Subgroups — C₂×C₆₇×#2837 #30715909

Order 17152.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2837	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#399×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#399×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#398×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#398×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#397×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#397×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#396×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#396×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#394×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#394×C₆₇	C₂	1	1	yes	maximal, characteristic
13	C₂×#394×C₆₇	C₂	1	1	yes	maximal, characteristic
14	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	#400×C₆₇	C₂²	1	8	yes	complemented
43	#399×C₆₇	C₂²	1	8	yes	complemented
44	#399×C₆₇	C₂²	1	8	yes	complemented
45	#398×C₆₇	C₂²	1	8	yes	complemented
46	#398×C₆₇	C₂²	1	8	yes	complemented
47	#397×C₆₇	C₂²	1	8	yes	complemented
48	#397×C₆₇	C₂²	1	8	yes	complemented
49	#396×C₆₇	C₂²	1	8	yes	complemented
50	#396×C₆₇	C₂²	1	8	yes	complemented
51	#394×C₆₇	C₂²	1	8	yes	—
52	#394×C₆₇	C₂²	1	8	yes	—
53	#394×C₆₇	C₂²	1	8	yes	—
54	#389×C₆₇	C₂²	1	8	yes	complemented
55	#388×C₆₇	C₂²	1	8	yes	complemented
56	#388×C₆₇	C₂²	1	8	yes	complemented
57	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
67	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
68	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₆₇	—	4	2	no	—
70	C₂²×D₄×C₆₇	—	4	2	no	—
71	C₂²×D₄×C₆₇	—	4	2	no	—
72	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
73	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
87	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
88	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
89	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
90	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
91	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
92	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
93	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
94	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
95	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
96	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
97	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
110	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
111	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
112	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
113	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
114	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
115	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
116	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
117	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
119	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₄²×C₆₇	—	4	2	no	—
133	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
134	#95×C₆₇	C₂³	1	4	yes	—
135	#95×C₆₇	C₂³	1	4	yes	—
136	#95×C₆₇	C₂³	1	4	yes	—
137	#95×C₆₇	C₂³	1	4	yes	—
138	#95×C₆₇	C₂³	1	4	yes	—
139	#95×C₆₇	C₂³	1	4	yes	—
140	#95×C₆₇	C₂³	1	4	yes	—
