Subgroups — C₆₇×#62836 #30742087

Order 17152.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3562	C₂	1	8	yes	maximal, complemented
2	C₆₇×#3554	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3546	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3542	C₂	1	8	yes	maximal, complemented
5	C₆₇×#3517	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3514	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3513	C₂	1	8	yes	maximal, complemented
8	C₆₇×#3511	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3510	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3508	C₂	1	4	yes	maximal, complemented
13	C₆₇×#3500	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3487	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3485	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
22	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
23	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
24	#562×C₆₇	C₂²	1	16	yes	complemented
25	#560×C₆₇	C₂²	1	16	yes	complemented
26	#559×C₆₇	C₂²	1	8	yes	complemented
27	#559×C₆₇	C₂²	1	4	yes	complemented
28	#559×C₆₇	C₂²	1	8	yes	complemented
29	#557×C₆₇	C₂²	1	4	yes	complemented
30	#556×C₆₇	C₂²	1	4	yes	complemented
31	#556×C₆₇	C₂²	1	8	yes	complemented
32	#555×C₆₇	C₂²	1	8	yes	complemented
33	#554×C₆₇	C₂²	1	8	yes	complemented
34	#553×C₆₇	C₂²	1	8	yes	complemented
35	#553×C₆₇	C₂²	1	8	yes	complemented
36	#553×C₆₇	C₂²	1	16	yes	complemented
37	#552×C₆₇	C₂²	1	8	yes	complemented
38	#551×C₆₇	C₂²	1	16	yes	complemented
39	#551×C₆₇	C₂²	1	16	yes	complemented
40	#550×C₆₇	C₂²	1	8	yes	complemented
41	#550×C₆₇	C₂²	1	8	yes	complemented
42	#550×C₆₇	C₂²	1	4	yes	complemented
43	#550×C₆₇	C₂²	1	4	yes	complemented
44	#550×C₆₇	C₂²	1	8	yes	complemented
45	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
46	#548×C₆₇	C₂²	1	8	yes	complemented
47	#548×C₆₇	C₂²	1	8	yes	complemented
48	#548×C₆₇	C₂²	1	8	yes	complemented
49	#547×C₆₇	C₂²	1	8	yes	complemented
50	#547×C₆₇	C₂²	1	4	yes	complemented
51	#547×C₆₇	C₂²	1	8	yes	complemented
52	#547×C₆₇	C₂²	1	8	yes	complemented
53	#546×C₆₇	C₂²	1	16	yes	complemented
54	#546×C₆₇	C₂²	1	8	yes	complemented
55	#546×C₆₇	C₂²	1	8	yes	complemented
56	#546×C₆₇	C₂²	1	8	yes	complemented
57	#546×C₆₇	C₂²	1	8	yes	complemented
58	#546×C₆₇	C₂²	1	8	yes	complemented
59	#546×C₆₇	C₂²	1	8	yes	complemented
60	D₄²×C₆₇	C₂²	1	8	yes	—
61	D₄²×C₆₇	C₂²	1	4	yes	complemented
62	#542×C₆₇	C₂²	1	8	yes	complemented
63	#542×C₆₇	C₂²	1	8	yes	complemented
64	#542×C₆₇	C₂²	1	8	yes	complemented
65	#541×C₆₇	C₂²	1	4	yes	complemented
66	#540×C₆₇	C₂²	1	8	yes	complemented
67	#540×C₆₇	C₂²	1	16	yes	complemented
68	#540×C₆₇	C₂²	1	4	yes	complemented
69	#540×C₆₇	C₂²	1	8	yes	complemented
70	#539×C₆₇	C₂²	1	16	yes	complemented
71	#538×C₆₇	C₂²	1	16	yes	complemented
72	#538×C₆₇	C₂²	1	16	yes	complemented
73	#537×C₆₇	C₂²	1	8	yes	complemented
74	#536×C₆₇	C₂²	1	2	yes	—
75	#536×C₆₇	C₂²	1	4	yes	complemented
76	#536×C₆₇	C₂²	1	4	yes	complemented
77	#536×C₆₇	C₂²	1	2	yes	complemented
78	#535×C₆₇	C₂²	1	2	yes	—
79	#535×C₆₇	C₂²	1	8	yes	complemented
80	#535×C₆₇	C₂²	1	8	yes	complemented
81	#535×C₆₇	C₂²	1	4	yes	complemented
82	#535×C₆₇	C₂²	1	4	yes	complemented
83	#535×C₆₇	C₂²	1	2	yes	complemented
84	#534×C₆₇	C₂²	1	8	yes	complemented
85	#533×C₆₇	C₂²	1	2	yes	complemented
86	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#533×C₆₇	C₂²	1	2	yes	complemented
89	#533×C₆₇	C₂²	1	4	yes	complemented
90	#532×C₆₇	C₂²	1	1	yes	characteristic
91	#532×C₆₇	C₂²	1	1	yes	characteristic
92	#532×C₆₇	C₂²	1	2	yes	complemented
93	#532×C₆₇	C₂²	1	4	yes	complemented
94	#532×C₆₇	C₂²	1	4	yes	complemented
95	#532×C₆₇	C₂²	1	4	yes	complemented
96	#532×C₆₇	C₂²	1	4	yes	complemented
97	#532×C₆₇	C₂²	1	2	yes	complemented
98	#532×C₆₇	C₂²	1	2	yes	complemented
99	#532×C₆₇	C₂²	1	2	yes	complemented
100	#532×C₆₇	C₂²	1	4	yes	complemented
101	#532×C₆₇	C₂²	1	4	yes	complemented
102	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
104	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
105	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
106	#529×C₆₇	C₂²	1	4	yes	complemented
107	#529×C₆₇	C₂²	1	4	yes	complemented
108	#529×C₆₇	C₂²	1	4	yes	complemented
109	#529×C₆₇	C₂²	1	4	yes	complemented
110	#529×C₆₇	C₂²	1	4	yes	complemented
111	#529×C₆₇	C₂²	1	2	yes	complemented
112	#529×C₆₇	C₂²	1	2	yes	complemented
113	#529×C₆₇	C₂²	1	8	yes	complemented
114	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
116	#525×C₆₇	C₂²	1	1	yes	characteristic
117	#525×C₆₇	C₂²	1	4	yes	complemented
118	#525×C₆₇	C₂²	1	4	yes	complemented
119	#525×C₆₇	C₂²	1	2	yes	complemented
120	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#525×C₆₇	C₂²	1	8	yes	complemented
122	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
123	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
124	#520×C₆₇	C₂²	1	8	yes	complemented
125	#519×C₆₇	C₂²	1	2	yes	complemented
126	#518×C₆₇	C₂²	1	2	yes	complemented
127	#518×C₆₇	C₂²	1	8	yes	complemented
128	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
129	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
131	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
132	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
133	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
134	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₆₇	—	4	8	no	—
136	H(5,𝔽₂)×C₆₇	—	4	8	no	—
137	C₂×#41×C₆₇	—	4	8	no	—
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	4	yes	—
142	C₂×#41×C₆₇	C₂³	1	4	yes	—
143	C₂×#41×C₆₇	C₂³	1	8	yes	—
144	C₂×#41×C₆₇	C₂³	1	8	yes	—
145	C₂×#41×C₆₇	C₂³	1	8	yes	—
146	C₂×#41×C₆₇	C₂³	1	8	yes	—
147	C₂×#41×C₆₇	C₂³	1	4	yes	—
148	C₂×#41×C₆₇	C₂³	1	4	yes	—
149	C₂×#41×C₆₇	C₂³	1	4	yes	—
150	C₂×#41×C₆₇	C₂³	1	4	yes	—
151	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
153	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
154	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
155	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
156	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
157	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
158	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
159	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
160	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
161	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
163	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
168	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
169	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
170	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
