8	yes	complemented
212	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
216	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
217	C₂³×D₇₃	—	2	8	no	—
218	C₂³×D₇₃	—	2	16	no	—
219	C₂³×D₇₃	—	4	2	no	—
220	C₂³×D₇₃	—	4	8	no	—
221	C₂³×D₇₃	—	4	8	no	—
222	C₂³×D₇₃	—	4	8	no	—
223	C₂³×D₇₃	—	4	4	no	—
224	C₂³×D₇₃	C₂⁴	1	4	yes	—
225	C₂³×D₇₃	C₂⁴	1	4	yes	—
226	C₂³×D₇₃	C₂⁴	1	2	yes	—
227	C₂³×D₇₃	C₂⁴	1	16	yes	—
228	C₂³×D₇₃	C₂⁴	1	8	yes	—
229	C₂×D₂₉₂	—	2	16	no	—
230	C₂×D₂₉₂	—	2	8	no	—
231	C₂×D₂₉₂	—	4	16	no	—
232	C₂×D₂₉₂	—	4	4	no	—
233	C₂×D₂₉₂	C₂⁴	1	8	yes	—
234	C₂×D₂₉₂	C₂⁴	1	16	yes	—
235	C₂×D₂₉₂	C₂⁴	1	8	yes	—
236	C₂×C₂²⋊D₇₃	—	2	8	no	—
237	C₂×C₂²⋊D₇₃	—	2	16	no	—
238	C₂×C₂²⋊D₇₃	—	2	8	no	—
239	C₂×C₂²⋊D₇₃	—	4	8	no	—
240	C₂×C₂²⋊D₇₃	—	4	8	no	—
241	C₂×C₂²⋊D₇₃	—	4	8	no	—
242	C₂×C₂²⋊D₇₃	—	4	8	no	—
243	C₂×C₂²⋊D₇₃	—	4	8	no	—
244	C₂×C₂²⋊D₇₃	—	4	64	no	—
245	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
246	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
247	C₂×C₂²⋊D₇₃	C₂⁴	1	8	yes	—
248	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
249	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
250	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
251	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
252	C₂×C₂²⋊D₇₃	C₂⁴	1	16	yes	—
253	D₄×D₇₃	—	4	32	no	—
254	D₄×D₇₃	—	4	64	no	—
255	D₄×D₇₃	—	4	64	no	—
256	C₂²×Dic₇₃	—	4	2	no	—
257	C₂²×Dic₇₃	—	4	8	no	—
258	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
259	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
260	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
261	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
262	C₂²×Dic₇₃	C₂⁴	1	16	yes	—
263	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
264	C₂×C₄×D₇₃	—	2	8	no	—
265	C₂×C₄×D₇₃	—	4	16	no	—
266	C₂×C₄×D₇₃	—	4	4	no	—
267	C₂×C₄×D₇₃	—	4	8	no	—
268	C₂×C₄×D₇₃	—	4	8	no	—
269	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
270	C₂×C₄×D₇₃	C₂⁴	1	8	yes	—
271	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
272	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
273	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
274	C₄⋊Dic₇₃	C₂⁴	1	8	yes	—
275	C₄⋊Dic₇₃	C₂⁴	1	16	yes	—
276	#11924007	C₂⁴	1	16	yes	—
277	#11924007	C₂⁴	1	16	yes	—
278	#11924007	C₂⁴	1	8	yes	—
279	#11924007	C₂⁴	1	8	yes	—
280	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
281	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
282	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
283	C₂²⋊Dic₇₃	C₂⁴	1	4	yes	—
284	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
285	C₂²⋊Dic₇₃	C₂⁴	1	8	yes	—
286	C₂²⋊Dic₇₃	C₂⁴	1	16	yes	—
287	#11924005	C₂⁴	1	16	yes	—
288	#11924005	C₂⁴	1	16	yes	—
289	#11924005	C₂⁴	1	8	yes	—
290	#11924005	C₂⁴	1	8	yes	—
291	#11924005	C₂⁴	1	16	yes	—
292	#11924005	C₂⁴	1	16	yes	—
293	C₄×Dic₇₃	C₂⁴	1	8	yes	—
294	C₄×Dic₇₃	C₂⁴	1	8	yes	—
295	C₂⁴×C₇₃	—	4	4	no	—
296	C₂⁴×C₇₃	—	4	8	no	—
297	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
298	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
299	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
300	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
301	C₂⁴×C₇₃	C₂⁴	1	8	yes	—
302	#41×C₇₃	—	4	16	no	—
303	C₂×Q₈×C₇₃	—	4	2	no	—