141	#95×C₆₇	C₂³	1	4	yes	—
142	#95×C₆₇	C₂³	1	4	yes	—
143	#95×C₆₇	C₂³	1	4	yes	—
144	C₂⁴×C₆₇	—	2	2	no	—
145	C₂⁴×C₆₇	—	2	2	no	—
146	C₂⁴×C₆₇	—	2	2	no	—
147	C₂⁴×C₆₇	—	2	2	no	—
148	C₂⁴×C₆₇	—	2	2	no	—
149	C₂⁴×C₆₇	—	2	2	no	—
150	C₂⁴×C₆₇	—	2	2	no	—
151	C₂⁴×C₆₇	—	2	2	no	—
152	C₂⁴×C₆₇	—	2	2	no	—
153	C₂⁴×C₆₇	—	2	2	no	—
154	C₂⁴×C₆₇	—	2	2	no	—
155	C₂⁴×C₆₇	—	2	2	no	—
156	C₂⁴×C₆₇	—	2	2	no	—
157	C₂⁴×C₆₇	—	2	2	no	—
158	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
159	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
160	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
161	C₂×D₄×C₆₇	—	4	4	no	—
162	C₂×D₄×C₆₇	—	4	4	no	—
163	C₂×D₄×C₆₇	—	4	4	no	—
164	C₂×D₄×C₆₇	—	4	16	no	—
165	C₂²×C₄×C₆₇	—	2	2	no	—
166	C₂²×C₄×C₆₇	—	2	2	no	—
167	C₂²×C₄×C₆₇	—	2	2	no	—
168	C₂²×C₄×C₆₇	—	2	2	no	—
169	C₂²×C₄×C₆₇	—	2	2	no	—
170	C₂²×C₄×C₆₇	—	2	2	no	—
171	C₂²×C₄×C₆₇	—	2	2	no	—
172	C₂²×C₄×C₆₇	—	2	2	no	—
173	C₂²×C₄×C₆₇	—	2	2	no	—
174	C₂²×C₄×C₆₇	—	2	2	no	—
175	C₂²×C₄×C₆₇	—	2	2	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	2	no	—
182	C₂²×C₄×C₆₇	—	2	2	no	—
183	C₂²×C₄×C₆₇	—	2	2	no	—
184	C₂²×C₄×C₆₇	—	2	2	no	—
185	C₂²×C₄×C₆₇	—	2	2	no	—
186	C₂²×C₄×C₆₇	—	2	2	no	—
187	C₂²×C₄×C₆₇	—	2	2	no	—
188	C₂²×C₄×C₆₇	—	2	2	no	—
189	C₂²×C₄×C₆₇	—	2	2	no	—
190	C₂²×C₄×C₆₇	—	2	2	no	—
191	C₂²×C₄×C₆₇	—	2	2	no	—
192	C₂²×C₄×C₆₇	—	2	2	no	—
193	C₂²×C₄×C₆₇	—	2	2	no	—
194	C₂²×C₄×C₆₇	—	2	2	no	—
195	C₂²×C₄×C₆₇	—	2	2	no	—
196	C₂²×C₄×C₆₇	—	2	2	no	—
197	C₂²×C₄×C₆₇	—	2	2	no	—
198	C₂²×C₄×C₆₇	—	2	2	no	—
199	C₂²×C₄×C₆₇	—	2	2	no	—
200	C₂²×C₄×C₆₇	—	2	2	no	—
201	C₂²×C₄×C₆₇	—	2	2	no	—
202	C₂²×C₄×C₆₇	—	2	2	no	—
203	C₂²×C₄×C₆₇	#41	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₄⋊C₄×C₆₇	—	2	8	no	—
218	C₄⋊C₄×C₆₇	—	4	4	no	—
219	C₄⋊C₄×C₆₇	—	4	4	no	—
220	C₄⋊C₄×C₆₇	—	4	4	no	—
221	C₄⋊C₄×C₆₇	—	4	4	no	—
222	C₄⋊C₄×C₆₇	—	4	4	no	—
223	C₄⋊C₄×C₆₇	—	4	4	no	—
224	C₄⋊C₄×C₆₇	—	4	4	no	—
225	C₄⋊C₄×C₆₇	—	4	4	no	—
226	C₄⋊C₄×C₆₇	—	4	4	no	—
227	C₄⋊C₄×C₆₇	—	4	4	no	—
228	C₂²⋊C₄×C₆₇	—	2	8	no	—
229	C₂²⋊C₄×C₆₇	—	2	8	no	—
230	C₂²⋊C₄×C₆₇	—	4	4	no	—
231	C₂²⋊C₄×C₆₇	—	4	4	no	—
232	C₂²⋊C₄×C₆₇	—	4	4	no	—
233	C₂²⋊C₄×C₆₇	—	4	4	no	—
234	C₂²⋊C₄×C₆₇	—	4	4	no	—
235	C₂²⋊C₄×C₆₇	—	4	4	no	—
236	C₂²⋊C₄×C₆₇	—	4	4	no	—
237	C₂²⋊C₄×C₆₇	—	4	4	no	—
238	C₂²⋊C₄×C₆₇	—	4	4	no	—
239	C₂²⋊C₄×C₆₇	—	4	4	no	—
240	C₄²×C₆₇	—	4	4	no	—
241	C₂³×C₆₇	—	2	2	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	2	no	—
244	C₂³×C₆₇	—	2	2	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	2	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	4	4	no	—
256	C₂³×C₆₇	—	4	4	no	—
257	C₂³×C₆₇	—	4	4	no	—
258	C₂³×C₆₇	—	4	4	no	—
259	C₂³×C₆₇	—	4	4	no	—
260	C₂³×C₆₇	—	4	4	no	—
261	C₂³×C₆₇	—	4	4	no	—
262	C₂³×C₆₇	—	4	4	no	—
263	C₂³×C₆₇	—	4	4	no	—
264	C₂³×C₆₇	—	4	4	no	—
265	C₂³×C₆₇	—	4	4	no	—
266	C₂³×C₆₇	—	4	4	no	—
267	C₂³×C₆₇	—	4	4	no	—
268	C₂³×C₆₇	—	4	4	no	—
269	C₂³×C₆₇	C₂×#41	1	2	yes	—
270	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
271	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
272	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
273	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
274	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
275	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