174	#127×C₆₇	C₂³	1	2	yes	—
175	#127×C₆₇	C₂³	1	2	yes	—
176	#127×C₆₇	C₂³	1	4	yes	—
177	#127×C₆₇	C₂³	1	1	yes	characteristic
178	#127×C₆₇	C₂³	1	4	yes	—
179	#127×C₆₇	C₂³	1	8	yes	—
180	#127×C₆₇	C₂³	1	1	yes	characteristic
181	#127×C₆₇	C₂³	1	4	yes	—
182	#127×C₆₇	C₂³	1	16	yes	—
183	#126×C₆₇	C₂³	1	8	yes	—
184	#126×C₆₇	C₂³	1	4	yes	—
185	#126×C₆₇	C₂³	1	4	yes	—
186	#126×C₆₇	C₂³	1	16	yes	—
187	#126×C₆₇	C₂³	1	16	yes	—
188	#126×C₆₇	C₂³	1	16	yes	—
189	#125×C₆₇	C₂³	1	2	yes	—
190	#125×C₆₇	C₂³	1	4	yes	—
191	#125×C₆₇	C₂³	1	2	yes	—
192	#125×C₆₇	C₂³	1	4	yes	—
193	#125×C₆₇	C₂³	1	8	yes	—
194	#125×C₆₇	C₂³	1	16	yes	—
195	#124×C₆₇	C₂³	1	1	yes	characteristic
196	#124×C₆₇	C₂³	1	4	yes	—
197	#124×C₆₇	C₂³	1	4	yes	—
198	#124×C₆₇	C₂³	1	8	yes	—
199	#124×C₆₇	C₂³	1	4	yes	—
200	#124×C₆₇	C₂³	1	4	yes	—
201	#124×C₆₇	C₂³	1	16	yes	—
202	#124×C₆₇	C₂³	1	1	yes	characteristic
203	#124×C₆₇	C₂³	1	2	yes	—
204	#124×C₆₇	C₂³	1	4	yes	—
205	#124×C₆₇	C₂³	1	4	yes	—
206	#124×C₆₇	C₂³	1	4	yes	—
207	#124×C₆₇	C₂³	1	4	yes	—
208	#124×C₆₇	C₂³	1	8	yes	—
209	#124×C₆₇	C₂³	1	16	yes	—
210	#124×C₆₇	C₂³	1	16	yes	—
211	#123×C₆₇	C₂³	1	2	yes	—
212	#123×C₆₇	C₂³	1	4	yes	—
213	#123×C₆₇	C₂³	1	8	yes	—
214	#123×C₆₇	C₂³	1	8	yes	—
215	#123×C₆₇	C₂³	1	16	yes	—
216	#123×C₆₇	C₂³	1	16	yes	—
217	#123×C₆₇	C₂³	1	2	yes	—
218	#123×C₆₇	C₂³	1	4	yes	—
219	#123×C₆₇	C₂³	1	4	yes	—
220	#123×C₆₇	C₂³	1	8	yes	—
221	#123×C₆₇	C₂³	1	16	yes	—
222	#123×C₆₇	C₂³	1	16	yes	—
223	#123×C₆₇	C₂³	1	16	yes	—
224	#123×C₆₇	C₂³	1	16	yes	—
225	#123×C₆₇	C₂³	1	16	yes	—
226	#123×C₆₇	C₂³	1	16	yes	—
227	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
228	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
229	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
230	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
231	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
232	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
233	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
234	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
235	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
236	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
237	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
238	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
239	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
240	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
241	#121×C₆₇	C₂³	1	8	yes	—
242	#121×C₆₇	C₂³	1	8	yes	—
243	#121×C₆₇	C₂³	1	8	yes	—
244	#121×C₆₇	C₂³	1	8	yes	—
245	#121×C₆₇	C₂³	1	2	yes	—
246	#121×C₆₇	C₂³	1	4	yes	—
247	#121×C₆₇	C₂³	1	4	yes	—
248	#121×C₆₇	C₂³	1	4	yes	—
249	#121×C₆₇	C₂³	1	4	yes	—
250	#121×C₆₇	C₂³	1	2	yes	—
251	#121×C₆₇	C₂³	1	4	yes	—
252	#121×C₆₇	C₂³	1	16	yes	—
253	#121×C₆₇	C₂³	1	8	yes	—
254	#121×C₆₇	C₂³	1	8	yes	—
255	#121×C₆₇	C₂³	1	8	yes	—
256	#121×C₆₇	C₂³	1	8	yes	—
257	#121×C₆₇	C₂³	1	8	yes	—
258	#121×C₆₇	C₂³	1	16	yes	—
259	#121×C₆₇	C₂³	1	16	yes	—
260	#121×C₆₇	C₂³	1	16	yes	—
261	#121×C₆₇	C₂³	1	16	yes	—
262	#121×C₆₇	C₂³	1	16	yes	—
263	#121×C₆₇	C₂³	1	16	yes	—
264	#121×C₆₇	C₂³	1	16	yes	—
265	#121×C₆₇	C₂³	1	16	yes	—
266	#120×C₆₇	C₂³	1	2	yes	—
267	#120×C₆₇	C₂³	1	4	yes	—
268	#120×C₆₇	C₂³	1	2	yes	—
269	#120×C₆₇	C₂³	1	8	yes	—
270	#120×C₆₇	C₂³	1	8	yes	—
271	#120×C₆₇	C₂³	1	16	yes	—
272	#120×C₆₇	C₂³	1	16	yes	—
273	#120×C₆₇	C₂³	1	16	yes	—
274	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
275	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
276	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
277	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
278	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
279	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
280	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
281	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
282	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
283	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
284	C₄×D₄×C₆₇	C₂³	1	8	yes	—
285	C₄×D₄×C₆₇	C₂³	1	8	yes	—
286	C₄×D₄×C₆₇	C₂³	1	8	yes	—
287	C₄×D₄×C₆₇	C₂³	1	8	yes	—
288	C₄×D₄×C₆₇	C₂³	1	4	yes	—
289	C₄×D₄×C₆₇	C₂³	1	2	yes	—
290	C₄×D₄×C₆₇	C₂³	1	4	yes	—
291	C₄×D₄×C₆₇	C₂³	1	4	yes	—
292	C₄×D₄×C₆₇	C₂³	1	8	yes	—
293	C₄×D₄×C₆₇	C₂³	1	4	yes	—
294	C₄×D₄×C₆₇	C₂³	1	8	yes	—
295	C₄×D₄×C₆₇	C₂³	1	4	yes	—
296	C₄×D₄×C₆₇	C₂³	1	8	yes	—
297	C₄×D₄×C₆₇	C₂³	1	4	yes	—
298	C₄×D₄×C₆₇	C₂³	1	4	yes	—
299	C₄×D₄×C₆₇	C₂³	1	4	yes	—
300	C₄×D₄×C₆₇	C₂³	1	4	yes	—
301	C₄×D₄×C₆₇	C₂³	1	4	yes	—
302	C₄×D₄×C₆₇	C₂³	1	4	yes	—
303	C₄×D₄×C₆₇	C₂³	1	2	yes	—
304	C₄×D₄×C₆₇	C₂³	1	16	yes	—
305	C₄×D₄×C₆₇	C₂³	1	16	yes	—
306	C₄×D₄×C₆₇	C₂³	1	8	yes	—
307	C₄×D₄×C₆₇	C₂³	1	8	yes	—
308	C₄×D₄×C₆₇	C₂³	1	8	yes	—
309	C₄×D₄×C₆₇	C₂³	1	8	yes	—
310	C₄×D₄×C₆₇	C₂³	1	16	yes	—
311	C₄×D₄×C₆₇	C₂³	1	16	yes	—
312	C₄×D₄×C₆₇	C₂³	1	8	yes	—
313	#117×C₆₇	C₂³	1	1	yes	characteristic
314	#117×C₆₇	C₂³	1	2	yes	—
315	#117×C₆₇	C₂³	1	1	yes	characteristic
316	#117×C₆₇	C₂³	1	4	yes	—
317	#117×C₆₇	C₂³	1	2	yes	—
318	#117×C₆₇	C₂³	1	4	yes	—
319	#117×C₆₇	C₂³	1	4	yes	—
320	#117×C₆₇	C₂³	1	4	yes	—
321	#117×C₆₇	C₂³	1	4	yes	—
322	#117×C₆₇	C₂³	1	2	yes	—
323	#117×C₆₇	C₂³	1	8	yes	—
324	#117×C₆₇	C₂³	1	8	yes	—
325	#117×C₆₇	C₂³	1	8	yes	—
326	#117×C₆₇	C₂³	1	16	yes	—
327	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
328	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
329	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
330	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
331	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
332	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
333	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
334	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
335	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
338	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
339	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
340	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
341	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
342	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
343	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
344	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
345	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
347	#41×C₆₇	—	2	4	no	—
348	#41×C₆₇	—	2	8	no	—
349	#41×C₆₇	—	2	4	no	—
350	#41×C₆₇	—	4	8	no	—
351	#41×C₆₇	—	4	16	no	—
352	#41×C₆₇	—	4	16	no	—
353	#41×C₆₇	—	4	16	no	—
354	#41×C₆₇	—	4	8	no	—
355	#41×C₆₇	—	4	16	no	—
356	#41×C₆₇	—	4	8	no	—
357	#41×C₆₇	—	4	8	no	—
358	#41×C₆₇	—	4	8	no	—
359	#41×C₆₇	—	4	8	no	—
360	C₂×Q₈×C₆₇	—	2	8	no	—
361	C₂×Q₈×C₆₇	—	4	8	no	—
362	C₂×Q₈×C₆₇	—	4	8	no	—