304	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
305	C₂×D₄×C₇₃	—	2	8	no	—
306	C₂×D₄×C₇₃	—	4	16	no	—
307	C₂×D₄×C₇₃	—	4	4	no	—
308	C₂×D₄×C₇₃	—	4	2	no	—
309	C₂×D₄×C₇₃	—	4	2	no	—
310	C₂×D₄×C₇₃	—	4	2	no	—
311	C₂×D₄×C₇₃	—	4	8	no	—
312	C₂×D₄×C₇₃	—	4	8	no	—
313	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
314	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
315	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
316	C₂×D₄×C₇₃	C₂⁴	1	16	yes	—
317	C₂×D₄×C₇₃	C₂⁴	1	16	yes	—
318	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
319	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
320	C₂²×C₄×C₇₃	—	2	4	no	—
321	C₂²×C₄×C₇₃	—	2	4	no	—
322	C₂²×C₄×C₇₃	—	2	4	no	—
323	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
325	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₇₃	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
334	C₂²⋊C₄×C₇₃	C₂⁴	1	16	yes	—
335	C₄²×C₇₃	C₂⁴	1	8	yes	—
336	C₂³×C₇₃	—	2	2	no	—
337	C₂³×C₇₃	—	2	2	no	—
338	C₂³×C₇₃	—	2	2	no	—
339	C₂³×C₇₃	—	2	8	no	—
340	C₂³×C₇₃	—	2	4	no	—
341	C₂³×C₇₃	—	2	4	no	—
342	C₂³×C₇₃	—	2	8	no	—
343	C₂³×C₇₃	—	2	8	no	—
344	C₂³×C₇₃	—	2	4	no	—
345	C₂³×C₇₃	—	4	8	no	—
346	C₂³×C₇₃	—	4	16	no	—
347	C₂³×C₇₃	—	8	16	no	—
348	C₂³×C₇₃	C₂⁵	1	2	yes	—
349	C₂³×C₇₃	C₂⁵	1	8	yes	—
350	C₂³×C₇₃	C₂⁵	1	2	yes	—
351	C₂³×C₇₃	C₂⁵	1	2	yes	—
352	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
353	C₂²×D₇₃	—	2	4	no	—
354	C₂²×D₇₃	—	2	4	no	—
355	C₂²×D₇₃	—	2	8	no	—
356	C₂²×D₇₃	—	2	8	no	—
357	C₂²×D₇₃	—	2	8	no	—
358	C₂²×D₇₃	—	2	16	no	—
359	C₂²×D₇₃	—	2	32	no	—
360	C₂²×D₇₃	—	4	4	no	—
361	C₂²×D₇₃	—	4	16	no	—
362	C₂²×D₇₃	—	4	16	no	—
363	C₂²×D₇₃	—	4	16	no	—
364	C₂²×D₇₃	—	4	16	no	—
365	C₂²×D₇₃	—	4	8	no	—
366	C₂²×D₇₃	—	8	32	no	—
367	C₂²×D₇₃	—	8	16	no	—
368	C₂²×D₇₃	H(5,𝔽₂)	1	8	yes	—
369	C₂²×D₇₃	C₂⁵	1	8	yes	—
370	C₂²×D₇₃	C₂⁵	1	4	yes	—
371	Q₈×C₇₃	—	4	4	no	—
372	D₄×C₇₃	—	2	16	no	—
373	D₄×C₇₃	—	4	8	no	—
374	D₄×C₇₃	—	4	4	no	—
375	D₄×C₇₃	—	4	4	no	—
376	D₄×C₇₃	—	4	4	no	—
377	D₄×C₇₃	—	4	16	no	—
378	D₄×C₇₃	—	4	16	no	—
379	C₂×C₄×C₇₃	—	2	2	no	—
380	C₂×C₄×C₇₃	—	2	2	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	2	8	no	—
383	C₂×C₄×C₇₃	—	2	8	no	—
384	C₂×C₄×C₇₃	—	2	8	no	—
385	C₂×C₄×C₇₃	—	2	8	no	—
386	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
387	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
388	C₂×C₄×C₇₃	C₂⁵	1	8	yes	—
389	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
390	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
391	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
392	C₂²⋊D₇₃	—	2	16	no	—
393	C₂²⋊D₇₃	—	2	32	no	—
394	C₂²⋊D₇₃	—	2	16	no	—
395	C₂²⋊D₇₃	—	4	16	no	—
396	C₂²⋊D₇₃	—	4	16	no	—
397	C₂²⋊D₇₃	—	4	16	no	—
398	C₂²⋊D₇₃	—	4	16	no	—
399	C₂²⋊D₇₃	—	4	16	no	—
400	C₂×Dic₇₃	—	2	4	no	—
401	C₂×Dic₇₃	—	2	4	no	—
402	C₂×Dic₇₃	—	2	8	no	—
403	C₂×Dic₇₃	—	2	4	no	—
404	C₂×Dic₇₃	—	4	4	no	—
405	C₂×Dic₇₃	—	4	16	no	—
406	C₂×Dic₇₃	C₂⁵	1	4	yes	—
407	C₂×Dic₇₃	C₂⁵	1	8	yes	—
408	C₂×Dic₇₃	C₂⁵	1	4	yes	—
409	C₂×Dic₇₃	C₂⁵	1	4	yes	—
410	D₂₉₂	—	2	32	no	—
411	D₂₉₂	—	2	16	no	—
412	D₂₉₂	—	4	8	no	—
413	C₄×D₇₃	—	2	16	no	—
414	C₄×D₇₃	—	4	8	no	—
415	C₄×D₇₃	—	4	16	no	—
416	C₄×D₇₃	—	4	16	no	—
417	C₂²×C₇₃	—	2	8	no	—
418	C₂²×C₇₃	—	2	2	no	—
419	C₂²×C₇₃	—	2	4	no	—
420	C₂²×C₇₃	—	2	8	no	—
421	C₂²×C₇₃	—	2	4	no	—