276	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
277	D₄×C₆₇	—	4	16	no	—
278	C₂×C₄×C₆₇	—	2	8	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	4	4	no	—
318	C₂×C₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	4	4	no	—
320	C₂×C₄×C₆₇	—	4	4	no	—
321	C₂×C₄×C₆₇	—	4	4	no	—
322	C₂×C₄×C₆₇	—	4	4	no	—
323	C₂×C₄×C₆₇	—	4	4	no	—
324	C₂×C₄×C₆₇	—	4	4	no	—
325	C₂×C₄×C₆₇	—	4	4	no	—
326	C₂×C₄×C₆₇	—	4	4	no	—
327	C₂×C₄×C₆₇	—	4	4	no	—
328	C₂×C₄×C₆₇	—	4	4	no	—
329	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
330	C₂²×C₆₇	—	4	2	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	—	4	2	no	—
336	C₂²×C₆₇	—	4	2	no	—
337	C₂²×C₆₇	—	4	2	no	—
338	C₂²×C₆₇	—	4	2	no	—
339	C₂²×C₆₇	—	4	2	no	—
340	C₂²×C₆₇	—	4	2	no	—
341	C₂²×C₆₇	—	4	2	no	—
342	C₂²×C₆₇	—	4	2	no	—
343	C₂²×C₆₇	—	4	2	no	—
344	C₂²×C₆₇	—	8	8	no	—
345	C₂²×C₆₇	—	8	8	no	—
346	C₂²×C₆₇	#539	1	4	yes	—
347	C₂²×C₆₇	#540	1	4	yes	—
348	C₂²×C₆₇	#542	1	4	yes	—
349	C₂²×C₆₇	#560	1	4	yes	—
350	C₂²×C₆₇	#562	1	4	yes	—
351	C₂²×C₆₇	#562	1	4	yes	—
352	C₂²×C₆₇	#563	1	4	yes	—
353	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
359	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
360	C₄×C₆₇	—	2	4	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	2	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	2	no	—
366	C₄×C₆₇	—	4	2	no	—
367	C₄×C₆₇	—	4	2	no	—
368	C₄×C₆₇	—	4	2	no	—
369	C₄×C₆₇	—	4	2	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₂×#2837	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₂×C₆₇	—	8	2	no	—
375	C₂×C₆₇	—	8	2	no	—
376	C₂×C₆₇	#2837	1	8	yes	direct product factor
377	C₂×C₆₇	C₂×#539	1	1	yes	characteristic
378	C₂×C₆₇	C₂×#540	1	1	yes	characteristic
379	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
380	C₂×C₆₇	C₂×#560	1	1	yes	characteristic
381	C₂×C₆₇	C₂×#562	1	1	yes	characteristic
382	C₂×C₆₇	C₂×#562	1	1	yes	characteristic
383	C₂×C₆₇	C₂×#563	1	1	yes	characteristic
384	#2837	C₂×C₆₇	1	16	yes	direct product factor
385	C₂×#400	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₂×#399	C₂×C₆₇	1	1	yes	characteristic, complemented
387	C₂×#399	C₂×C₆₇	1	1	yes	characteristic, complemented
388	C₂×#398	C₂×C₆₇	1	1	yes	characteristic, complemented
389	C₂×#398	C₂×C₆₇	1	1	yes	characteristic, complemented
390	C₂×#397	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂×#397	C₂×C₆₇	1	1	yes	characteristic, complemented
392	C₂×#396	C₂×C₆₇	1	1	yes	characteristic, complemented
393	C₂×#396	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₂×#394	C₂×C₆₇	1	1	yes	characteristic
395	C₂×#394	C₂×C₆₇	1	1	yes	characteristic
396	C₂×#394	C₂×C₆₇	1	1	yes	characteristic
397	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
398	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₆₇	C₂×#2837	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
405	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
411	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
412	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
420	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
423	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
425	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
426	#400	C₂²×C₆₇	1	8	yes	complemented