363	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
364	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
366	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
367	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
368	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
370	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
371	C₂×D₄×C₆₇	—	2	8	no	—
372	C₂×D₄×C₆₇	—	4	8	no	—
373	C₂×D₄×C₆₇	—	4	16	no	—
374	C₂×D₄×C₆₇	—	4	8	no	—
375	C₂×D₄×C₆₇	—	4	8	no	—
376	C₂×D₄×C₆₇	—	4	8	no	—
377	C₂×D₄×C₆₇	—	4	16	no	—
378	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
379	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
380	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
381	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
382	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
383	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
385	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
386	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
387	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
389	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
390	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
391	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
392	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
393	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
394	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
395	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
396	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
397	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
398	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
399	C₂²×C₄×C₆₇	—	2	4	no	—
400	C₂²×C₄×C₆₇	—	4	4	no	—
401	C₂²×C₄×C₆₇	—	4	8	no	—
402	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
409	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
410	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
412	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
414	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
415	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
416	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
418	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
419	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
420	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
421	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
422	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
423	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
425	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
426	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
427	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
429	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
430	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
431	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
432	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
433	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
439	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
442	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
443	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
444	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
445	C₂²⋊C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
447	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
448	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
449	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
451	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
452	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
453	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
454	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
455	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
456	C₂²⋊C₄×C₆₇	C₂⁴	1	2	yes	—
457	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
458	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
459	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
460	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
461	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
463	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
464	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
465	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
466	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
467	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
468	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
469	C₄²×C₆₇	C₂⁴	1	2	yes	—
470	C₄²×C₆₇	C₂⁴	1	2	yes	—
471	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
472	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₄²×C₆₇	C₂⁴	1	2	yes	—
474	C₄²×C₆₇	C₂⁴	1	2	yes	—
475	C₄²×C₆₇	C₂⁴	1	2	yes	—
476	C₄²×C₆₇	C₂⁴	1	2	yes	—
477	C₄²×C₆₇	C₂⁴	1	8	yes	—
478	C₄²×C₆₇	C₂⁴	1	2	yes	—
479	C₄²×C₆₇	C₂⁴	1	4	yes	—
480	C₄²×C₆₇	C₂⁴	1	4	yes	—
481	C₄²×C₆₇	C₂⁴	1	4	yes	—
482	C₄²×C₆₇	C₂⁴	1	2	yes	—
483	C₄²×C₆₇	C₂⁴	1	16	yes	—
484	C₂³×C₆₇	—	2	2	no	—
485	C₂³×C₆₇	—	2	8	no	—
486	C₂³×C₆₇	—	4	2	no	—
487	C₂³×C₆₇	—	4	8	no	—
488	C₂³×C₆₇	—	4	8	no	—
489	C₂³×C₆₇	—	4	16	no	—
490	C₂³×C₆₇	C₂⁵	1	2	yes	—
491	C₂³×C₆₇	C₂⁵	1	4	yes	—
492	C₂³×C₆₇	C₂⁵	1	8	yes	—
493	C₂³×C₆₇	C₂⁵	1	2	yes	—
494	C₂³×C₆₇	C₂⁵	1	2	yes	—
495	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
496	Q₈×C₆₇	—	2	8	no	—
497	Q₈×C₆₇	—	2	8	no	—
498	Q₈×C₆₇	—	2	2	no	—
499	Q₈×C₆₇	—	2	4	no	—
500	Q₈×C₆₇	—	2	2	no	—
501	Q₈×C₆₇	—	2	8	no	—
502	Q₈×C₆₇	—	4	8	no	—
503	Q₈×C₆₇	—	4	4	no	—
504	D₄×C₆₇	—	2	4	no	—
505	D₄×C₆₇	—	2	8	no	—
506	D₄×C₆₇	—	2	4	no	—
507	D₄×C₆₇	—	2	8	no	—
508	D₄×C₆₇	—	2	8	no	—
509	D₄×C₆₇	—	2	2	no	—
510	D₄×C₆₇	—	2	4	no	—
511	D₄×C₆₇	—	2	2	no	—
512	D₄×C₆₇	—	2	16	no	—
513	D₄×C₆₇	—	2	8	no	—
514	D₄×C₆₇	—	4	8	no	—
515	D₄×C₆₇	—	4	8	no	—
516	D₄×C₆₇	—	4	8	no	—
517	D₄×C₆₇	—	4	16	no	—
518	D₄×C₆₇	—	4	16	no	—
519	D₄×C₆₇	—	4	4	no	—
520	D₄×C₆₇	—	4	4	no	—
521	D₄×C₆₇	—	4	4	no	—
522	D₄×C₆₇	—	4	8	no	—
523	D₄×C₆₇	—	4	16	no	—
524	D₄×C₆₇	—	4	8	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	8	no	—
527	C₂×C₄×C₆₇	—	2	4	no	—
528	C₂×C₄×C₆₇	—	2	4	no	—
529	C₂×C₄×C₆₇	—	2	4	no	—
530	C₂×C₄×C₆₇	—	2	8	no	—
531	C₂×C₄×C₆₇	—	2	4	no	—
532	C₂×C₄×C₆₇	—	2	4	no	—
533	C₂×C₄×C₆₇	—	2	4	no	—
534	C₂×C₄×C₆₇	—	2	4	no	—
535	C₂×C₄×C₆₇	—	2	8	no	—
536	C₂×C₄×C₆₇	—	2	8	no	—
537	C₂×C₄×C₆₇	—	4	2	no	—
538	C₂×C₄×C₆₇	—	4	2	no	—
539	C₂×C₄×C₆₇	—	4	2	no	—
540	C₂×C₄×C₆₇	—	4	16	no	—
541	C₂×C₄×C₆₇	—	4	8	no	—
542	C₂×C₄×C₆₇	—	4	8	no	—
543	C₂×C₄×C₆₇	—	4	8	no	—
544	C₂×C₄×C₆₇	—	4	8	no	—
545	C₂×C₄×C₆₇	—	4	16	no	—
546	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