422	C₂²×C₇₃	—	2	4	no	—
423	C₂²×C₇₃	—	2	8	no	—
424	C₂²×C₇₃	—	2	2	no	—
425	C₂²×C₇₃	—	2	2	no	—
426	C₂²×C₇₃	—	4	4	no	—
427	C₂²×C₇₃	—	4	4	no	—
428	C₂²×C₇₃	—	4	16	no	—
429	C₂²×C₇₃	—	4	4	no	—
430	C₂²×C₇₃	—	8	16	no	—
431	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
432	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
433	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
434	C₂×D₇₃	—	2	4	no	—
435	C₂×D₇₃	—	2	4	no	—
436	C₂×D₇₃	—	2	16	no	—
437	C₂×D₇₃	—	2	8	no	—
438	C₂×D₇₃	—	2	8	no	—
439	C₂×D₇₃	—	2	8	no	—
440	C₂×D₇₃	—	4	16	no	—
441	C₂×D₇₃	—	4	16	no	—
442	C₂×D₇₃	—	8	32	no	—
443	C₂×D₇₃	—	8	16	no	—
444	C₂×D₇₃	C₂×H(5,𝔽₂)	1	8	yes	—
445	C₄×C₇₃	—	2	8	no	—
446	C₄×C₇₃	—	2	2	no	—
447	C₄×C₇₃	—	2	2	no	—
448	C₄×C₇₃	—	2	2	no	—
449	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	—
450	Dic₇₃	—	2	4	no	—
451	Dic₇₃	—	2	4	no	—
452	Dic₇₃	—	2	8	no	—
453	Dic₇₃	—	2	4	no	—
454	C₂×#3537	—	73	1	no	maximal, Sylow
455	C₂×C₇₃	—	4	2	no	—
456	C₂×C₇₃	—	4	2	no	—
457	C₂×C₇₃	—	4	8	no	—
458	C₂×C₇₃	—	4	2	no	—
459	C₂×C₇₃	#3537	1	4	yes	complemented
460	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	2	yes	—
461	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
462	D₇₃	—	2	8	no	—
463	D₇₃	—	4	8	no	—
464	#3537	—	73	32	no	—
465	C₂×#560	—	73	2	no	—
466	C₂×#560	—	73	2	no	—
467	C₂×#553	—	73	2	no	—
468	C₂×#553	—	73	2	no	—
469	C₂×D₄²	—	73	2	no	—
470	C₂×D₄²	—	73	2	no	—
471	C₂×D₄²	—	73	2	no	—
472	C₂×D₄²	—	73	2	no	—
473	C₂×#540	—	73	2	no	—
474	C₂×#538	—	73	4	no	—
475	C₂×#535	—	73	1	no	—
476	C₂×#535	D₇₃	1	1	yes	characteristic, complemented
477	C₂×#534	—	73	4	no	—
478	C₂×#525	—	73	1	no	—
479	C₂²×#121	—	73	2	no	—
480	C₇₃	C₂×#3537	1	1	yes	characteristic, complemented, Sylow
481	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
482	C₂³×D₄	—	73	4	no	—
483	C₂³×D₄	—	73	4	no	—
484	C₂³×D₄	—	73	2	no	—
485	C₂³×D₄	—	73	4	no	—
486	C₂³×D₄	—	73	1	no	—
487	C₂³×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
488	C₂⁴×C₄	—	73	1	no	—
489	#560	—	73	32	no	—
490	#560	—	73	32	no	—
491	#553	—	73	32	no	—
492	#553	—	73	32	no	—
493	D₄²	—	73	32	no	—
494	D₄²	—	73	32	no	—
495	D₄²	—	73	32	no	—
496	D₄²	—	73	32	no	—
497	#540	—	73	32	no	—
498	#538	—	73	64	no	—
499	#535	—	73	16	no	—
500	#535	C₂×D₇₃	1	16	yes	complemented
501	#534	—	73	64	no	—
502	C₂×#127	—	73	2	no	—
503	C₂×#127	—	73	2	no	—
504	C₂×#127	C₂×D₇₃	1	2	yes	complemented
505	C₂×#126	—	73	4	no	—
506	C₂×#126	—	73	4	no	—
507	C₂×#125	—	73	2	no	—
508	C₂×#124	—	73	2	no	—
509	C₂×#124	C₂×D₇₃	1	2	yes	complemented
510	#525	—	73	16	no	—
511	C₂×#123	—	73	1	no	—
512	C₂×#123	—	73	1	no	—
513	C₂×#123	—	73	4	no	—
514	C₂×#123	—	73	4	no	—
515	C₂×#123	—	73	4	no	—
516	C₂×#123	—	73	4	no	—
517	C₂×C₂²⋊Q₈	—	73	2	no	—
518	C₂×#121	—	73	2	no	—
519	C₂×#121	—	73	4	no	—
520	C₂×#121	—	73	2	no	—
521	C₂×#121	—	73	4	no	—
522	C₂×#121	—	73	4	no	—
523	C₂×#121	—	73	4	no	—
524	C₂×#121	—	73	4	no	—
525	C₂×#121	—	73	2	no	—
526	C₂×#121	—	73	2	no	—
527	C₂×#121	—	73	32	no	—
528	C₂×#121	—	73	2	no	—
529	C₂×#121	—	73	4	no	—
530	C₂×#121	—	73	4	no	—
531	C₂×#121	—	73	4	no	—
532	C₂×#121	C₂×D₇₃	1	2	yes	complemented
533	C₂×#121	C₂×D₇₃	1	2	yes	complemented
534	C₂×#120	—	73	4	no	—
535	C₂×#120	—	73	1	no	—
536	C₂×#120	—	73	1	no	—
537	C₂×#120	—	73	2	no	—