427	#399	C₂²×C₆₇	1	8	yes	complemented
428	#399	C₂²×C₆₇	1	8	yes	complemented
429	#398	C₂²×C₆₇	1	8	yes	complemented
430	#398	C₂²×C₆₇	1	8	yes	complemented
431	#397	C₂²×C₆₇	1	8	yes	complemented
432	#397	C₂²×C₆₇	1	8	yes	complemented
433	#396	C₂²×C₆₇	1	8	yes	complemented
434	#396	C₂²×C₆₇	1	8	yes	complemented
435	#394	C₂²×C₆₇	1	8	yes	—
436	#394	C₂²×C₆₇	1	8	yes	—
437	#394	C₂²×C₆₇	1	8	yes	—
438	#389	C₂²×C₆₇	1	8	yes	complemented
439	#388	C₂²×C₆₇	1	8	yes	complemented
440	#388	C₂²×C₆₇	1	8	yes	complemented
441	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
451	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
452	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
453	C₂²×D₄	—	4	2	no	—
454	C₂²×D₄	—	4	2	no	—
455	C₂²×D₄	—	4	2	no	—
456	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
457	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
470	C₂×C₄⋊C₄	—	2	4	no	—
471	C₂×C₄⋊C₄	—	4	2	no	—
472	C₂×C₄⋊C₄	—	4	2	no	—
473	C₂×C₄⋊C₄	—	4	2	no	—
474	C₂×C₄⋊C₄	—	4	2	no	—
475	C₂×C₄⋊C₄	—	4	2	no	—
476	C₂×C₄⋊C₄	—	4	2	no	—
477	C₂×C₄⋊C₄	—	4	2	no	—
478	C₂×C₄⋊C₄	—	4	2	no	—
479	C₂×C₄⋊C₄	—	4	2	no	—
480	C₂×C₄⋊C₄	—	4	2	no	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
492	C₂×C₂²⋊C₄	—	2	4	no	—
493	C₂×C₂²⋊C₄	—	2	4	no	—
494	C₂×C₂²⋊C₄	—	4	2	no	—
495	C₂×C₂²⋊C₄	—	4	2	no	—
496	C₂×C₂²⋊C₄	—	4	2	no	—
497	C₂×C₂²⋊C₄	—	4	2	no	—
498	C₂×C₂²⋊C₄	—	4	2	no	—
499	C₂×C₂²⋊C₄	—	4	2	no	—
500	C₂×C₂²⋊C₄	—	4	2	no	—
501	C₂×C₂²⋊C₄	—	4	2	no	—
502	C₂×C₂²⋊C₄	—	4	2	no	—
503	C₂×C₂²⋊C₄	—	4	2	no	—
504	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
516	C₂×C₄²	—	4	2	no	—
517	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
518	#95	C₂³×C₆₇	1	4	yes	—
519	#95	C₂³×C₆₇	1	4	yes	—
520	#95	C₂³×C₆₇	1	4	yes	—
521	#95	C₂³×C₆₇	1	4	yes	—
522	#95	C₂³×C₆₇	1	4	yes	—
523	#95	C₂³×C₆₇	1	4	yes	—
524	#95	C₂³×C₆₇	1	4	yes	—
525	#95	C₂³×C₆₇	1	4	yes	—
526	#95	C₂³×C₆₇	1	4	yes	—
527	#95	C₂³×C₆₇	1	4	yes	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	2	no	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	—	2	2	no	—
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
543	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
544	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
545	C₂×D₄	—	4	4	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	16	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	#41×C₆₇	1	4	yes	—
588	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	—	4	4	no	—
604	C₄⋊C₄	—	4	4	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₄⋊C₄	—	4	4	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₄²	—	4	4	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	4	4	no	—
640	C₂³	—	4	4	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	4	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	4	4	no	—
653	C₂³	C₂×#41×C₆₇	1	2	yes	—
654	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
655	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
656	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
657	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
658	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
659	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