547	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
548	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
549	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
550	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
551	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
552	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
553	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
554	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
555	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
556	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
557	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
558	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
559	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
560	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
561	C₂²×C₆₇	—	2	2	no	—
562	C₂²×C₆₇	—	2	2	no	—
563	C₂²×C₆₇	—	2	2	no	—
564	C₂²×C₆₇	—	2	4	no	—
565	C₂²×C₆₇	—	2	2	no	—
566	C₂²×C₆₇	—	2	8	no	—
567	C₂²×C₆₇	—	2	2	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	4	no	—
570	C₂²×C₆₇	—	2	4	no	—
571	C₂²×C₆₇	—	2	16	no	—
572	C₂²×C₆₇	—	2	8	no	—
573	C₂²×C₆₇	—	4	4	no	—
574	C₂²×C₆₇	—	8	8	no	—
575	C₂²×C₆₇	—	16	8	no	—
576	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
577	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
578	C₄×C₆₇	—	2	2	no	—
579	C₄×C₆₇	—	2	2	no	—
580	C₄×C₆₇	—	2	4	no	—
581	C₄×C₆₇	—	2	2	no	—
582	C₄×C₆₇	—	2	8	no	—
583	C₄×C₆₇	—	2	2	no	—
584	C₄×C₆₇	—	2	4	no	—
585	C₄×C₆₇	—	2	2	no	—
586	C₄×C₆₇	—	2	2	no	—
587	C₄×C₆₇	—	2	4	no	—
588	C₄×C₆₇	—	2	8	no	—
589	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
590	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
591	C₄×C₆₇	#585	1	4	yes	—
592	#62836	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
593	C₂×C₆₇	—	2	2	no	—
594	C₂×C₆₇	—	4	2	no	—
595	C₂×C₆₇	—	4	2	no	—
596	C₂×C₆₇	—	4	8	no	—
597	C₂×C₆₇	—	4	4	no	—
598	C₂×C₆₇	—	4	2	no	—
599	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂×C₆₇	C₂×#585	1	2	yes	—
601	#3562	C₂×C₆₇	1	8	yes	complemented
602	#3554	C₂×C₆₇	1	4	yes	complemented
603	#3546	C₂×C₆₇	1	4	yes	complemented
604	#3542	C₂×C₆₇	1	8	yes	complemented
605	#3517	C₂×C₆₇	1	4	yes	complemented
606	#3514	C₂×C₆₇	1	4	yes	complemented
607	#3513	C₂×C₆₇	1	8	yes	complemented
608	#3511	C₂×C₆₇	1	4	yes	complemented
609	#3510	C₂×C₆₇	1	2	yes	complemented
610	#3509	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#3508	C₂×C₆₇	1	4	yes	complemented
613	#3500	C₂×C₆₇	1	2	yes	complemented
614	#3499	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3487	C₂×C₆₇	1	2	yes	complemented
617	#3485	C₂×C₆₇	1	2	yes	complemented
618	#3444	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3444	C₂×C₆₇	1	1	yes	characteristic, complemented
620	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
621	C₆₇	#62836	1	1	yes	characteristic, direct product factor, Sylow
622	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
623	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
624	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
625	#562	C₂²×C₆₇	1	16	yes	complemented
626	#560	C₂²×C₆₇	1	16	yes	complemented
627	#559	C₂²×C₆₇	1	8	yes	complemented
628	#559	C₂²×C₆₇	1	8	yes	complemented
629	#559	C₂²×C₆₇	1	4	yes	complemented
630	#557	C₂²×C₆₇	1	4	yes	complemented
631	#556	C₂²×C₆₇	1	4	yes	complemented
632	#556	C₂²×C₆₇	1	8	yes	complemented
633	#555	C₂²×C₆₇	1	8	yes	complemented
634	#554	C₂²×C₆₇	1	8	yes	complemented
635	#553	C₂²×C₆₇	1	8	yes	complemented
636	#553	C₂²×C₆₇	1	8	yes	complemented
637	#553	C₂²×C₆₇	1	16	yes	complemented
638	#552	C₂²×C₆₇	1	8	yes	complemented
639	#551	C₂²×C₆₇	1	16	yes	complemented
640	#551	C₂²×C₆₇	1	16	yes	complemented
641	#550	C₂²×C₆₇	1	8	yes	complemented
642	#550	C₂²×C₆₇	1	8	yes	complemented
643	#550	C₂²×C₆₇	1	4	yes	complemented
644	#550	C₂²×C₆₇	1	8	yes	complemented
645	#550	C₂²×C₆₇	1	4	yes	complemented
646	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
647	#548	C₂²×C₆₇	1	8	yes	complemented
648	#548	C₂²×C₆₇	1	8	yes	complemented
649	#548	C₂²×C₆₇	1	8	yes	complemented
650	#547	C₂²×C₆₇	1	8	yes	complemented
651	#547	C₂²×C₆₇	1	8	yes	complemented
652	#547	C₂²×C₆₇	1	8	yes	complemented
653	#547	C₂²×C₆₇	1	4	yes	complemented
654	#546	C₂²×C₆₇	1	8	yes	complemented
655	#546	C₂²×C₆₇	1	8	yes	complemented
656	#546	C₂²×C₆₇	1	8	yes	complemented
657	#546	C₂²×C₆₇	1	16	yes	complemented
658	#546	C₂²×C₆₇	1	8	yes	complemented
659	#546	C₂²×C₆₇	1	8	yes	complemented
660	#546	C₂²×C₆₇	1	8	yes	complemented
661	D₄²	C₂²×C₆₇	1	8	yes	—
662	D₄²	C₂²×C₆₇	1	4	yes	complemented
663	#542	C₂²×C₆₇	1	8	yes	complemented
664	#542	C₂²×C₆₇	1	8	yes	complemented
665	#542	C₂²×C₆₇	1	8	yes	complemented
666	#541	C₂²×C₆₇	1	4	yes	complemented
667	#540	C₂²×C₆₇	1	8	yes	complemented
668	#540	C₂²×C₆₇	1	8	yes	complemented
669	#540	C₂²×C₆₇	1	4	yes	complemented
670	#540	C₂²×C₆₇	1	16	yes	complemented
671	#539	C₂²×C₆₇	1	16	yes	complemented
672	#538	C₂²×C₆₇	1	16	yes	complemented
673	#538	C₂²×C₆₇	1	16	yes	complemented
674	#537	C₂²×C₆₇	1	8	yes	complemented
675	#536	C₂²×C₆₇	1	2	yes	—
676	#536	C₂²×C₆₇	1	2	yes	complemented
677	#536	C₂²×C₆₇	1	4	yes	complemented
678	#536	C₂²×C₆₇	1	4	yes	complemented
679	#535	C₂²×C₆₇	1	2	yes	—
680	#535	C₂²×C₆₇	1	2	yes	complemented
681	#535	C₂²×C₆₇	1	8	yes	complemented
682	#535	C₂²×C₆₇	1	4	yes	complemented
683	#535	C₂²×C₆₇	1	4	yes	complemented
684	#535	C₂²×C₆₇	1	8	yes	complemented
685	#534	C₂²×C₆₇	1	8	yes	complemented
686	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#533	C₂²×C₆₇	1	2	yes	complemented
689	#533	C₂²×C₆₇	1	2	yes	complemented
690	#533	C₂²×C₆₇	1	4	yes	complemented
691	#532	C₂²×C₆₇	1	1	yes	characteristic
692	#532	C₂²×C₆₇	1	1	yes	characteristic
693	#532	C₂²×C₆₇	1	4	yes	complemented
694	#532	C₂²×C₆₇	1	4	yes	complemented
695	#532	C₂²×C₆₇	1	4	yes	complemented
696	#532	C₂²×C₆₇	1	4	yes	complemented
697	#532	C₂²×C₆₇	1	2	yes	complemented
698	#532	C₂²×C₆₇	1	2	yes	complemented
699	#532	C₂²×C₆₇	1	2	yes	complemented
700	#532	C₂²×C₆₇	1	2	yes	complemented
701	#532	C₂²×C₆₇	1	4	yes	complemented
702	#532	C₂²×C₆₇	1	4	yes	complemented
703	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
705	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
706	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
707	#529	C₂²×C₆₇	1	4	yes	complemented
708	#529	C₂²×C₆₇	1	4	yes	complemented
709	#529	C₂²×C₆₇	1	2	yes	complemented
710	#529	C₂²×C₆₇	1	2	yes	complemented
711	#529	C₂²×C₆₇	1	4	yes	complemented
712	#529	C₂²×C₆₇	1	4	yes	complemented
713	#529	C₂²×C₆₇	1	4	yes	complemented
714	#529	C₂²×C₆₇	1	8	yes	complemented