538	C₂×#120	—	73	4	no	—
539	C₂×#120	—	73	2	no	—
540	C₂×#120	—	73	4	no	—
541	C₂×#120	—	73	4	no	—
542	C₂×#120	C₂×D₇₃	1	2	yes	complemented
543	C₂×#120	C₂×D₇₃	1	2	yes	complemented
544	C₂×C₄×D₄	—	73	2	no	—
545	C₂×C₄×D₄	—	73	2	no	—
546	C₂×C₄×D₄	—	73	2	no	—
547	C₂×C₄×D₄	—	73	2	no	—
548	C₂×C₄×D₄	—	73	4	no	—
549	C₂×C₄×D₄	—	73	4	no	—
550	C₂×#117	—	73	1	no	—
551	C₂×#117	—	73	1	no	—
552	C₂×#117	C₂×D₇₃	1	1	yes	characteristic, complemented
553	C₂²×C₄⋊C₄	—	73	2	no	—
554	C₂²×C₂²⋊C₄	—	73	4	no	—
555	C₂⁵	—	73	2	no	—
556	C₂⁵	—	73	4	no	—
557	C₂⁵	—	73	1	no	—
558	C₂⁵	C₂²×D₇₃	1	2	yes	—
559	C₂×#41	—	4	4	no	—
560	C₂×#41	C₂²×D₇₃	1	8	yes	complemented
561	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
562	C₂²×D₄	—	4	4	no	—
563	C₂²×D₄	—	292	4	no	—
564	C₂²×D₄	—	292	16	no	—
565	C₂²×D₄	—	292	16	no	—
566	C₂²×D₄	—	292	16	no	—
567	C₂²×D₄	—	292	8	no	—
568	C₂²×D₄	—	73	4	no	—
569	C₂²×D₄	—	73	4	no	—
570	C₂²×D₄	—	73	4	no	—
571	C₂²×D₄	—	73	4	no	—
572	C₂²×D₄	—	73	4	no	—
573	C₂²×D₄	—	73	32	no	—
574	C₂²×D₄	—	73	32	no	—
575	C₂²×D₄	—	73	16	no	—
576	C₂²×D₄	—	73	32	no	—
577	C₂²×D₄	—	73	2	no	—
578	C₂²×D₄	—	73	4	no	—
579	C₂²×D₄	—	73	2	no	—
580	C₂²×D₄	—	73	2	no	—
581	C₂²×D₄	—	73	8	no	—
582	C₂²×D₄	—	73	4	no	—
583	C₂²×D₄	—	73	2	no	—
584	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
585	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
586	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
587	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
588	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
589	C₂²×D₄	C₂²×D₇₃	1	4	yes	—
590	C₂²×D₄	C₂²×D₇₃	1	4	yes	—
591	C₂²×D₄	C₂²×D₇₃	1	8	yes	complemented
592	C₂³×C₄	—	292	4	no	—
593	C₂³×C₄	—	73	4	no	—
594	C₂³×C₄	—	73	1	no	—
595	C₂³×C₄	—	73	2	no	—
596	C₂³×C₄	—	73	4	no	—
597	C₂³×C₄	—	73	4	no	—
598	C₂³×C₄	—	73	8	no	—
599	C₂³×C₄	—	73	2	no	—
600	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
601	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
602	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
603	#127	—	73	16	no	—
604	#127	—	73	16	no	—
605	#127	C₂²×D₇₃	1	16	yes	complemented
606	#126	—	73	32	no	—
607	#126	—	73	32	no	—
608	#125	—	73	16	no	—
609	#124	—	73	16	no	—
610	#124	C₂²×D₇₃	1	16	yes	complemented
611	#123	—	73	8	no	—
612	#123	—	73	8	no	—
613	#123	—	73	32	no	—
614	#123	—	73	32	no	—
615	#123	—	73	32	no	—
616	#123	—	73	32	no	—
617	C₂²⋊Q₈	—	73	16	no	—
618	#121	—	73	16	no	—
619	#121	—	73	32	no	—
620	#121	—	73	16	no	—
621	#121	—	73	32	no	—
622	#121	—	73	32	no	—
623	#121	—	73	32	no	—
624	#121	—	73	32	no	—
625	#121	—	73	16	no	—
626	#121	—	73	16	no	—
627	#121	—	73	16	no	—
628	#121	—	73	32	no	—
629	#121	—	73	32	no	—
630	#121	—	73	32	no	—
631	#121	C₂²×D₇₃	1	16	yes	complemented
632	#121	C₂²×D₇₃	1	16	yes	complemented
633	#120	—	73	32	no	—
634	#120	—	73	8	no	—
635	#120	—	73	8	no	—
636	#120	—	73	16	no	—
637	#120	—	73	32	no	—
638	#120	—	73	16	no	—
639	#120	—	73	32	no	—
640	#120	—	73	32	no	—
641	#120	C₂²×D₇₃	1	16	yes	complemented
642	#120	C₂²×D₇₃	1	16	yes	complemented
643	C₄×D₄	—	73	16	no	—
644	C₄×D₄	—	73	16	no	—
645	C₄×D₄	—	73	16	no	—
646	C₄×D₄	—	73	16	no	—
647	C₄×D₄	—	73	32	no	—
648	C₄×D₄	—	73	32	no	—
649	#117	—	73	8	no	—
650	#117	—	73	8	no	—
651	#117	C₂²×D₇₃	1	8	yes	complemented
652	C₂×C₄⋊C₄	—	73	2	no	—