660	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
661	D₄	—	4	16	no	—
662	C₂×C₄	—	2	8	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	8	8	no	—
729	C₂²	—	8	8	no	—
730	C₂²	#539×C₆₇	1	4	yes	—
731	C₂²	#540×C₆₇	1	4	yes	—
732	C₂²	#542×C₆₇	1	4	yes	—
733	C₂²	#560×C₆₇	1	4	yes	—
734	C₂²	#562×C₆₇	1	4	yes	—
735	C₂²	#562×C₆₇	1	4	yes	—
736	C₂²	#563×C₆₇	1	4	yes	—
737	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
738	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
739	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
740	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
741	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
742	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
743	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
744	C₄	—	2	4	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₂	—	8	2	no	—
758	C₂	—	8	2	no	—
759	C₂	C₆₇×#2837	1	8	yes	direct product factor
760	C₂	C₂×#539×C₆₇	1	1	yes	characteristic
761	C₂	C₂×#540×C₆₇	1	1	yes	characteristic
762	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
763	C₂	C₂×#560×C₆₇	1	1	yes	characteristic
764	C₂	C₂×#562×C₆₇	1	1	yes	characteristic
765	C₂	C₂×#562×C₆₇	1	1	yes	characteristic
766	C₂	C₂×#563×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2837	C₂	direct (N × H)
2. C₂×#400×C₆₇	C₂	semidirect
3. C₂×#399×C₆₇	C₂	semidirect
4. C₂×#399×C₆₇	C₂	semidirect
5. C₂×#398×C₆₇	C₂	semidirect
6. C₂×#398×C₆₇	C₂	semidirect
7. C₂×#397×C₆₇	C₂	semidirect
8. C₂×#397×C₆₇	C₂	semidirect
9. C₂×#396×C₆₇	C₂	semidirect
10. C₂×#396×C₆₇	C₂	semidirect
14. C₂×#389×C₆₇	C₂	semidirect
15. C₂×#388×C₆₇	C₂	semidirect
16. C₂×#388×C₆₇	C₂	semidirect
42. #400×C₆₇	C₂²	semidirect
43. #399×C₆₇	C₂²	semidirect
44. #399×C₆₇	C₂²	semidirect
45. #398×C₆₇	C₂²	semidirect
46. #398×C₆₇	C₂²	semidirect
47. #397×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #396×C₆₇	C₂²	semidirect
50. #396×C₆₇	C₂²	semidirect
54. #389×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #388×C₆₇	C₂²	semidirect
373. C₂×#2837	C₆₇	direct (N × H)
376. C₂×C₆₇	#2837	direct (N × H)
384. #2837	C₂×C₆₇	direct (N × H)
385. C₂×#400	C₂×C₆₇	semidirect
386. C₂×#399	C₂×C₆₇	semidirect
387. C₂×#399	C₂×C₆₇	semidirect
388. C₂×#398	C₂×C₆₇	semidirect
389. C₂×#398	C₂×C₆₇	semidirect
390. C₂×#397	C₂×C₆₇	semidirect
391. C₂×#397	C₂×C₆₇	semidirect
392. C₂×#396	C₂×C₆₇	semidirect
393. C₂×#396	C₂×C₆₇	semidirect
397. C₂×#389	C₂×C₆₇	semidirect
398. C₂×#388	C₂×C₆₇	semidirect
399. C₂×#388	C₂×C₆₇	semidirect
400. C₆₇	C₂×#2837	direct (N × H)
426. #400	C₂²×C₆₇	semidirect
427. #399	C₂²×C₆₇	semidirect
428. #399	C₂²×C₆₇	semidirect
429. #398	C₂²×C₆₇	semidirect
430. #398	C₂²×C₆₇	semidirect
431. #397	C₂²×C₆₇	semidirect
432. #397	C₂²×C₆₇	semidirect
433. #396	C₂²×C₆₇	semidirect
434. #396	C₂²×C₆₇	semidirect
438. #389	C₂²×C₆₇	semidirect
439. #388	C₂²×C₆₇	semidirect
440. #388	C₂²×C₆₇	semidirect
759. C₂	C₆₇×#2837	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2837	2
C₂×#400×C₆₇	2
C₂×#399×C₆₇	2
C₂×#398×C₆₇	2
C₂×#397×C₆₇	2
C₂×#396×C₆₇	2
C₂×#394×C₆₇	2
C₂×#389×C₆₇	2
C₂×#388×C₆₇	2
C₂×#2837	67

Subgroups — C2×C67×#2837 #30715909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2837 #30715909