715	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
716	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
717	#525	C₂²×C₆₇	1	1	yes	characteristic
718	#525	C₂²×C₆₇	1	2	yes	complemented
719	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	#525	C₂²×C₆₇	1	4	yes	complemented
721	#525	C₂²×C₆₇	1	4	yes	complemented
722	#525	C₂²×C₆₇	1	8	yes	complemented
723	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
724	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
725	#520	C₂²×C₆₇	1	8	yes	complemented
726	#519	C₂²×C₆₇	1	2	yes	complemented
727	#518	C₂²×C₆₇	1	2	yes	complemented
728	#518	C₂²×C₆₇	1	8	yes	complemented
729	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
730	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
732	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
733	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
734	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
735	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	2₋¹⁺⁴	—	4	8	no	—
737	H(5,𝔽₂)	—	4	8	no	—
738	C₂×#41	—	4	8	no	—
739	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×#41	C₂³×C₆₇	1	2	yes	—
741	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×#41	C₂³×C₆₇	1	4	yes	—
743	C₂×#41	C₂³×C₆₇	1	4	yes	—
744	C₂×#41	C₂³×C₆₇	1	8	yes	—
745	C₂×#41	C₂³×C₆₇	1	8	yes	—
746	C₂×#41	C₂³×C₆₇	1	8	yes	—
747	C₂×#41	C₂³×C₆₇	1	8	yes	—
748	C₂×#41	C₂³×C₆₇	1	4	yes	—
749	C₂×#41	C₂³×C₆₇	1	4	yes	—
750	C₂×#41	C₂³×C₆₇	1	4	yes	—
751	C₂×#41	C₂³×C₆₇	1	4	yes	—
752	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
753	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
754	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
755	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
756	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
757	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
758	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
759	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
760	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
761	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
762	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
763	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
764	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
765	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
766	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
767	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
768	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
769	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
770	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
771	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
772	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
773	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
774	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
775	#127	C₂³×C₆₇	1	2	yes	—
776	#127	C₂³×C₆₇	1	2	yes	—
777	#127	C₂³×C₆₇	1	4	yes	—
778	#127	C₂³×C₆₇	1	1	yes	characteristic
779	#127	C₂³×C₆₇	1	4	yes	—
780	#127	C₂³×C₆₇	1	8	yes	—
781	#127	C₂³×C₆₇	1	1	yes	characteristic
782	#127	C₂³×C₆₇	1	4	yes	—
783	#127	C₂³×C₆₇	1	16	yes	—
784	#126	C₂³×C₆₇	1	8	yes	—
785	#126	C₂³×C₆₇	1	4	yes	—
786	#126	C₂³×C₆₇	1	4	yes	—
787	#126	C₂³×C₆₇	1	16	yes	—
788	#126	C₂³×C₆₇	1	16	yes	—
789	#126	C₂³×C₆₇	1	16	yes	—
790	#125	C₂³×C₆₇	1	2	yes	—
791	#125	C₂³×C₆₇	1	4	yes	—
792	#125	C₂³×C₆₇	1	2	yes	—
793	#125	C₂³×C₆₇	1	4	yes	—
794	#125	C₂³×C₆₇	1	8	yes	—
795	#125	C₂³×C₆₇	1	16	yes	—
796	#124	C₂³×C₆₇	1	1	yes	characteristic
797	#124	C₂³×C₆₇	1	4	yes	—
798	#124	C₂³×C₆₇	1	4	yes	—
799	#124	C₂³×C₆₇	1	8	yes	—
800	#124	C₂³×C₆₇	1	4	yes	—
801	#124	C₂³×C₆₇	1	4	yes	—
802	#124	C₂³×C₆₇	1	16	yes	—
803	#124	C₂³×C₆₇	1	1	yes	characteristic
804	#124	C₂³×C₆₇	1	2	yes	—
805	#124	C₂³×C₆₇	1	4	yes	—
806	#124	C₂³×C₆₇	1	4	yes	—
807	#124	C₂³×C₆₇	1	4	yes	—
808	#124	C₂³×C₆₇	1	4	yes	—
809	#124	C₂³×C₆₇	1	8	yes	—
810	#124	C₂³×C₆₇	1	16	yes	—
811	#124	C₂³×C₆₇	1	16	yes	—
812	#123	C₂³×C₆₇	1	2	yes	—
813	#123	C₂³×C₆₇	1	4	yes	—
814	#123	C₂³×C₆₇	1	8	yes	—
815	#123	C₂³×C₆₇	1	8	yes	—
816	#123	C₂³×C₆₇	1	16	yes	—
817	#123	C₂³×C₆₇	1	16	yes	—
818	#123	C₂³×C₆₇	1	2	yes	—
819	#123	C₂³×C₆₇	1	4	yes	—
820	#123	C₂³×C₆₇	1	4	yes	—
821	#123	C₂³×C₆₇	1	8	yes	—
822	#123	C₂³×C₆₇	1	16	yes	—
823	#123	C₂³×C₆₇	1	16	yes	—
824	#123	C₂³×C₆₇	1	16	yes	—
825	#123	C₂³×C₆₇	1	16	yes	—
826	#123	C₂³×C₆₇	1	16	yes	—
827	#123	C₂³×C₆₇	1	16	yes	—
828	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
829	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
830	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
831	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
832	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
834	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
835	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
836	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
837	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
838	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
839	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
840	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
841	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
842	#121	C₂³×C₆₇	1	8	yes	—
843	#121	C₂³×C₆₇	1	8	yes	—
844	#121	C₂³×C₆₇	1	8	yes	—
845	#121	C₂³×C₆₇	1	8	yes	—
846	#121	C₂³×C₆₇	1	2	yes	—
847	#121	C₂³×C₆₇	1	4	yes	—
848	#121	C₂³×C₆₇	1	4	yes	—
849	#121	C₂³×C₆₇	1	4	yes	—
850	#121	C₂³×C₆₇	1	4	yes	—
851	#121	C₂³×C₆₇	1	2	yes	—
852	#121	C₂³×C₆₇	1	4	yes	—
853	#121	C₂³×C₆₇	1	16	yes	—
854	#121	C₂³×C₆₇	1	8	yes	—
855	#121	C₂³×C₆₇	1	8	yes	—
856	#121	C₂³×C₆₇	1	8	yes	—
857	#121	C₂³×C₆₇	1	8	yes	—
858	#121	C₂³×C₆₇	1	8	yes	—
859	#121	C₂³×C₆₇	1	16	yes	—
860	#121	C₂³×C₆₇	1	16	yes	—
861	#121	C₂³×C₆₇	1	16	yes	—
862	#121	C₂³×C₆₇	1	16	yes	—
863	#121	C₂³×C₆₇	1	16	yes	—
864	#121	C₂³×C₆₇	1	16	yes	—
865	#121	C₂³×C₆₇	1	16	yes	—
866	#121	C₂³×C₆₇	1	16	yes	—
867	#120	C₂³×C₆₇	1	2	yes	—
868	#120	C₂³×C₆₇	1	4	yes	—
869	#120	C₂³×C₆₇	1	2	yes	—
870	#120	C₂³×C₆₇	1	8	yes	—
871	#120	C₂³×C₆₇	1	8	yes	—
872	#120	C₂³×C₆₇	1	16	yes	—
873	#120	C₂³×C₆₇	1	16	yes	—
874	#120	C₂³×C₆₇	1	16	yes	—
875	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
876	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
877	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
878	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
879	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
880	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
881	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