653	C₂×C₄⋊C₄	—	73	4	no	—
654	C₂×C₄⋊C₄	—	73	2	no	—
655	C₂×C₄⋊C₄	—	73	2	no	—
656	C₂×C₄⋊C₄	—	73	2	no	—
657	C₂×C₄⋊C₄	—	73	4	no	—
658	C₂×C₄⋊C₄	—	73	4	no	—
659	C₂×C₄⋊C₄	—	73	16	no	—
660	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
661	C₂×C₂²⋊C₄	—	73	4	no	—
662	C₂×C₂²⋊C₄	—	73	2	no	—
663	C₂×C₂²⋊C₄	—	73	1	no	—
664	C₂×C₂²⋊C₄	—	73	1	no	—
665	C₂×C₂²⋊C₄	—	73	4	no	—
666	C₂×C₂²⋊C₄	—	73	2	no	—
667	C₂×C₂²⋊C₄	—	73	2	no	—
668	C₂×C₂²⋊C₄	—	73	4	no	—
669	C₂×C₂²⋊C₄	—	73	4	no	—
670	C₂×C₂²⋊C₄	—	73	2	no	—
671	C₂×C₂²⋊C₄	—	73	2	no	—
672	C₂×C₂²⋊C₄	—	73	4	no	—
673	C₂×C₂²⋊C₄	—	73	4	no	—
674	C₂×C₂²⋊C₄	—	73	32	no	—
675	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
676	C₂×C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
678	C₂×C₄²	—	73	2	no	—
679	C₂×C₄²	—	73	2	no	—
680	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
681	C₂⁴	—	4	4	no	—
682	C₂⁴	—	4	8	no	—
683	C₂⁴	—	292	2	no	—
684	C₂⁴	—	292	8	no	—
685	C₂⁴	—	292	8	no	—
686	C₂⁴	—	292	4	no	—
687	C₂⁴	—	292	8	no	—
688	C₂⁴	—	73	8	no	—
689	C₂⁴	—	73	16	no	—
690	C₂⁴	—	73	4	no	—
691	C₂⁴	—	73	2	no	—
692	C₂⁴	—	73	4	no	—
693	C₂⁴	—	146	8	no	—
694	C₂⁴	—	146	16	no	—
695	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
696	C₂⁴	C₂³×D₇₃	1	4	yes	—
697	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
698	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
699	C₂⁴	C₂³×D₇₃	1	8	yes	—
700	#41	—	4	16	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	4	16	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	8	no	—
707	C₂×D₄	—	4	8	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	292	4	no	—
712	C₂×D₄	—	292	16	no	—
713	C₂×D₄	—	292	64	no	—
714	C₂×D₄	—	292	64	no	—
715	C₂×D₄	—	292	64	no	—
716	C₂×D₄	—	292	32	no	—
717	C₂×D₄	—	292	8	no	—
718	C₂×D₄	—	292	8	no	—
719	C₂×D₄	—	292	8	no	—
720	C₂×D₄	—	292	8	no	—
721	C₂×D₄	—	292	8	no	—
722	C₂×D₄	—	73	16	no	—
723	C₂×D₄	—	73	16	no	—
724	C₂×D₄	—	73	16	no	—
725	C₂×D₄	—	73	16	no	—
726	C₂×D₄	—	73	16	no	—
727	C₂×D₄	—	73	8	no	—
728	C₂×D₄	—	73	16	no	—
729	C₂×D₄	—	73	8	no	—
730	C₂×D₄	—	73	8	no	—
731	C₂×D₄	—	73	16	no	—
732	C₂×D₄	—	73	8	no	—
733	C₂×D₄	—	146	16	no	—
734	C₂×D₄	—	146	8	no	—
735	C₂×D₄	—	146	16	no	—
736	C₂×D₄	—	146	8	no	—
737	C₂×D₄	—	146	8	no	—
738	C₂×D₄	C₂³×D₇₃	1	8	yes	—
739	C₂×D₄	C₂³×D₇₃	1	4	yes	—
740	C₂×D₄	C₂³×D₇₃	1	4	yes	—
741	C₂×D₄	C₂³×D₇₃	1	8	yes	—
742	C₂×D₄	C₂³×D₇₃	1	4	yes	—
743	C₂×D₄	C₂³×D₇₃	1	16	yes	—
744	C₂×D₄	C₂³×D₇₃	1	16	yes	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	292	4	no	—
749	C₂²×C₄	—	292	8	no	—
750	C₂²×C₄	—	292	8	no	—
751	C₂²×C₄	—	292	16	no	—
752	C₂²×C₄	—	292	2	no	—
753	C₂²×C₄	—	292	8	no	—
754	C₂²×C₄	—	73	16	no	—
755	C₂²×C₄	—	73	4	no	—
756	C₂²×C₄	—	73	8	no	—
757	C₂²×C₄	—	73	16	no	—
758	C₂²×C₄	—	73	16	no	—
759	C₂²×C₄	—	73	2	no	—
760	C₂²×C₄	—	73	4	no	—
761	C₂²×C₄	—	73	2	no	—
762	C₂²×C₄	—	73	2	no	—
763	C₂²×C₄	—	73	8	no	—
764	C₂²×C₄	—	146	8	no	—
765	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
766	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
767	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
768	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
770	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
771	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
772	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
773	C₄⋊C₄	—	73	16	no	—
774	C₄⋊C₄	—	73	8	no	—
775	C₄⋊C₄	—	73	8	no	—
776	C₄⋊C₄	—	73	16	no	—
777	C₄⋊C₄	—	73	8	no	—
778	C₄⋊C₄	—	73	8	no	—
779	C₄⋊C₄	—	73	16	no	—
780	C₄⋊C₄	C₂³×D₇₃	1	8	yes	—
781	C₂²⋊C₄	—	73	16	no	—
782	C₂²⋊C₄	—	73	8	no	—
783	C₂²⋊C₄	—	73	4	no	—
784	C₂²⋊C₄	—	73	4	no	—
785	C₂²⋊C₄	—	73	16	no	—
786	C₂²⋊C₄	—	73	8	no	—
787	C₂²⋊C₄	—	73	8	no	—
788	C₂²⋊C₄	—	73	16	no	—
789	C₂²⋊C₄	—	73	16	no	—
790	C₂²⋊C₄	—	73	8	no	—
791	C₂²⋊C₄	—	73	8	no	—
792	C₂²⋊C₄	—	73	16	no	—
793	C₂²⋊C₄	—	73	16	no	—
794	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
795	C₂²⋊C₄	C₂³×D₇₃	1	8	yes	—
796	C₂²⋊C₄	C₂³×D₇₃	1	16	yes	—
797	C₄²	—	73	8	no	—
798	C₄²	—	73	8	no	—
799	C₄²	C₂³×D₇₃	1	8	yes	—
800	C₂³	—	2	8	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	8	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	8	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	16	no	—
811	C₂³	—	8	16	no	—
812	C₂³	—	292	4	no	—
813	C₂³	—	292	16	no	—
814	C₂³	—	292	16	no	—
815	C₂³	—	292	8	no	—
816	C₂³	—	292	16	no	—
817	C₂³	—	292	16	no	—
818	C₂³	—	584	16	no	—
819	C₂³	—	584	32	no	—
820	C₂³	—	73	8	no	—
821	C₂³	—	73	4	no	—
822	C₂³	—	73	8	no	—
823	C₂³	—	146	16	no	—
824	C₂³	—	146	32	no	—
825	C₂³	—	146	8	no	—
826	C₂³	—	146	8	no	—
827	C₂³	—	146	8	no	—
828	C₂³	—	146	4	no	—
829	C₂³	—	146	4	no	—
830	C₂³	C₂⁴×D₇₃	1	2	yes	—
831	C₂³	C₂⁴×D₇₃	1	8	yes	—
832	C₂³	C₂⁴×D₇₃	1	2	yes	—
833	C₂³	C₂⁴×D₇₃	1	2	yes	—
834	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
835	Q₈	—	4	4	no	—
836	D₄	—	2	16	no	—
837	D₄	—	4	8	no	—
838	D₄	—	4	16	no	—
839	D₄	—	4	16	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	292	8	no	—
844	D₄	—	292	16	no	—
845	D₄	—	292	16	no	—
846	D₄	—	292	16	no	—
847	D₄	—	292	16	no	—
848	D₄	—	292	16	no	—
849	D₄	—	146	32	no	—
850	D₄	—	146	16	no	—
851	D₄	—	146	32	no	—
852	D₄	—	146	16	no	—
853	D₄	—	146	16	no	—
854	C₂×C₄	—	2	8	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	8	no	—
860	C₂×C₄	—	2	8	no	—
861	C₂×C₄	—	292	8	no	—
862	C₂×C₄	—	292	16	no	—
863	C₂×C₄	—	292	16	no	—
864	C₂×C₄	—	292	4	no	—
865	C₂×C₄	—	292	16	no	—
866	C₂×C₄	—	73	4	no	—
867	C₂×C₄	—	73	4	no	—
868	C₂×C₄	—	73	8	no	—
869	C₂×C₄	—	73	4	no	—
870	C₂×C₄	—	146	4	no	—
871	C₂×C₄	—	146	8	no	—
872	C₂×C₄	—	146	4	no	—
873	C₂×C₄	—	146	4	no	—
874	C₂×C₄	—	146	16	no	—
875	C₂×C₄	#14556636	1	4	yes	—
876	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
877	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
878	C₂×C₄	C₂⁴×D₇₃	1	8	yes	—
879	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
880	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	8	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	8	no	—
890	C₂²	—	4	4	no	—
891	C₂²	—	4	16	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	8	16	no	—
895	C₂²	—	292	16	no	—
896	C₂²	—	292	16	no	—
897	C₂²	—	584	16	no	—
898	C₂²	—	584	32	no	—
899	C₂²	—	73	8	no	—
900	C₂²	—	146	8	no	—
901	C₂²	—	146	8	no	—
902	C₂²	—	146	8	no	—
903	C₂²	—	146	16	no	—
904	C₂²	—	146	4	no	—
905	C₂²	—	146	4	no	—
906	C₂²	H(5,𝔽₂)×D₇₃	1	4	yes	—
907	C₂²	C₂×#14556636	1	2	yes	—
908	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
909	C₄	—	2	8	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	146	4	no	—
914	C₄	—	146	8	no	—