882	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
883	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
884	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
885	C₄×D₄	C₂³×C₆₇	1	8	yes	—
886	C₄×D₄	C₂³×C₆₇	1	8	yes	—
887	C₄×D₄	C₂³×C₆₇	1	8	yes	—
888	C₄×D₄	C₂³×C₆₇	1	8	yes	—
889	C₄×D₄	C₂³×C₆₇	1	4	yes	—
890	C₄×D₄	C₂³×C₆₇	1	2	yes	—
891	C₄×D₄	C₂³×C₆₇	1	4	yes	—
892	C₄×D₄	C₂³×C₆₇	1	4	yes	—
893	C₄×D₄	C₂³×C₆₇	1	8	yes	—
894	C₄×D₄	C₂³×C₆₇	1	4	yes	—
895	C₄×D₄	C₂³×C₆₇	1	8	yes	—
896	C₄×D₄	C₂³×C₆₇	1	4	yes	—
897	C₄×D₄	C₂³×C₆₇	1	8	yes	—
898	C₄×D₄	C₂³×C₆₇	1	4	yes	—
899	C₄×D₄	C₂³×C₆₇	1	4	yes	—
900	C₄×D₄	C₂³×C₆₇	1	4	yes	—
901	C₄×D₄	C₂³×C₆₇	1	4	yes	—
902	C₄×D₄	C₂³×C₆₇	1	4	yes	—
903	C₄×D₄	C₂³×C₆₇	1	4	yes	—
904	C₄×D₄	C₂³×C₆₇	1	2	yes	—
905	C₄×D₄	C₂³×C₆₇	1	16	yes	—
906	C₄×D₄	C₂³×C₆₇	1	16	yes	—
907	C₄×D₄	C₂³×C₆₇	1	8	yes	—
908	C₄×D₄	C₂³×C₆₇	1	8	yes	—
909	C₄×D₄	C₂³×C₆₇	1	8	yes	—
910	C₄×D₄	C₂³×C₆₇	1	8	yes	—
911	C₄×D₄	C₂³×C₆₇	1	16	yes	—
912	C₄×D₄	C₂³×C₆₇	1	16	yes	—
913	C₄×D₄	C₂³×C₆₇	1	8	yes	—
914	#117	C₂³×C₆₇	1	1	yes	characteristic
915	#117	C₂³×C₆₇	1	2	yes	—
916	#117	C₂³×C₆₇	1	1	yes	characteristic
917	#117	C₂³×C₆₇	1	4	yes	—
918	#117	C₂³×C₆₇	1	2	yes	—
919	#117	C₂³×C₆₇	1	4	yes	—
920	#117	C₂³×C₆₇	1	4	yes	—
921	#117	C₂³×C₆₇	1	4	yes	—
922	#117	C₂³×C₆₇	1	4	yes	—
923	#117	C₂³×C₆₇	1	2	yes	—
924	#117	C₂³×C₆₇	1	8	yes	—
925	#117	C₂³×C₆₇	1	8	yes	—
926	#117	C₂³×C₆₇	1	8	yes	—
927	#117	C₂³×C₆₇	1	16	yes	—
928	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
929	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
930	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
931	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
932	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
933	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
934	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
935	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
936	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
937	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
939	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
940	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
941	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
942	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
943	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
944	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
945	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
946	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
948	#41	—	2	4	no	—
949	#41	—	2	8	no	—
950	#41	—	2	4	no	—
951	#41	—	4	8	no	—
952	#41	—	4	16	no	—
953	#41	—	4	16	no	—
954	#41	—	4	16	no	—
955	#41	—	4	8	no	—
956	#41	—	4	8	no	—
957	#41	—	4	8	no	—
958	#41	—	4	8	no	—
959	#41	—	4	8	no	—
960	#41	—	4	16	no	—
961	C₂×Q₈	—	2	8	no	—
962	C₂×Q₈	—	4	8	no	—
963	C₂×Q₈	—	4	8	no	—
964	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
965	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
967	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
968	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
969	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
971	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
972	C₂×D₄	—	2	8	no	—
973	C₂×D₄	—	4	8	no	—
974	C₂×D₄	—	4	8	no	—
975	C₂×D₄	—	4	8	no	—
976	C₂×D₄	—	4	16	no	—
977	C₂×D₄	—	4	8	no	—
978	C₂×D₄	—	4	16	no	—
979	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
980	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
981	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
982	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
983	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
984	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
986	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
987	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
988	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
990	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
991	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
992	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
993	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
994	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
995	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
996	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
997	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
998	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
999	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1000	C₂²×C₄	—	2	4	no	—
1001	C₂²×C₄	—	4	4	no	—
1002	C₂²×C₄	—	4	8	no	—
1003	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1004	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1005	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1010	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1011	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1012	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1013	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1015	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1018	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1019	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
1020	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1021	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
1022	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1023	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1024	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1026	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1027	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1028	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1029	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1030	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1031	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1032	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1033	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1034	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1036	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1037	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1038	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1039	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1040	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1041	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1042	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1043	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1044	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1045	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1046	