915	C₄	—	146	4	no	—
916	C₄	—	146	4	no	—
917	C₄	C₂×#14556636	1	4	yes	—
918	C₂	—	4	2	no	—
919	C₂	—	4	8	no	—
920	C₂	—	4	2	no	—
921	C₂	—	4	2	no	—
922	C₂	—	292	8	no	—
923	C₂	—	146	8	no	—
924	C₂	#22624164	1	4	yes	direct product factor
925	C₂	C₂×H(5,𝔽₂)×D₇₃	1	2	yes	—
926	C₂	C₂²×#14556636	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂×#535×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#535	D₇₃
hypocenter	C₇₃	C₂×#3537
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×#535

Complements

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

N	H ≅ G/N	type
1. #22624164	C₂	direct (N × H)
2. C₂×#17989326	C₂	semidirect
3. C₂×#17989324	C₂	semidirect
4. C₂×#17989284	C₂	semidirect
5. C₂×#17989281	C₂	semidirect
6. C₂×#17989222	C₂	semidirect
7. C₂×#17989221	C₂	semidirect
8. C₂×D₄×C₂²⋊D₇₃	C₂	semidirect
9. C₂×#17989219	C₂	semidirect
10. C₂×#17989190	C₂	semidirect
11. C₂×#17989171	C₂	semidirect
12. C₂×#17989151	C₂	semidirect
13. C₂×#17989147	C₂	semidirect
14. C₂×#17989094	C₂	semidirect
15. C₂×#121×D₇₃	C₂	semidirect
16. C₂×#535×C₇₃	C₂	semidirect
17. C₂³×D₂₉₂	C₂²	semidirect
18. C₂³×C₂²⋊D₇₃	C₂²	semidirect
19. C₂²×D₄×D₇₃	C₂²	semidirect
20. C₂²×D₄×D₇₃	C₂²	semidirect
21. C₂²×D₄×D₇₃	C₂²	semidirect
22. C₂³×C₄×D₇₃	C₂²	semidirect
23. #17989326	C₂²	semidirect
24. #17989324	C₂²	semidirect
25. #17989284	C₂²	semidirect
26. #17989281	C₂²	semidirect
27. #17989222	C₂²	semidirect
28. #17989221	C₂²	semidirect
29. D₄×C₂²⋊D₇₃	C₂²	semidirect
30. #17989219	C₂²	semidirect
31. #17989190	C₂²	semidirect
32. #17989171	C₂²	semidirect
33. #17989151	C₂²	semidirect
34. #17989147	C₂²	semidirect
35. C₂×#14556587	C₂²	semidirect
36. C₂×#14556587	C₂²	semidirect
37. C₂×#14556585	C₂²	semidirect
38. C₂×#14556584	C₂²	semidirect
39. C₂×#14556582	C₂²	semidirect
40. C₂×#14556580	C₂²	semidirect
41. #17989094	C₂²	semidirect
42. C₂×#14556575	C₂²	semidirect
43. C₂×#14556573	C₂²	semidirect
44. C₂×#14556573	C₂²	semidirect
45. C₂×#14556572	C₂²	semidirect
46. C₂×#14556572	C₂²	semidirect
47. C₂×#14556572	C₂²	semidirect
48. C₂×#14556567	C₂²	semidirect
49. C₂×#14556566	C₂²	semidirect
50. C₂×#14556565	C₂²	semidirect
51. C₂×#14556565	C₂²	semidirect
52. C₂×#14556564	C₂²	semidirect
53. C₂×#14556564	C₂²	semidirect
54. C₂×#14556564	C₂²	semidirect
55. C₂×#14556563	C₂²	semidirect
56. C₂×#14556563	C₂²	semidirect
57. C₂×#14556563	C₂²	semidirect
58. C₂×#14556562	C₂²	semidirect
59. C₂×#14556562	C₂²	semidirect
60. C₂×#14556562	C₂²	semidirect
61. C₂×#14556562	C₂²	semidirect
62. #121×D₇₃	C₂²	semidirect
63. C₂×#14556561	C₂²	semidirect
64. C₂×#14556560	C₂²	semidirect
65. C₂×#14556559	C₂²	semidirect
66. C₂×#14556559	C₂²	semidirect
67. C₂×#14556559	C₂²	semidirect
68. C₂×#14556559	C₂²	semidirect
69. C₂×#14556559	C₂²	semidirect
70. C₂×#14556559	C₂²	semidirect
71. C₂×C₄×D₂₉₂	C₂²	semidirect
72. C₂×D₄×Dic₇₃	C₂²	semidirect
73. C₂×#14556553	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
75. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
76. C₂×#14556551	C₂²	semidirect
77. C₂×#14556550	C₂²	semidirect
78. C₂×#14556550	C₂²	semidirect
79. C₂×C₄⋊C₄×D₇₃	C₂²	semidirect
80. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
81. C₂²×#41×C₇₃	C₂²	semidirect
82. C₂³×D₄×C₇₃	C₂²	semidirect