C₂²⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1047	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1048	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1049	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1050	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1051	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1052	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1053	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1054	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1055	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1056	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1057	C₂²⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1058	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1059	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1060	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1061	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1062	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1063	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1064	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1065	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1066	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1067	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1068	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1070	C₄²	C₂⁴×C₆₇	1	2	yes	—
1071	C₄²	C₂⁴×C₆₇	1	2	yes	—
1072	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1073	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1074	C₄²	C₂⁴×C₆₇	1	2	yes	—
1075	C₄²	C₂⁴×C₆₇	1	2	yes	—
1076	C₄²	C₂⁴×C₆₇	1	2	yes	—
1077	C₄²	C₂⁴×C₆₇	1	2	yes	—
1078	C₄²	C₂⁴×C₆₇	1	8	yes	—
1079	C₄²	C₂⁴×C₆₇	1	2	yes	—
1080	C₄²	C₂⁴×C₆₇	1	4	yes	—
1081	C₄²	C₂⁴×C₆₇	1	4	yes	—
1082	C₄²	C₂⁴×C₆₇	1	4	yes	—
1083	C₄²	C₂⁴×C₆₇	1	2	yes	—
1084	C₄²	C₂⁴×C₆₇	1	16	yes	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	8	no	—
1087	C₂³	—	4	2	no	—
1088	C₂³	—	4	8	no	—
1089	C₂³	—	4	8	no	—
1090	C₂³	—	4	16	no	—
1091	C₂³	C₂⁵×C₆₇	1	2	yes	—
1092	C₂³	C₂⁵×C₆₇	1	4	yes	—
1093	C₂³	C₂⁵×C₆₇	1	8	yes	—
1094	C₂³	C₂⁵×C₆₇	1	2	yes	—
1095	C₂³	C₂⁵×C₆₇	1	2	yes	—
1096	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1097	Q₈	—	2	8	no	—
1098	Q₈	—	2	8	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	4	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	8	no	—
1103	Q₈	—	4	8	no	—
1104	Q₈	—	4	4	no	—
1105	D₄	—	2	4	no	—
1106	D₄	—	2	8	no	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	8	no	—
1109	D₄	—	2	8	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	16	no	—
1114	D₄	—	2	8	no	—
1115	D₄	—	4	8	no	—
1116	D₄	—	4	8	no	—
1117	D₄	—	4	16	no	—
1118	D₄	—	4	8	no	—
1119	D₄	—	4	16	no	—
1120	D₄	—	4	8	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	8	no	—
1125	D₄	—	4	16	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	8	no	—
1128	C₂×C₄	—	2	4	no	—
1129	C₂×C₄	—	2	4	no	—
1130	C₂×C₄	—	2	4	no	—
1131	C₂×C₄	—	2	8	no	—
1132	C₂×C₄	—	2	4	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	8	no	—
1137	C₂×C₄	—	2	8	no	—
1138	C₂×C₄	—	4	16	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	8	no	—
1143	C₂×C₄	—	4	8	no	—
1144	C₂×C₄	—	4	8	no	—
1145	C₂×C₄	—	4	8	no	—
1146	C₂×C₄	—	4	16	no	—
1147	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
1148	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1149	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1150	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1151	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1152	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1153	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1154	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1155	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1156	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1157	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1158	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1159	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1160	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1161	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	4	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	8	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	4	no	—
1171	C₂²	—	2	4	no	—
1172	C₂²	—	2	16	no	—
1173	C₂²	—	2	8	no	—
1174	C₂²	—	4	4	no	—
1175	C₂²	—	8	8	no	—
1176	C₂²	—	16	8	no	—
1177	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1178	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	4	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	8	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	4	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	4	no	—
1189	C₄	—	2	8	no	—
1190	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1191	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1192	C₄	#585×C₆₇	1	4	yes	—
1193	C₂	—	2	2	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	4	8	no	—
1196	C₂	—	4	2	no	—
1197	C₂	—	4	4	no	—
1198	C₂	—	4	2	no	—
1199	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1200	C₂	C₂×#585×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3562	C₂	semidirect
2. C₆₇×#3554	C₂	semidirect
3. C₆₇×#3546	C₂	semidirect
4. C₆₇×#3542	C₂	semidirect
5. C₆₇×#3517	C₂	semidirect
6. C₆₇×#3514	C₂	semidirect
7. C₆₇×#3513	C₂	semidirect
8. C₆₇×#3511	C₂	semidirect
9. C₆₇×#3510	C₂	semidirect
10. C₆₇×#3509	C₂	semidirect
11. C₆₇×#3508	C₂	semidirect
12. C₆₇×#3508	C₂	semidirect
13. C₆₇×#3500	C₂	semidirect
14. C₆₇×#3499	C₂	semidirect
15. C₆₇×#3498	C₂	semidirect
16. C₆₇×#3487	C₂	semidirect
17. C₆₇×#3485	C₂	semidirect
18. C₆₇×#3444	C₂	semidirect
19. C₆₇×#3444	C₂	semidirect
20. C₂×#532×C₆₇	C₂	semidirect
21. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
23. C₂²×#41×C₆₇	C₂²	semidirect
24. #562×C₆₇	C₂²	semidirect
25. #560×C₆₇	C₂²	semidirect
26. #559×C₆₇	C₂²	semidirect
27. #559×C₆₇	C₂²	semidirect
28. #559×C₆₇	C₂²	semidirect
29. #557×C₆₇	C₂²	semidirect
30. #556×C₆₇	C₂²	semidirect
31. #556×C₆₇	C₂²	semidirect
32. #555×C₆₇	C₂²	semidirect
33. #554×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
35. #553×C₆₇	C₂²	semidirect
36. #553×C₆₇	C₂²	semidirect
37. #552×C₆₇	C₂²	semidirect
38. #551×C₆₇	C₂²	semidirect
39. #551×C₆₇	C₂²	semidirect
40. #550×C₆₇	C₂²	semidirect
41. #550×C₆₇	C₂²	semidirect
42. #550×C₆₇	C₂²	semidirect
43. #550×C₆₇	C₂²	semidirect
44. #550×C₆₇	C₂²	semidirect
45. D₄×Q₈×C₆₇	C₂²	semidirect
46. #548×C₆₇	C₂²	semidirect
47. #548×C₆₇	C₂²	semidirect
48. #548×C₆₇	C₂²	semidirect
49. #547×C₆₇	C₂²	semidirect
50. #547×C₆₇	C₂²	semidirect
51. #547×C₆₇	C₂²	semidirect
52. #547×C₆₇	C₂²	semidirect
53. #546×C₆₇	C₂²	semidirect
54. #546×C₆₇	C₂²	semidirect
55. #546×C₆₇	C₂²	semidirect
56. #546×C₆₇	C₂²	semidirect
57. #546×C₆₇	C₂²	semidirect
58. #546×C₆₇	C₂²	semidirect
59. #546×C₆₇	C₂²	semidirect
61. D₄²×C₆₇	C₂²	semidirect
62. #542×C₆₇	C₂²	semidirect
63. #542×C₆₇	C₂²	semidirect
64. #542×C₆₇	C₂²	semidirect
65. #541×C₆₇	C₂²	semidirect
66. #540×C₆₇	C₂²	semidirect
67. #540×C₆₇	C₂²	semidirect
68. #540×C₆₇	C₂²	semidirect
69. #540×C₆₇	C₂²	semidirect
70. #539×C₆₇	C₂²	semidirect
71. #538×C₆₇	C₂²	semidirect
72. #538×C₆₇	C₂²	semidirect
73. #537×C₆₇	C₂²	semidirect
75. #536×C₆₇	C₂²	semidirect
76. #536×C₆₇	C₂²	semidirect
77. #536×C₆₇	C₂²	semidirect
79. #535×C₆₇	C₂²	semidirect
80. #535×C₆₇	C₂²	semidirect
81. #535×C₆₇	C₂²	semidirect
82. #535×C₆₇	C₂²	semidirect
83. #535×C₆₇	C₂²	semidirect
84. #534×C₆₇	C₂²	semidirect
85. #533×C₆₇	C₂²	semidirect
86. #533×C₆₇	C₂²	semidirect
87. #533×C₆₇	C₂²	semidirect
88. #533×C₆₇	C₂²	semidirect
89. #533×C₆₇	C₂²	semidirect
92. #532×C₆₇	C₂²	semidirect
93. #532×C₆₇	C₂²	semidirect
94. #532×C₆₇	C₂²	semidirect
95. #532×C₆₇	C₂²	semidirect
96. #532×C₆₇	C₂²	semidirect
97. #532×C₆₇	C₂²	semidirect
98. #532×C₆₇	C₂²	semidirect
99. #532×C₆₇	C₂²	semidirect
100. #532×C₆₇	C₂²	semidirect
101. #532×C₆₇	C₂²	semidirect
102. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
103. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
105. C₂×#127×C₆₇	C₂²	semidirect
106. #529×C₆₇	C₂²	semidirect
107. #529×C₆₇	C₂²	semidirect
108. #529×C₆₇	C₂²	semidirect
109. #529×C₆₇	C₂²	semidirect
110. #529×C₆₇	C₂²	semidirect
111. #529×C₆₇	C₂²	semidirect
112. #529×C₆₇	C₂²	semidirect
113. #529×C₆₇	C₂²	semidirect
114. C₂×#124×C₆₇	C₂²	semidirect
115. C₂×#124×C₆₇	C₂²	semidirect
117. #525×C₆₇	C₂²	semidirect
118. #525×C₆₇	C₂²	semidirect
119. #525×C₆₇	C₂²	semidirect
120. #525×C₆₇	C₂²	semidirect
121. #525×C₆₇	C₂²	semidirect
122. C₂×#123×C₆₇	C₂²	semidirect
123. C₂×#121×C₆₇	C₂²	semidirect
124. #520×C₆₇	C₂²	semidirect
125. #519×C₆₇	C₂²	semidirect
126. #518×C₆₇	C₂²	semidirect
127. #518×C₆₇	C₂²	semidirect
129. C₄×#41×C₆₇	C₂²	semidirect
130. C₄×#41×C₆₇	C₂²	semidirect
131. C₄×#41×C₆₇	C₂²	semidirect
132. C₄×#41×C₆₇	C₂²	semidirect
133. C₂×C₄×D₄×C₆₇	C₂²	semidirect
134. C₂²×C₄²×C₆₇	C₂²	semidirect
592. #62836	C₆₇	direct (N × H)
601. #3562	C₂×C₆₇	semidirect
602. #3554	C₂×C₆₇	semidirect
603. #3546	C₂×C₆₇	semidirect
604. #3542	C₂×C₆₇	semidirect
605. #3517	C₂×C₆₇	semidirect
606. #3514	C₂×C₆₇	semidirect
607. #3513	C₂×C₆₇	semidirect
608. #3511	C₂×C₆₇	semidirect
609. #3510	C₂×C₆₇	semidirect
610. #3509	C₂×C₆₇	semidirect
611. #3508	C₂×C₆₇	semidirect
612. #3508	C₂×C₆₇	semidirect
613. #3500	C₂×C₆₇	semidirect
614. #3499	C₂×C₆₇	semidirect
615. #3498	C₂×C₆₇	semidirect
616. #3487	C₂×C₆₇	semidirect
617. #3485	C₂×C₆₇	semidirect
618. #3444	C₂×C₆₇	semidirect
619. #3444	C₂×C₆₇	semidirect
620. C₂×#532	C₂×C₆₇	semidirect
621. C₆₇	#62836	direct (N × H)
622. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
624. C₂²×#41	C₂²×C₆₇	semidirect
625. #562	C₂²×C₆₇	semidirect
626. #560	C₂²×C₆₇	semidirect
627. #559	C₂²×C₆₇	semidirect
628. #559	C₂²×C₆₇	semidirect
629. #559	C₂²×C₆₇	semidirect
630. #557	C₂²×C₆₇	semidirect
631. #556	C₂²×C₆₇	semidirect
632. #556	C₂²×C₆₇	semidirect
633. #555	C₂²×C₆₇	semidirect
634. #554	C₂²×C₆₇	semidirect
635. #553	C₂²×C₆₇	semidirect
636. #553	C₂²×C₆₇	semidirect
637. #553	C₂²×C₆₇	semidirect
638. #552	C₂²×C₆₇	semidirect
639. #551	C₂²×C₆₇	semidirect
640. #551	C₂²×C₆₇	semidirect
641. #550	C₂²×C₆₇	semidirect
642. #550	C₂²×C₆₇	semidirect
643. #550	C₂²×C₆₇	semidirect
644. #550	C₂²×C₆₇	semidirect
645. #550	C₂²×C₆₇	semidirect
646. D₄×Q₈	C₂²×C₆₇	semidirect
647. #548	C₂²×C₆₇	semidirect
648. #548	C₂²×C₆₇	semidirect
649. #548	C₂²×C₆₇	semidirect
650. #547	C₂²×C₆₇	semidirect
651. #547	C₂²×C₆₇	semidirect
652. #547	C₂²×C₆₇	semidirect
653. #547	C₂²×C₆₇	semidirect
654. #546	C₂²×C₆₇	semidirect
655. #546	C₂²×C₆₇	semidirect
656. #546	C₂²×C₆₇	semidirect
657. #546	C₂²×C₆₇	semidirect
658. #546	C₂²×C₆₇	semidirect
659. #546	C₂²×C₆₇	semidirect
660. #546	C₂²×C₆₇	semidirect
662. D₄²	C₂²×C₆₇	semidirect
663. #542	C₂²×C₆₇	semidirect
664. #542	C₂²×C₆₇	semidirect
665. #542	C₂²×C₆₇	semidirect
666. #541	C₂²×C₆₇	semidirect
667. #540	C₂²×C₆₇	semidirect
668. #540	C₂²×C₆₇	semidirect
669. #540	C₂²×C₆₇	semidirect
670. #540	C₂²×C₆₇	semidirect
671. #539	C₂²×C₆₇	semidirect
672. #538	C₂²×C₆₇	semidirect
673. #538	C₂²×C₆₇	semidirect
674. #537	C₂²×C₆₇	semidirect
676. #536	C₂²×C₆₇	semidirect
677. #536	C₂²×C₆₇	semidirect
678. #536	C₂²×C₆₇	semidirect
680. #535	C₂²×C₆₇	semidirect
681. #535	C₂²×C₆₇	semidirect
682. #535	C₂²×C₆₇	semidirect
683. #535	C₂²×C₆₇	semidirect
684. #535	C₂²×C₆₇	semidirect
685. #534	C₂²×C₆₇	semidirect
686. #533	C₂²×C₆₇	semidirect
687. #533	C₂²×C₆₇	semidirect
688. #533	C₂²×C₆₇	semidirect
689. #533	C₂²×C₆₇	semidirect
690. #533	C₂²×C₆₇	semidirect
693. #532	C₂²×C₆₇	semidirect
694. #532	C₂²×C₆₇	semidirect
695. #532	C₂²×C₆₇	semidirect
696. #532	C₂²×C₆₇	semidirect
697. #532	C₂²×C₆₇	semidirect
698. #532	C₂²×C₆₇	semidirect
699. #532	C₂²×C₆₇	semidirect
700. #532	C₂²×C₆₇	semidirect
701. #532	C₂²×C₆₇	semidirect
702. #532	C₂²×C₆₇	semidirect
703. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
704. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
706. C₂×#127	C₂²×C₆₇	semidirect
707. #529	C₂²×C₆₇	semidirect
708. #529	C₂²×C₆₇	semidirect
709. #529	C₂²×C₆₇	semidirect
710. #529	C₂²×C₆₇	semidirect
711. #529	C₂²×C₆₇	semidirect
712. #529	C₂²×C₆₇	semidirect
713. #529	C₂²×C₆₇	semidirect
714. #529	C₂²×C₆₇	semidirect
715. C₂×#124	C₂²×C₆₇	semidirect
716. C₂×#124	C₂²×C₆₇	semidirect
718. #525	C₂²×C₆₇	semidirect
719. #525	C₂²×C₆₇	semidirect
720. #525	C₂²×C₆₇	semidirect
721. #525	C₂²×C₆₇	semidirect
722. #525	C₂²×C₆₇	semidirect
723. C₂×#123	C₂²×C₆₇	semidirect
724. C₂×#121	C₂²×C₆₇	semidirect
725. #520	C₂²×C₆₇	semidirect
726. #519	C₂²×C₆₇	semidirect
727. #518	C₂²×C₆₇	semidirect
728. #518	C₂²×C₆₇	semidirect
730. C₄×#41	C₂²×C₆₇	semidirect
731. C₄×#41	C₂²×C₆₇	semidirect
732. C₄×#41	C₂²×C₆₇	semidirect
733. C₄×#41	C₂²×C₆₇	semidirect
734. C₂×C₄×D₄	C₂²×C₆₇	semidirect
735. C₂²×C₄²	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3562	2
C₆₇×#3554	2
C₆₇×#3546	2
C₆₇×#3542	2
C₆₇×#3517	2
C₆₇×#3514	2
C₆₇×#3513	2
C₆₇×#3511	2
C₆₇×#3510	2
C₆₇×#3509	2
C₆₇×#3508	2
C₆₇×#3500	2
C₆₇×#3499	2
C₆₇×#3498	2
C₆₇×#3487	2
C₆₇×#3485	2
C₆₇×#3444	2
C₂×#532×C₆₇	2
#62836	67

Subgroups — C67×#62836 #30742087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#62836 #30742087