83. #535×C₇₃	C₂²	semidirect
84. C₂×#127×C₇₃	C₂²	semidirect
85. C₂×#124×C₇₃	C₂²	semidirect
86. C₂×#121×C₇₃	C₂²	semidirect
87. C₂×#121×C₇₃	C₂²	semidirect
88. C₂×#120×C₇₃	C₂²	semidirect
89. C₂×#120×C₇₃	C₂²	semidirect
90. C₂×#117×C₇₃	C₂²	semidirect
98. C₂²×D₂₉₂	C₂³	semidirect
108. C₂²×C₂²⋊D₇₃	C₂³	semidirect
112. C₂×D₄×D₇₃	C₂³	semidirect
113. C₂×D₄×D₇₃	C₂³	semidirect
114. C₂×D₄×D₇₃	C₂³	semidirect
122. C₂²×C₄×D₇₃	C₂³	semidirect
123. #14556587	C₂³	semidirect
124. #14556587	C₂³	semidirect
125. #14556585	C₂³	semidirect
126. #14556584	C₂³	semidirect
127. #14556582	C₂³	semidirect
128. #14556580	C₂³	semidirect
129. #14556575	C₂³	semidirect
130. #14556573	C₂³	semidirect
131. #14556573	C₂³	semidirect
132. #14556572	C₂³	semidirect
133. #14556572	C₂³	semidirect
134. #14556572	C₂³	semidirect
135. #14556567	C₂³	semidirect
136. #14556566	C₂³	semidirect
137. #14556565	C₂³	semidirect
138. #14556565	C₂³	semidirect
139. #14556564	C₂³	semidirect
140. #14556564	C₂³	semidirect
141. #14556564	C₂³	semidirect
142. #14556563	C₂³	semidirect
143. #14556563	C₂³	semidirect
144. #14556563	C₂³	semidirect
145. #14556562	C₂³	semidirect
146. #14556562	C₂³	semidirect
147. #14556562	C₂³	semidirect
148. #14556562	C₂³	semidirect
149. #14556561	C₂³	semidirect
150. #14556560	C₂³	semidirect
151. #14556559	C₂³	semidirect
152. #14556559	C₂³	semidirect
153. #14556559	C₂³	semidirect
154. #14556559	C₂³	semidirect
155. #14556559	C₂³	semidirect
156. #14556559	C₂³	semidirect
157. C₄×D₂₉₂	C₂³	semidirect
158. D₄×Dic₇₃	C₂³	semidirect
159. #14556553	C₂³	semidirect
160. C₄×C₂²⋊D₇₃	C₂³	semidirect
161. C₄×C₂²⋊D₇₃	C₂³	semidirect
162. #14556551	C₂³	semidirect
163. #14556550	C₂³	semidirect
164. #14556550	C₂³	semidirect
172. C₄⋊C₄×D₇₃	C₂³	semidirect
186. C₂²⋊C₄×D₇₃	C₂³	semidirect
191. C₂×#41×C₇₃	C₂³	semidirect
201. C₂²×D₄×C₇₃	C₂³	semidirect
205. #127×C₇₃	C₂³	semidirect
206. #124×C₇₃	C₂³	semidirect
207. #121×C₇₃	C₂³	semidirect
208. #121×C₇₃	C₂³	semidirect
209. #120×C₇₃	C₂³	semidirect
210. #120×C₇₃	C₂³	semidirect
211. #117×C₇₃	C₂³	semidirect
459. C₂×C₇₃	#3537	semidirect
476. C₂×#535	D₇₃	semidirect
480. C₇₃	C₂×#3537	semidirect
481. C₂²×#41	C₂×D₇₃	semidirect
487. C₂³×D₄	C₂×D₇₃	semidirect
500. #535	C₂×D₇₃	semidirect
504. C₂×#127	C₂×D₇₃	semidirect
509. C₂×#124	C₂×D₇₃	semidirect
532. C₂×#121	C₂×D₇₃	semidirect
533. C₂×#121	C₂×D₇₃	semidirect
542. C₂×#120	C₂×D₇₃	semidirect
543. C₂×#120	C₂×D₇₃	semidirect
552. C₂×#117	C₂×D₇₃	semidirect
560. C₂×#41	C₂²×D₇₃	semidirect
591. C₂²×D₄	C₂²×D₇₃	semidirect
605. #127	C₂²×D₇₃	semidirect
610. #124	C₂²×D₇₃	semidirect
631. #121	C₂²×D₇₃	semidirect
632. #121	C₂²×D₇₃	semidirect
641. #120	C₂²×D₇₃	semidirect
642. #120	C₂²×D₇₃	semidirect
651. #117	C₂²×D₇₃	semidirect
924. C₂	#22624164	direct (N × H)

Maximal subgroups

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

subgroup	index
#22624164	2
C₂×#17989326	2
C₂×#17989324	2
C₂×#17989284	2
C₂×#17989281	2
C₂×#17989222	2
C₂×#17989221	2
C₂×D₄×C₂²⋊D₇₃	2
C₂×#17989219	2
C₂×#17989190	2
C₂×#17989171	2
C₂×#17989151	2
C₂×#17989147	2
C₂×#17989094	2
C₂×#121×D₇₃	2
C₂×#535×C₇₃	2
C₂×#3537	73

Subgroups — C2×#22624164 #33993217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22624164 #33993217